We study spectrum sharing between two dense low-earth orbit (LEO) satellite constellations, an incumbent primary system and a secondary system that must respect interference protection constraints on the primary system. In particular, we propose a secondary satellite selection framework and algorithm that maximizes capacity while guaranteeing that the time-average interference and absolute interference inflicted upon each primary ground user never exceeds specified thresholds. We solve this NP-hard constrained, combinatorial satellite selection problem through Lagrangian relaxation to decompose it into simpler problems which can then be solved through subgradient methods. A high-fidelity simulation is developed based on public FCC filings and technical specifications of the Starlink and Kuiper systems. We use this case study to illustrate the effectiveness of our approach and that explicit protection is indeed necessary for healthy coexistence. We further demonstrate that deep learning models can be used to predict the primary satellite system associations, which helps the secondary system avoid inflicting excessive interference and maximize its own capacity.

Deep neural network (DNN)-based algorithms are emerging as an important tool for many physical and MAC layer functions in future wireless communication systems, including for large multi-antenna channels. However, training such models typically requires a large dataset of high-dimensional channel measurements, which are very difficult and expensive to obtain. This paper introduces a novel method for generating synthetic wireless channel data using diffusion-based models to produce user-specific channels that accurately reflect real-world wireless environments. Our approach employs a conditional denoising diffusion implicit model (cDDIM) framework, effectively capturing the relationship between user location and multi-antenna channel characteristics. We generate synthetic high fidelity channel samples using user positions as conditional inputs, creating larger augmented datasets to overcome measurement scarcity. The utility of this method is demonstrated through its efficacy in training various downstream tasks such as channel compression and beam alignment. Our diffusion-based augmentation approach achieves over a 1-2 dB gain in NMSE for channel compression, and an 11 dB SNR boost in beamforming compared to prior methods, such as noise addition or the use of generative adversarial networks (GANs).

This paper introduces a novel deep learning-based user-side feedback reduction framework, termedself-nomination. The goal of self-nomination is to reduce the number of users (UEs) feeding back channel state information (CSI) to the base station (BS), by letting each UE decide whether to feed back based on its estimated likelihood of being scheduled and its potential contribution to precoding in a multiuser MIMO (MU-MIMO) downlink. Unlike SNR- or SINR-based thresholding methods, the proposed approach uses rich spatial channel statistics and learns nontrivial correlation effects that affect eventual MU-MIMO scheduling decisions. To train the self-nomination network under an average feedback constraint, we propose two different strategies: one based on direct optimization with gradient approximations, and another using policy gradient-based optimization with a stochastic Bernoulli policy to handle non-differentiable scheduling. The framework also supports proportional-fair scheduling by incorporating dynamic user weights. Numerical results confirm that the proposed self-nomination method significantly reduces CSI feedback overhead. Compared to baseline feedback methods, self-nomination can reduce feedback by as much as 65%, saving not only bandwidth but also allowing many UEs to avoid feedback altogether (and thus, potentially enter a sleep mode). Self-nomination achieves this significant savings with negligible reduction in sum-rate or fairness.

In this paper, we consider a matrix function generalization of the Laplace transform of a random variable, termed the matrix Laplace transform. We characterize the conditions under which the matrix Laplace transform exists, establish its relation to the higher order moments and CCDF of a random variable, and derive the matrix Laplace transform of general Poisson shot noise. Techniques leveraging matrix Laplace transforms can provide improved tractability in the analysis of wireless networks using stochastic geometry. In particular, when one considers the underlying point process of transmitters in the network to follow a Poisson Point Process (PPP), techniques exploiting matrix Laplace transforms provide tractable expressions for the coverage probability of the network when the fading power on the desired signal follows a general phase-type distribution, the metadistribution of the SINR when the fading power on the desired signal follows an exponential distribution, and the distribution of the interference power observed by the typical user in the network.

We develop tractable characterizations of the interference resulting from terrestrial cellular networks radiating towards passive satellite sensing receivers. Such a setting has important implications for the future allocation and terrestrial use of spectrum in the 100 to 300 GHz band. Building on a recently developed stochastic geometry approach, we focus on the outage probability experienced by to a constellation of satellite sensors, which depends upon the distribution of the interference experienced by a typical satellite sensor. The distribution is a function of spatial and temporal randomness. We obtain upper bounds on the outage probability using a large deviation technique for Poisson shot noise, which is a novel adaptation of the Chernoff technique. This analytical method allows for the distribution of the interference to be tightly and tractably bounded. Our analysis theoretically confirms that the satellite sensor's outage probability decreases exponentially as the interference constraint is relaxed, and allows bounding of very low outage probability values, which would be very difficult to simulate.

We consider a generalization of the Laplace transform of Poisson shot noise defined as an integral transform with respect to a matrix exponential. We denote this as the matrix Laplace transform and establish that it is in general a matrix function extension of the scalar Laplace transform. We show that the matrix Laplace transform of Poisson shot noise admits an expression analogous to that implied by Campbell’s theorem. We demonstrate the utility of this generalization of Campbell’s theorem in two important applications: the characterization of a Poisson shot noise process and the derivation of the complementary CDF (CCDF) and meta-distribution of signal-to-interference-and-noise (SINR) models in Poisson networks. In the former application, we demonstrate how the higher order moments of Poisson shot noise may be obtained directly from the elements of its matrix Laplace transform. We further show how the CCDF of this object may be bounded using a summation of the first row of its matrix Laplace transform. For the latter application, we show how the CCDF of SINR models with phase-type distributed desired signal power may be obtained via an expectation of the matrix Laplace transform of the interference and noise, analogous to the canonical case of SINR models with Rayleigh fading. Additionally, when the power of the desired signal is exponentially distributed, we establish that the meta-distribution may be obtained in terms of the limit of a sequence expressed in terms of the matrix Laplace transform of a related Poisson shot noise process.

This work provides a rigorous assessment of the feasibility of spectrum sharing between large low-earth orbit (LEO) satellite constellations. For concreteness, we focus on the existing Starlink system and the soon-to-be-launched Kuiper system, the latter of which is prohibited from inflicting excessive interference onto incumbent Starlink ground users. We carefully model and study the potential downlink interference between the two systems at 20 GHz and investigate how strategic satellite selection may be used by Kuiper to serve its own ground users while also protecting Starlink ground users. We then extend this notion of satellite selection to the case where Kuiper has limited knowledge of Starlink’s serving satellite. Throughout our analysis, we examine the distribution of interference and SINR over time as each constellation orbits the globe. Our findings reveal that there is virtually always the potential for very high or extremely low interference, depending on which Starlink and Kuiper satellites are being used to serve their ground users. Consequently, we show that Kuiper can protect Starlink ground users, with high probability, by strategically selecting which of its satellites are used to serve its ground users. Simultaneously, Kuiper is capable of delivering near-maximal downlink SINR to its own ground users. This highlights a potential feasible route to the coexistence of two dense LEO satellite systems, even in scenarios where one system has limited knowledge of the other’s serving satellites.

This paper proposes and analyzes novel deep learning methods for downlink (DL) single-user multiple-input multiple-output (MIMO) and multi-user MIMO (MU-MIMO) systems operating in time division duplex mode. A motivating application is the 6G upper midbands (7-24 GHz), where the base station (BS) antenna arrays are large, user equipment array sizes are moderate, and theoretically optimal approaches are practically infeasible for several reasons. To deal with uplink (UL) pilot overhead and low signal power issues, we introduce the channel-adaptive pilot, as part of the novel analog channel state information feedback mechanism. Deep neural network (DNN)-generated pilots are used to linearly transform the UL channel matrix into lower-dimensional latent vectors. Meanwhile, the BS employs a second DNN that processes the received UL pilots to directly generate near-optimal DL precoders. The training is end-to-end which exploits synergies between the two DNNs. For MU-MIMO precoding, we propose a DNN structure inspired by theoretically optimum linear precoding. The proposed methods are evaluated against genie-aided upper bounds and conventional approaches, using realistic upper midband datasets. Numerical results demonstrate the potential of our approach to achieve significantly increased sum-rate, particularly at moderate to high signal-to-noise ratio and when UL pilot overhead is constrained.

This paper presents a sensor-aided pose-aware beamwidth adaptation design for a conceptual extended reality (XR) Head-Mounted Display (HMD) equipped with a 2D planar array. The beam is tracked and adapted on the user side by leveraging HMD orientation estimates. The beamwidth adaptation scheme is effected by selective deactivation of elements in the 2D antenna array, employing the angular estimation covariance matrix to overlap the beam with the estimation confidence interval. The proposed method utilizes the estimation correlations to adapt the beamwidth along the confidence interval of these estimates. Compared to a beamwidth adaptation without leveraging estimation correlations, the proposed method demonstrates the gain of leveraging estimation correlations by improving the coverage area for a given outage probability threshold by approximately 16 %, or equivalently increasing the power efficiency up to 18 %.

This work investigates the in-band coexistence between two dense low-earth orbit (LEO) satellite communication systems by analyzing two preeminent large-scale constellations, namely Starlink and Kuiper, both which have been granted non-exclusive rights to operate at 20 GHz. Through extensive simulation of Starlink and Kuiper based on their public filings, we examine downlink performance of both systems when Kuiper is obliged to protect Starlink by not inflicting prohibitive interference onto its ground users. We show that Kuiper is capable of reliably satisfying a strict protection constraint at virtually all times by strategically selecting which overhead satellites are used to serve its ground users. In fact, while protecting Starlink users in this way, our results show that Kuiper can remarkably also deliver near-maximal downlink SINR to its own ground users, revealing a feasible route to fruitful coexistence of both systems. For instance, as the constellations orbit the globe, we show that Kuiper is always capable of keeping its inflicted interference at least 12 dB below noise and in doing so sacrifices only about 1 dB in SINR over 80% of the time.

For millimeter wave (mmWave) communication, fast and accurate beam alignment is essential but challenging. Site-specific beam adaptation using deep learning is a very promising paradigm for beam alignment, but such methods typically require a lot of clean channel measurements for training, which can be difficult or even impossible to achieve in practice. This paper introduces a novel method to learn beam alignment policies using only uplink (UL) pilot measurements. The proposed method integrates a generative adversarial network (GAN)-based channel estimation (CE) model with an unsupervised deep learning model beam alignment engine (BAE). We introduce an efficient form of dataset amplification for improved training that leverages the randomness of the deep generative model (DGM) and an early stopping mechanism. Our experiments show that the GAN-BAE method achieves a better signal-to-noise ratio (SNR) by nearly 3 dB compared to compressed sensing (CS) methods such as orthogonal matching pursuit (OMP) and EM-GM-AMP (an Approximate Message Passing algorithm), especially when there are limited pilot measurements from each mobile user.

Wireless use cases such as spectrum sharing and Massive Machine Type Communications (mMTC) can benefit from the detection of unknown signals, which includes estimating their received power as well as other key characteristics such as bandwidth, modulation type, and waveform. While conventional signal detection methods are susceptible to noise, deep learning (DL) models offer a more robust alternative. Previously, DL models were used for solving simpler problems, focusing mainly on modulation recognition. We propose an advanced DL neural network structure that extracts the parameters of 5G NR frequency range 2 (FR2) mmWave test model waveforms. We evaluate our framework on a state-of-the-art signal generator and vector signal analyzer (VSA) that mimics real-world detection. Our work shows that incorporating curriculum training (CT) on both additive white Gaussian noise (AWGN) and frequency shift error enhances the model's accuracy across all SNR and frequency shift ranges. We further enhance the accuracy by employing the error vector magnitude (EVM) function to prioritize the top five scored parameters and validate selected parameters. As a result, our method consistently achieves an accuracy rate exceeding 90% when extracting the key parameters from 5G NR FR2 mmWave waveforms at diverse noise levels.

Coexistence between 5G cellular networks and incumbent radar systems is necessary for an increasing number of spectral bands, including highly valuable spectrum such as the C-band. This paper presents a novel coexistence framework that intelligently adjusts 5G antenna parameters to mitigate interference reaching known radar systems, while simultaneously maximizing cellular network performance. The framework leverages Gaussian process regression and differential evolution to navigate high-dimensional, non-convex spaces while effectively managing uncertainty. We propose a practical approach that utilizes user RSRP measurements to characterize communication interference on radar, addressing the non-cooperative nature of radar systems. Evaluation on AT&T Labs' high-fidelity simulator demonstrates over a 12% increase in sum-log-rate and around a 3.6 dB increase in median SINR compared to the exhaustive search with common parameter configurations across all base stations, while decreasing interference on radar to its lowest achievable level in our simulation setup.

This work investigates the joint optimization of coverage, capacity, and cell load by tuning several cell-specific antenna and cell association parameters via data-driven methods. We are particularly focused on the complexities of macrocell and small cell coexistence, and demonstrate an automated learning method whereby macrocells and small cells can strategically adapt their coverage areas. Coupled with adaptive offloading using a tunable small cell bias, we demonstrate significant throughput and coverage improvement in a realistic 5G network simulator developed by AT&T Labs. Concretely, we formulate an optimization problem to maximize network coverage and the application-layer data rate experienced by users, accounting for delays from congestion, cell loading, and packet retransmissions. We propose an algorithm that approaches the optimum via Gaussian process models and the evolutionary search: efficiently navigating the high-dimensional, nonconvex space while managing uncertainty. Our results show that the joint optimization of antenna tuning and load balancing - exemplified by load-aware cell shaping - more than doubles the cell edge throughput and increases the cell edge SINR by 8 dB, compared to bias-only optimization. Furthermore, our algorithm and overall approach appear viable for implementation.

Ultradense cell-free massive multiple-input multiple-output (CF-MMIMO) has emerged as a promising technology expected to meet the future ubiquitous connectivity requirements and ever-growing data traffic demands in sixth generation (6G). This article provides a contemporary overview of ultradense CF-MMIMO networks and addresses important unresolved questions on their future deployment. We first present a comprehensive survey of state-of-the-art research on CF-MMIMO and ultradense networks. Then, we discuss the key challenges of CF-MMIMO under ultradense scenarios such as low-complexity architecture and processing, low-complexity/scalable resource allocation, fronthaul limitation, massive access, synchronization, and channel acquisition. Finally, we answer key open questions, considering different design comparisons and discussing suitable methods dealing with the key challenges of ultradense CF-MMIMO. The discussion aims to provide a valuable roadmap for interesting future research directions in this area, facilitating the development of CF-MMIMO for 6G.

From an information theoretic perspective, joint communication and sensing (JCAS) represents a natural generalization of communication network functionality. However, it requires the re-evaluation of network performance from a multi-objective perspective. We develop a novel mathematical framework for characterizing the sensing and communication coverage probability and ergodic rate in JCAS networks. We employ a formulation of sensing parameter estimation based on mutual information to extend the notions of coverage probability and ergodic rate to the radar setting. We define sensing coverage probability as the probability that the rate of information extracted about the parameters of interest associated with a typical radar target exceeds some threshold, and sensing ergodic rate as the spatial average of the aforementioned rate of information. Using this framework, we analyze the downlink sensing and communication coverage and rate of a mmWave JCAS network employing a shared waveform, directional beamforming, and monostatic sensing. Leveraging tools from stochastic geometry, we derive upper and lower bounds for these quantities. We also develop several general technical results including: i) a generic method for obtaining closed form upper and lower bounds on the Laplace Transform of a shot noise process, ii) a new analog of Hölder’s Inequality to the setting of harmonic means, and iii) a relation between the Laplace and Mellin Transforms of a non-negative random variable. We use the derived bounds to numerically investigate the performance of JCAS networks under varying base station and blockage density. Among several insights, our numerical analysis indicates that network densification improves sensing SINR performance – in contrast to communications.

Cellular networks are becoming increasingly heterogeneous with higher base station (BS) densities and ever more frequency bands, making BS selection and band assignment key decisions in terms of user service rate and coverage. In this paper, we decompose the mobility-aware user association task into (i) forecasting of user data rate and then (ii) convex utility maximization for user association accounting for the effects of BS load and handover overheads. Using a linear combination of normalized mean-squared error (NMSE) and normalized discounted cumulative gain (NDCG) as a novel loss function, a recurrent deep neural network is trained to reliably forecast the mobile users’ future data rates. Based on the forecast, the controller optimizes the association decisions to maximize the service rate-based network utility using our computationally efficient (speed up of 100× versus generic convex solver) algorithm based on the Frank-Wolfe method. Using an industry-grade network simulator developed by Meta, we show that the proposed model predictive control (MPC) approach improves the 5th percentile service rate by 3.5× compared to the traditional signal strength-based association, reduces the median number of handovers by 7× compared to a handover agnostic strategy, and achieves service rates close to a genie-aided scheme. Furthermore, our model-based approach is significantly more sample-efficient (needs 100× less training data) compared to model-free reinforcement learning (RL), and generalizes well across different user drop scenarios.

Beam alignment is a critical bottleneck in millimeter wave communication. An ideal beam alignment technique should achieve high beamforming gain with low latency, scale well to systems with higher carrier frequencies, larger antenna arrays and multiple user equipment, and not require hard-to-obtain context information. These qualities are collectively lacking in existing methods. We depart from the conventional codebook-based (CB) approach where the optimal beam is chosen from quantized codebooks and instead propose a grid-free beam alignment method that directly synthesizes the transmit and receive beams from the continuous search space using measurements from a few site-specific probing beams found via a deep learning pipeline. In realistic settings, the proposed method achieves a far superior signal-to-noise ratio (SNR)-latency trade-off compared to the CB baselines: it aligns near-optimal beams 100x faster or equivalently finds beams with 10–15 dB higher average SNR in the same number of searches, relative to an exhaustive search over a conventional codebook.

We propose a novel framework for optimizing antenna parameter settings in a heterogeneous cellular network. We formulate an optimization problem for both coverage and capacity– in both the downlink (DL) and uplink (UL)– which configures the tilt angle, vertical half-power beamwidth (HPBW), and horizontal HPBW of each cell’s antenna array across the network. The novel data-driven framework proposed for this nonconvex problem, inspired by Bayesian optimization (BO) and differential evolution algorithms, is sample-efficient and converges quickly, while being scalable to large networks. By jointly optimizing DL and UL performance, we take into account the different signal power and interference characteristics of these two links, allowing a graceful trade-off between coverage and capacity in each one. Our experiments on a state-of-the-art 5G NR cellular system-level simulator developed by AT&T Labs show that the proposed algorithm consistently and significantly outperforms the 3GPP default settings, random search, and conventional BO. In one realistic setting, and compared to conventional BO, our approach increases the average sum-log-rate by over 60% while decreasing the outage probability by over 80%. Compared to the 3GPP default settings, the gains from our approach are considerably larger. The results also indicate that the practically important combination of DL throughput and UL coverage can be greatly improved by joint UL-DL optimization.

As cellular networks embrace heterogeneity with higher base station (BS) densities and ever more frequency bands, BS selection and band assignment become increasingly key decisions in terms of rate and coverage optimization. In this paper, we propose a novel learning-based model predictive control (MPC) approach for BS selection and band assignment while accounting for user mobility. We formulate a convex utility maximization problem that accounts for the effects of BS load and handover overheads on the user's service rate. Using a linear combination of normalized mean-squared error (NMSE) and$\mathbf{top}-m$loss as a novel loss function, a recurrent deep neural network is trained to reliably forecast the mobile users' future rates. The MPC controller then uses this forecast to optimize the association decisions to maximize the service rate-based network utility. Using an industry-grade network simulator developed by Meta, we show that the proposed approach improves the 5th percentile service rate by$2.7\times$compared to the traditional signal strength-based association and its performance approaches that of a genie-aided scheme in terms of the achieved service rate and the number of handovers triggered.

Characterizing self-interference is essential to the design and evaluation of in-band full-duplex communication systems. Until now, little has been understood about this coupling in full-duplex systems operating at millimeter wave (mmWave) frequencies, and it has been shown that the highly-idealized models proposed for such do not align with practice. This work presents the first spatial and statistical model of mmWave self-interference backed by measurements, enabling engineers to draw realizations that exhibit the large-scale and small-scale spatial characteristics observed in our nearly 6.5 million measurements taken at 28 GHz. Core to our model is its use of system and model parameters having real-world meaning, which facilitates its extension to systems beyond our own phased array platform through proper parameterization. We demonstrate this by collecting nearly 13 million additional measurements to show that our model can generalize to two other system configurations. We assess our model by comparing it against actual measurements to confirm its ability to align spatially and in distribution with real-world self-interference. In addition, using both measurements and our model of self-interference, we evaluate an existing beamforming-based full-duplex mmWave solution to illustrate that our model can be reliably used to design new solutions and validate the performance improvements they may offer.

Integrated access and backhaul (IAB) facilitates cost-effective deployment of millimeter wave (mmWave) cellular networks through multihop self-backhauling. Full-duplex (FD) technology, particularly for mmWave systems, is a potential means to overcome latency and throughput challenges faced by IAB networks. We derive practical and tractable throughput and latency constraints using queueing theory and formulate a network utility maximization problem to evaluate both full-duplex (FD)-IAB and half-duplex (HD)-IAB networks. We use this to characterize the network-level improvements seen when upgrading from conventional HD IAB nodes to FD ones by deriving closed-form expressions for (i) latency gain of FD-IAB over HD-IAB and (ii) the maximum number of hops that a HD- and FD-IAB network can support while satisfying latency and throughput targets. Extensive simulations illustrate that FD-IAB can facilitate reduced latency, higher throughput, deeper networks, and fairer service. Compared to HD-IAB, FD-IAB can improve throughput by$8\times $and reduce latency by$4\times $for a fourth-hop user. In fact, upgrading IAB nodes with FD capability can allow the network to support latency and throughput targets that its HD counterpart fundamentally cannot meet. The gains are more profound for users further from the donor and can be achieved even when residual self-interference is significantly above the noise floor.

This work develops LoneSTAR, a novel enabler of full-duplex millimeter wave (mmWave) communication systems through the design of analog beamforming codebooks. LoneSTAR codebooks deliver high beamforming gain and broad coverage while simultaneously reducing the self-interference coupled by transmit and receive beams at a full-duplex mmWave transceiver. Our design framework accomplishes this by tolerating some variability in transmit and receive beamforming gain to strategically shape beams that reject self-interference spatially while accounting for digitally-controlled analog beamforming networks and self-interference channel estimation error. By leveraging the coherence time of the self-interference channel, a mmWave system can use the same LoneSTAR design over many time slots to serve several downlink-uplink user pairs in a full-duplex fashion without the need for additional self-interference cancellation. Compared to those using conventional codebooks, full-duplex mmWave systems employing LoneSTAR codebooks can mitigate higher levels of self-interference, tolerate more cross-link interference, and demand lower SNRs in order to outperform half-duplex operation—all while supporting beam alignment. This makes LoneSTAR a potential standalone solution for enabling simultaneous transmission and reception in mmWave systems, from which it derives its name.

Beam alignment - finding optimal analog beam-forming (BF) weights - is a critical bottleneck for millimeter wave (mmWave) systems. Existing beam alignment approaches typically assume that devices adopt codebooks of analog beams with uniform coverage, from which a good beam pair is selected after an exhaustive search or sweeping a few candidate beams. In this work, we propose a beam alignment method that is grid-less - the analog beam is synthesized from the continuous set instead of being chosen from a quantized codebook, and one-shot - near-optimal BF weights are directly predicted without searching even a small number of candidates. With unsupervised training, the proposed method uses a few learned probing beams to sense the channel and predict the BF weights. Our experiments show that it can get within 0.32 dB of the hard theoretical upper bound, outperforms the exhaustive search in terms of the signal-to-noise ratio (SNR), reduces the beam sweeping latency by over 20×, while scaling optimally to multiple UEs and fitting within the 5G NR beam alignment framework.

In this paper, we jointly optimize the capacity and coverage of both uplink and downlink transmissions by tuning the downtilt angle, vertical half-power beamwidth (HPBW), and horizontal HPBW of each cell's antenna array across a heterogeneous cellular network. We formulate an optimization problem and propose a novel sample-efficient algorithm to solve this non-convex problem. We evaluate our framework on a state-of-the-art cellular system-level simulator developed by AT&T Labs by comparing it with the 3GPP baseline. Example results tuned to optimize uplink coverage and downlink rate indicate that jointly optimizing the uplink and downlink directions improves uplink median and 5% outage SINR by (i) 1.6 dB and 4.5 dB, respectively, compared to downlink only-optimization and by (ii) 6.7 dB and 14.6 dB compared to the 3GPP baseline. Simultaneously, we can increase downlink median and outage SINR by comparable amounts compared to uplink-only optimization, but with larger gains in median SINR and downlink sum-rate. Our results indicate that there are significant gains to be harvested from site-specific data-driven base station parameter optimization, and they can be achieved in a scalable and automated fashion.

Machine-learning based transceivers have received increasing attention for next-generation wireless systems. We investigate the application of two meta-learning algorithms – Model Agnostic Meta Learning (MAML) and Reptile – to a deep learning-based Wi-Fi channel estimation and tracking system, called DeepWiPHY. The meta-learning algorithms were compared against conventional methods such as random initialization, cross-evaluation, and retraining on multiple channel models with varying severity of multipath fading. Comparisons were made fairly with respect to the complexity of the adaptation of the model necessary for a new environment. The results indicate that perhaps surprisingly, conventional training methods are adequate and in fact can outperform meta-learning methods over a wide variety of channels. The key is to train the receiver using the worst-case (most severe) multipath channel model, which then allows strong performance across a wide class of channels without requiring the additional burden of meta-learning.

We present measurements of the 28 GHz self-interference channel for full-duplex sectorized multi-panel millimeter wave (mmWave) systems, such as integrated access and backhaul. We measure the isolation between the input of a transmitting phased array panel and the output of a co-located receiving phased array panel, each of which is electronically steered across a number of directions in azimuth and elevation. In total, nearly 6.5 million measurements were taken in an anechoic chamber to densely inspect the directional nature of the coupling between 256-element phased arrays. We observe that highly directional mmWave beams do not necessarily offer widespread high isolation between transmitting and receiving arrays. Rather, our measurements indicate that steering the transmitter or receiver away from the other tends to offer higher isolation but even slight steering changes can lead to drastic variations in isolation. These measurements can be useful references when developing mmWave full-duplex solutions and can motivate a variety of future topics including beam/user selection and beamforming codebook design.

In mmWave networks, a large or nearby object can obstruct multiple communication links, which results in spatial correlation in the blocking probability between a user and two or more base stations (BSs). This paper characterizes this blocking correlation and derives its impact on the signal-to-interference-plus-noise ratio (SINR) of a mmWave cellular network. We first present an exact analysis of a 1D network and highlight the impact of blocking correlation in the derived expressions. Gaining insights from the 1D analysis, we develop an analytical framework for a 2D network where we characterize the sum interference at the user by considering the correlation between the blocking of serving and interfering links. Using this, we derive the SINR coverage probability. Via simulations, we demonstrate that including blockage correlation in the analysis is required for accurate characterization of the system performance, in particular when the blocking objects tend to be large.

Modern millimeter wave (mmWave) communication systems rely on beam alignment to deliver sufficient beamforming gain to close the link between devices. We present a novel beam selection methodology for multi-panel, full-duplex mmWave systems, which we call Steer, that delivers high beamforming gain while significantly reducing the full-duplex self-interference coupled between the transmit and receive beams. Steer does not necessitate changes to conventional beam alignment methodologies nor additional over-the-air feedback, making it compatible with existing cellular standards. Instead, Steer uses conventional beam alignment to identify the general directions beams should be steered, and then it makes use of a minimal number of self-interference measurements to jointly select transmit and receive beams that deliver high gain in these directions while coupling low self-interference. We implement Steer on an industry-grade 28 GHz phased array platform and use further simulation to show that full-duplex operation with beams selected by Steer can notably outperform both half-duplex and full-duplex operation with beams chosen via conventional beam selection. For instance, Steer can reliably reduce self-interference by more than 20 dB and improve SINR by more than 10 dB, compared to conventional beam selection. Our experimental results highlight that beam alignment can be used not only to deliver high beamforming gain in full-duplex mmWave systems but also to mitigate self-interference to levels near or below the noise floor, rendering additional self-interference cancellation unnecessary with Steer.

Beam alignment – the process of finding an optimal directional beam pair – is a challenging procedure crucial to millimeter wave (mmWave) communication systems. We propose a novel beam alignment method that learns a site-specific probing codebook and uses the probing codebook measurements to predict the optimal narrow beam. An end-to-end neural network (NN) architecture is designed to jointly learn the probing codebook and the beam predictor. The learned codebook consists of site-specific probing beams that can capture particular characteristics of the propagation environment. The proposed method relies on beam sweeping of the learned probing codebook, does not require additional context information, and is compatible with the beam sweeping-based beam alignment framework in 5G. Using realistic ray-tracing datasets, we demonstrate that the proposed method can achieve high beam alignment accuracy and signal-to-noise ratio (SNR) while significantly – by roughly a factor of 3 in our setting – reducing the beam sweeping complexity and latency.

Beamforming with high dimensional antenna arrays provides the gain needed to enable high bandwidth communication in the sub-terahertz (THz) band. The resulting narrow beams, however, come at the cost of increased sensitivity to beam alignment errors. A potential remedy to this problem is to introduce a form a macrodiversity through non-coherent joint transmission (NC-JT). We employ a stochastic geometry framework to analyze the performance of a THz network employing user-centric base station clustering and NC-JT. We derive semi-closed form lower bounds for the coverage probability and ergodic capacity experienced by a typical user in the network. Our model includes THz networks without joint transmission as a special case. Overall, our analysis indicates that joint transmission from a few base stations improves coverage and capacity by mitigating the impact of beam misalignment. Moreover, in certain settings, NC-JT is a more efficient usage a network access points compared to the non-cooperative case, and reduces the sensitivity of coverage and capacity to the choice of user beamwidth.

We present measurements and analysis of self-interference in multi-panel millimeter wave (mmWave) full-duplex communication systems at 28 GHz. In an anechoic chamber, we measure the self-interference power between the input of a transmitting phased array and the output of a colocated receiving phased array, each of which is electronically steered across a number of directions in azimuth and elevation. These self-interference power measurements shed light on the potential for a full-duplex communication system to successfully receive a desired signal while transmitting in-band. Our nearly 6.5 million measurements illustrate that more self-interference tends to be coupled when the transmitting and receiving phased arrays steer their beams toward one another but that slight shifts in steering direction (on the order of one degree) can lead to significant fluctuations in self-interference power. We analyze these measurements to characterize the spatial variability of self-interference to better quantify and statistically model this sensitivity. Our analyses and statistical results can be useful references when developing and evaluating mmWave full-duplex systems and motivate a variety of future topics including beam selection, beamforming codebook design, and self-interference channel modeling.

Cellular networks continue to trend rapidly towards more bands and carrier frequencies, along with higher base station density, requiring complex decisions to be made when associating a mobile user with a band and cell. This paper develops a novel approach to optimizing frequency band and cell selection while taking into account user mobility and handovers. This is a complex problem because of the uncertain link failure events, handover related overheads, and the significant difference in the propagation characteristics between different frequency bands. The network dynamics due to user mobility are modeled as a Markov decision process, and we develop a recurrent Q-learning framework to exploit the relationship between user trajectories and the history of SINR measurements. The effective cell boundaries are therefore based on user trajectories and velocities rather than just position and signal strength. Detailed system-level simulations show that the proposed learning-based approach improves the throughput of the edge users by 54% and the median throughput by 34% compared to traditional SINR-based association and achieves a superior rate/coverage tradeoff (quantified as sum-log-rate) compared to SINR or signal-strength-based associations.

Beam alignment - the process of finding an optimal directional beam pair - is a challenging procedure crucial to millimeter wave (mmWave) communication systems. In this work, we propose a beam alignment method that learns a site-specific probing codebook and uses the probing codebook measurements to predict the optimal narrow beam. A novel neural network (NN) architecture is designed to jointly learn the probing codebook and the beam predictor in an end-to-end fashion. The learned codebook consists of site-specific probing beams that can capture particular characteristics of the propagation environment. The proposed method relies on beam sweeping of the learned probing codebook, does not require additional context information and is compatible with the beam sweeping-based beam alignment framework in 5G. We demonstrate using realistic ray-tracing data that the proposed method can achieve high beam alignment accuracy and signal-to-noise ratio (SNR) while significantly reducing the beam sweeping complexity and latency.

The coming extension of cellular technology to base-stations in low-earth orbit (LEO) requires a fresh look at terrestrial 3GPP channel models. Relative to such models, sky-to-ground cellular channels will exhibit less diffraction, deeper shadowing, larger Doppler shifts, and possibly far stronger cross-cell interference: consequences of high elevation angles and extreme “sectorization” of LEO satellite transmissions into partially-overlapping spot beams. To permit forecasting of expected signal-to-noise ratio (SNR), interference-to-noise ratio (INR), and probability of outage, we characterize the powers of desired and interference signals as received by ground users from such a LEO satellite. In particular, building on the Shadowed Rician (SR) channel model, we observe that co-cell and cross-cell sky-to-ground signals travel along similar paths, whereas terrestrial co- and cross-cell signals travel along very different paths. We characterize SNR, signal-to-interference ratio (SIR), and INR using transmit beam profiles and linear relationships that we establish between certain SR random variables. These tools allow us to simplify certain density functions and moments, facilitating future analysis. Numerical results yield insight into the key question of whether emerging LEO systems should be viewed as interference- or noise-limited.

We develop a novel stochastic geometry framework to quantify the SINR coverage probability of a Terahertz (THz) cellular network. THz frequencies will require highly directional beams, leading to inevitably imperfect beam alignment. We derive a tractable and accurate semi-closed form lower bound for the coverage probability of a typical user in the network, introducing a novel approach of characterizing non line-of-sight (NLOS) links as equivalent LoS links using a non-homogeneous Poisson Point Process. We use the coverage bound to investigate the SINR scaling trends with base station density and array directivity at the base station and user. Dense base station deployments are required to achieve sufficient coverage and our analysis exposes a tradeoff between directivity (array gain) and loss in SINR due to misalignment.

This paper develops a novel methodology for designing analog beamforming codebooks for full-duplex millimeter wave (mmWave) transceivers, the first such codebooks to the best of our knowledge. Our design reduces the self-interference coupled by transmit-receive beam pairs and simultaneously delivers high beamforming gain over desired coverage regions, allowing mmWave full-duplex systems to support beam alignment while minimizing self-interference. To do so, our methodology allows some variability in beamforming gain to strategically shape beams that reject self-interference while still having substantial gain. We present an algorithm for approximately solving our codebook design problem while accounting for the non-convexity posed by digitally-controlled phase shifters and attenuators. Numerical results suggest that our design can outperform or nearly match existing codebooks in sum spectral efficiency across a wide range of self-interference power levels. Results show that our design offers an extra 20–50 dB of robustness to selfinterference, depending on hardware constraints.

Finding an optimum configuration of base station (BS) antenna parameters is a challenging, non-convex problem for cellular networks. The chosen configuration has major implications for coverage and throughput in real-world systems, as it effects signal strength differently throughout the cell, as well as dictating the interference caused to other cells. In this paper, we propose a novel and sample-efficient data-driven methodology for optimizing antenna downtilt angles. Our approach combines Bayesian optimization (BO) with Differential Evolution (DE): BO decreases the computational burden of DE, while DE helps BO avoid the curse of dimensionality. We evaluate the performance on a realistic state-of-the-art cellular system simulator developed by AT&T Labs, that includes all layers of the protocol stack and sophisticated channel models. Our results show that the proposed algorithm outperforms Bayesian optimization, random selection, and the baseline settings adopted in 3GPP by nontrivial amounts in terms of both capacity and coverage. Also, our approach is notably more time-efficient than DE alone.

This paper presents a novel compressed sensing (CS) approach to high dimensional wireless channel estimation by optimizing the input to a deep generative network. Channel estimation using generative networks relies on the assumption that the reconstructed channel lies in the range of a generative model. Channel reconstruction using generative priors outperforms conventional CS techniques and requires fewer pilots. It also eliminates the need of a priori knowledge of the sparsifying basis, instead using the structure captured by the deep generative model as a prior. Using this prior, we also perform channel estimation from one-bit quantized pilot measurements, and propose a novel optimization objective function that attempts to maximize the correlation between the received signal and the generator's channel estimate while minimizing the rank of the channel estimate. Our approach significantly outperforms sparse signal recovery methods such as Orthogonal Matching Pursuit (OMP) and Approximate Message Passing (AMP) algorithms such as EM-GM-AMP for narrowband mmWave channel reconstruction, and its execution time is not noticeably affected by the increase in the number of received pilot symbols.

The increasing number of wireless devices operating in unlicensed spectrum motivates the development of intelligent adaptive approaches to spectrum access. We consider decentralized contention-based medium access for base stations (BSs) operating on unlicensed shared spectrum, where each BS autonomously decides whether or not to transmit on a given resource. The contention decision attempts to maximize not its own downlink throughput, but rather a network-wide objective. We formulate this problem as a decentralized partially observable Markov decision process with a novel reward structure that provides long term proportional fairness in terms of throughput. We then introduce a two-stage Markov decision process in each time slot that uses information from spectrum sensing and reception quality to make a medium access decision. Finally, we incorporate these features into a distributed reinforcement learning framework for contention-based spectrum access. Our formulation provides decentralized inference, online adaptability and also caters to partial observability of the environment through recurrent Q-learning. Empirically, we find its maximization of the proportional fairness metric to be competitive with a genie-aided adaptive energy detection threshold, while being robust to channel fading and small contention windows.

We abstract the core logical functions from applications that require ultra-low-latency wireless communications to provide a novel definition for reliability. Real-time applications - such as intelligent transportation, remote surgery, and industrial automation - involve a significant element of control and decision making. Such systems involve three logical components: observers (e.g. sensors) measuring the state of an environment or dynamical system, a centralized executive (e.g. controller) deciding on the state, and agents (e.g. actuators) that implement the executive's decisions. The executive harvests the observers' measurements and decides on the short-term trajectory of the system by instructing its agents to take appropriate actions. All observation packets (typically uplink) and action packets (typically downlink) must be delivered by hard deadlines to ensure the proper functioning of the controlled system. In-full on-time delivery cannot be guaranteed in wireless systems due to inherent uncertainties in the channel such as fading and unpredictable interference; accordingly, the executive will have to drop some packets. We develop a novel framework to formulate the Observer Selection Problem (OSP) through which the executive schedules a sequence of observations that maximize its knowledge about the current state of the system. To solve this problem efficiently yet optimally, we devise a branch-and-bound algorithm that systematically prunes the search space. Our work is different from existing work on real-time communications in that communication reliability is not conveyed by packet loss or error rate, but rather by the extent of the executive's knowledge about the state of the system it controls.

Communication at high carrier frequencies such as millimeter wave (mmWave) and terahertz (THz) requires channel estimation for very large bandwidths at low SNR. Hence, allocating an orthogonal pilot tone for each coherence bandwidth leads to excessive number of pilots. We leverage generative adversarial networks (GANs) to accurately estimate frequency selective channels with few pilots at low SNR. The proposed estimator first learns to produce channel samples from the true but unknown channel distribution via training the generative network, and then uses this trained network as a prior to estimate the current channel by optimizing the network's input vector in light of the current received signal. Our results show that at an SNR of -5 dB, even if a transceiver with one-bit phase shifters is employed, our design achieves the same channel estimation error as an LS estimator with SNR = 20 dB or the LMMSE estimator at 2.5 dB, both with fully digital architectures. Additionally, the GAN-based estimator reduces the required number of pilots by about 70% without significantly increasing the estimation error and required SNR. We also show that the generative network does not appear to require retraining even if the number of clusters and rays change considerably.

Optimizing a hybrid beamforming transmitter is a non-convex problem and requires channel state information, leading in most cases to nontrivial feedback overhead. We propose a methodology relying on the principles of deep generative models and unfolding to achieve near-optimal hybrid beamforming with reduced feedback and computational complexity. We first represent the channel as a low-dimensional manifold via a generative adversarial network (GAN) and search the optimum digital and analog precoders in this low-dimensional space. To decrease the search complexity, we find an iteration rule by formulating hybrid beamforming as a bi-level optimization problem and then unfold each iteration as a neural layer. This results in a novel model-based deep neural network that incorporates domain knowledge. Our results show that this method (i) approaches the capacity-achieving spectral efficiency, (ii) provides a superior energy and spectral efficiency tradeoff, (iii) decreases feedback overhead, and (iv) reduces the complexity significantly, by optimizing a single low-dimensional vector per channel coherence time, with the neural network itself trained offline. The achieved spectral efficiency is robust when tested with realistic 3GPP channel models, even if the offline training relies on a simple geometric channel model.

In cellular systems, the user equipment (UE) can request a change in the frequency band when its rate drops below a threshold on the current band. The UE is then instructed by the base station (BS) to measure the quality of candidate bands, which requires a measurement gap in the data transmission, thus lowering the data rate. We propose an online-learning based band switching approach that does not require any measurement gap. Our proposed classifier-based band switching policy instead exploits spatial and spectral correlation between radio frequency signals in different bands based on knowledge of the UE location. We focus on switching between a lower (e.g., 3.5 GHz) band and a millimeter wave band (e.g., 28 GHz), and design and evaluate two classification models that are trained on a ray-tracing dataset. A key insight is that measurement gaps are overkill, in that only the relative order of the bands is necessary for band selection, rather than a full channel estimate. Our proposed machine learning-based policies achieve roughly 30% improvement in mean effective rates over those of the industry standard policy, while achieving misclassification errors well below 0.5% and maintaining resilience against blockage uncertainty.

Full-duplex millimeter wave (mmWave) communication has shown increasing promise for self-interference cancellation via hybrid precoding and combining. This paper proposes a novel mmWave multiple-input multiple-output (MIMO) design for configuring the analog and digital beamformers of a full-duplex transceiver. This work is the first to holistically consider the key practical constraints of analog beamforming codebooks, a minimal number of radio frequency (RF) chains, limited channel knowledge, beam alignment, and a limited receive dynamic range. To prevent self-interference from saturating receive components, such as LNAs and ADCs, a design framework is developed that limits the degree of self-interference on a per-antenna and per-RF chain basis. We present a means for constructing analog beamforming candidates from beam alignment measurements to afford our design greater flexibility in its aim to reduce self-interference. Numerical results evaluate the design in a variety of settings and validate the need to prevent receiver-side saturation. These results and corresponding insights serve as useful design references and benchmarks for practical full-duplex mmWave transceivers.

In this work, we develop DeepWiPHY, a deep learning-based architecture to replace the channel estimation, common phase error (CPE) correction, sampling rate offset (SRO) correction, and equalization modules of IEEE 802.11ax based orthogonal frequency division multiplexing (OFDM) receivers. We first train DeepWiPHY with a synthetic dataset, which is generated using representative indoor channel models and includes typical radio frequency (RF) impairments that are the source of nonlinearity in wireless systems. To further train and evaluate DeepWiPHY with real-world data, we develop a passive sniffing-based data collection testbed composed of Universal Software Radio Peripherals (USRPs) and commercially available IEEE 802.11ax products. The comprehensive evaluation of DeepWiPHY with synthetic and real-world datasets (110 million synthetic OFDM symbols and 14 million real-world OFDM symbols) confirms that, even without fine-tuning the neural network's architecture parameters, DeepWiPHY achieves comparable performance to or outperforms the conventional WLAN receivers, in terms of both bit error rate (BER) and packet error rate (PER), under a wide range of channel models, signal-to-noise (SNR) levels, and modulation schemes.

System level simulations of large 5G networks are essential to evaluate and design algorithms related to network issues such as scheduling, mobility management, interference management, and cell planning. In this paper, we look back to the idea of spatial indexing and its advantages, applications, and future potentials in accelerating large 5G network simulations. We introduce a multi-level inheritance based architecture which is used to index all elements of a heterogeneous network (HetNet) on a single geometry tree. Then, we define spatial queries to accelerate searches in distance, azimuth, and elevation. We demonstrate that spatial indexing can accelerate location-based searches by 3 orders of magnitude. Further, the proposed design is implemented as an open source platform freely available to all.

This paper proposes a novel deep learning-based error correction coding scheme for AWGN channels under the constraint of one-bit quantization in receivers. Specifically, it is first shown that the optimum error correction code that minimizes the probability of bit error can be obtained by perfectly training a special autoencoder, in which “perfectly” refers to converging the global minima. However, perfect training is not possible in most cases. To approach the performance of a perfectly trained autoencoder with a suboptimum training, we propose utilizing turbo codes as an implicit regularization, i.e., using a concatenation of a turbo code and an autoencoder. It is empirically shown that this design gives nearly the same performance as to the hypothetically perfectly trained autoencoder, and we also provide a theoretical proof of why that is so. The proposed coding method is as bandwidth efficient as the integrated (outer) turbo code, since the autoencoder exploits the excess bandwidth from pulse shaping and packs signals more intelligently thanks to sparsity in neural networks. Our results show that the proposed coding scheme at finite block lengths outperforms conventional turbo codes even for QPSK modulation. Furthermore, the proposed coding method can make one-bit quantization operational even for 16-QAM.

This paper proposes a deep learning-based channel estimation method for multi-cell interference-limited massive MIMO systems, in which base stations equipped with a large number of antennas serve multiple single-antenna users. The proposed estimator employs a specially designed deep neural network (DNN) based on the deep image prior (DIP) network to first denoise the received signal, followed by conventional least-squares (LS) estimation. We analytically prove that our LS-type deep channel estimator can approach minimum mean square error (MMSE) estimator performance for high-dimensional signals, while avoiding complex channel inversions and knowledge of the channel covariance matrix. This analytical result, while asymptotic, is observed in simulations to be operational for just 64 antennas and 64 subcarriers per OFDM symbol. The proposed method also does not require any training and utilizes several orders of magnitude fewer parameters than conventional DNNs. The proposed deep channel estimator is also robust to pilot contamination and can even completely eliminate it under certain conditions.

Multihop self-backhauling is a key enabling technology for millimeter wave cellular deployments. We consider the multihop link scheduling problem with the objective of minimizing the end-to-end delay experienced by a typical packet. This is a complex problem, and so we model the system as a network of queues and formulate it as a Markov decision process over a continuous action space. This allows us to leverage the deep deterministic policy gradient algorithm from reinforcement learning to learn the delay minimizing scheduling policy under two scenarios: 1) an ideal setup where a centralized scheduler performs all per slot scheduling decisions and has full instantaneous knowledge of network state and 2) a centralized scheduler, but where network state feedback and scheduling decisions are limited to once per frame, which is many slots. For the second scenario, we model the scheduler with a recurrent neural network to capture the evolution of the network state over the frame. Detailed system-level simulations show that for the more realistic second scenario, the delay experienced by the 5thpercentile packets under backpressure based scheduling and max-min scheduling can be up to 230% and 260%, respectively more than that under the proposed scheduler.

This paper studies the effect of the user hand grip on the design of beamforming codebooks for 5G millimeter-wave (mmWave) mobile handsets. The high-frequency structure simulator (HFSS) is used to characterize the radiation fields for fourteen possible handgrip profiles based on experiments we conducted. The loss from hand blockage on the antenna gains can be up to 20-25 dB, which implies that the possible hand grip profiles need to be taken into account while designing beam codebooks. Specifically, we consider three different codebook adaption schemes: a grip-aware scheme, where perfect knowledge of the hand grip is available; a semi-aware scheme, where just the application (voice call, messaging, etc.) and the orientation of the mobile handset is known; and a grip-agnostic scheme, where the codebook ignores hand blockage. Our results show that the ideal grip-aware scheme can provide more than 50% gain in terms of the spherical coverage over the agnostic scheme, depending on the grip and orientation. Encouragingly, the more practical semi-aware scheme we propose provides performance approaching the fully grip-aware scheme. Overall, we demonstrate that 5G mmWave handsets are different from pre-5G handsets: the user grip needs to be explicitly factored into the codebook design.

The interactions between the cells, most notably due to their coupled interference and the large number of users, render the optimization of antenna parameters prohibitively complex. To cope with this problem, we propose a novel practical deep learning (DL) based reinforcement learning (RL) algorithm to jointly optimize antenna tilt angle and vertical and horizontal half-power beamwidths of the macrocells in a heterogeneous cellular network (HetNet). In the proposed algorithm, DL is used to extract the features by learning the locations of users, and mean field RL is used to learn the average interference values for different antenna settings. Our results illustrate that the proposed deep RL algorithm can approach the optimum weighted sum rate with hundreds of online trials, as opposed to millions of trials for standard Q-learning, assuming relatively low environmental dynamics. Furthermore, the proposed algorithm is compact and implementable, and empirically appears to provide a performance guarantee regardless of the amount of environmental dynamics.

This paper proposes a deep learning-based error correction coding for AWGN channels under the constraint of one-bit quantization in receivers. An autoencoder is designed and integrated with a turbo code that acts as an implicit regularization. This implicit regularizer facilitates approaching the Shannon bound for the one-bit quantized AWGN channels even if the autoencoder is trained suboptimally, since one-bit quantization stymies ideal training. Our empirical results show that the proposed coding scheme gives better results at finite block lengths than conventional turbo codes even for QPSK modulation, which can achieve the Shannon bound at infinite block length despite one-bit quantization. Furthermore, the proposed coding method makes one- bit quantization operational even for 16-QAM, which is unprecedented.

Beam alignment is a challenging and time-consuming process for millimeter wave (mmWave) initial access (IA). We propose a beam training method that is assisted by machine learning (ML), where we train ML models to predict the optimal Access Point (AP) and optimal beam for a user equipment (UE) given its Global Positioning System (GPS) coordinates. After a (possibly offline) training phase during which exhaustive or hierarchical beam training is performed, our beam training method predicts a few candidate APs and beams knowing only the location of the UE. We train the models and evaluate the performance with realistic mmWave beamforming (BF) data generated from state-of-the- art ray tracing software. We show that even with dynamic scatterers and imperfect knowledge of the UE locations, our beam training method can reliably find the optimal AP and the optimal beam for a UE while reducing the search time by 4x for AP selection and over 10x for beam selection.

Many control applications demand stringent latency and reliability requirements that cannot be met by existing wireless technologies. Prior work has modeled a pilot-assisted, variable-rate communication procedure that describes the transmission of commands from a centralized controller to a number of agents (e.g. actuators) through a number of access points (APs). This procedure comprises two phases with pre-allocated time budgets per transmission cycle. There is a training phase where channel states between AP-agent pairs are estimated, and a downlink phase where the commands are sequentially transmitted at adapted rates before the start of a new cycle - a hard deadline. System reliability is compromised, though, when the agents fail to receive the controller's commands before the start of a subsequent cycle. In this paper, we calculate a closed-form expression for the probability of hard-deadline violation when there are two agents. We find upper and lower bounds on this probability when there are more agents. We observe that these bounds approximate the probability of hard-deadline violation which reflects the reliability of the system.

This paper develops novel deep learning-based architectures and design methodologies for an orthogonal frequency division multiplexing (OFDM) receiver under the constraint of one-bit complex quantization. Single bit quantization reduces greatly the complexity and power consumption but makes accurate channel estimation and data detection difficult. This is particularly true for multicarrier waveforms that have high peak-to-average power ratio in the time domain and fragile subcarrier orthogonality in the frequency domain. The severe distortion for one-bit quantization typically results in an error floor even at moderately low signal-to-noise-ratio (SNR) such as 5 dB. For channel estimation (using pilots), we design a novel generative supervised deep neural network that can be trained with a reasonable number of pilots. After channel estimation, a neural network-based receiver-specifically, an autoencoder-jointly learns a precoder and decoder for data symbol detection. Since quantization prevents end-to-end training, we propose a two-step sequential training policy for this model. With synthetic data, our deep learning-based channel estimation can outperform least squares channel estimation for unquantized (full-resolution) OFDM at average SNRs up to 14 dB. For data detection, our proposed design achieves lower bit error rate (BER) in fading than unquantized OFDM at average SNRs up to 10 dB.

We consider a downlink periodic wireless communications system, where multiple access points cooperatively transmit packets to a number of devices, e.g., actuators in an industrial control system. Each period consists of two phases: an uplink training phase and a downlink data transmission phase. Each actuator must successfully receive its unique packet within a single transmission phase; else, an outage is declared. Such an outage can be caused by two events: a transmission error due to transmission at a rate that the channel cannot actually support or time overflow, where the downlink data phase is too short, given the channel conditions to successfully communicate all the packets. We determine the closed-form expressions for the time overflow probability when there are just two field devices, as well as the transmission error probability for an arbitrary number of devices. In addition, we provide upper and lower bounds on the time overflow probability for an arbitrary number of devices. We propose a novel variable-rate transmission method that eliminates time overflow. Detailed system-level simulations are used to identify system design guidelines, such as the optimal amount of training time, as well as for benchmarking the proposed system design versus non-cooperative cellular, cooperative fixed-rate, and cooperative relaying.

This paper studies the asymptotic properties of average area spectral efficiency (ASE) of a downlink cellular network in the limit of very dense base station (BS) and user densities. This asymptotic analysis relies on three assumptions: 1) interference is treated as noise; 2) the BS locations are drawn from a Poisson point process; and 3) the path loss function is bounded above satisfying mild regularity conditions. We consider three possible definitions of the average ASE, all of which give units of bits per second per unit bandwidth per unit area. When there is no constraint on the minimum operational signal-to-interference-plus-noise ratio (SINR) and instantaneous full channel state information (CSI) is available at the transmitter, the average ASE is proven to saturate to a constant, which we derive in a closed form. For the other two ASE definitions, wherein either a minimum SINR is enforced or CSI is not available, the average ASE is instead shown to collapse to zero at high BS density. We provide several familiar case studies for the class of considered path loss models, and demonstrate that our results cover most previous models and results on ultradense networks as special cases.

Self-organizing networks (SONs) can help to manage the severe interference in dense heterogeneous networks (HetNets). Given their need to automatically configure power and other settings, machine learning is a promising tool for data-driven decision making in SONs. In this paper, a HetNet is modeled as a dense two-tier network with conventional macrocells overlaid with denser small cells (e.g. femto or pico cells). First, a distributed framework based on the multi-agent Markov decision process is proposed that models the power optimization problem in the network. Second, we present a systematic approach for designing a reward function based on the optimization problem. Third, we introduce Q-learning-based distributed power allocation algorithm (Q-DPA) as a self-organizing mechanism that enables the ongoing transmit power adaptation as new small cells are added to the network. Furthermore, the sample complexity of the Q-DPA algorithm to achieve ϵ-optimality with high probability is provided. We demonstrate, at the density of several thousands femtocells per km2, the required quality of service of a macrocell user can be maintained via the proper selection of independent or cooperative learning and appropriate Markov state models.

We show that two point processes Φeqand Φeq2, which were claimed by Yin and Haas to be equivalent in terms of their signal-to-interference-plus-noise ratio (SINR), are, in fact, not SINR equivalent. We discuss the importance of this distinction and explain how the correction impacts the results derived in the original paper.

Future 5G cellular networks supporting delay-sensitive, low-latency communications could employ random access communication to reduce the overhead compared to scheduled access techniques used in 4G networks. We consider a wireless communication system where multiple devices transmit payloads of a given fixed size in a random access fashion over shared radio resources to a common receiver. We allow retransmissions and assume Chase combining at the receiver. The radio resources are partitioned in the time and frequency dimensions, and we determine the optimal partition granularity to maximize throughput, subject to given constraints on latency and outage. In the regime of high and low signal-to-noise ratio (SNR), we derive explicit expressions for the granularity and throughput, first using a Shannon capacity approximation and then using finite block length analysis. Numerical results show that the throughput scaling results are applicable over a range of SNRs. The proposed analytical framework can provide insights for resource allocation strategies in reliable and delay-sensitive random access systems and in specific 5G use cases for massive, short packet uplink access.

Owing to its flexibility in modeling real-world spatial configurations of users and base stations (BSs), the Poisson cluster process (PCP) has recently emerged as an appealing way to model and analyze heterogeneous cellular networks (HetNets). Despite its undisputed relevance to HetNets-corroborated by the models used in the industry-the PCP's use in performance analysis has been limited. This is primarily because of the lack of analytical tools to characterize the performance metrics, such as the coverage probability of a user connected to the strongest BS. In this paper, we develop an analytical framework for the evaluation of the coverage probability, or equivalently the complementary cumulative density function (CCDF) of signal-tointerference-and-noise ratio (SINR), of a typical user in a K-tier HetNet under a max power-based association strategy, where the BS locations of each tier follow either a Poisson point process (PPP) or a PCP. The key enabling step involves conditioning on the parent PPPs of all the PCPs, which allows us to express the coverage probability as a product of sum-product and probability generating functionals (PGFLs) of the parent PPPs. In addition to several useful insights, our analysis provides a rigorous way to study the impact of the cluster size on the SINR distribution, which was not possible using the existing PPP-based models.

Competing cellular operators aggressively share infrastructure in many major US markets. If operators also share spectrum licenses, intra- cellular interference will become correlated with inter-cellular interference. We propose a mathematical framework to model a two-operator millimeter-wave (mmWave) cellular network with co- located base-stations (BSs). We then characterize the SINR distribution for an arbitrary network to understand the impact of varying the spatial correlation between the operators' networks. An interesting observation is that sharing spectrum and infrastructure yields a higher rate coverage probability for higher rate thresholds, but has a lower coverage for lower thresholds. This suggests that networks catering for low-rate, limited-QoS devices, are at a disadvantage when spectrum and infrastructure are shared.

This paper studies the asymptotic properties of area spectral efficiency (ASE) of a downlink cellular network in the limit of very dense base station (BS) and user densities. This asymptotic analysis relies on three assumptions: (1) interference is treated as noise; (2) the BS locations are drawn from a Poisson point process; (3) the path loss function is bounded above satisfying mild regularity conditions. When there is no constraint on the minimum operational SINR and instantaneous full channel state information is available at the transmitter, the ASE is proven to saturate to a constant, which we derive in closed form. We provide several familiar case studies for the class of considered path loss models, and demonstrate that our results cover most previous models and results on ultradense networks as special cases.

We propose a new cellular network model that captures both deterministic and random aspects of base station (BS) deployments. Namely, the BS locations are modeled as the superposition of two independent stationary point processes: a random shifted grid with intensity λgand a Poisson point process (PPP) with intensity λp. Grid and PPP deployments are special cases with λp→ 0 and λg→ 0 , with actual deployments in between these two extremes, as we demonstrate with deployment data. Assuming that each user is associated with the BS that provides the strongest average received signal power, we obtain the probability that a typical user is associated with either a grid or PPP BS. Assuming Rayleigh fading channels, we derive the expression for the coverage probability of the typical user, resulting in the following observations. First, the association and the coverage probability of the typical user are fully characterized as functions of intensity ratio ρλ= λp/λg. Second, the user association is biased toward the BSs located on a grid. Finally, the proposed model predicts the coverage probability of the actual deployment with great accuracy.

Cell search is the process for a user to detect its neighboring base stations (BSs) and make a cell selection decision. Due to the importance of beamforming in 5G cellular networks including both the millimeter wave and sub-6 GHz networks, there is a need for a better understanding of the directional cell search delay performance. A cellular network with fixed BS and user locations is considered, so as to take into account the strong temporal correlations that exist for the SINR experienced by each BS and user in this context. For Poisson cellular networks with Rayleigh fading channels, a closed-form expression for the spatially averaged mean cell search delay of all users is derived. This mean cell search delay for a noise-limited network is proved to be infinite whenever the non-line-of-sight path loss exponent is larger than two. For interference-limited networks, a phase transition for the mean cell search delay is shown to exist in terms of the number of BS beams M: the mean cell search delay is infinite when M is smaller than a threshold and finite otherwise. Beam-sweeping is also demonstrated to be effective in decreasing the cell search delay, especially for cell edge users.

Distance-based attenuation is a critical aspect of wireless communications. As opposed to the ubiquitous powerlaw path loss model, this paper proposes a stretched exponential path loss model that is suitable for short-range communication. In this model, the signal power attenuates over a distance r as e-αrβ, where α and β are tunable parameters. Using experimental propagation measurements, we show that the proposed model is accurate for short to moderate distances in the range r ∈ (5, 300) meters and so is a suitable model for dense and ultradense networks. We integrate this path loss model into a downlink cellular network with base stations modeled by a Poisson point process, and derive expressions for the coverage probability, potential throughput, and area spectral efficiency. Although the most general result for coverage probability has a double integral, several special cases are given, where the coverage probability has a compact or even closed form. We then show that the potential throughput is maximized for a particular BS density and then collapses to zero for high densities, assuming a fixed signal-to-interference-plus-noise ratio (SINR) threshold. We next prove that the area spectral efficiency, which assumes an adaptive SINR threshold, is nondecreasing with the BS density and converges to a constant for high densities.

Blocking objects (blockages) between a transmitter and receiver cause wireless communication links to transition from line-of-sight (LOS) to non-LOS propagation, which can greatly reduce the received power, particularly at the higher frequencies such as millimeter wave. We consider a cellular network in which a mobile user attempts to connect to two or more base stations (BSs) simultaneously, to increase the probability of at least one LOS link, which is a form of macrodiversity. We develop a framework for determining the LOS probability as a function of the number of BSs, when taking into account the correlation between blockages: for example, a single blockage close to the device-including the user's own body-could block multiple BSs. We consider the impact of the size of blocking objects on the system's n th order LOS probability and show that macrodiversity gains are higher when the blocking objects are small. We also show that the BS density must scale as the square of the blockage density to maintain a given level of LOS probability.

We use stochastic geometry to analyze the performance of an energy-efficient joint downlink/uplink (UL) radio-frequency (RF) wake-up solution for Internet of Things (IoT) devices over cellular networks. When the IoT device has no data to transmit, it turns its main circuitry completely OFF and switches to a deep sleep mode. The transition back to the active mode is only achieved upon receiving enough power at the device's front end. After wake up, the device initiates regular UL communication with its serving base station (BS). The device experiences a successful wake-up event when the total received power includes a wake-up signal transmitted from its serving BS, and the UL signal-to-interference-and-noise ratio (SINR) is above a predefined threshold. On the other hand, the device experiences a false wake-up event when the wake up is due to received power from neighboring BSs excluding the serving BS. We derive lower and upper bounds for the success and false wake-up probabilities in addition to closed-form expression for the UL SINR coverage probability after successful wake up. We present performance results as a function of various key design parameters and highlight the effectiveness and tradeoffs of RF wake up for IoT devices.

We study optimal geographic content placement for device-to-device (D2D) networks in which each file's popularity follows the Zipf distribution. The locations of the D2D users (caches) are modeled by a Poisson point process and have limited communication range and finite storage. Inspired by the Matérn hard-core (type II) point process that captures pairwise interactions between nodes, we devise a novel spatially correlated caching strategy called hard-core placement (HCP) such that the D2D nodes caching the same file are never closer to each other than the exclusion radius. The exclusion radius plays the role of a substitute for caching probability. We derive and optimize the exclusion radii to maximize the hit probability, which is the probability that a given D2D node can find a desired file at another node's cache within its communication range. Contrasting it with independent content placement, which is used in most prior work, our HCP strategy often yields a significantly higher cache hit probability. We further demonstrate that the HCP strategy is effective for small cache sizes and a small communication radius, which are likely conditions for D2D.

We consider a single cell wireless uplink in which randomly arriving devices transmit their payload to a receiver. Given SNR per user, payload size per device, a fixed latency constraint T, total available bandwidth W, i.e., total symbol resources is given by N = TW. The total bandwidth W is evenly partitioned into B bins. Each time slot of duration T is split into a maximum number of retransmission attempts M. Hence, the N resources are partitioned into N/MB resources each bin per retransmission. We characterize the maximum average rate or number of Poisson arrivals that can successfully complete the random access procedure such that the probability of outage is sufficiently small. We analyze the proposed setting for i) noise-limited regime and ii) interference-limited regime. We show that in the noise-limited regime the devices share the resources, and in the interference-limited regime, the resources split such that devices do not experience any interference. We then incorporate Rayleigh fading to model the channel power gain distribution. Although the variability of the channel causes a drop in the number of arrivals that can successfully complete the random access phase, similar scaling results extend to the Rayleigh fading case.

We propose a new cellular network model that captures both strong repulsion and randomness between base stations. The base stations are modeled by superposition of a random shifted grid with intensity λgfor the grid base stations and an independent Poisson point process with intensity λpfor the random base stations. Assuming that the typical user is associated with the base station that provides the strongest average receive signal power, we derive the association probability of the typical user. In Rayleigh fading channels, the coverage probability of the typical user at the origin is derived.

We propose a distributed bidding-aided Matern carrier sense multiple access (CSMA) policy for device-to-device (D2D) content distribution. The network is composed of D2D receivers and potential D2D transmitters, i.e., transmitters are turned on or off by the scheduling algorithm. Each D2D receiver determines the value of its request, by bidding on the set of potential transmitters in its communication range. Given a medium access probability, a fraction of the potential transmitters are jointly scheduled, i.e., turned on, determined jointly by the auction policy and the power control scheme. The bidding-aided scheduling algorithm exploits (i) the local demand distribution, (ii) spatial distribution of D2D node locations, and (iii) the cache configurations of the potential transmitters. We contrast the performance of the bidding-aided CSMA policy with other well-known CSMA schemes that do not take into account (i)-(iii), demonstrate that our algorithm achieves a higher spectral efficiency in terms of the number of bits transmitted per unit time per unit bandwidth per user. The gain becomes even more visible under randomized configurations and requests rather than more skewed placement configurations and deterministic demand distributions.

We use 3-D ray tracing to evaluate the performance of millimeter wave (mmWave) cellular in a realistic model of MetLife stadium, NJ, USA. We model thousands of human blockages using the dielectric properties at 28 GHz. Using this setup, we contrast the coverage and capacity performance with and without human blockages. Our study highlights that incorporating human models is essential for performance evaluation and also for deployment choice. We study the scaling in achievable data rates of three dense deployments in the stadium, and conclude that meeting the minimum 100 Mbps 5G requirement in stadiums can be challenging with a unicast mode of transmission. Broadcasting popular content in conjunction with a multiplexed unicast mode can provide minimum 100 Mbps rate for the broadcasted content.

We provide a comprehensive overview of mathematical models and analytical techniques for millimeter wave (mmWave) cellular systems. The two fundamental physical differences from conventional sub-6-GHz cellular systems are: 1) vulnerability to blocking and 2) the need for significant directionality at the transmitter and/or receiver, which is achieved through the use of large antenna arrays of small individual elements. We overview and compare models for both of these factors, and present a baseline analytical approach based on stochastic geometry that allows the computation of the statistical distributions of the downlink signal-to-interference-plus-noise ratio (SINR) and also the per link data rate, which depends on the SINR as well as the average load. There are many implications of the models and analysis: 1) mmWave systems are significantly more noise-limited than at sub-6 GHz for most parameter configurations; 2) initial access is much more difficult in mmWave; 3) self-backhauling is more viable than in sub-6-GHz systems, which makes ultra-dense deployments more viable, but this leads to increasingly interference-limited behavior; and 4) in sharp contrast to sub-6-GHz systems cellular operators can mutually benefit by sharing their spectrum licenses despite the uncontrolled interference that results from doing so. We conclude by outlining several important extensions of the baseline model, many of which are promising avenues for future research.

I Would like to take this opportunity as I step down as EIC after three years to review the state of the Transactions. I believe that the Transactions should be an ever-evolving institution that always strives for a higher level of excellence across multiple dimensions such as quality, impact, timeliness, and efficiency.

Initial deployments of millimeter wave (mm-wave) cellular networks are likely to be enabled with self-backhauling. In this paper, we propose a random spatial model to analyze uplink (UL) and downlink (DL) signal to interference plus noise ratio distribution and mean rates corresponding to different access-backhaul and UL-DL resource allocation schemes in a self-backhauled mm-wave cellular network with Poisson point process (PPP) deployment of users and base stations (BSs). In particular, we focus on heuristic implementations of static and dynamic time division duplexing (TDD) for access links with synchronized or unsynchronized access-backhaul (SAB or UAB) time splits. We propose PPP approximations to characterize the distribution of the new types of interference encountered with dynamic TDD and UAB. These schemes offer better resource utilization than static TDD and SAB, however, potentially higher interference makes their choice non-trivial and the offered gains sensitive to different network parameters, including UL/DL traffic asymmetry, user load per BS or number of slave BSs per master BS. One can harness notable gains from UAB and/or dynamic TDD only if backhaul links are designed to have much larger throughput than the access links.

Initial access is the process which allows a mobile user to first connect to a cellular network. It consists of two main steps: cell search (CS) on the downlink and random access (RA) on the uplink. Millimeter wave (mm-wave) cellular systems typically must rely on directional beamforming (BF) in order to create a viable connection. The BF direction must, therefore, be learned-as well as used-in the initial access process for mm-wave cellular networks. This paper considers four simple but representative initial access protocols that use various combinations of directional BF and omnidirectional transmission and reception at the mobile and the BS, during the CS and RA phases. We provide a system-level analysis of the success probability for CS and RA for each one, as well as of the initial access delay and user-perceived downlink throughput (UPT). For a baseline exhaustive search protocol, we find the optimal BS beamwidth and observe that in terms of initial access delay it is decreasing as blockage becomes more severe, but is relatively constant (about π/12) for UPT. Of the considered protocols, the best tradeoff between initial access delay and UPT is achieved under a fast CS protocol.

Sharing the spectrum among multiple operators seems promising in millimeter wave (mmWave) systems. One explanation is the highly directional transmission in mmWave, which reduces the interference caused by one network on the other networks sharing the same resources. In this paper, we model a mmWave cellular system where an operator that primarily owns an exclusive-use license of a certain band can sell a restricted secondary license of the same band to another operator. This secondary network has a restriction on the maximum interference it can cause to the original network. Using stochastic geometry, we derive expressions for the coverage and rate of both networks, and establish the feasibility of secondary licensing in licensed mmWave bands. Results show that the restricted secondary operator can achieve good coverage with a small impact on the original operator. Our results also illustrate that the spectrum sharing gains increase with narrow beams and when the network densifies.

The severe power limitations of machine-to-machine (M2M) devices challenge their access connectivity and reliable communication over cellular networks. In this work, we propose a new solution to reduce the power consumption of M2M over cellular by minimizing the power dissipated during inactive intervals. When the M2M device has no data to transmit, it will turn its main circuitry off and switch to a new deep sleep mode. The transition back to the active mode is only achieved upon receiving a radio frequency (RF) wake-up signal from the device's serving base station (BS). We use stochastic geometry to analyze the performance of the proposed wake-up solution. In the proposed model, the M2M device leaves the deep sleep mode when it receives enough power to be activated. The device experiences a successful wake-up event when the total received power includes a wake-up signal transmitted from its serving base station. On the other hand, the device experiences a false wake-up event when it wakes up due to received power from neighboring base station excluding the serving base station. The performance of the proposed model is evaluated in terms of the probabilities of these two events. We use Poisson point processes (PPPs) to derive tractable expressions for the performance metrics, and we present insights for network design and optimization.

In conventional applications of time division duplex (TDD) in cellular systems, the time resource split between uplink (UL) and downlink (DL) is fixed across all base stations (BSs) in the network. This leads to under utilization of BS resources when there is a mismatch between the expected and experienced UL/DL traffic in a given cell. A dynamic split that varies in each cell is desirable, but is challenging due to the high interference experienced by UL receivers in one cell from DL transmissions in adjacent cells. This paper analyzes the performance of UL users in dynamic TDD enabled next generation cellular networks using a stochastic geometry framework. The analysis highlights the trade-off between spectral efficiency and resource utilization for dynamic TDD. With appropriate interference mitigation, dynamic TDD offers a significant gain in data rates as compared to static TDD, which is higher when the BSs are lightly loaded and/or the fraction of UL users is low.

Machine-to-machine (M2M) communication's severe power limitations challenge the interconnectivity, access management, and reliable communication of data. In densely deployed M2M networks, coordinating and aggregating the generated data is critical. We propose an energy efficient data aggregation scheme for a hierarchical M2M network with truncated power control. We optimize the number of hierarchical stages and perform a coverage probability-based uplink analysis for M2M devices. Our analysis exposes the key tradeoffs between the coverage characteristics for successive and parallel transmission schemes that can be either half-duplex or full-duplex. Comparing the rate performances of the transmission models, we observe that successive and half-duplex parallel modes have better coverage characteristics compared to full-duplex parallel scheme.

We study the optimal geographic content placement problem for device-to-device (D2D) networks in which the content popularity follows the Zipf law. We consider a D2D caching model where the locations of the D2D users (caches) are modeled by a Poisson point process (PPP) and have limited communication range and finite storage. Unlike most related work which assumes independent placement of content, and does not capture the locations of the users, we model the spatial properties of the network including spatial correlation in terms of the cached content. We propose two novel spatial correlation models, the exchangeable content model and a Matérn (MHC) content placement model, and analyze and optimize the hit probability, which is the probability of a given D2D node finding a desired file at another node within its communication range. We contrast these results to the independent placement model, and show that exchangeable placement performs worse. On the other hand, MHC placement yields a higher cache hit probability than independent placement for small cache sizes.

We consider a multi-antenna downlink cellular network using either single-user maximal ratio transmission (MRT) or multi-user zero-forcing (ZF) transmission. The locations of the base stations are modeled by a Poisson point process to allow the inter-cell interference to be tractably analyzed. A tight lower bound on the optimum number of feedback bits maximizing the net spectral efficiency is derived, whereby the cost of feedback sent via uplink is subtracted from the corresponding gain in downlink spectral efficiency. When using MRT, the optimum number of feedback bits is shown to scale linearly with the number of antennas, and logarithmically with the channel coherence time. With ZF, the optimum amount of feedback scales the same as with MRT, but additionally also increases linearly with the pathloss exponent.

Sharing the spectrum among multiple operators seems promising in millimeter wave (mmWave) systems. One explanation is the highly directional transmission in mmWave, which reduces the interference caused by one network on the other networks sharing the same resources. In this paper, we model a mmWave cellular system, where an operator that primarily owns an exclusive-use license of a certain band can sell a restricted secondary license of the same band to another operator. This secondary network has a restriction on the maximum interference it can cause to the original network. Using stochastic geometry, we derive expressions for the coverage and the rate of both networks, and establish the feasibility of secondary licensing in licensed mmWave bands. To explain economic tradeoffs, we consider a revenue-pricing model for both operators in the presence of a central licensing authority. Our results show that the original operator and central network authority can benefit from secondary licensing when the maximum interference threshold is properly adjusted. This means that the original operator and central licensing authority have an incentive to permit a secondary network to restrictively share the spectrum. Our results also illustrate that the spectrum sharing gains increase with narrow beams and when the network densifies.

The highly directional and adaptive antennas used in mmWave communication open up the possibility of uncoordinated sharing of spectrum licenses between commercial cellular operators. There are several advantages to sharing including a reduction in license costs and an increase in spectrum utilization. In this paper, we establish the theoretical feasibility of spectrum license sharing among mmWave cellular operators. We consider a heterogeneous multi-operator system containing multiple independent cellular networks, each owned by an operator. We then compute the signal-to-interference-and-noise ratio and rate distribution for downlink mobile users of each network. Using the analysis, we compare the systems with fully shared licenses and exclusive licenses for different access rules and explore the trade-offs between system performance and spectrum cost. We show that sharing spectrum licenses increases the per-user rate when antennas have narrow beams and is also favored when there is a low density of users. We also consider a multi-operator system where BSs of all the networks are co-located to show that the simultaneous sharing of spectrum and infrastructure is also feasible. We show that all networks can share licenses with less bandwidth and still achieve the same per-user median rate as if they each had an exclusive license to spectrum with more bandwidth.

Large antenna arrays will be needed in future millimeter wave (mmWave) cellular networks, enabling a large number of different possible antenna architectures and multiple-input multiple-output (MIMO) techniques. It is still unclear which MIMO technique is most desirable as a function of different network parameters. This paper, therefore, compares the coverage and rate performance of hybrid beamforming enabled multiuser (MU) MIMO and single-user spatial multiplexing (SM) with single-user analog beamforming (SU-BF). A stochastic geometry model for coverage and rate analysis is proposed for MU-MIMO mmWave cellular networks, taking into account important mmWave-specific hardware constraints for hybrid analog/digital precoders and combiners, and a blockage-dependent channel model which is sparse in angular domain. The analytical results highlight the coverage, rate, and power consumption tradeoffs in multiuser mmWave networks. With perfect channel state information at the transmitter and round robin scheduling, MU-MIMO is usually a better choice than SM or SU-BF in mmWave cellular networks. This observation, however, neglects any overhead due to channel acquisition or computational complexity. Incorporating the impact of such overheads, our results can be re-interpreted so as to quantify the minimum allowable efficiency of MU-MIMO to provide higher rates than SM or SU-BF.

We derive a general and closed-form result for the success probability in downlink multiple-antenna (MIMO) heterogeneous cellular networks (HetNets), utilizing a novel Toeplitz matrix representation. This main result, which is equivalently the signal-to-interference ratio (SIR) distribution, includes multiuser MIMO, single-user MIMO and per-tier biasing for K different tiers of randomly placed base stations (BSs), assuming zero-forcing precoding and perfect channel state information. The large SIR limit of this result admits a simple closed form that is accurate at moderate SIRs, e.g., above 5 dB. These results reveal that the SIR-invariance property of SISO HetNets does not hold for MIMO HetNets; instead the success probability may decrease as the network density increases. We prove that the maximum success probability is achieved by activating only one tier of BSs, while the maximum area spectral efficiency (ASE) is achieved by activating all the BSs. This reveals a unique tradeoff between the ASE and link reliability in multiuser MIMO HetNets. To achieve the maximum ASE while guaranteeing a certain link reliability, we develop efficient algorithms to find the optimal BS densities. It is shown that as the link reliability requirement increases, more BSs and more tiers should be deactivated.

Device-to-device (D2D) communication is a promising approach to optimize the utilization of air interface resources in 5G networks, since it allows decentralized opportunistic short-range communication. For D2D to be useful, mobile nodes must possess content that other mobiles want. Thus, intelligent caching techniques are essential for D2D. In this paper, we use results from stochastic geometry to derive the probability of successful content delivery in the presence of interference and noise. We employ a general transmission strategy, where multiple files are cached at the users and different files can be transmitted simultaneously throughout the network. We then formulate an optimization problem, and find the caching distribution that maximizes the density of successful receptions (DSR) under a simple transmission strategy, where a single file is transmitted at a time throughout the network. We model file requests by a Zipf distribution with exponent γr, which results in an optimal caching distribution that is also a Zipf distribution with exponent γc, which is related to γr through a simple expression involving the path loss exponent. We solve the optimal content placement problem for more general demand profiles under Rayleigh, Ricean, and Nakagami small-scale fading distributions. Our results suggest that it is required to flatten the request distribution to optimize the caching performance. We also develop strategies to optimize content caching for the more general case with multiple files, and bound the DSR for that scenario.

Machine-to-machine (M2M) communication's severe power limitations challenge the interconnectivity, access management, and reliable communication of data. In densely deployed M2M networks, controlling and aggregating the generated data is critical. We propose an energy-efficient data aggregation scheme for a hierarchical M2M network. We develop a coverage probability-based optimal data aggregation scheme for M2M devices to minimize the average total energy expenditure per unit area per unit time or simply the energy density of an M2M communication network. Our analysis exposes the key tradeoffs between the energy density of the M2M network and the coverage characteristics for successive and parallel transmission schemes that can be either half-duplex or full-duplex. Comparing the rate and energy performances of the transmission models, we observe that successive mode and half-duplex parallel mode have better coverage characteristics compared to full-duplex parallel scheme. Simulation results show that the uplink coverage characteristics dominate the trend of the energy consumption for both successive and parallel schemes.

Two key traits of 5G cellular networks are much higher base station (BS) densities-especially in the case of low-power BSs-and the use of massive MIMO at these BSs. This paper explores how massive MIMO can be used to jointly maximize the offloading gains and minimize the interference challenges arising from adding small cells. We consider two interference management approaches: joint transmission (JT) with local precoding, where users are served simultaneously by multiple BSs without requiring channel state information exchanges among cooperating BSs, and resource blanking, where some macro BS resources are left blank to reduce the interference in the small cell downlink. A key advantage offered by massive MIMO is channel hardening, which enables to predict instantaneous rates a priori. This allows us to develop a unified framework, where resource allocation is cast as a network utility maximization (NUM) problem, and to demonstrate large gains in cell-edge rates based on the NUM solution. We propose an efficient dual subgradient based algorithm, which converges towards the NUM solution. A scheduling scheme is also proposed to approach the NUM solution. Simulations illustrate more than 2x rate gain for 10th percentile users vs. an optimal association without interference management.

Millimeter wave (mmWave) links will offer high capacity but are poor at penetrating into or diffracting around solid objects. Thus, we consider a hybrid cellular network with traditional sub-6 GHz macrocells coexisting with denser mmWave small cells, where a mobile user can connect to either opportunistically. We develop a general analytical model to characterize and derive the uplink and downlink cell association in the view of the signal-to-interference-and-noise-ratio and rate coverage probabilities in such a mixed deployment. We offer extensive validation of these analytical results (which rely on several simplifying assumptions) with simulation results. Using the analytical results, different decoupled uplink and downlink cell association strategies are investigated and their superiority is shown compared with the traditional coupled approach. Finally, small cell biasing in mmWave is studied, and we show that unprecedented biasing values are desirable due to the wide bandwidth.

We leverage stochastic geometry to characterize key performance metrics for neighboring Wi-Fi and LTE networks in unlicensed spectrum. Our analysis focuses on a single unlicensed frequency band, where the locations for the Wi-Fi access points and LTE eNodeBs are modeled as two independent homogeneous Poisson point processes. Three LTE coexistence mechanisms are investigated: 1) LTE with continuous transmission and no protocol modifications; 2) LTE with discontinuous transmission; and 3) LTE with listen-before-talk and random back-off. For each scenario, we derive the medium access probability, the signal-to-interference-plus-noise ratio coverage probability, the density of successful transmissions (DST), and the rate coverage probability for both Wi-Fi and LTE. Compared with the baseline scenario where one Wi-Fi network coexists with an additional Wi-Fi network, our results show that Wi-Fi performance is severely degraded when LTE transmits continuously. However, LTE is able to improve the DST and rate coverage probability of Wi-Fi while maintaining acceptable data rate performance when it adopts one or more of the following coexistence features: a shorter transmission duty cycle, lower channel access priority, or more sensitive clear channel assessment thresholds.

We consider a downlink cellular network where multi-antenna base stations (BSs) transmit data to single-antenna users by using one of two linear precoding methods with limited feedback: 1) maximum ratio transmission (MRT) for serving a single user or 2) zero forcing (ZF) for serving multiple users. The BS and user locations are drawn from a Poisson point process, allowing expressions for the signal-to-interference coverage probability and the ergodic spectral efficiency to be derived as a function of system parameters, such as the number of BS antennas and feedback bits, and the pathloss exponent. We find a tight lower bound on the optimum number of feedback bits to maximize the net spectral efficiency, which captures the overall system gain by considering both of downlink and uplink spectral efficiency using limited feedback. Our main finding is that, when using MRT, the optimum number of feedback bits scales linearly with the number of antennas, and logarithmically with the channel coherence time. When using ZF, the feedback scales in the same ways as MRT, but also linearly with the pathloss exponent. The derived results provide system-level insights into the preferred channel codebook size by averaging the effects of short-term fading and long-term pathloss.

This paper studies the interplay between massive MIMO and device-to-device (D2D) networking in a single cell setting, where cellular uplink resources are shared by D2D. The spatial positions of underlaid D2D transmitters are modeled by a Poisson point process. All the transmissions (both cellular and D2D) are SIMO (i.e., single-input multiple-output) with the base station (BS) having a very large antenna array. Assuming perfect channel state information at the receivers, we study cellular and D2D spectral efficiency. In the asymptotic regime where the number of BS antennas goes to infinity, we find that the received signal-to-interference-plus-noise ratio (SINR) of any cellular user increases unboundedly and the effects of noise, fast fading, and the interfering signals from the other co-channel cellular users and the infinite D2D transmitters vanish completely. In the non-asymptotic regime, we derive simple analytical lower bounds for both cellular and D2D spectral efficiency, which allow for efficient numerical evaluation.

Existing cellular network analyses are based on the standard power law path loss model. If the base stations are modeled by a Poisson point process, this leads to a tractable analysis of coverage probability and other metrics for downlink cellular networks. Yet, it is also well-known that the standard path loss model is idealized and does not capture the distance-dependence of the path loss exponent. This paper considers a more precise and general model, the dual-slope path loss model, where the path loss exponents are different for short links and long links differentiated by a critical distance. We derive compact expressions on the coverage probability and its tight closed-form estimate under this model. The analytical results show that the SINR does not monotonically increase with network density (as under the standard path loss model). Rather, ultra-densification leads to worse or even zero coverage when the near-field path loss exponent is 2 or less.

This paper proposes a random network model for a device-to-device (D2D) underlaid cellular system using stochastic geometry and develops centralized and distributed power control algorithms. The goal of centralized power control is twofold: ensure that the cellular users have sufficient coverage probability by limiting the interference created by underlaid D2D users, while scheduling as many D2D links as possible. For the distributed power control method, the optimal on-off power control strategy is proposed, which maximizes the sum rate of the D2D links. Expressions are derived for the coverage probabilities of cellular, D2D links, and the sum rate of the D2D links in terms of the density of D2D links and the path-loss exponent. The analysis reveals the impact of key system parameters on the network performance. For example, the bottleneck of D2D underlaid cellular networks is the cross-tier interference between D2D links and the cellular user, not the D2D intratier interference when the density of D2D links is sparse. Simulation results verify the exactness of the derived coverage probabilities and the sum rate of D2D links.

Millimeter wave (mmWave) cellular systems will require high-gain directional antennas and dense base station (BS) deployments to overcome a high near-field path loss and poor diffraction. As a desirable side effect, high-gain antennas offer interference isolation, providing an opportunity to incorporate self-backhauling, i.e., BSs backhauling among themselves in a mesh architecture without significant loss in the throughput, to enable the requisite large BS densities. The use of directional antennas and resource sharing between access and backhaul links leads to coverage and rate trends that significantly differ from conventional UHF cellular systems. In this paper, we propose a general and tractable mmWave cellular model capturing these key trends and characterize the associated rate distribution. The developed model and analysis are validated using actual building locations from dense urban settings and empirically derived path loss models. The analysis shows that, in sharp contrast to the interference-limited nature of UHF cellular networks, the spectral efficiency of mmWave networks (besides the total rate) also increases with the BS density, particularly at the cell edge. Increasing the system bandwidth does not significantly influence the cell edge rate, although it boosts the median and peak rates. With self-backhauling, different combinations of the wired backhaul fraction (i.e., the fraction of BSs with a wired connection) and the BS density are shown to guarantee the same median rate (QoS).

Although the Poisson point process (PPP) has been widely used to model base station (BS) locations in cellular networks, it is an idealized model that neglects the spatial correlation among BSs. This paper proposes the use of the determinantal point process (DPP) to take into account these correlations, in particular the repulsiveness among macro BS locations. DPPs are demonstrated to be analytically tractable by leveraging several unique computational properties. Specifically, we show that the empty space function, the nearest neighbor function, the mean interference, and the signal-to-interference ratio (SIR) distribution have explicit analytical representations and can be numerically evaluated for cellular networks with DPP-configured BSs. In addition, the modeling accuracy of DPPs is investigated by fitting three DPP models to real BS location data sets from two major U.S. cities. Using hypothesis testing for various performance metrics of interest, we show that these fitted DPPs are significantly more accurate than popular choices such as the PPP and the perturbed hexagonal grid model.

This paper develops a novel analytical framework for asynchronous wireless networks deploying multicarrier transmission over flat-fading channels. Nodes in the network have different notions of timing; therefore, from the viewpoint of a typical receiver, the received signals from different transmitters are asynchronous, leading to a loss of orthogonality between subcarriers. We first develop a detailed link-level analysis based on OFDM, based on which we propose a tractable system-level signal-to-interference-plus-noise ratio (SINR) model for asynchronous OFDM networks. The proposed model is used to analytically characterize several important statistics in asynchronous networks with spatially distributed transmitters, including: (i) the number of decodable transmitters; (ii) the decoding probability of the nearest transmitter; and (iii) the system throughput. The system-level loss from lack of synchronization is quantified, and to mitigate the loss, we compare and discuss four possible solutions including extended cyclic prefix, advanced receiver timing, dynamic receiver timing positioning, and semi-static receiver timing positioning with multiple timing hypotheses. The model and results are general, and apply to ad hoc networks, cellular systems, and neighbor discovery in device-to-device (D2D) networks.

Cellular network performance can significantly benefit from direct device-to-device (D2D) communication, but interference from cochannel D2D communication limits the performance gain. In hybrid networks consisting of D2D and cellular links, finding the optimal interference management is challenging. In particular, we show that the problem of maximizing network throughput while guaranteeing predefined service levels to cellular users is non-convex and hence intractable. Instead, we adopt a distributed approach that is computationally extremely efficient, and requires minimal coordination, communication and cooperation among the nodes. The key algorithmic idea is a signaling mechanism that can be seen as a fictional pricing mechanism, that the base stations optimize and transmit to the D2D users, who then play a best response (i.e., selfishly) to this signal. Numerical results show that our algorithms converge quickly, have low overhead, and achieve a significant throughput gain, while maintaining the quality of cellular links at a predefined service level.

Existing cellular network analyses, and even simulations, typically use the standard path loss model where received power decays like ||x||-αover a distance ||x}}. This standard path loss model is quite idealized, and in most scenarios the path loss exponent α is itself a function of ||x||, typically an increasing one. Enforcing a single path loss exponent can lead to orders of magnitude differences in average received and interference powers versus the true values. In this paper, we study multi-slope path loss models, where different distance ranges are subject to different path loss exponents. We focus on the dual-slope path loss function, which is a piece-wise power law and continuous and accurately approximates many practical scenarios. We derive the distributions of SIR, SNR, and finally SINR before finding the potential throughput scaling, which provides insight on the observed cell-splitting rate gain. The exact mathematical results show that the SIR monotonically decreases with network density, while the converse is true for SNR, and thus the network coverage probability in terms of SINR is maximized at some finite density. With ultra-densification (network density goes to infinity), there exists a phase transition in the near-field path loss exponent α0: if α0>1 unbounded potential throughput can be achieved asymptotically; if α0<;1, ultra-densification leads in the extreme case to zero throughput.

In a device-to-device (D2D) underlaid cellular network, the uplink spectrum is reused by the D2D transmissions, causing mutual interference with the ongoing cellular transmissions. Massive MIMO is appealing in such a context as the base station's (BS's) large antenna array can nearly null the D2D-to-BS interference. The multi-user transmission in massive MIMO, however, may lead to increased cellular-to-D2D interference. This paper studies the interplay between massive MIMO and underlaid D2D networking in a multi-cell setting. We investigate cellular and D2D spectral efficiencies under both perfect and imperfect channel state information (CSI) at the receivers that employ partial zero-forcing. Compared to the case without D2D, there is a loss in cellular spectral efficiency due to D2D underlay. With perfect CSI, the loss can be completely overcome if the number of canceled D2D interfering signals is scaled with the number of BS antennas at an arbitrarily slow rate. With imperfect CSI, in addition to pilot contamination, a new asymptotic effect termed underlay contamination arises. In the non-asymptotic regime, simple analytical lower bounds are derived for both the cellular and D2D spectral efficiencies.

Load balancing by proactively offloading users onto small and otherwise lightly-loaded cells is critical for tapping the potential of dense heterogeneous cellular networks (HCNs). Offloading has mostly been studied for the downlink, where it is generally assumed that a user offloaded to a small cell will communicate with it on the uplink as well. The impact of coupled downlink-uplink offloading is not well understood. Uplink power control and spatial interference correlation further complicate the mathematical analysis as compared to the downlink. We propose an accurate and tractable model to characterize the uplink SINR and rate distribution in a multi-tier HCN as a function of the association rules and power control parameters. Joint uplink downlink rate coverage is also characterized. Using the developed analysis, it is shown that the optimal degree of channel inversion (for uplink power control) increases with load imbalance in the network. In sharp contrast to the downlink, minimum path loss association is shown to be optimal for uplink rate. Moreover, with minimum path loss association and full channel inversion, uplink SIR is shown to be invariant of infrastructure density. It is further shown that a decoupled association-employing differing association strategies for uplink and downlink-leads to significant improvement in joint uplink-downlink rate coverage over the standard coupled association in HCNs.

In this paper, we study the coverage probability of a K-tier multiple-input multiple-output heterogeneous cellular network (MIMO HetNet) assuming (i) zero-forcing precoding at all the base stations (BSs), (ii) Rayleigh fading, (iii) independent Poisson Point Process (PPP) model for the locations of BSs of each tier, and (iv) general cell selection rule that maximizes average received signal-to-interference-plus-noise ratio (SINR) at the users. Our analysis highlights key differences between MIMO HetNets and the more familiar single antenna HetNets in terms of cell selection. While it is challenging to derive exact cell selection rule to maximize average downlink SINR in MIMO HetNets, we show that adding an appropriately chosen per-tier selection bias yields a close approximation. The bias value for each tier is given in closed form. One interpretation of this result is that MIMO HetNets may balance load more naturally across different tiers in certain special cases compared to single antenna HetNets where an artificial selection bias is often needed for load balancing.

The use of dense millimeter wave (mmWave) cellular networks with highly directional beamforming stands as an intriguing solution to the current spectrum congestion problem. Due to significantly different propagation characteristics at such high frequencies, however, the coverage and rate trends differ drastically from conventional microwave networks. This paper aims to gain insights into the coverage and rate performance of mmWave cellular networks in major metropolitan cities. Our results confirm that, unlike conventional cellular networks, mmWave networks operating at 73 GHz carrier frequency are pre-dominantly noise-limited. Though larger system bandwidth leads to higher peak rates, it does not improve the cell edge rates. It is observed that dense base station (BS) deployment is the key to achieve both better coverage and rates in mmWave cellular networks. Further, based on actual building locations, we show the inadequacy of existing blockage models and validate a better blockage model.

The macro base station (BS) deployments in modern cellular networks are neither regular nor completely random. We use determinantal point process (DPP) models to study the repulsiveness among macro base stations observed in cellular networks. Three DPP models are fitted to base station location data sets from two major US cities. Hypothesis testing is used to validate the goodness-of-fit for these DPP models. Based on performance metrics including the K-function, the L-function and coverage probability, DPP models are shown to be accurate in modeling real BS deployments. On the contrary, the Poisson point process and perturbed hexagonal grid model are shown to be less realistic. Different DPP models are compared, and several computational properties of these models are also discussed.

In this paper, we study physical layer security for the downlink of cellular networks. In a cellular network, the confidential messages transmitted to each mobile user can be eavesdropped by the other users in the same cell and also by the users in the other cells. We model the locations of base stations and mobile users as two independent two-dimensional Poisson point processes. By combining tools from stochastic geometry and random matrix theory, we analyze the secrecy rates achievable with regularized channel inversion (RCI) precoding under Rayleigh fading. Our analysis shows that unlike isolated cells, the secrecy rate in a cellular network does not grow monotonically with the transmit power. Moreover, we find that the network tends to be in secrecy outage if the transmit power grows unbounded. Furthermore, we show that there exists an optimal value for the base station deployment density that maximizes the secrecy rate.

In this paper, we consider the broadcast channel with confidential messages and eavesdroppers (BCCE), where a multi-antenna base station simultaneously communicates to multiple potentially malicious users, in the presence of external eavesdroppers randomly located according to a Poisson point process (PPP). By using techniques from stochastic geometry and random matrix theory, we obtain explicit expressions for the secrecy outage probability and mean secrecy rate achievable with regularized channel inversion precoding. We show that both these metrics scale as -4fe, where N is the number of transmit antennas and Aeis the density of external eavesdroppers.

Base station (BS) cooperation is set to play a key role in managing interference in dense heterogeneous cellular networks (HCNs). Non-coherent joint transmission (JT) is particularly appealing due to its low complexity, smaller overhead, and ability for load balancing. However, a general analysis of this technique is difficult mostly due to the lack of tractable models. This paper addresses this gap and presents a tractable model for analyzing non-coherent JT in HCNs, while incorporating key system parameters such as user-centric BS clustering and channel-dependent cooperation activation. Assuming all BSs of each tier follow a stationary Poisson point process, the coverage probability for non-coherent JT is derived. Using the developed model, it is shown that for small cooperative clusters of small-cell BSs, non-coherent JT by small cells provides spectral efficiency gains without significantly increasing cell load. Further, when cooperation is aggressively triggered intra-cluster frequency reuse within small cells is favorable over intra-cluster coordinated scheduling.

In this paper, we develop a tractable and accurate framework for a Device-to-Device (D2D) enabled downlink cellular network with a dedicated spectrum approach, meaning that D2D links use a frequency band orthogonal to the cellular users. Using stochastic geometry, we provide accurate expressions for SINR distributions and average rates, under an assumption of interference randomization via time and/or frequency hopping. The obtained analytical results allow us to easily explore and optimize the impact of system parameters. For example, we find the optimal frequency hopping probability for the D2D users, i.e. how often they should randomly access a subband. We also propose an optimization approach for mode selection, i.e. when should potential D2D users transmit directly, and when should they fall back to the cellular mode. This can be viewed as an optimized lower bound to other more sophisticated scheduling schemes.

What will 5G be? What it will not be is an incremental advance on 4G. The previous four generations of cellular technology have each been a major paradigm shift that has broken backward compatibility. Indeed, 5G will need to be a paradigm shift that includes very high carrier frequencies with massive bandwidths, extreme base station and device densities, and unprecedented numbers of antennas. However, unlike the previous four generations, it will also be highly integrative: tying any new 5G air interface and spectrum together with LTE and WiFi to provide universal high-rate coverage and a seamless user experience. To support this, the core network will also have to reach unprecedented levels of flexibility and intelligence, spectrum regulation will need to be rethought and improved, and energy and cost efficiencies will become even more critical considerations. This paper discusses all of these topics, identifying key challenges for future research and preliminary 5G standardization activities, while providing a comprehensive overview of the current literature, and in particular of the papers appearing in this special issue.

In this paper, we study physical layer security for the downlink of cellular networks, where the confidential messages transmitted to each mobile user can be eavesdropped by both (i) the other users in the same cell and (ii) the users in the other cells. The locations of base stations and mobile users are modeled as two independent two-dimensional Poisson point processes. Using the proposed model, we analyze the secrecy rates achievable by regularized channel inversion (RCI) precoding by performing a large-system analysis that combines tools from stochastic geometry and random matrix theory. We obtain approximations for the probability of secrecy outage and the mean secrecy rate, and characterize regimes where RCI precoding achieves a nonzero secrecy rate. We find that unlike isolated cells, the secrecy rate in a cellular network does not grow monotonically with the transmit power, and the network tends to be in secrecy outage if the transmit power grows unbounded. Furthermore, we show that there is an optimal value for the base station deployment density that maximizes the secrecy rate, and this value is a decreasing function of the signal-to-noise ratio.

We model and analyze heterogeneous cellular networks with multiple antenna BSs (multi-antenna HetNets) with K classes or tiers of base stations (BSs), which may differ in terms of transmit power, deployment density, number of transmit antennas, number of users served, transmission scheme, and path loss exponent. We show that the cell selection rules in multi-antenna HetNets may differ significantly from the single-antenna HetNets due to the possible differences in multi-antenna transmission schemes across tiers. While it is challenging to derive exact cell selection rules even for maximizing signal-to-interference-plus-noise-ratio (SINR) at the receiver, we show that adding an appropriately chosen tier-dependent cell selection bias in the received power yields a close approximation. Assuming arbitrary selection bias for each tier, simple expressions for downlink coverage and rate are derived. For coverage maximization, the required selection bias for each tier is given in closed form. Due to this connection with biasing, multi-antenna HetNets may balance load more naturally across tiers in certain regimes compared to single-antenna HetNets, where a large cell selection bias is often needed to offload traffic to small cells.

Despite being ubiquitous in practice, the performance of maximal-ratio combining (MRC) in the presence of interference is not well understood. Because the interference received at each antenna originates from the same set of interferers but partially decorrelates over the fading channel, it possesses a complex correlation structure. This paper develops a realistic analytic model that accurately accounts for the interference correlation using stochastic geometry. Modeling interference by a Poisson shot noise process with independent Nakagami fading, we derive the link success probability for dual-branch interference-aware MRC. Using this result, we show that the common assumption that all receive antennas experience equal interference power underestimates the true performance, although this gap rapidly decays with increasing the Nakagami parameter mIof the interfering links. In contrast, ignoring interference correlation leads to a highly optimistic performance estimate for MRC, especially for large mI. In the low outage probability regime, our success probability expression can be considerably simplified. Observations based from the analysis include the following: 1) For small path loss exponents, MRC and minimum mean square error combining exhibit similar performance, and 2) the gains of MRC over selection combining are smaller in the interference-limited case than in the well-studied noise-limited case.

We develop a new tractable model for K-tier heterogeneous cellular networks (HetNets), where each base station (BS) is powered solely by a self-contained energy harvesting module. The BSs across tiers differ in terms of the energy harvesting rate, energy storage capacity, transmit power and deployment density. Since a BS may not always have enough energy, it may need to be kept OFF and allowed to recharge while nearby users are served by neighboring BSs that are ON. We show that the fraction of time a kthtier BS can be kept ON, termed availability ρk, is a fundamental metric of interest. Using tools from random walk theory, fixed point analysis and stochastic geometry, we characterize the set of K-tuples (ρ1, ρ2, ... ρK), termed the availability region, that is achievable by general uncoordinated operational strategies, where the decision to toggle the current ON/OFF state of a BS is taken independently of the other BSs. If the availability vector corresponding to the optimal system performance, e.g., in terms of rate, lies in this availability region, there is no performance loss due to the presence of unreliable energy sources. As a part of our analysis, we model the temporal dynamics of the energy level at each BS as a birth-death process, derive the energy utilization rate, and use hitting/stopping time analysis to prove that there exists a fundamental limit on ρkthat cannot be surpassed by any uncoordinated strategy.

In this paper, we consider the broadcast channel with confidential messages and external eavesdroppers (BCCE), where a multi-antenna base station simultaneously communicates to multiple potentially malicious users, in the presence of randomly located external eavesdroppers. Using the proposed model, we study the secrecy rates achievable with regularized channel inversion (RCI) precoding by performing a large-system analysis that combines results from stochastic geometry and random matrix theory, where the number of users K and the number of transmit antennas N both grow to infinity in a fixed ratio. We obtain explicit expressions for the probability of secrecy outage and an upper bound on the rate loss due to the presence of external eavesdroppers. We show that both these quantities scale as \fraclambda_esqrt{N} as the density of external eavesdroppers λ_e grows, irrespective of their collusion strategy. Furthermore, we derive a practical rule for the choice of the regularization parameter, which is agnostic of channel state information and location of eavesdroppers, and yet provides close to optimal performance.

This paper addresses two fundamental and interrelated issues in device-to-device (D2D) enhanced cellular networks. The first issue is how D2D users should access spectrum, and we consider two choices: overlay (orthogonal spectrum between D2D and cellular UEs) and underlay (non-orthogonal). The second issue is how D2D users should choose between communicating directly or via the base station, a choice that depends on distance between the potential D2D transmitter and receiver. We propose a tractable hybrid network model where the positions of mobiles are modeled by random spatial Poisson point process, with which we present a general analytical approach that allows a unified performance evaluation for these questions. Then, we derive analytical rate expressions and apply them to optimize the two D2D spectrum sharing scenarios under a weighted proportional fair utility function. We find that as the proportion of potential D2D mobiles increases, the optimal spectrum partition in the overlay is almost invariant (when D2D mode selection threshold is large) while the optimal spectrum access factor in the underlay decreases. Further, from a coverage perspective, we reveal a tradeoff between the spectrum access factor and the D2D mode selection threshold in the underlay: as more D2D links are allowed (due to a more relaxed mode selection threshold), the network should actually make less spectrum available to them to limit their interference.

Multicast device-to-device (D2D) transmission is important for applications like local file transfer in commercial networks and is also a required feature in public safety networks. In this paper we propose a tractable baseline multicast D2D model, and use it to analyze important multicast metrics like the coverage probability, mean number of covered receivers and throughput. In addition, we examine how the multicast performance would be affected by certain factors like dynamics (due to e.g., mobility) and network assistance. Take the mean number of covered receivers as an example. We find that simple repetitive transmissions help but the gain quickly diminishes as the number of repetitions increases. Meanwhile, dynamics and network assistance (i.e., allowing the network to relay the multicast signals) can help cover more receivers. We also explore how to optimize multicasting, e.g. by choosing the optimal multicast rate and the optimal number of retransmission times.

In heterogeneous cellular networks (HCNs), it is desirable to offload mobile users to small cells, which are typically significantly less congested than the macrocells. To achieve sufficient load balancing, the offloaded users often have much lower SINR than they would on the macrocell. This SINR degradation can be partially alleviated through interference avoidance, for example time or frequency resource partitioning, whereby the macrocell turns off in some fraction of such resources. Naturally, the optimal offloading strategy is tightly coupled with resource partitioning; the optimal amount of which in turn depends on how many users have been offloaded. In this paper, we propose a general and tractable framework for modeling and analyzing joint resource partitioning and offloading in a two-tier cellular network. With it, we are able to derive the downlink rate distribution over the entire network, and an optimal strategy for joint resource partitioning and offloading. We show that load balancing, by itself, is insufficient, and resource partitioning is required in conjunction with offloading to improve the rate of cell edge users in co-channel heterogeneous networks.

While the performance of maximum ratio combining (MRC) is well understood for a single isolated link, the same is not true in the presence of interference, which is typically correlated across antennas due to the common locations of interferers. For tractability, prior work focuses on the two extreme cases where the interference power across antennas is either assumed to be fully correlated or fully uncorrelated. In this paper, we address this shortcoming and characterize the performance of MRC in the presence of spatially-correlated interference across antennas. Modeling the interference field as a Poisson point process, we derive the exact distribution of the signal-to-interference ratio (SIR) for the case of two receive antennas, and upper and lower bounds for the general case. Using these results, we study the diversity behavior of MRC and characterize the critical density of simultaneous transmissions for a given outage constraint. The exact SIR distribution is also useful in benchmarking simpler correlation models. We show that the full-correlation assumption is considerably pessimistic (up to 30% higher outage probability for typical values) and the no-correlation assumption is significantly optimistic compared to the true performance.

This paper presents a tractable model for analyzing noncoherent joint-transmission base station (BS) cooperation, taking into account the irregular BS deployment typically encountered in practice. In addition to cellular-network specific aspects, such as BS density, channel fading, average path loss, and interference, the model also captures relevant cooperation mechanisms, including user-centric BS clustering and channel-dependent cooperation activation. The locations of all BSs are modeled by a Poisson point process. Using tools from stochastic geometry, the signal-to-interference-plus-noise ratio (SINR) distribution with cooperation is precisely characterized in a generality-preserving form. The result is then applied to practical design problems of recent interest. We find that increasing the network-wide BS density improves the SINR, while the gains increase with the path loss exponent. For pilot-based channel estimation, the average spectral efficiency saturates at cluster sizes of around seven BSs for typical values, irrespective of backhaul quality. Finally, it is shown that intra-cluster frequency reuse is favorable in moderately loaded cells with generous cooperation activation, while intra-cluster coordinated scheduling may be better in lightly loaded cells with conservative cooperation activation.

We develop a new tractable model for K-tier cellular networks, where each base station (BS) is solely powered by a self-contained energy harvesting module instead of a conventional power-line source. The BSs across tiers differ in terms of the energy harvesting rate, energy storage capacity, transmit power and deployment density. Since a BS may not always have enough energy, it may need to be kept OFF and allowed to recharge while its load is served by the neighboring BSs that are ON. Using tools from random walk theory and stochastic geometry, we characterize the fraction of time each type of BS can be kept ON, termed availability, for general uncoordinated strategies, where each BS toggles its ON/OFF state independently of the others. As a part of our analysis, we model the temporal dynamics of the energy level at each BS as a birth-death process, derive energy utilization rate for each BS class, and use hitting/stopping time analysis to study availabilities. We prove that there is a fundamental limit on the availabilities, which cannot be surpassed by any uncoordinated strategy. As a part of the proof, we construct the strategy that achieves this limit.

In this paper we jointly address two fundamental issues in device-to-device (D2D) overlaid cellular networks: 1) how to partition the spectrum assuming orthogonal cellular and D2D transmissions, and 2) what is the optimal threshold for distance-based D2D mode selection? To this end, we first derive rate expressions for both cellular and D2D users. Three design criteria - (weighted) max-sum, max-min and proportional fairness - are considered and optimal spectrum partition rules are derived. Finally we validate our model and give rules of thumb for optimizing the spectrum partition and mode selection.

Mobile users proactively offloaded from macro cells to small cells in heterogeneous cellular networks (HCNs) encounter less congestion but higher interference. Resource partitioning protects the offloaded users from macro tier interference by muting the macro tier on certain fraction of resources and scheduling the offloaded users on those resources. However, the extent to which joint offloading and resource partitioning is needed remains unanswered. This is partly due to the lack of tractable frameworks to analyze downlink rate in the presence of such techniques. In this paper, we develop a tractable framework to analyze joint resource partitioning and offloading in a two-tier cellular network and derive the downlink rate distribution over the entire network. Each tier of base stations is modeled as a Poisson point process (PPP) where each tier differs in transmit power and deployment density. Using the developed analysis, we show that the optimal combination of load balancing and resource partitioning improves the rate of cell edge users in co-channel heterogeneous networks.

Device-to-device (D2D) communication is emerging as a potentially attractive way to increase cellular network capacity and flexibility. However, as we describe, analyzing the performance of D2D schemes is non-trivial. In this paper, we consider a D2D overlaid cellular network model, that incorporates many of the leading models for the D2D links and access control. We show that using a Poisson point process (PPP) model for the base stations (BSs), and also a modified Matern hardcore point process (MHC) that can capture BS repulsion, we can extend tools and ideas from stochastic geometry to give compact expressions for important performance metrics, including outage probability. Extending the scope of stochastic geometry is itself an important goal, as this has proven difficult in the past. This allows a tractable approach to understand the performance of D2D overlaid cellular networks. Our simulation results subsequently demonstrate that both the PPP and the modified MHC give good approximations of true BS deployments. In particular, our simulations show the modified MHC process is more accurate than the PPP BS model, at the cost of some additional computational effort.

The rate distribution in heterogeneous networks (HetNets) greatly benefits from load balancing, by which mobile users are pushed onto lightly-loaded small cells despite the resulting loss in SINR. This offloading can be made more aggressive and robust if the macrocells leave a fraction of time/frequency resource blank, which reduces the interference to the offloaded users. We investigate the joint optimization of this technique - referred to in 3GPP as enhanced intercell interference coordination (eICIC) via almost blank subframes (ABSs) - with offloading in this paper. Although the joint cell association and blank resource (BR) problem is nominally combinatorial, by allowing users to associate with multiple base stations (BSs), the problem becomes convex, and upper bounds the performance versus a binary association. We show both theoretically and through simulation that the optimal solution of the relaxed problem still results in an association that is mostly binary. The optimal association differs significantly when the macrocell is on or off; in particular the offloading can be much more aggressive when the resource is left blank by macro BSs. Further, we observe that jointly optimizing the offloading with BR is important. The rate gain for cell edge users (the worst 3-10%) is very large - on the order of 5-10x - versus a naive association strategy without macrocell blanking.

Heterogeneous networks (HetNets) and carrier aggregation (CA) are two distinct features of next-generation cellular networks. Small cells in HetNets are vital for data off-loading and can significantly improve area and cell edge spectral efficiency compared to using just macrocells. CA further increases the transmission bandwidth and thus network capacity by aggregating multiple component carriers on the physical layer. In this paper, we propose a tractable multi-band multi-tier model to study multi-flow CA in HetNets, where base station positions in each tier follow an independent Poisson point process. Our model incorporates an appropriate notion of load which allows the study of the impact of biasing on HetNet performance. For a typical HetNet consisting of two tiers, macro cells and small cells, and two bands, 800MHz band and 2.4GHz band, we observe that the gain (in terms of UE ergodic rate) is about 35% to 40% if the small cells adopt optimal biasing factor compared to the case without biasing. Our model also incorporates the impact of band deployment. For the typical HetNet described, our study suggests that deploying the 800MHz band and 2.4GHz band in both the macro and small cells helps the HetNet best exploit the CA feature.

Current wireless networks are becoming increasingly heterogeneous both in terms of the radio access technologies (RATs) and the base station capabilities. Downlink rate or throughput in such heterogeneous networks is a crucial metric and has been primarily studied using system level simulations. To derive the distribution of rate analytically we develop a fairly general tractable model that consists of M different RATs, each deploying up to K different classes of access points (APs), where each class differs in transmit power, path loss exponent, and deployment density. Each class of APs is modeled as an independent Poisson point process (PPP), with mobile user locations modeled as another independent PPP, all channels further consisting of i.i.d. Rayleigh fading. Using a weighted association strategy, the distribution of rate over the entire network is derived. Further, it is shown that in a two-RAT setting there exists an optimum fraction of traffic that should be associated with each RAT to maximize rate coverage, defined as the fraction of users achieving a given rate.

This paper analyzes large-scale networks that share the spectrum with interference cancellation (IC). The efficiency of spectrum sharing is determined primarily by interference, which in turn depends on the spatial densities, the interference cancellation method, and the spectrum sharing method, i.e., underlay or overlay. By assuming the Poisson distribution for transmitters, equal transmission power in the same system, and an interference-limited environment, this paper finds the performance gain from IC in terms of spectrum-sharing transmission capacity (S-TC), defined as the number of successful transmissions per unit area while guaranteeing the target outage probabilities of all coexisting systems. The effectiveness of IC is characterized by the coefficient of cancellation (CoC), and specific CoC values are derived for two simple IC scenarios, the strong interferer and the close interferer cancellation, with the assumption of having perfect information for channel states of interfering links and interferer locations. The sum S-TC optimal spatial densities of the two systems are given. Finally, CoC conditions to determine the superiority of an underlay or overlay method are presented. We verify that the underlay method could be preferred depending on the CoCs of coexisting systems; that is starkly different from the case without IC, in which the overlay method is always better.

Carrier aggregation (CA) and small cells are two distinct features of next-generation cellular networks. Cellular networks with different types of small cells are often referred to as HetNets. In this paper, we introduce a load-aware model for CA-enabled multi-band HetNets. Under this model, the impact of biasing can be more appropriately characterized; for example, it is observed that with large enough biasing, the spectral efficiency of small cells may increase while its counterpart in a fully-loaded model always decreases. Further, our analysis reveals that the peak data rate does not depend on the base station density and transmit powers; this strongly motivates other approaches e.g. CA to increase the peak data rate. Last but not least, different band deployment configurations are studied and compared. We find that with large enough small cell density, spatial reuse with small cells outperforms adding more spectrum for increasing user rate. More generally, universal cochannel deployment typically yields the largest rate; and thus a capacity loss exists in orthogonal deployment. This performance gap can be reduced by appropriately tuning the HetNet coverage distribution (e.g. by optimizing biasing factors).

In this paper, we analyze a multiple-input multiple-output (MIMO) interference channel where nodes are randomly distributed on a plane as a spatial Poisson cluster point process. A Poisson cluster point process consists of clusters with fixed number of points randomly distributed as with the cluster centers distributed randomly on the plane. The nodes in each cluster use interference alignment (IA) to suppress intra-cluster interference but unlike most work on IA, we do not neglect inter-cluster interference. We also connect the accuracy of channel state information to the distance between the nodes, i.e., the quality of CSI degrades with increasing distance. Accounting for the training and feedback overhead, we derive the transmission capacity of this MIMO IA ad hoc network and then compare it to open-loop (interference-blind) spatial multiplexing. Finally, we present exemplary system setups where spatial multiplexing outperforms IA due to the imperfect channel state information or the non-aligned inter-cluster interference.

The design and evaluation of Inter-cell Interference Coordination (ICIC) techniques has been the focus of significant research as wireless networks are increasingly faced with the challenge of balancing fairness to users at the cell-edge with high spectral efficiency. This work considers the use of Fractional frequency reuse (FFR), in the cellular uplink, which is well-suited for modern cellular networks due to its low complexity and coordination requirements and resource allocation flexibility. These approaches have typically been modeled using deterministic grids for the base station deployments and analyzed through system-level simulations, which do not lead to fundamental insights or tractable expressions of relevant metrics of coverage probability or average rate for a typical user. Instead, this work utilizes Poisson point processes for the underlying spatial models for user and base station locations. From the derived expressions we quantify the coverage gains with Strict FFR relative to universal reuse and Soft Frequency Reuse (SFR), as well as the performance tradeoff SFR achieves for edge and inner users through greater bandwidth efficiency. We additionally illustrate how the analytical model can be directly related to traffic or coverage requirements and gives insight into selecting power control parameters and resource allocations under Strict FFR and SFR to achieve system capacity gains over universal frequency reuse.

We consider information dissemination in a largen-user wireless network in whichkusers wish to share a unique message with all other users. Each of thenusers only has knowledge of its own contents and state information; this corresponds to a one-sided push-only scenario. The goal is to disseminate all messages efficiently, hopefully achieving an order-optimal spreading rate over unicast wireless random networks. First, we show that a random-push strategy-where a user sends its own or a received packet at random-is order-wise suboptimal in a random geometric graph: specifically, Ω(√n) times slower than optimal spreading. It is known that this gap can be closed if each user has “full” mobility, since this effectively creates a complete graph. We instead consider velocity-constrained mobility where at each time slot the user moves locally using a discrete random walk with velocityv(n) that is much lower than full mobility. We propose a simple two-stage dissemination strategy that alternates between individual message flooding (“self promotion”) and random gossiping. We prove that this scheme achieves a close to optimal spreading rate (within only a logarithmic gap) as long as the velocity is at leastv(n)=ω(√(logn/k)). The key insight is that the mixing property introduced by the partial mobility helps users to spread in space within a relatively short period compared to the optimal spreading time, which macroscopically mimics message dissemination over a complete graph.

Multicell cooperation (MCC) is an approach for mitigating intercell interference in dense cellular networks. Existing studies on MCC performance typically rely on either oversimplified Wyner-type models or complex system-level simulations. The promising theoretical results (typically using Wyner models) seem to materialize neither in complex simulations nor in practice. To more accurately investigate the theoretical performance of MCC, this paper models an entire plane of interfering cells as a Poisson random tessellation. The base stations (BSs) are then clustered using a regular lattice, whereby BSs in the same cluster mitigate mutual interference by beamforming with perfect channel state information. Techniques from stochastic geometry and large-deviation theory are applied to analyze the outage probability as a function of the mobile locations, scattering environment, and the average number of cooperating BSs per clusterl. For mobiles near the centers of BS clusters, it is shown that outage probability diminishes asO(e-lν1) with 0 ≤ ν1≤ 1 if scattering is sparse, and asO(l-ν2) with ν2proportional to the signal diversity order if scattering is rich. For randomly located mobiles, regardless of scattering, outage probability is shown to scale asO(l-ν3) with 0 ≤ ν3≤ 0.5. These results confirm analytically that cluster-edge mobiles are the bottleneck for network coverage and provide a plausible analytic framework for more realistic analysis of other multicell techniques.

Cooperation is viewed as a key ingredient for interference management in wireless networks. This paper shows that cooperation has fundamental limitations. First, it is established that in systems that rely on pilot-assisted channel estimation, the spectral efficiency is upper-bounded by a quantity that does not depend on the transmit powers; in this framework, cooperation is possible only within clusters of limited size, which are subject to out-of-cluster interference whose power scales with that of the in-cluster signals. Second, an upper bound is also shown to exist if the cooperation extends to an entire (large) system operating as a single cluster; here, pilot-assisted transmission is necessarily transcended. Altogether, it is concluded that cooperation cannot in general change an interference-limited network to a noise-limited one. Consequently, the existing literature that routinely assumes that the high-power spectral efficiency scales with the log-scale transmit power provides only a partial characterization. The complete characterization proposed in this paper subdivides the high-power regime into a degree-of-freedom regime, where the scaling with the log-scale transmit power holds approximately, and a saturation regime, where the spectral efficiency hits a ceiling that is independent of the power. Using a cellular system as an example, it is demonstrated that the spectral efficiency saturates at power levels of operational relevance.

In this paper, we consider delay-constrained wireless multi-hop ad hoc networks where a packet should be delivered to the destination within the maximum allowed delay while satisfying the target outage probability. The proposed performance metric for analyzing networks is the delay-constrained random access transport capacity (D-RATC), which quantifies the maximum end-to-end (e2e) link achievable rate per unit area of a delay-constrained network using a random access protocol. The scaling of the D-RATC is obtained for various slotted ALOHA (SA) protocols and it is shown that the SA protocol is order-optimal for delay-constrained random networks when interference control is used with an additional feature such as rate control or admission control. If interference control is not used, the SA protocol suffers from the negatively infinite scaling exponent except the case of using rate control where a finite but suboptimal scaling exponent may be achieved. Also, it is shown that multi-hop control does not affect the scaling exponent but just improves the D-RATC pre-constant.

Random spatial models are attractive for modeling heterogeneous cellular networks (HCNs) due to their realism, tractability, and scalability. A major limitation of such models to date in the context of HCNs is the neglect of network traffic and load: all base stations (BSs) have typically been assumed to always be transmitting. Small cells in particular will have a lighter load than macrocells, and so their contribution to the network interference may be significantly overstated in a fully loaded model. This paper incorporates a flexible notion of BS load by introducing a new idea of conditionally thinning the interference field. For a K-tier HCN where BSs across tiers differ in terms of transmit power, supported data rate, deployment density, and now load, we derive the coverage probability for a typical mobile, which connects to the strongest BS signal. Conditioned on this connection, the interfering BSs of the ith tier are assumed to transmit independently with probability p%, which models the load. Assuming - reasonably - that smaller cells are more lightly loaded than macrocells, the analysis shows that adding such access points to the network always increases the coverage probability. We also observe that fully loaded models are quite pessimistic in terms of coverage.

We develop a general downlink model for multi-antenna heterogeneous cellular networks (HetNets), where base stations (BSs) across tiers may differ in terms of transmit power, target signal-to-interference-ratio (SIR), deployment density, number of transmit antennas and the type of multi-antenna transmission. In particular, we consider and compare space division multiple access (SDMA), single user beamforming (SU-BF), and baseline single-input single-output (SISO) transmission. For this general model, the main contributions are: (i) ordering results for both coverage probability and per user rate in closed form for any BS distribution for the three considered techniques, using novel tools from stochastic orders, (ii) upper bounds on the coverage probability assuming a Poisson BS distribution, and (iii) a comparison of the area spectral efficiency (ASE). The analysis concretely demonstrates, for example, that for a given total number of transmit antennas in the network, it is preferable to spread them across many single-antenna BSs vs. fewer multi-antenna BSs. Another observation is that SU-BF provides higher coverage and per user data rate than SDMA, but SDMA is in some cases better in terms of ASE.

Despite the central role of mobility in wireless networks, analytical study on its impact on network performance is notoriously difficult. This paper aims to address this gap by proposing a random waypoint (RWP) mobility model defined on the entire plane and applying it to analyze two key cellular network parameters: handover rate and sojourn time. We first analyze the stochastic properties of the proposed model and compare it to two other models: the classical RWP mobility model and a synthetic truncated Levy walk model which is constructed from real mobility trajectories. The comparison shows that the proposed RWP mobility model is more appropriate for the mobility simulation in emerging cellular networks, which have ever-smaller cells. Then we apply the proposed model to cellular networks under both deterministic (hexagonal) and random (Poisson) base station (BS) models. We present analytic expressions for both handover rate and sojourn time, which have the expected property that the handover rate is proportional to the square root of BS density. Compared to an actual BS distribution, we find that the Poisson-Voronoi model is about as accurate in terms of mobility evaluation as hexagonal model, though being more pessimistic in that it predicts a higher handover rate and lower sojourn time.

Cellular uplink analysis has typically been undertaken by either a simple approach that lumps all interference into a single deterministic or random parameter in a Wyner-type model, or via complex system level simulations that often do not provide insight into why various trends are observed. This paper proposes a novel middle way using point processes that is both accurate and also results in easy-to-evaluate integral expressions based on the Laplace transform of the interference. We assume mobiles and base stations are randomly placed in the network with each mobile pairing up to its closest base station. Compared to related recent work on downlink analysis, the proposed uplink model differs in two key features. First, dependence is considered between user and base station point processes to make sure each base station serves a single mobile in the given resource block. Second, per-mobile power control is included, which further couples the transmission of mobiles due to location-dependent channel inversion. Nevertheless, we succeed in deriving the coverage (equivalently outage) probability of a typical link in the network. This model can be used to address a wide variety of system design questions in the future. In this paper we focus on the implications for power control and show that partial channel inversion should be used at low signal-to-interference-plus-noise ratio (SINR), while full power transmission is optimal at higher SINR.

Pushing data traffic from cellular to WiFi is an example of inter radio access technology (RAT) offloading. While this clearly alleviates congestion on the over-loaded cellular network, the ultimate potential of such offloading and its effect on overall system performance is not well understood. To address this, we develop a general and tractable model that consists of M different RATs, each deploying up to K different tiers of access points (APs), where each tier differs in transmit power, path loss exponent, deployment density and bandwidth. Each class of APs is modeled as an independent Poisson point process (PPP), with mobile user locations modeled as another independent PPP, all channels further consisting of i.i.d. Rayleigh fading. The distribution of rate over the entire network is then derived for a weighted association strategy, where such weights can be tuned to optimize a particular objective. We show that the optimum fraction of traffic offloaded to maximize SINR coverage is not in general the same as the one that maximizes rate coverage, defined as the fraction of users achieving a given rate.

Coordinated multi-point (CoMP) communication is attractive for heterogeneous cellular networks (HCNs) for interference reduction. However, previous approaches to CoMP face two major hurdles in HCNs. First, they usually ignore the inter-cell overhead messaging delay, although it results in an irreducible performance bound. Second, they consider the grid or Wyner model for base station locations, which is not appropriate for HCN BS locations which are numerous and haphazard. Even for conventional macrocell networks without overlaid small cells, SINR results are not tractable in the grid model nor accurate in the Wyner model. To overcome these hurdles, we develop a novel analytical framework which includes the impact of overhead delay for CoMP evaluation in HCNs. This framework can be used for a class of CoMP schemes without user data sharing. As an example, we apply it to downlink CoMP zero-forcing beamforming (ZFBF), and see significant divergence from previous work. For example, we show that CoMP ZFBF does not increase throughput when the overhead channel delay is larger than 60% of the channel coherence time. We also find that, in most cases, coordinating with only one other cell is nearly optimum for downlink CoMP ZFBF.

For small cell technology to significantly increase the capacity of tower-based cellular networks, mobile users will need to be actively pushed onto the more lightly loaded tiers (corresponding to, e.g., pico and femtocells), even if they offer a lower instantaneous SINR than the macrocell base station (BS). Optimizing a function of the long-term rate for each user requires (in general) a massive utility maximization problem over all the SINRs and BS loads. On the other hand, an actual implementation will likely resort to a simple biasing approach where a BS in tier j is treated as having its SINR multiplied by a factor Aj≥ 1, which makes it appear more attractive than the heavily-loaded macrocell. This paper bridges the gap between these approaches through several physical relaxations of the network-wide association problem, whose solution is NP hard. We provide a low-complexity distributed algorithm that converges to a near-optimal solution with a theoretical performance guarantee, and we observe that simple per-tier biasing loses surprisingly little, if the bias values Ajare chosen carefully. Numerical results show a large (3.5x) throughput gain for cell-edge users and a 2x rate gain for median users relative to a maximizing received power association.

Heterogeneous cellular networks (HCNs) are characterized by cells whose coverage areas may vary by orders of magnitude. It is natural therefore that their user populations (and hence traffic loads) will vary similarly. Yet, to date, random spatial models developed for HCNs generally assume that all base stations (BSs) are always transmitting and hence implicitly have the same load. This paper incorporates a flexible notion of BS load by conditionally thinning the interference field, conditional on the connection of a typical mobile to its serving BS. We derive the coverage probability - i.e. the Signal-to-Interference-Ratio (SIR) distribution - for a typical mobile in a K-tier HCN where each tier has an arbitrary load characterized by a traffic factor pk∈ [0, 1], where pk= 1 is fully loaded. Fully-loaded models are observed to be extremely pessimistic in terms of coverage, and the analysis shows that adding lightly loaded access points (e.g. pico or femtocells) to the macrocell network always increases the coverage probability.

The cellular uplink has typically been studied using simple Wyner-type analytical models where interference is modeled as a constant or a single random variable, or via complex system-level simulations for a given set of parameters, which are often insufficient to evaluate performance in all operational regimes. In this paper, we take a fresh look at this classic problem using tools from point process theory and stochastic geometry, and develop a new tractable model for the cellular uplink which provides easy-to-evaluate expressions for important performance metrics such as coverage probability. The main idea is to model the locations of mobiles as a realization of a Poisson Point Process where each base station (BS) is located uniformly in the Voronoi cell of the mobile it serves, thereby capturing the dependence in two spatial processes. In addition to modeling interference accurately, it provides a natural way to model per-mobile power control, which is an important aspect of the uplink and one of the reasons why uplink analysis is more involved than its downlink counterpart. We also show that the same framework can be used to study regular as well as irregular BS deployments by choosing an appropriate distribution for the distance of a mobile to its serving BS. We verify the accuracy of this framework with an actual urban/suburban cellular network.

Mobility modeling and analysis is a key issue in wireless networks. In this paper we propose a new and quite general random waypoint (RWP) mobility model which is valid over the entire plane. We derive key properties of the proposed mobility model including transition length, transition time and spatial node distribution. Then the RWP mobility model is applied to study the handover rate in cellular networks under both deterministic (hexagonal) and random (Poisson) base station (BS) models. Closed form expressions for handover rate can be obtained. These results show the expected property that the handover rate is proportional to the square root of base station density. Also, we find that Poisson-Voronoi model for BS coverage areas is about as accurate in terms of mobility (particularly handover) evaluation as the ubiquitous hexagonal model.

In industry, cellular tower locations have primarily been modeled by a deterministic hexagonal grid. Since real deployments are rarely regular, the even spacing between nodes in the grid and constant Voronoi cell areas make the hexagonal grid unrealistic. In this paper we use tools from spatial statistics to show that a purely random node placement and a hexagonal grid distribution with the points perturbed also have unrealistic spatial relationships between nodes, and that pairwise interactions between nodes are necessary, and in most cases sufficient, for modeling spatial qualities of cellular networks. We detail the benefits of using pairwise point interactions in modeling both a coverage-centric tower deployment and a capacity-centric tower deployment. We propose using pairwise and saturated pairwise interaction point processes from the Gibbs process family of point processes: the Strauss Hardcore process for inhibitive point patterns and the Geyer Saturation process for clustered point patterns. Due to its relationship with the coverage areas, we also propose that the Voronoi cell area distribution can be used as a test statistic in general spatial modeling of cellular networks.

We investigate how a heterogeneous cellular network should self-organize by proposing a load-aware user association scheme. This is an important consideration, in order to move traffic off congested cells and onto more lightly loaded cells. Although the network-wide optimal association problem is NP hard, a closely related utility maximization problem can be made convex by applying relaxations on the association metric. We then address a low-complexity distributed algorithm that converges to a near-optimal solution with theoretical guarantee on its performance, requiring limited information and no coordination. This is directly related to range extension and small-cell biasing, which is how cell associations are likely to work in practice. Our load-aware association scheme provides theoretical guidance on the best “biasing factor” for different tiers of base stations. Numerical results show a 3.5x throughput gain for cell-edge users and a 2x gain for median users relative to the standard max-SINR association where a mobile connects to the strongest base station.

Interference modeling is central to the analysis of many interference limited systems. The aggregate interference due to many individual interferers is often very difficult to characterize exactly, especially when lognormal shadowing and path loss is considered. Some results are available for homogeneous sources where the individual components have the same distribution, but many more detailed studies involve heterogeneous sources. Hence, in this paper we build upon previous models for homogeneous sources to develop three general purpose approaches to modeling the aggregate interference from heterogeneous sources which include both shadowing and path-loss. These models are the inverse gamma, inverse generalized gamma and extreme value distributions. These models are motivated by prior work as well as by three distinct interference scenarios relating to cognitive radio systems, digital television and femtocells. The models are fitted to these wide ranging examples and numerical results show good agreement, both for interference and SINR distributions.

Multi-cell cooperation (MCC) is a promising approach for mitigating inter-cell interference in dense cellular networks. To study the MCC performance, existing work typically relies on the over-simplified Wyner-type models that fail to account for mobile spatial statistics, irregular locations of base stations (BSs) and the resultant highly variable path-loss. Unsurprisingly, real-world systems show gains far below those predicted using such idealized models. This paper adopts a stochastic-geometry model for a cellular downlink network with MCC where cells are modeled as a Poisson random tessellation generated by Poisson distributed BSs, these BSs are then clustered using a hexagonal lattice, and BSs in the same cluster mitigate mutual interference by spatial interference avoidance. We analyze the effects of scattering on network coverage as the average number of cooperative BSs, K, increases. For mobiles near the centers of cooperative BS clusters, we show that the outage probability diminishes with increasing K at least sub-exponentially for sparse scattering and following a power law for rich scattering where the exponent is proportional to the signal diversity order. For randomly located mobiles, the outage probability is shown to decrease with increasing K following a power law independent with scattering.

Quality of Experience (QoE) has taken a center stage in the performance evaluation of multimedia delivery technologies. The Third Generation Partnership Project (3GPP) Long Term Evolution (LTE) system is the latest generation of wireless cellular technology expected to deliver higher data rates and meet the burgeoning data demand. With the projected dominant share of video services in mobile traffic, providing satisfactory QoE to video users is a key objective for LTE system design. In this paper, we present a QoE-based evaluation methodology to assess the LTE system video capacity in terms of the number of unicast video consumers that can be simultaneously supported for a given target QoE. We define and use the notion of rebuffering outage capacity to quantify the video service capacity. Our evaluation further incorporates adaptive streaming, a promising technology for video delivery over wireless, and presents its consequent QoE-capacity tradeoff. The impact of QoE-based outage criteria is also investigated on the downlink video capacity. Finally, we propose a QoE-aware radio resource management (RRM) framework which allows the network operator to further enhance the video capacity. Our results demonstrate that there is a significant potential to optimize video capacity through QoE awareness both at the application level and radio access network (RAN) level.

Cooperation in a large wireless network with pilotassisted coherent communication is shown to have certain fundamental limitations, namely that even perfect cooperation cannot in general change an interference-limited network to a noise-limited one. Specifically, we demonstrate the existence of a spectral efficiency upper bound that does not grow with the transmit power, when channels are estimated via pilot signals. This is because pilot-assisted channel estimation is only possible within finite cooperation clusters, resulting in out-of-cluster interference that scales with the transmit power. Making the clusters excessively large can actually worsen this effect, nor does sidestepping the pilot-assisted channel estimation via noncoherent demodulation provide an escape. Using a cellular system as an example, it is demonstrated that the spectral efficiency saturates at power levels of operational relevance, indicating that the lackluster gains from cooperation observed in practice may be based on fundamental information-theoretic limitations, rather than current technology imperfections.

Femtocells, despite their name, pose a potentially large disruption to the carefully planned cellular networks that now connect a majority of the planet's citizens to the Internet and with each other. Femtocells - which by the end of 2010 already outnumbered traditional base stations and at the time of publication are being deployed at a rate of about five million a year - both enhance and interfere with this network in ways that are not yet well understood. Will femtocells be crucial for offloading data and video from the creaking traditional network? Or will femtocells prove more trouble than they are worth, undermining decades of careful base station deployment with unpredictable interference while delivering only limited gains? Or possibly neither: are femtocells just a "flash in the pan"; an exciting but short-lived stage of network evolution that will be rendered obsolete by improved WiFi offloading, new backhaul regulations and/or pricing, or other unforeseen technological developments? This tutorial article overviews the history of femtocells, demystifies their key aspects, and provides a preview of the next few years, which the authors believe will see a rapid acceleration towards small cell technology. In the course of the article, we also position and introduce the articles that headline this special issue.

Cellular networks are in a major transition from a carefully planned set of large tower-mounted base-stations (BSs) to an irregular deployment of heterogeneous infrastructure elements that often additionally includes micro, pico, and femtocells, as well as distributed antennas. In this paper, we develop a tractable, flexible, and accurate model for a downlink heterogeneous cellular network (HCN) consisting of K tiers of randomly located BSs, where each tier may differ in terms of average transmit power, supported data rate and BS density. Assuming a mobile user connects to the strongest candidate BS, the resulting Signal-to-Interference-plus-Noise-Ratio (SINR) is greater than 1 when in coverage, Rayleigh fading, we derive an expression for the probability of coverage (equivalently outage) over the entire network under both open and closed access, which assumes a strikingly simple closed-form in the high SINR regime and is accurate down to -4 dB even under weaker assumptions. For external validation, we compare against an actual LTE network (for tier 1) with the other K-1 tiers being modeled as independent Poisson Point Processes. In this case as well, our model is accurate to within 1-2 dB. We also derive the average rate achieved by a randomly located mobile and the average load on each tier of BSs. One interesting observation for interference-limited open access networks is that at a given \sinr, adding more tiers and/or BSs neither increases nor decreases the probability of coverage or outage when all the tiers have the same target-SINR.

The unpredictability of the wireless medium poses a major challenge to delivering a high quality of experience (QoE) for real-time video services. Bursty co-channel interference is a prominent cause of wireless throughput variability, which leads to video QoE degradation, even for a fixed average channel quality. In this paper, we propose and analyze a network-level resource management algorithm termed interference shaping to smooth out the throughput variations (and hence improve the QoE) of video users by decreasing the peak rate of co-channel best effort users. Wireless link capacity variations are mapped to the real-time video packet loss rate, and the interference shaping QoE gain for video users is quantified by benchmarking against a modified multi-scale structural similarity (H-MS-SSIM) index. H-MS-SSIM is an accurate perceptual video quality metric that incorporates the important hysteresis effect whereby the current QoE (which is subjective) may strongly depend on the recent past. The proposed technique increases mean QoE and reduces the QoE variability over time, with a net perceptual increase of about 2-3x in illustrative settings while incurring insignificant decrease in the QoE for co-channel best effort users. Interference shaping can be implemented in both unicast and multicast real-time video streaming with much higher potential gains for multicast.

Interference management techniques are critical to the performance of heterogeneous cellular networks, which will have dense and overlapping coverage areas, and experience high levels of interference. Fractional frequency reuse (FFR) is an attractive interference management technique due to its low complexity and overhead, and significant coverage improvement for low-percentile (cell-edge) users. Instead of relying on system simulations based on deterministic access point locations, this paper instead proposes an analytical model for evaluating Strict FFR and Soft Frequency Reuse (SFR) deployments based on the spatial Poisson point process. Our results both capture the non-uniformity of heterogeneous deployments and produce tractable expressions which can be used for system design with Strict FFR and SFR. We observe that the use of Strict FFR bands reserved for the users of each tier with the lowest average \sinr provides the highest gains in terms of coverage and rate, while the use of SFR allows for more efficient use of shared spectrum between the tiers, while still mitigating much of the interference. Additionally, in the context of multi-tier networks with closed access in some tiers, the proposed framework shows the impact of cross-tier interference on closed access FFR, and informs the selection of key FFR parameters in open access.

This paper develops upper bounds on the end-to-end transmission capacity of multihop wireless networks. Potential source-destination paths are dynamically selected from a pool of randomly located relays, from which a closed-form lower bound on the outage probability is derived in terms of the expected number of potential paths. This is in turn used to provide an upper bound on the number of successful transmissions that can occur per unit area, which is known as the transmission capacity. The upper bound results from assuming independence among the potential paths, and can be viewed as the maximum diversity case. A useful aspect of the upper bound is its simple form for an arbitrary-sized network, which allows insights into how the number of hops and other network parameters affect spatial throughput in the nonasymptotic regime. The outage probability analysis is then extended to account for retransmissions with a maximum number of allowed attempts. In contrast to prevailing wisdom, we show that predetermined routing (such as nearest neighbor) is suboptimal, since more hops are not useful once the network is interference-limited. Our results also make clear that randomness in the location of relay sets and dynamically varying channel states is helpful in obtaining higher aggregate throughput, and that dynamic route selection should be used to exploit path diversity.

The spatial correlations in transmitter node locations introduced by common multiple access protocols make the analysis of interference, outage, and other related metrics in a wireless network extremely difficult. Most works therefore assume that nodes are distributed either as a Poisson point process (PPP) or a grid, and utilize the independence properties of the PPP (or the regular structure of the grid) to analyze interference, outage and other metrics. But, the independence of node locations makes the PPP a dubious model for nontrivial MACs which intentionally introduce correlations, e.g., spatial separation, while the grid is too idealized to model real networks. In this paper, we introduce a new technique based on the factorial moment expansion of functionals of point processes to analyze functions of interference, in particular outage probability. We provide a Taylor-series type expansion of functions of interference, wherein increasing the number of terms in the series provides a better approximation at the cost of increased complexity of computation. Various examples illustrate how this new approach can be used to find outage probability in both Poisson and non-Poisson wireless networks.

Interference between nodes is a critical impairment in mobile ad hoc networks. This paper studies the role of multiple antennas in mitigating such interference. Specifically, a network is studied in which receivers apply zero-forcing beamforming to cancel the strongest interferers. Assuming a network with Poisson-distributed transmitters and independent Rayleigh fading channels, the transmission capacity is derived, which gives the maximum number of successful transmissions per unit area. Mathematical tools from stochastic geometry are applied to obtain the asymptotic transmission capacity scaling and characterize the impact of inaccurate channel state information (CSI). It is shown that, if each node cancels interferers, the transmission capacity decreases as as the outage probability vanishes. For fixed , as grows, the transmission capacity increases as where is the path-loss exponent. Moreover, CSI inaccuracy is shown to have no effect on the transmission capacity scaling as vanishes, provided that the CSI training sequence has an appropriate length, which we derive. Numerical results suggest that canceling merely one interferer by each node may increase the transmission capacity by an order of magnitude or more, even when the CSI is imperfect.

Communication in decentralized wireless networks is limited by interference. Because transmissions typically last for more than a single contention time slot, interference often exhibits a strong statistical dependence over time that results in temporally correlated communication performance. The temporal dependence in interference increases as user mobility decreases and/or the total transmission time increases. We propose a network model that spans the extremes of temporal independence to long-term temporal dependence. Using the proposed model, closed-form single hop communication performance metrics are derived that are asymptotically exact in the low outage regime. The primary contributions are (i) deriving the joint temporal statistics of network interference and showing that it follows a multivariate symmetric alpha stable distribution; (ii) utilizing the joint interference statistics to derive closed-form expressions for local delay, throughput outage probability, and average network throughput; and (iii) using the joint interference statistics to redefine and analyze the network transmission capacity that captures the throughput-delay-reliability tradeoffs in single hop transmissions. Simulation results verify the closed-form expressions derived in this paper and we demonstrate up to 2× gain in network throughput and reliability by optimizing certain parameters of medium access control layer protocol in view of the temporal correlations.

In this paper we develop a tractable framework for SINR analysis in downlink heterogeneous cellular networks (HCNs) with flexible cell association policies. The HCN is modeled as a multi-tier cellular network where each tier's base stations (BSs) are randomly located and have a particular transmit power, path loss exponent, spatial density, and bias towards admitting mobile users. For example, as compared to macrocells, picocells would usually have lower transmit power, higher path loss exponent (lower antennas), higher spatial density (many picocells per macrocell), and a positive bias so that macrocell users are actively encouraged to use the more lightly loaded picocells. In the present paper we implicitly assume all base stations have full queues; future work should relax this. For this model, we derive the outage probability of a typical user in the whole network or a certain tier, which is equivalently the downlink SINR cumulative distribution function. The results are accurate for all SINRs, and their expressions admit quite simple closed-forms in some plausible special cases. We also derive the average ergodic rate of the typical user, and the minimum average user throughput - the smallest value among the average user throughputs supported by one cell in each tier. We observe that neither the number of BSs or tiers changes the outage probability or average ergodic rate in an interference-limited full-loaded HCN with unbiased cell association (no biasing), and observe how biasing alters the various metrics.

The tremendous capacity gains promised by space division multiple access (SDMA) depend critically on the accuracy of the transmit channel state information. In the broadcast channel, even without any network interference, it is known that such gains collapse due to interstream interference if the feedback is delayed or low rate. In this paper, we investigate SDMA in the presence of interference from many other simultaneously active transmitters distributed randomly over the network. In particular we consider zero-forcing beamforming in a decentralized (ad hoc) network where each receiver provides feedback to its respective transmitter. We derive closed-form expressions for the outage probability, network throughput, transmission capacity, and average achievable rate and go on to quantify the degradation in network performance due to residual self-interference as a function of key system parameters. One particular finding is that as in the classical broadcast channel, the per-user feedback rate must increase linearly with the number of transmit antennas and SINR (in dB) for the full multiplexing gains to be preserved with limited feedback. We derive the throughput-maximizing number of streams, establishing that single-stream transmission is optimal in most practically relevant settings. In short, SDMA does not appear to be a prudent design choice for interference-limited wireless networks.

Most work on wireless network throughput ignores the temporal correlation inherent to wireless channels because it degrades tractability. To better model and quantify the temporal variations of wireless network throughput, this paper introduces a metric termed ergodic transmission capacity (ETC), which includes spatial and temporal ergodicity. All transmitters in the network form a homogeneous Poisson point process and all channels are modeled by a finite state Markov chain. The bounds on outage probability and ETC are characterized, and their scaling behaviors for a sparse and dense network are discussed. From these results, we show that the ETC can be characterized by the inner product of the channel-state related vector and the invariant probability vector of the Markov chain. This indicates that distributed channel-aware scheduling (DCAS) does not always increase ETC. Finally, we look at outage probability with interference management from a stochastic geometry point of view. The improved bounds on outage probability and ETC due to interference management are characterized and they provide some useful insights on how to effectively manage interference in sparse and dense networks.

In this paper we analyze a constant multiple-input multiple-output interference channel where a set of active users are cooperating through interference alignment while a set of secondary users desire access to the channel. We find the minimum number of secondary transmit antennas required so that a secondary user can use the channel without affecting the sum rate of the active users, under a zero-forcing equalization assumption. When the secondary users have enough antennas, we derive several secondary user precoders that approximately maximize the secondary users' sum rate without changing the sum rate of the active users. When the secondary users do not have enough antennas, we perform numerical optimization to find secondary user precoders that cause minimum degradation to the sum rate of the active users. Through simulations, we confirm that i) with enough antennas at the secondary users, gains equivalent to the case of all the users cooperating through interference alignment is obtainable, and ii) when the secondary users do not have enough antennas, large rate losses at the active users can be avoided.channels

Most multiuser precoding techniques require accurate channel state information at the transmitter (CSIT) to maintain orthogonality between the users. Such techniques have proven quite fragile in time-varying channels because the CSIT is inherently imperfect due to quantization error and feedback delay. An alternative approach recently proposed by Maddah-Ali and Tse (MAT) allows for significant multiplexing gain in the multi-input single-output (MISO) broadcast channel (BC) even with CSIT that is "completely stale", i.e., uncorrelated with the current channel state. With K users, their scheme claims to lose only a log(K) factor relative to the full K degrees of freedom (DoF) attainable in the MISO BC with perfect CSIT for large K. However, their result does not consider the cost of the feedback, which is potentially very large in high mobility (short channel coherence time). In this paper, we more closely examine the MAT scheme and compare its maximum net DoF gain to single user transmission (which always achieves 1 DoF) and partial CSIT linear precoding (which achieves up to K). In particular, assuming the channel coherence time is N symbol periods and the feedback delay is Nfd, we show that when N; (1+o(1)) (Nfd+ K/ log K)(1-log-1K)-1(long coherence time), zero-forcing precoding outperforms the other two. The MAT scheme is optimal for intermediate coherence times, which for practical parameter choices is indeed quite a large and significant range, even accounting for the feedback cost.

In this paper, we investigate spatial intercell interference cancellation - an efficient technique to mitigate intercell interference in multicell networks. We consider a practical model for channel state information (CSI), where the transmit CSI is acquired through downlink training and uplink feedback. Due to the requirement of channel information from multiple base stations, the training and feedback design is quite different from conventional single-cell processing systems. We optimize training and feedback, where both analog and digital feedback is considered. For analog feedback, it is shown that the downlink training optimization provides a more significant performance gain than feedback optimization; while conversely for digital feedback over a finite-rate feedback channel, the feedback bit allocation is more important than the training optimization.

Multi-cell cooperation is a promising approach for mitigating inter-cell interference in dense cellular networks. Quantifying the performance of multi-cell cooperation is challenging as it integrates physical-layer techniques and network topologies. For tractability, existing work typically relies on the over-simplified Wyner-type models. In this paper, we propose a new stochastic- geometry model for a cellular network with multi-cell cooperation, which accounts for practical factors including the irregular locations of base stations (BSs) and the resultant path-losses. In particular, the proposed network-topology model has three key features: i) the cells are modeled using a Poisson random tessellation generated by Poisson distributed BSs, ii) multi-antenna BSs are clustered using a hexagonal lattice and BSs in the same cluster mitigate mutual interference by spatial interference avoidance, iii) BSs near cluster edges access a different sub- channel from that by other BSs, shielding cluster-edge mobiles from strong interference. Using this model and assuming sparse scattering, we analyze the shapes of the outage probabilities of mobiles served by cluster-interior BSs as the average number K of BSs per cluster increases. The outage probability of a mobile near a cluster center is shown to be proportional to e(-c(2- √v)2) K where v is the fraction of BSs lying in the interior of clusters and c is a constant. Moreover, the outage probability of a typical mobile is proved to scale proportionally with e(-c(2- √v)2) K where c' is a constant.

In this paper we develop a tractable framework for SINR analysis in downlink heterogeneous cellular networks (HCNs) with flexible cell association. The HCN is modeled as a multi-tier cellular network where each tier's base stations (BSs) are randomly located and have a unique transmit power, path loss exponent, spatial density, and bias towards admitting users. We implicitly assume every BS has full queues. From this model, we derive the outage probability of a typical user in the network, which can be viewed as a spatial average of SINR over all users in the network. We observe that deploying more or less BSs does not change the outage probability in interference-limited HCN with unbiased cell association, and observe how biasing affects the metric.

Fractional frequency reuse (FFR) is an interference management technique well-suited to OFDMA-based cellular networks wherein the cells are partitioned into spatial regions with different frequency reuse factors. These techniques are of further relevance when considered in the context of heterogeneous networks whose performance is often limited by intercell and inter-tier interference. To date, FFR techniques have typically been evaluated through system-level simulations using a hexagonal grid for the base station locations. This paper instead focuses on analytically evaluating the two main types of FFR deployments - Strict FFR and Soft Frequency Reuse (SFR) - using a Poisson point process to model the access point locations. Under reasonable assumptions for modern cellular networks, our results reduce to tractable expressions which provide insight into system design guidelines and the relative merits of Strict FFR and SFR, compared to universal reuse for a two-tier network with open access between tiers.

Fractional frequency reuse (FFR) is an interference management technique well-suited to OFDMA-based cellular networks wherein the cells are partitioned into spatial regions with different frequency reuse factors. To date, FFR techniques have been typically been evaluated through system-level simulations using a hexagonal grid for the base station locations. This paper instead focuses on analytically evaluating the two main types of FFR deployments - Strict FFR and Soft Frequency Reuse (SFR) - using a Poisson point process to model the base station locations. The results are compared with the standard grid model and an actual urban deployment. Under reasonable special cases for modern cellular networks, our results reduce to simple closed-form expressions, which provide insight into system design guidelines and the relative merits of Strict FFR, SFR, universal reuse, and fixed frequency reuse.

In this paper we consider an interference channel where a set of primary active users are cooperating through interference alignment over a constant multiple-input-multiple-output channel while a set of secondary users desire access to the channel. We present the conditions under which a secondary user can be admitted to the network. For the admitted users, we derive several beamforming designs maximizing approximately the secondary users' sum-rate based on the number of the secondary users, the number of antennas at the secondary users and the total number of streams in the network of active users.

It is common practice to model the base station (BS) locations in a cellular system by a grid, such as a hexagonal or square lattice. This model is usually analytically intractable as well as quite idealized. Therefore, system designers resort to complex simulations to evaluate network performance. In this paper, we introduce a new model for the base station locations based on a homogeneous Poisson point process (PPP), whereby the mobiles communicate with their nearest base stations. We obtain the distribution of the signal-to-interference-noise ratio (SINR), compute the average ergodic rate, and analytically verify the trade-off between coverage and rate with frequency reuse. We compare our results with actual BS locations as well as the grid model. In addition to being tractable, we also observe that the performance predicted by the PPP model lower bounds the actual performance, and is about as predictive as the grid model which provides upper bounds.

A fundamental choice in femtocell deployments is the set of users which are allowed to access each femtocell. Closed access restricts the set to specifically registered users, while open access allows any mobile subscriber to use any femtocell. The main results of the paper are lemmas which provide expressions for the SINR distribution for various zones within a cell as a function of this MBS-femto distance. The average sum throughput (or any other SINR-based metric) of home and cellular users under open and closed access can be readily determined from these expressions. We show that unlike in the uplink, the interests of home and cellular users are in conflict, with home users preferring closed access and cellular users preferring open access. The conflict is most pronounced for femtocells near the cell edge, when there are many cellular users and fewer femtocells.

The effect of limited feedback on point-to-multipoint communication is investigated in multi-antenna wireless ad hoc networks. We consider zero-forcing beamforming with quantized channel direction information and derive new closed-form expressions for the outage probability, throughput, transmission capacity, and average user rate. Expressions for the performance degradation due to finite rate feedback, the optimal number of streams, and the required feedback rate scaling are provided. Our results indicate that the optimized system operating points depend on different network parameters such as pathloss exponent, node density, and outage constraints.

The efficiency of spectrum sharing can be improved by interference suppression and/or cancellation. This paper analyzes the performance of spectrum sharing networks with interference cancellation (IC) based on the spectrum-sharing transmission capacity (S-TC), defined as the number of successful transmissions per unit area while guaranteeing all target outage probabilities of spectrum-sharing systems. The effectiveness of IC can be characterized by the coefficient of cancellation (CoC) and a specific CoC for strong interferer cancellation (S-IC) method is derived. It is verified that the performance of S-IC is affected solely by system parameters of its own system and the S-TC region can increase in various forms depending on CoCs, which should be considered in analysis of spectrum-sharing efficiency.

Compared to real cellular systems where users are spatially distributed and interference levels vary by several orders of magnitude over a cell, in the Wyner model user locations are fixed and the interference intensity is characterized by a single fixed parameter. Although it is a fairly extreme simplification, the Wyner model has been extensively used to analyze cellular networks. Does it capture some of the main trends of such networks or not? In this study of downlink cellular networks, we show that from an outage point of view, the Wyner model is highly inaccurate since outage is primarily a function of user location. However, in the case of average throughput, the Wyner model may in some special cases be an acceptable simplification if the interference parameter is set appropriately. In particular, we show that it is relatively accurate in terms of the average throughput for CDMA systems with single-cell processing and perfect channel inversion, and for the sum throughput of multicell processing with equal transmit power per user. In short, the Wyner model appears to be a reasonable approximation for SINR mean-based metrics like sum and average throughput for certain scenarios, but is unreasonable in nearly all cases for SINR tail-based metrics like outage probability.

Information dissemination in a large network is typically achieved when each user shares its own information or resources with each other user. Consider n users randomly located over a fixed region, and k of them wish to flood their individual messages among all other users, where each user only has knowledge of its own contents and state information. The goal is to disseminate all messages using a low-overhead strategy that is one-sided and distributed while achieving an order-optimal spreading rate over a random geometric graph. In this paper, we investigate the random-push gossip-based algorithm where message selection is based on the sender's own state in a random fashion. It is first shown that random-push is inefficient in static random geometric graphs. Specifically, it is Ω(√n) times slower than optimal spreading. This gap can be closed if each user is mobile, and at each time moves “locally” using a random walk with velocity v(n). We propose an efficient dissemination strategy that alternates between individual message flooding and random gossiping. We show that this scheme achieves the optimal spreading rate as long as the velocity satisfies v(n) = ω(√log n/k). The key insight is that the mixing introduced by this velocity-limited mobility approximately uniformizes the locations of all copies of each message within the optimal spreading time, which emulates a balanced geometry-free evolution over a complete graph.

Most work on wireless network throughput ignore the temporal correlation inherent to wireless channels, due to trouble with tractability. In order to better capture the temporal variations of wireless network throughput, this paper introduces the metric of ergodic spatial throughput (EST), which includes spatial and temporal ergodicity. All transmitters in the network form a stationary Poisson point process and all channels are modeled by a finite state Markov chain. The bounds on EST are characterized, and their scaling behaviors for a sparse and dense network are discussed. From these results, we show that the EST can be characterized by the inner product of the channel state vector and the invariant probability vector of the Markov chain. This indicates that channel-aware opportunistic transmission (CAOT) may not always increase the EST.

Cellular networks are usually modeled by placing the base stations on a grid, with mobile users either randomly scattered or placed deterministically. These models have been used extensively but suffer from being both highly idealized and not very tractable, so complex system-level simulations are used to evaluate coverage/outage probability and rate. More tractable models have long been desirable. We develop new general models for the multi-cell signal-to-interference-plus-noise ratio (SINR) using stochastic geometry. Under very general assumptions, the resulting expressions for the downlink SINR CCDF (equivalent to the coverage probability) involve quickly computable integrals, and in some practical special cases can be simplified to common integrals (e.g., the Q-function) or even to simple closed-form expressions. We also derive the mean rate, and then the coverage gain (and mean rate loss) from static frequency reuse. We compare our coverage predictions to the grid model and an actual base station deployment, and observe that the proposed model is pessimistic (a lower bound on coverage) whereas the grid model is optimistic, and that both are about equally accurate. In addition to being more tractable, the proposed model may better capture the increasingly opportunistic and dense placement of base stations in future networks.

The benefit of multi-antenna receivers is investigated in wireless ad hoc networks, and the main finding is that network throughput can be made to scale linearly with the number of receive antennas N_r even if each transmitting node uses only a single antenna. This is in contrast to a large body of prior work in single-user, multiuser, and ad hoc wireless networks that have shown linear scaling is achievable when multiple receive and transmit antennas (i.e., MIMO transmission) are employed, but that throughput increases logarithmically or sublinearly with N_r when only a single transmit antenna (i.e., SIMO transmission) is used. The linear gain is achieved by using the receive degrees of freedom to simultaneously suppress interference and increase the power of the desired signal, and exploiting the subsequent performance benefit to increase the density of simultaneous transmissions instead of the transmission rate. This result is proven in the transmission capacity framework, which presumes single-hop transmissions in the presence of randomly located interferers, but it is also illustrated that the result holds under several relaxations of the model, including imperfect channel knowledge, multihop transmission, and regular networks (i.e., interferers are deterministically located on a grid).

This paper proposes an adaptive multi-mode transmission strategy to improve the spectral efficiency achieved in the multiple-input multiple-output (MIMO) broadcast channel with delayed and quantized channel state information. The adaptive strategy adjusts the number of active users, denoted as the transmission mode, to balance transmit array gain, spatial division multiplexing gain, and residual inter-user interference. Accurate closed-form approximations are derived for the achievable rates for different modes, which help identify the active mode that maximizes the average sum throughput for given feedback delay and channel quantization error. The proposed transmission strategy can be easily combined with round-robin scheduling to serve a large number of users. As instantaneous channel information is not exploited, the proposed algorithm cannot provide multiuser diversity gain, but it is still able to provide throughput gain over single-user MIMO at moderate signal-to-noise ratio. In addition, it has a light feedback overhead and only requires feedback of instantaneous channel state information from a small number of users. In the system with a feedback load constraint, it is shown that the proposed algorithm provides performance close to that achieved by opportunistic scheduling with instantaneous feedback from a large number of users.

In many wireless systems, interference is the main performance-limiting factor, and is primarily dictated by the locations of concurrent transmitters. In many earlier works, the locations of the transmitters is often modeled as a Poisson point process for analytical tractability. While analytically convenient, the PPP only accurately models networks whose nodes are placed independently and use ALOHA as the channel access protocol, which preserves the independence. Correlations between transmitter locations in non-Poisson networks, which model intelligent access protocols, makes the outage analysis extremely difficult. In this paper, we take an alternative approach and focus on an asymptotic regime where the density of interferers η goes to 0. We prove for general node distributions and fading statistics that the success probability Ps~ 1 - γηκfor η → 0, and provide values of γ and κ for a number of important special cases. We show that κ is lower bounded by 1 and upper bounded by a value that depends on the path loss exponent and the fading. This new analytical framework is then used to characterize the transmission capacity of a very general class of networks, defined as the maximum spatial density of active links given an outage constraint.

In this paper, a lower bound on the capacity of wireless ad hoc erasure networks is derived in closed form in the case where n nodes are uniformly and independently distributed in the unit area square. It holds almost surely and is asymptotically tight. Nodes are assumed to have fixed transmit power; hence, two nodes should be within a specified distance rnto overcome noise. With interference determining outages, each transmitter-receiver pair is modeled as an erasure channel with a broadcast constraint, i.e., each node can transmit only one signal across all its outgoing links. A lower bound of Θ(nrn) for the network capacity is derived when erasures across distinct links are independent, with constant erasure probabilities. When erasures are correlated, the lower bound Θ(1/(rn)) is proved. If the broadcast constraint is relaxed, the gain is a function of rnand the link erasure probabilities, and is at most a constant if the erasure probabilities grow sufficiently large with n. Finally, the case where the erasure probabilities are random variables, for example due to randomness in geometry or channels, is analyzed. In this setting, it is shown somewhat surprisingly that variability in erasure probabilities increases network capacity.

Multicast transmission, wherein the same packet must be delivered to multiple receivers, is an important aspect of sensor and tactical networks and has several distinctive traits as opposed to more commonly studied unicast networks. Specially, these include 1) identical packets must be delivered successfully to several nodes, 2) outage at any receiver requires the packet to be retransmitted at least to that receiver, and 3) the multicast rate is dominated by the receiver with the weakest link in order to minimize outage and retransmission. A first contribution of this paper is the development of a tractable multicast model and throughput metric that captures each of these key traits in a multicast wireless network. We utilize a Poisson cluster process (PCP) consisting of a distinct Poisson point process (PPP) for the transmitters and receivers, and then define the multicast transmission capacity (MTC) as the maximum achievable multicast rate per transmission attempt times the maximum intensity of multicast clusters under decoding delay and multicast outage constraints. A multicast cluster is a contiguous area over which a packet is multicasted, and to reduce outage it can be tessellated intovsmaller regions of multicast. The second contribution of the paper is the analysis of several key aspects of this model, for which we develop the following main result. Assuming τ/vtransmission attempts are allowed for each tessellated region in a multicast cluster, we show that the MTC is Θ(ρkxlog(k)vy) where ρ,xandyare functions of τ andvdepending on the network size and intensity, andkis the average number of the intended receivers in a cluster. We derive {ρ,x,y} for a number of regimes of interest, and also show that an appropriate number of retransmissions can significantly enhance the MTC.

This paper investigates the theoretical limits of white space sensing in a cognitive radio (CR) network limited by channel correlation. In a log-normal shadowing channel, the received signal power is correlated based on the distance between the sensors and this makes sensing the presence of a signal difficult, even with several cooperative sensors. In the proposed system, each sensor uses the spectral covariance sensing (SCS) algorithm to detect the primary signal and then sends its decision statistic to the base station (BS). The BS, using the Neyman Pearson log-likelihood ratio test, makes the final decision. We analyze the probability of a false alarm (PFA) and compare it with that of the cooperative energy detector. We show that an asymptotic lower bound on the PFAis an order of magnitude lower than that of the energy detector. We also demonstrate improvements in the cooperation gain in terms of the effective number of independent sensors, and the required number of sensors for a given detection metric. The results of this paper show that cooperative SCS detection has far better white space sensing properties than cooperative energy detection in correlated channels.

This paper analyzes spectrum sharing between multiple systems. The efficiency of spectrum sharing is determined primarily by interference, which is a function of the spatial densities of the transmitters in systems dependent on the chosen spectrum sharing method. One method is underlay, which allows all systems to concurrently use the whole spectrum, and the other is overlay, in which a system only utilizes its own assigned spectrum. We define the spectrum-sharing transmission capacity (S-TC) as the number of successful transmissions per unit area subject to outage probability constraints for each system. To prevent some systems from monopolizing access to the spectrum, we also propose a fair coexistence constraint and derive the optimal spatial densities and relative transmission powers both with and without this constraint in terms of the sum S-TC. Through analytical results, the overlay and underlay methods are compared, verifying that the overlay method is generally preferred, and the underlay method is equally good only for optimal transmission power ratios under a fair coexistence constraint.

This paper evaluates the outage probability of cognitive relay networks with cooperation between secondary users based on the underlay approach, while adhering to the interference constraint on the primary user, i.e., the limited amount of interference which the primary user can tolerate. A relay selection criterion, suitable for cognitive relay networks, is provided, and using it, we derive the outage probability. It is shown that the outage probability of cognitive relay networks is higher than that of conventional relay networks due to the interference constraint, and we quantify the increase. In addition, the outage probability is affected by the distance ratio of the interference link (between the secondary transmitter and the primary receiver) to the relaying link (between the secondary transmitter and the secondary receiver). We also prove that cognitive relay networks achieve the same full selection diversity order as conventional relay networks, and that the decrease in outage probability achieved by increasing the selection diversity (the number of relays) is not less than that in conventional relay networks.

Fractional frequency reuse (FFR) is an interference management technique well-suited to OFDMA-based cellular networks wherein the bandwidth of the cells is partitioned into regions with different frequency reuse factors. To date, FFR techniques have been typically been evaluated through system-level simulations using a hexagonal grid for the base station locations. This paper instead focuses on analytically evaluating the two main types of FFR deployments - Strict FFR and Soft Frequency Reuse (SFR) - using a Poisson point process to model the base station locations. The results are compared with the standard grid model and an actual urban deployment. Under reasonable special cases for modern cellular networks, our results reduce to simple closed-form expressions, which provide insight into system design guidelines and the relative merits of Strict FFR, SFR, universal reuse, and fixed frequency reuse. Finally, a SINR-proportional resource allocation strategy is proposed based on the analytical expressions and we observe that FFR provides an increase in the sum-rate as well as the well-known benefit of improved coverage for cell-edge users.

We propose a new graphical model approach to cooperative multiple-input multiple-output (MIMO) cellular networks. The objective is to optimize downlink transmit beamforming at each BS in order to maximize the sum throughput over the entire network. While ideal centralized beamforming requires full channel state information (CSI) sharing among all BSs in the network and huge computational complexity for combinatorial optimization, the proposed graphical model enables distributed beamforming which requires only local CSI sharing between neighboring BSs and efficiently solves the optimization problem in a distributed manner. As distributed solvers for this problem, we derive message-passing algorithms which can be implemented with polynomial-time computational complexity. Furthermore, we make a slight approximation on the objective function to derive a simpler graphical model, providing further complexity saving. Simulation results indicate that the proposed distributed downlink beamforming achieves average cell throughput typically within just 2% of ideal centralized beamforming.

The Wyner model has been widely used to model and analyze cellular networks due to its simplicity and analytical tractability. Its key aspects include fixed user locations and the deterministic and homogeneous interference intensity. While clearly a significant simplification of a real cellular system, which has random user locations and interference levels that vary by several orders of magnitude over a cell, a common presumption by theorists is that the Wyner model nevertheless captures the essential aspects of cellular interactions. But is this true? To answer this question, we compare the Wyner model to a model that includes random user locations and fading. We consider both uplink and downlink transmissions and both outage-based and average-based metrics. For the uplink, for both metrics, we conclude that the Wyner model is in fact quite accurate for systems with a sufficient number of simultaneous users, e.g., a CDMA system. Conversely, it is broadly inaccurate otherwise. Turning to the downlink, the Wyner model becomes inaccurate even for systems with a large number of simultaneous users. In addition, we derive an approximation for the main parameter in the Wyner model - the interference intensity term, which depends on the path loss exponent.

Information-theoretic security constraints reduce the connectivity of wireless networks in the presence of eavesdroppers, which motivates better modeling of such networks and the development of techniques that are robust to eavesdropping. In this letter, we are concerned with the existence of secure connections from a typical transmitter to the legitimate receiver(s) over fading channels, where the legitimate nodes and eavesdroppers are all randomly located. We consider non-colluding and colluding eavesdroppers, and derive the network secure connectivity for both eavesdropper strategies. We mathematically show how nodes with multiple transmit antenna elements can improve secure connectivity by forming a directional antenna or using eigen-beamforming. Compared with single antenna transmission, a large connectivity improvement can be achieved by both multi-antenna transmission techniques even with a small number of antennas.

This paper studies the throughput of large-scale decentralized wireless networks with physical layer security constraints. In particular, we are interested in the question of how much throughput needs to be sacrificed for achieving a certain level of security. We consider random networks where the legitimate nodes and the eavesdroppers are distributed according to independent two-dimensional Poisson point processes. The transmission capacity framework is used to characterize the area spectral efficiency of secure transmissions with constraints on both the quality of service (QoS) and the level of security. This framework illustrates the dependence of the network throughput on key system parameters, such as the densities of legitimate nodes and eavesdroppers, as well as the QoS and security constraints. One important finding is that the throughput cost of achieving a moderate level of security is quite low, while throughput must be significantly sacrificed to realize a highly secure network. We also study the use of a secrecy guard zone, which is shown to give a significant improvement on the throughput of networks with high security requirements.

Multi-gigabit per second wireless network devices are emerging for personal area networks (PAN) in the 60 GHz band. Such devices are typically power hungry, largely due to the requisite high speed analog to digital converters (ADCs) that can consume from tens to hundreds of milliwatts of power. This paper studies the use of analog equalization before the ADC to reduce the required ADC resolution. We provide a novel analysis that uses a superposition model for multipath energy and derive a closed-form expression that relates ADC resolution to the channel state, and also the bit error rate (BER) for MQAM constellations. Simulations verify that analog equalization can reduce the link bit-error rate by up to several orders of magnitude, without increasing the number of quantization bits in the ADC.

Fractional frequency reuse (FFR) is an interference coordination technique well-suited to OFDMA based wireless networks wherein cells are partitioned into spatial regions with different frequency reuse factors. This work focuses on evaluating the two main types of FFR deployments: Strict FFR and Soft Frequency Reuse (SFR). Relevant metrics are discussed, including outage probability, network throughput, spectral efficiency, and average cell- edge user SINR. In addition to analytical expressions for outage probability, system simulations are used to compare Strict FFR and SFR with universal frequency reuse based on a typical OFDMA deployment and uniformly distributed users. Based on the analysis and numerical results, system design guidelines and a detailed picture of the tradeoffs associated with the FFR systems are presented, showing that Strict FFR provides the greatest overall network throughput and highest cell-edge user SINR, while SFR balances the requirements of interference reduction and resource efficiency.

We propose a new method for computing transmit beamforming vectors for downlink multicell multiple- input multiple-output (MIMO) networks. The key novelty of the work is the application of graphical model theory to the intercell interference problem. An index restriction beamforming strategy is adopted to mitigate intercell interference, and is implemented with the well-known message-passing algorithm known as belief-propagation. The advantage of combining restricted index beamforming with belief propagation is only local channel information is required, and the computational complexity is lower than competing methods for base station cooperation. Numerical results show that the network throughput of downlink multicell MIMO systems is increased by the proposed cooperative method especially for cell edge users while the computational complexity is kept similar to non- cooperative methods.

This paper investigates open vs. closed access in the uplink of femtocell networks, for the particular case of orthogonal multiple access protocols like TDMA or OFDMA. Open access reduces near-far interference and provides an inexpensive way to expand the capacity of the operator's network. Additionally, with a cap on the amount of resources allocated to the cellular users, open access ensures the femtocell owner still monopolizes a large portion of the femtocell's capacity and backhaul. Seemingly open access is the appropriate approach for both two parties. We show mathematically and through simulations that the reality is more complicated and depends heavily on cellular user density: for example, closed access is typically preferable at high user densities in orthogonal multiple access. The results of this paper suggest that OFDMA or TDMA femtocells should adapt their access mechanism to the average cellular user density, which changes slowly.

The Wyner model has been widely used to model and analyze cellular networks due to its simplicity and analytical tractability. The key aspects of this model are fixed user location and deterministic and homogeneous interference intensity. While clearly a significant simplification of a real cellular system, which has random user locations and interference levels that can vary by several orders of magnitude over a cell, a common presumption is that the Wyner model nevertheless captures the essential aspects of cellular interactions. But is this true? In this study of uplink cellular networks, we argue that the Wyner model is only accurate for systems with a sufficient number of simultaneous users. Therefore, it is a reasonable abstraction for CDMA multicell networks but quite inaccurate for those employing TDMA. With single-cell signal processing, the Wyner model fails to capture the fact that intracell TDMA is advantageous over CDMA in terms of ergodic symmetric throughput and that random user locations increase throughput. In the case of multi-cell processing, it is shown that intracell TDMA is suboptimal in terms of ergodic symmetric capacity, which is in sharp contrast to results obtained under the Wyner model wherein intracell TDMA is proved to be optimal.

Despite the shortage of available frequency spectrum, recent studies have shown that the actual usage of the allocated spectrum is scarce. The IEEE is developing the 802.22 standard for spectral reuse in TV bands that uses cognitive radio (CR) technology. One of the essential and challenging features of CR is spectrum sensing. This paper proposes a novel spectrum sensing algorithm using spectral covariance of the received signal. The proposed spectral covariance sensing (SCS) algorithm exploits different statistical correlations of the signal and noise in the frequency domain. Test statistics are computed from the covariance matrix of spectrogram and compared with the decision threshold. Detection performance is theoretically analyzed and verified through extensive simulation according to the IEEE 802.22 requirements. We show that SCS achieved 3dB better sensitivity to pilot location detector with the same sensing time. It is also shown that SCS is very robust to the noise uncertainty, which is one of the critical performance measures of spectrum sensing. The results of the paper suggest that SCS is an efficient and viable sensing scheme for IEEE 802.22 systems.

This paper evaluates the achievable transmission capacity of the secondary system in cognitive radio networks, defined by the spatial density of successful transmissions while guaranteeing the target outage probabilities of the secondary and the primary systems. By using stochastic geometry, the effects of the spatial densities and the transmission powers on the achievable transmission capacity is presented. Subsequently, the optimal spatial density of the secondary system and the optimal transmission power ratio of the primary system to the secondary system are derived. Furthermore, the maximum achievable transmission capacity is defined using the derived optimal values. From the theoretical results, it is shown that the optimal transmission power ratio is affected by not the density of the primary system, but the system parameters including the target outage probability. In addition, the achievable transmission capacity of the secondary system decreases as the spatial density of the primary system increases at the decreasing rate determined by the system parameters of the primary system.

This paper develops an upper bound on the end-to-end transmission capacity of multi-hop wireless networks, in which all nodes are randomly distributed. Potential source-destination paths are dynamically selected from a pool of randomly located relays, from which a closed-form bound on the outage probability is derived in terms of the number of potential paths. This in turn gives an upper bound on the number of successful transmissions that can occur per unit area, which is known as the transmission capacity. The upper bound results from assuming independence among the potential paths, and can be viewed as the maximum diversity case. A useful aspect of the upper bound is its simple form for an arbitrary-sized network, which allows us to immediately observe how the number of hops and other network traits affect spatial throughput. Our analysis indicates that predetermined routing approach (such as nearest-neighbor) cannot achieve optimal throughput: more hops are not necessarily helpful in interference-limited networks compared with single-hop direct transmission.

The relative locations of concurrent transmitting nodes play an important role in the performance of wireless networks because it largely determines their mutual interference. In most prior work the set of interfering transmitters has been modeled by a homogeneous Poisson distribution, which assumes independence in the transmitting node positions, and hence precludes intelligent scheduling protocols. One of the main difficulties in extending the numerous Poisson results is the absence of an analytical form for the probability generating functional and the Palm characterization of the underlying spatial node distribution. In this paper we take an alternative approach based on the second-order product density of the node distribution, which is asymptotically tight as the outage probability tends to zero. Unlike the probability generating functional, the second order product density can be easily obtained for a wide range of point processes and hence this approach is useful in analyzing complex wireless networks and MAC protocols. We use this approach to then provide accurate approximations of the transmission capacity of wireless ad hoc networks for three plausible point processes, corresponding to ALOHA, clustering, and carrier sensing schedulers. The mathematical framework introduced can be used to analyze other relevant metrics.

Multicast transmission has several distinctive traits as opposed to more commonly studied unicast networks. Specially, these include (i) identical packets must be delivered successfully to several nodes, (ii) outage could simultaneously happen at different receivers, and (iii) the multicast rate is dominated by the receiver with the weakest link in order to minimize outage and retransmission. To capture these key traits, we utilize a Poisson cluster process consisting of a distinct Poisson point process (PPP) for the transmitters and receivers, and then define the multicast transmission capacity (MTC) as the maximum achievable multicast rate times the number of multicast clusters per unit volume, accounting for outages and retransmissions. Our main result shows that if τ transmission attempts are allowed in a multicast cluster, the MTC is Θ(ρkxlog(k)) where ρ and x are functions of τ depending on the network size and density, and k is the average number of the intended receivers in a cluster. We also show that an appropriate number of retransmissions can significantly enhance the MTC.

This paper provides a simple closed-form SINR expression for interference alignment over MIMO channels with channel uncertainty. Assuming linear processing (specifically, zero-forcing) at the transmitters and receivers and a complex Gaussian interference channel, we show that random matrix theory can be successfully applied to find the SINR distribution of each stream for each user with channel uncertainty. Perfect channel knowledge constitutes a special case. This SINR distribution allows easy calculation of useful performance metrics like symbol error-rate and achievable sum rate.

A novel capacity scaling law for multiple-input multiple-output (MIMO) broadcast channels is derived considering a random user distribution. The random locations cause unequal average SNRs amongst the users, whereas prior work typically assumes that all users have the same average SNR. Most centralized wireless networks, e.g. cellular systems, are more accurately captured by the proposed model. For a large number of users, the average sum capacity is shown to scale like M log K instead of M log log K, where M and K denote the number of transmit antennas and the number of users within a cell. This means that the average sum capacity of cellular MIMO broadcast channels grows significantly faster than previous results indicate.

Downlink spatial intercell interference cancellation (ICIC) is considered for mitigating other-cell interference using multiple transmit antennas. A principle question we explore is whether it is better to do ICIC or simply standard single-cell beamforming. We explore this question analytically and show that beamforming is preferred for all users when the edge SNR (signal-to-noise ratio) is low (10 dB), for example in an urban setting. At medium SNR, a proposed adaptive strategy, where multiple base stations jointly select transmission strategies based on the user location, outperforms both while requiring a lower feedback rate than the pure ICIC approach. The employed metric is sum rate, which is normally a dubious metric for cellular systems, but surprisingly we show that even with this reward function the adaptive strategy also improves fairness. When the channel information is provided by limited feedback, the impact of the induced quantization error is also investigated. The analysis provides insights on the feedback design, and it is shown that ICIC with well-designed feedback strategies still provides significant throughput gain.

This paper surveys and unifies a number of recent contributions that have collectively developed a metric for decentralized wireless network analysis known as transmission capacity. Although it is notoriously difficult to derive general end-to-end capacity results for multi-terminal or adhoc networks, the transmission capacity (TC) framework allows for quantification of achievable single-hop rates by focusing on a simplified physical/MAC-layer model. By using stochastic geometry to quantify the multi-user interference in the network, the relationship between the optimal spatial density and success probability of transmissions in the network can be determined, and expressed-often fairly simply-in terms of the key network parameters. The basic model and analytical tools are first discussed and applied to a simple network with path loss only and we present tight upper and lower bounds on transmission capacity (via lower and upper bounds on outage probability). We then introduce random channels (fading/shadowing) and give TC and outage approximations for an arbitrary channel distribution, as well as exact results for the special cases of Rayleigh and Nakagami fading. We then apply these results to show how TC can be used to better understand scheduling, power control, and the deployment of multiple antennas in a decentralized network. The paper closes by discussing shortcomings in the model as well as future research directions.

We develop a new metric for quantifying end-to-end throughput in multihop wireless networks, which we term random access transport capacity, since the interference model presumes uncoordinated transmissions. The metric quantifies the average maximum rate of successful end-to-end transmissions, multiplied by the communication distance, and normalized by the network area. We show that a simple upper bound on this quantity is computable in closed-form in terms of key network parameters when the number of retransmissions is not restricted and the hops are assumed to be equally spaced on a line between the source and destination. We also derive the optimum number of hops and optimal per hop success probability and show that our result follows the well-known square root scaling law while providing exact expressions for the preconstants, which contain most of the design-relevant network parameters. Numerical results demonstrate that the upper bound is accurate for the purpose of determining the optimal hop count and success (or outage) probability.

In Orthogonal Frequency Division Multiplexing, a simple clipping method is widely used in order to reduce the peak-to-average power ratio since it is easy to implement. The performance analysis of the clipping approach has been previously introduced in the literature. Clipping, however, is a nonlinear process and may cause two major undesirable effects: (i) spectral regrowth, which causes unacceptable out-of-band radiation; and (ii) distortion of the desired signal, which increases bit-error-rate (BER). The out-of-band radiation can and often is suppressed by filtering, which leads to peak regrowth. Therefore, iterative clipping and filtering is required until the desired clipping level is achieved. However, this iterative process makes BER estimation difficult. This letter provides expressions and analytical techniques for estimating the attenuation factor, error vector magnitude, and BER, using a noise enhancement factor that is obtained by simulation. Simulation results show strong agreement with our semi-analytical results for 1024 subcarriers.

This paper proposes a novel, highly effective spectrum sensing algorithm for cognitive radio and white space applications. The proposed spectral covariance sensing (SCS) algorithm exploits the different statistical correlations of the received signal and noise in the frequency domain. Test statistics are computed from the covariance matrix of a partial spectrogram and compared with a decision threshold to determine whether a primary signal or arbitrary type is present or not. This detector is analyzed theoretically and verified through realistic open-source simulations using actual digital television signals captured in the US. Compared to the state of the art in the literature, SCS improves sensitivity by 3 dB for the same dwell time, which is a very significant improvement for this application. Further, it is shown that SCS is highly robust to noise uncertainty, whereas many other spectrum sensors are not.

We develop a realistic model for multiple-input multiple-output (MIMO) broadcast channels, where each randomly located user's average SNR depends on its distance from the transmitter. With perfect channel state information at the transmitter (CSIT), the average sum capacity is proven to scale for many users like αM/2 log K instead of M log log K, where α, M, and K denote the path loss exponent, the number of transmit antennas, and the number of users in a cell. With only partial CSIT, the sum capacity at high SNR eventually saturates due to interference, and the saturation value scales for large B like MB/M-1, where B denotes the quantization resolution for channel feedback.

Femtocells are assuming an increasingly important role in the coverage and capacity of cellular networks. In contrast to existing cellular systems, femtocells are end-user deployed and controlled, randomly located, and rely on third party backhaul (e.g. DSL or cable modem). Femtocells can be configured to be either open access or closed access. Open access allows an arbitrary nearby cellular user to use the femtocell, whereas closed access restricts the use of the femtocell to users explicitly approved by the owner. Seemingly, the network operator would prefer an open access deployment since this provides an inexpensive way to expand their network capabilities, whereas the femtocell owner would prefer closed access, in order to keep the femtocell's capacity and backhaul to himself. We show mathematically and through simulations that the reality is more complicated for both parties, and that the best approach depends heavily on whether the multiple access scheme is orthogonal (TDMA or OFDMA, per subband) or non-orthogonal (CDMA). In a TDMA/OFDMA network, closed-access is typically preferable at high user densities, whereas in CDMA, open access can provide gains of more than 300% for the home user by reducing the near-far problem experienced by the femtocell. The results of this paper suggest that the interests of the femtocell owner and the network operator are more compatible than typically believed, and that CDMA femtocells should be configured for open access whereas OFDMA or TDMA femtocells should adapt to the cellular user density.

In a two tier cellular network comprised of a central macrocell underlaid with shorter range femtocell hotspots cross-tier interference limits overall capacity with universal frequency reuse. To quantify near-far effects, this paper derives a fundamental relation providing the largest feasible cellular signal-to-interference plus noise ratio (SINR), given any set of feasible femtocell SINRs. A distributed utility-based SINR adaptation at femtocells is proposed in order to alleviate cross-tier interference at the macrocell. The Foschini-Miljanic (FM) algorithm is a special case of the adaptation. Each femtocell maximizes their individual utility consisting of a SINR based reward less an incurred cost (cross-tier interference). Results show greater than 30% improvement in mean femtocell SINRs relative to FM. An algorithm is proposed that adaptively curtails transmission powers of the strongest femtocell interferers. Simulations show that a cell-edge user can achieve its SINR target even with 100 femtocells/cell-site (with typical cellular parameters).

In two-tier networks - comprising a conventional cellular network overlaid with shorter range femtocell hotspots - with universal frequency reuse, the near-far effect from crosstier interference diminishes coverage for users in either tier. Equipping the macrocell and femtocell basestations (BSs) with multiple antennas can enhance robustness against the near-far problem. Given a per-tier outage probability constraint, this work derives coverage radii wherein cross-tier interference bottlenecks cellular and hotspot coverage. Single-user (SU) multiple antenna transmission at each tier is shown to provide significantly superior coverage and spatial reuse relative to multiuser (MU) transmission. We propose a decentralized carrier sensing approach to regulate femtocell transmission powers for ensuring reliable cellular coverage. Simulations using typical path loss scenarios show that our interference management strategy provides reliable cellular coverage with about 60 femtocells per cellsite.

This paper investigates the impact of delayed channel state information at the transmitter (CSIT) on the MIMO broadcast channel with block diagonalization (BD) preceding. First, an upper bound for the achievable throughput is provided, which shows that BD is more robust to imperfect CSIT than zero-forcing precoding as it has fewer inter-user interfering streams. Due to residual inter-user interference, the throughput of BD still saturates at high SNR, which motivates switching between single-user and multi-user precoding. An accurate closed-form approximation is derived for the achievable throughput of the BD system, which provides guidance on the preferred transmission technique for a given scenario.

The benefit of multiple antenna communication is investigated in wireless ad hoc networks, and the primary finding is that throughput can be made to scale linearly with the number of receive antennas even if each transmitting node uses only a single antenna. The linear throughput gain is achieved by (i) using the receive antennas to cancel the signals of nearby interferers as well as to increase signal power (i.e., for array gain), and (ii) maintaining a constant per-link rate and increasing the spatial density of simultaneous transmissions linearly with the number of antennas at each receiver. Numerical results show that even a few receive antennas provide substantial throughput gains, thereby illustrating that the asymptotic linear scaling result is also indicative of performance for reasonable numbers of antennas.

In this paper, a lower bound on the capacity of wireless ad hoc erasure networks is derived in closed form in the canonical case where n nodes are uniformly and independently distributed in the unit area square. The bound holds almost surely and is asymptotically tight. We assume all nodes have fixed transmit power and hence two nodes should be within a specified distance rnof each other to overcome noise. In this context, interference determines outages, so we model each transmitter-receiver pair as an erasure channel with a broadcast constraint, i.e. each node can transmit only one signal across all its outgoing links. A lower bound of ¿-(nrn) for the capacity of this class of networks is derived. Finally, the case where the erasure probabilities are themselves random variables, for example due to randomness in geometry or channels, is analyzed. We prove somewhat surprisingly that in this setting, variability in erasure probabilities increases network capacity.

In the multiple-input multiple-output (MIMO) broadcast channel with imperfect channel state information (CSI), neither the capacity nor the optimal transmission technique have been fully discovered. In this paper, we derive achievable ergodic rates for a multi-antenna fading broadcast channel when CSI at the transmitter (CSIT) is delayed and quantized. It is shown that not all possible users should be supported with spatial division multiplexing due to the residual inter-user interference caused by imperfect CSIT. Based on the derived achievable rates, we propose a multi-mode transmission strategy to maximize the throughput, which adaptively adjusts the number of active users based on the channel statistics information.

We consider transmission of packets in two-hop wireless ad hoc networks in which relay nodes are deployed between the source-destination pairs. Based on results from extreme value theory and product tails, we derive throughput scaling laws when opportunistic relay selection is performed. Assuming partial channel state information at each transmitter (CSIT) and decode- and-forward, half-duplex relays, we investigate how the per-hop throughput depends on the channel gain asymptotic distribution and the relay deployment. In dense networks with lambdatnodes per m2and fixed relay distances, we provide specific scaling laws for Rayleigh, lognormal, and Weibull fading, showing that the throughput is upper bounded by thetas(radic(lambdat)). Interestingly, with variable relay distances and location-aware relay selection, we analytically show that regularly varying channel distributions result in enhanced multi-relay diversity gain, achieving linear throughput scaling thetas(radic(lambdat)).

Wireless networks are fundamentally limited by the intensity of the received signals and by their interference. Since both of these quantities depend on the spatial location of the nodes, mathematical techniques have been developed in the last decade to provide communication-theoretic results accounting for the networks geometrical configuration. Often, the location of the nodes in the network can be modeled as random, following for example a Poisson point process. In this case, different techniques based on stochastic geometry and the theory of random geometric graphs -including point process theory, percolation theory, and probabilistic combinatorics-have led to results on the connectivity, the capacity, the outage probability, and other fundamental limits of wireless networks. This tutorial article surveys some of these techniques, discusses their application to model wireless networks, and presents some of the main results that have appeared in the literature. It also serves as an introduction to the field for the other papers in this special issue.

The one tutorial and 22 papers in this special issue focus on geometry and random graph for the analysis and design of wireless networks. The papers are organized into five groups: Topology; Outage, throughput, capacity, and scaling laws; Connectivity and coverage; Co-existence of disparate wireless networks and cognitive radio; and Distributed algorithms.

Two-tier networks, comprising a conventional cellular network overlaid with shorter range hotspots (e.g. femtocells, distributed antennas, or wired relays), offer an economically viable way to improve cellular system capacity. The capacity-limiting factor in such networks is interference. The cross-tier interference between macrocells and femtocells can suffocate the capacity due to the near-far problem, so in practice hotspots should use a different frequency channel than the potentially nearby high-power macrocell users. Centralized or coordinated frequency planning, which is difficult and inefficient even in conventional cellular networks, is all but impossible in a two-tier network. This paper proposes and analyzes an optimum decentralized spectrum allocation policy for two-tier networks that employ frequency division multiple access (including OFDMA). The proposed allocation is optimal in terms of area spectral efficiency (ASE), and is subjected to a sensible quality of service (QoS) requirement, which guarantees that both macrocell and femtocell users attain at least a prescribed data rate. Results show the dependence of this allocation on the QoS requirement, hotspot density and the co-channel interference from the macrocell and femtocells. Design interpretations are provided.

Space-time block codes (STBCs) from coordinate interleaved orthogonal designs (CIODs) offer several advantages including full-diversity and single-symbol decodability. In an effort to assess their performance in quasi-static frequency nonselective i.i.d. Nakagami-m fading channels, we analyze the error rate, outage capacity, and information outage probability. First, based on an accurate closed-form formula for the average symbol pairwise error rate (SPER), we derive tight union upper and lower bounds on the symbol-error rate (SER). Second, we apply Gaussian and Gamma approximations to provide closed form expressions for the outage capacity. Third, using high signal-to-noise ratio (SNR) and moment-matching approximation techniques, we also derive accurate closed-form approximations for the information outage probability (IOP). Finally, we show that STBCs from CIODs provide full-diversity by deriving SER based and IOP-based asymptotic and instantaneous diversity orders. Monte-Carlo simulations show that the analytical results agree with simulation experiments.

Two-tier femtocell networks- comprising a conventional cellular network plus embedded femtocell hotspots- offer an economically viable solution to achieving high cellular user capacity and improved coverage. With universal frequency reuse and DS-CDMA transmission however, the ensuing cross-tier interference causes unacceptable outage probability. This paper develops an uplink capacity analysis and interference avoidance strategy in such a two-tier CDMA network. We evaluate a network-wide area spectral efficiency metric called the operating contour (OC) defined as the feasible combinations of the average number of active macrocell users and femtocell base stations (BS) per cell-site that satisfy a target outage constraint. The capacity analysis provides an accurate characterization of the uplink outage probability, accounting for power control, path loss and shadowing effects. Considering worst case interference at a corner femtocell, results reveal that interference avoidance through a time-hopped CDMA physical layer and sectorized antennas allows about a 7x higher femtocell density, relative to a split spectrum two-tier network with omnidirectional femtocell antennas. A femtocell exclusion region and a tier selection based handoff policy offers modest improvements in the OCs. These results provide guidelines for the design of robust shared spectrum two-tier networks.

In a two tier cellular network - comprised of a central macrocell underlaid with shorter range femtocell hotspots - cross-tier interference limits overall capacity with universal frequency reuse. To quantify near-far effects with universal frequency reuse, this paper derives a fundamental relation providing the largest feasible cellular Signal-to-Interference-Plus-Noise Ratio (SINR), given any set of feasible femtocell SINRs. We provide a link budget analysis which enables simple and accurate performance insights in a two-tier network. A distributed utility- based SINR adaptation at femtocells is proposed in order to alleviate cross-tier interference at the macrocell from cochannel femtocells. The Foschini-Miljanic (FM) algorithm is a special case of the adaptation. Each femtocell maximizes their individual utility consisting of a SINR based reward less an incurred cost (interference to the macrocell). Numerical results show greater than 30% improvement in mean femtocell SINRs relative to FM. In the event that cross-tier interference prevents a cellular user from obtaining its SINR target, an algorithm is proposed that reduces transmission powers of the strongest femtocell interferers. The algorithm ensures that a cellular user achieves its SINR target even with 100 femtocells/cell-site (with typical cellular parameters) and requires a worst case SINR reduction of only 16% at femtocells. These results motivate design of power control schemes requiring minimal network overhead in two-tier networks with shared spectrum.

In two-tier networks comprising a conventional cellular network overlaid with shorter range hotspots (e.g. femtocells, distributed antennas, or wired relays) with universal frequency reuse, the near-far effect from cross-tier interference creates dead spots where reliable coverage cannot be guaranteed to users in either tier. Equipping the macrocell and femtocells with multiple antennas enhances robustness against the near-far problem. This work derives the maximum number of simultaneously transmitting multiple antenna femtocells meeting a per-tier outage probability constraint. Coverage dead zones are presented wherein cross-tier interference bottlenecks cellular and femtocell coverage. Two operating regimes are shown namely 1) a cellular-limited regime in which femtocell users experience unacceptable cross-tier interference and 2) a hotspot-limited regime wherein both femtocell users and cellular users are limited by hotspot interference. Our analysis accounts for the per-tier transmit powers, the number of transmit antennas (single antenna transmission being a special case) and terrestrial propagation such as the Rayleigh fading and the path loss exponents. Single-user (SU) multiple antenna transmission at each tier is shown to provide significantly superior coverage and spatial reuse relative to multiuser (MU) transmission. We propose a decentralized carrier-sensing approach to regulate femtocell transmission powers based on their location. Considering a worst-case cell-edge location, simulations using typical path loss scenarios show that our interference management strategy provides reliable cellular coverage with about 60 femtocells per cell-site.

Opportunistic scheduling algorithms must balance throughput improvement (multiuser diversity) with externally imposed constraints on delay and fairness. For K users each with a weighted fairness constraint, the optimum solution is typically infeasible due to interdependence in the achievable rates. The contribution of this paper is a novel algorithm for achieving resource-sharing constraints with low complexity. This technique, termed resource-redistributive opportunistic (RRO) scheduling, consists of an initial allocation and then a stochastic diversion of resources from surplus users to underserved users. This conceptually and numerically simple approach is shown to have some appealing properties. First, we derive the exact average throughput of the RRO scheduler for non-identically distributed user channels, and show that RRO achieves 90-95% of the optimum weighted fairness capacity, which requires O(K-3) complexity conservatively. Second, extreme value theory is used to prove that for large K the throughput loss of the proposed scheduler is linear with the degree of weighted fairness, and the throughput loss rate is only a half of that of the redistribution strategy based on round-robin.

We derive an upper bound on the capacity of cognitive radio using the interference temperature concept. We do not assume any cooperation between the primary and the secondary user. First, assuming all four links associated with the primary/secondary transmitter/receiver experience Rayleigh fading, the capacity is achieved via the water-filling power allocation strategy, subject to an average secondary to primary interference to signal ratio (ISR) constraint and a peak ISR constraint. Second, we extend our result to the case with path loss as well as channel fading to reflect the geometric relations between link pairs and network size. Finally, we numerically show that for KPprimary receivers which are opportunistically scheduled, the capacity of cognitive radio asymptotically grows as logloglogKP.

A clustered base transceiver station (BTS) coordination strategy is proposed for a large cellular MIMO network, which includes full intra-cluster coordination-to enhance the sum rate-and limited inter-cluster coordination-to reduce interference for the cluster edge users. Multi-cell block diagonalization is used to coordinate the transmissions across multiple BTSs in the same cluster. To satisfy per-BTS power constraints, three combined precoder and power allocation algorithms are proposed with different performance and complexity tradeoffs. For inter-cluster coordination, the coordination area is chosen to balance fairness for edge users and the achievable sum rate. It is shown that a small cluster size (about 7 cells) is sufficient to obtain most of the sum rate benefits from clustered coordination while greatly relieving channel feedback requirement. Simulations show that the proposed coordination strategy efficiently reduces interference and provides a considerable sum rate gain for cellular MIMO networks.

Interference between nodes directly limits the capacity of mobile ad hoc networks. This paper focuses on spatial interference cancellation with perfect channel state information (CSI), and analyzes the corresponding network capacity. Specifically, by using multiple antennas, zero-forcing beamforming is applied at each receiver for canceling the strongest interferers. Given spatial interference cancellation, the network transmission capacity is analyzed in this paper, which is defined as the maximum transmitting node density under constraints on outage and the signal-to-interference-plus-noise ratio. Assuming that the locations of network nodes are Poisson distributed and spatially i.i.d. Rayleigh fading channels, mathematical tools from stochastic geometry are applied for deriving scaling laws for transmission capacity. Specifically, for a large number of antennas per node, the transmission capacity scales with the number of antennas raised to a fractional power, which depends only on the path-loss exponent. Moreover, for small target outage probability, transmission capacity is proved to increase following a power law, where the exponent is the inverse of the size of antenna array or larger depending on the pass-loss exponent. As shown by simulations, spatial interference cancellation increases transmission capacity by an order of magnitude or more even if only one extra antenna is added to each node.

This letter proposes an approximate waterfill power loading scheme using limited feedback in orthogonal frequency division multiplexing (OFDM) systems. The proposed technique achieves nearly the capacity of optimal waterfill power loading, while significantly reducing feedback by using order information for the subcarrier channel gains. Furthermore, the proposed power loading technique can circumvent the practical shortcomings of previous limited feedback power loading techniques by simply exploiting order mapping and interpolation. The advantages are particularly visible at low SNR or for many subcarriers, both of which will be very common in emerging wireless broadband OFDM standards.

The capacity and robustness of cellular MIMO systems is very sensitive to other-cell interference which will in practice necessitate network level interference reduction strategies. As an alternative to traditional static frequency reuse patterns, this paper investigates intercell scheduling among neighboring base stations. We show analytically that cooperatively scheduled transmission, which is well within the capability of present systems, can achieve an expanded multiuser diversity gain in terms of ergodic capacity as well as almost the same amount of interference reduction as conventional frequency reuse. This capacity gain over conventional frequency reuse isO(Mtsquare-root of log Ns) for dirty paper coding andO(min (Mr, Mt) square-root of logNs) for time division, where Nsis the number of cooperating base stations employing opportunistic scheduling in anMtxMrMIMO system. From a theoretical standpoint, an interesting aspect of this analysis comes from an altered view of multiuser diversity in the context of a multi-cell system. Previously, multiuser diversity capacity gain has been known to grow as O(log logK), from selecting the maximum ofKexponentially-distributed powers. Because multicell considerations such as the positions of the users, lognormal shadowing, and pathless affect the multiuser diversity gain, we find instead that the gain isO(square-root of 2logicK), from selecting the maximum of a compound Iognormal-exponential distribution. Finding the maximum of such a distribution is an additional contribution of the paper.

This paper derives the outage probability and transmission capacity of ad hoc wireless networks with nodes employing multiple antenna diversity techniques, for a general class of signal distributions. This analysis allows system performance to be quantified for fading or non-fading environments. The transmission capacity is given for interference-limited uniformly random networks on the entire plane with path loss exponent alpha > 2 in which nodes use: (1) static beamforming through M sectorized antennas, for which the increase in transmission capacity is shown to be thetas(M2) if the antennas are without sidelobes, but less in the event of a nonzero sidelobe level; (2) dynamic eigenbeamforming (maximal ratio transmission/combining), in which the increase is shown to be thetas(M2/alpha); (3) various transmit antenna selection and receive antenna selection combining schemes, which give appreciable but rapidly diminishing gains; and (4) orthogonal space-time block coding, for which there is only a small gain due to channel hardening, equivalent to Nakagami-m fading for increasing m. It is concluded that in ad hoc networks, static and dynamic beamforming perform best, selection combining performs well but with rapidly diminishing returns with added antennas, and that space-time block coding offers only marginal gains.

This paper addresses the following question, which is of interest in the design of a multiuser decentralized network. Given a total system bandwidth of W Hz and a fixed data rate constraint of R bps for each transmission, how many frequency slots N of size W/N should the band be partitioned into in order to maximize the number of simultaneous links in the network? Dividing the available spectrum results in two competing effects. On the positive side, a larger N allows for more parallel, non- interfering communications to take place in the same area. On the negative side, a larger N increases the SINR requirement for each link because the same information rate must be achieved over less bandwidth. Exploring this tradeoff and determining the optimum value of N in terms of the system parameters is the focus of the paper. Using stochastic geometry, the optimal SINR threshold - which directly corresponds to the optimal spectral efficiency - is derived for both the low SNR (power-limited) and high SNR (interference-limited) regimes. This leads to the optimum choice of the number of frequency bands N in terms of the path loss exponent, power and noise spectral density, desired rate, and total bandwidth.

We consider a new approach to power control in decentralized wireless networks, termed fractional power control (FPC). Transmission power is chosen as the current channel quality raised to an exponent -s, where s is a constant between 0 and 1. The choices s = 1 and s = 0 correspond to the familiar cases of channel inversion and constant power transmission, respectively. Choosing s isin (0,1) allows all intermediate policies between these two extremes to be evaluated, and we see that usually neither extreme is ideal. We derive closed-form approximations for the outage probability relative to a target SINR in a decentralized (ad hoc or unlicensed) network as well as for the resulting transmission capacity, which is the number of users/m2that can achieve this SINR on average. Using these approximations, which are quite accurate over typical system parameter values, we prove that using an exponent of s* = 1/2 minimizes the outage probability, meaning that the inverse square root of the channel strength is a sensible transmit power scaling for networks with a relatively low density of interferers. We also show numerically that this choice of s is robust to a wide range of variations in the network parameters. Intuitively, s* = 1/2 balances between helping disadvantaged users while making sure they do not flood the network with interference.

Space-time block codes (STBCs) from coordinate interleaved orthogonal designs (CIODs) have attracted considerable attention lately due to their full-diversity and single-symbol decodability for multiple antenna systems. In this letter, we analyze the information outage probability of STBCs from symmetric structured CIODs in quasi-static frequency-nonselective Rayleigh fading channels. By using the probability density function (PDF) and the cumulative distribution function (CDF) of the product of two i.i.d. chi-square random variables and then exploiting a moment-matching approximation technique, we derive an accurate closed-form approximation for the information outage probability of symmetric CIODs and a corresponding asymptotic diversity order, the results of which can be used to theoretically predict the performance of symmetric CIODs with various antenna configurations in non-ergodic Rayleigh fading channels. Some simulations are performed to verify the accuracy of the derived formulas and illustrate the theoretical results.

Block diagonalization is one approach for linear preceding in the multiple-input multiple-output broadcast channel that sends multiple interference free data streams to different users in the same cell. Unfortunately, block diagonalization neglects other-cell interference (OCI), which limits the performance of users at the edge of the cell. This paper presents an OCI-aware enhancement to block diagonalization that uses a whitening filter for interference suppression at the receiver and a novel precoder using the interference-plus-noise covariance matrix for each user at the transmitter. For complex Gaussian matrix channels, the asymptotic sum rate of the proposed system is analyzed under a large antenna assumption for isotropic inputs and compared to conventional block diagonalization. The capacity loss due to OCI is quantified in terms of results from single-user MIMO capacity. Several numerical examples compare achievable sum rates, the proposed asymptotic rates, and the capacity loss, in low and high interference regimes.

In a cellular distributed antenna system (DAS), distributed antenna elements (AEs) are connected to the base station via an offline dedicated link, e.g. fiber optics or line-of-sight RF. Distributed antennas have been recently shown to provide considerable gains in coverage and capacity, at much lower cost than decreasing cell size. Previous studies have neglected the key sources of randomness in such systems, notably (i) random channel effects (fading and shadowing) and (ii) the random quantity and locations of both the mobile users and the AEs. Typically, path loss has been the focus, and the AEs are assumed to be regularly spaced, both of which are significant idealizations. First, we develop an analytical framework that allows random channels to be accommodated. We use this approach to show that selection transmission (using a single AE) is preferable to maximum ratio transmission (which uses all the AEs) in a multicell environment. Interestingly, the opposite is true in an isolated cell. Second, since AEs are placed opportunistically (on tall structures with backhaul access) rather than regularly, we develop a stochastic geometry-inspired approach to determine the outage probability as a function of the number of randomly placed AEs, which we model as a point process. With selection transmission, the outage probability is shown to decrease exponentially with the number of AEs and users. In the most general setup - with multiple distributed antennas and users, and both AE selection and user selection - we show that randomly deployed AEs provide nearly the same performance as regularly spaced AEs.

Two-tier femtocell networks-comprising a conventional macrocellular network plus embedded femtocell hotspots- offer an economically viable solution to achieving high cellular user capacity and improved coverage. This paper develops an uplink capacity analysis and interference avoidance strategy in such a two-tier CDMA network with universal frequency reuse. We evaluate a network-wide area spectral efficiency metric called the Operating Contour (OC) defined as the combinations of the average macrocell users and femtocell BS per cell-site that meet a target outage constraint. A contribution of this work is an accurate characterization of the uplink outage probability taking cross-tier power control, path-loss and shadowing into account. Considering worst case interference at a corner femtocell, results reveal that interference avoidance through a time-hopped CDMA physical layer and sectorized antennas allows about a 7x higher femtocell BS density, relative to a split spectrum network with omnidirectional femtocell antennas. These results provide guidelines for the design of robust shared spectrum two-tier networks.

Block diagonalization is a preceding technique for multiuser MIMO systems that pre-cancels inter-user interference at the transmitter side. When there are a large number of base station antennas but a limited number of RF amplifiers, the system performance can be significantly improved by switching a subset of antennas to the RF chains and exploiting antenna selection diversity. The optimal antenna subset can be obtained by exhaustively searching over all possible antenna combinations. This brute-force search, however, is prohibitively complicated and impractical. To reduce the complexity, in this paper we propose several low-complexity suboptimal transmit selection algorithms that minimize a symbol error rate (SER) upper bound or maximize a capacity lower bound. Simulation results show that our proposed algorithms perform very close to the optimal exhaustive search, while the complexity is much lower.

Block diagonalization is one approach for linear preceding in the multiple-input multiple-output broadcast channel that sends multiple interference free data streams to different users in the same cell. Unfortunately, block diagonalization neglects other cell interference, which limits the performance of users at the edge of the cell. This paper presents an OCI-aware enhancement to block diagonalization that uses a whitening filter for interference suppression at the receiver and a novel precoder using the interference-plus-noise covariance matrix for each user at the transmitter. For complex Gaussian matrix channels, the asymptotic sum rate of the proposed system is analyzed under a large antenna assumption for isotropic inputs and compared to conventional block diagonalization.

A cellular distributed antenna system with randomly located distributed antenna elements (AEs) and mobile users is considered. The AEs are connected to the base station via an offline dedicated link (such as fiber optics or line-of- sight RF). A user is served by selecting the AE with the best channel to it (often the closest one). The outage probability is derived for both AE selection and user selection individually for an isolated cell, and shown to decrease exponentially with the number of AEs and users. Due to selection diversity, fading and shadowing typically are desirable effects that decrease the likelihood of outage. In a more general setup - with multiple distributed antennas and both AE selection and user selection - the outage probability decreases exponentially with the number of users but not with the number of AEs. Due to diminishing returns, there is no need to deploy more AEs than a certain extent, which is determined by the transmit power of AEs. With a sufficient number of AEs, randomly deployed AEs can provide nearly the same performance as regularly deployed AEs, and both have a common outage probability floor which is determined by user density.

Block diagonalization is a downlink preceding technique that pre-cancels inter-user interference in multiuser MIMO systems. When there are a large number of users, the system throughput can be significantly increased by selecting a subset of users and a subset of receive antennas for each user. The optimal user and antenna subset can be obtained by exhaustively searching over all possible user and antenna combinations to find the one with the highest sum throughput. This brute-force solution, however, is prohibitively complicated. To reduce the complexity, in this paper we propose a low-complexity suboptimal user and antenna selection algorithm. For most system configurations, we show that our proposed algorithm achieves up to 98% of the optimal sum throughput of the exhaustive search, where the complexity is orders of magnitude lower than the exhaustive search method.

On a multi-antenna downlink channel, separation of multiple users by transmit beamforming enables simultaneous transmission from the base station to the users, resulting in high sum throughput. This paper proposes and analyzes a practical algorithm for joint scheduling and orthogonal beamforming, which is enabled by feedback of quantized channel state information (CSI). In this approach, each user quantizes CSI using a codebook comprised of multiple orthonormal vector sets and sends back quantized CSI. Using feedback CSI, the base station jointly selects a set of orthogonal beamforming vectors and schedules a subset of feedback users for downlink transmission such that the throughput is maximized. For moderate to large numbers of users, the proposed algorithm achieves higher sum capacities than the conventional ones.

Space division multiple access (SDMA) is capable of achieving sum capacity that grows double logarithmically with the number of users. The sum rate for channel state information (CSI) feedback, however, increases linearly with the number of users, reducing the effective uplink capacity. To address this problem, a novel SDMA design is proposed, where the sum feedback rate is upper-bounded by a constant. This design consists of algorithms for CSI quantization, threshold based CSI feedback, and joint beamforming and scheduling. The key feature of the proposed approach is the use of feedback thresholds to select feedback users with large channel gains and small CSI quantization errors such that the sum feedback rate constraint is satisfied. Despite this constraint, the proposed SDMA design is shown to achieve a sum capacity growth rate close to the optimal one. Numerical results show that the proposed SDMA design is capable of attaining higher sum capacities than existing ones, even though the sum feedback rate is bounded.

For a wireless multi-antenna network with a large number of users, the sum capacity scales at most linearly with the number of antennas and double logarithmically the number of users. Achieving this optimal capacity scaling potentially requires feedback of channel state information (CSI) from all users, leading to overflow of the feedback channel. This paper proposes a limited feedback strategy that provides feedback control such that a sum CSI feedback rate constraint is satisfied. It is proved that a wireless multi-antenna network using the proposed limited feedback strategy achieves the optimal capacity scaling for the broadcast channel.

This paper derives the exact outage probability and transmission capacity of ad hoc wireless networks with nodes employing multiple antenna diversity techniques. The analysis enables a direct comparison of the number of simultaneous transmissions achieving a certain data rate under different diversity techniques. Preliminary results derive the outage probability and transmission capacity for a general class of signal distributions which facilitates quantifying the gain for fading or non-fading environments. The transmission capacity is then given for uniformly random networks with path loss exponent alpha > 2 in which nodes: (1) perform maximal ratio transmission/combining on M antennas with Theta(M 2/alpha ) gains; (2) various antenna selection combining schemes which give appreciable but rapidly diminishing gains; and (3) orthogonal space-time block coding, for which there is only a small gain due to channel hardening. It is concluded that in ad hoc networks, beamforming performs best, selection combining performs well for smaller numbers of antennas, and that space-time block coding offers only marginal gains.

This paper addresses the following question, which is of interest in the design of a multiuser decentralized network: given a total system bandwidth of W Hz and a fixed data rate constraint of R bps for each transmission, how many frequency slots N of size W/N should the band be partitioned into to maximize the number of simultaneous transmissions in the network? Dividing the available spectrum reduces the number of users on each band and therefore decreases multiuser interference level, but also increases the SINR requirement for each transmission because the same information rate must be achieved over a smaller bandwidth. Exploring this tradeoff between bandwidth and SINR and determining the optimum value of N in terms of the system parameters is the focus of the paper. Using stochastic geometry, we analytically derive the optimal SINR threshold on this tradeoff curve and show that it is a function of only the path loss exponent. Furthermore, the optimal SINR point lies between the low-SINR (power-limited) and high-SINR (bandwidth-limited) regimes.

This paper analyzes the capacity of MIMO channels in the presence of both antenna correlation and co-channel interference. We investigate the optimization of the input covariance, characterize the optimality of beamforming, and study the behavior of the input covariance in the low and high-power regimes. For the special case of separable correlations, we also derive analytical expressions for the key statistical properties of the spectral efficiency achievable with an arbitrary input covariance. Altogether, our analysis enables assessing the joint impact of correlation and interference on the capacity of multiantenna architectures in a cellular system.

In this paper, a novel transmission technique for the multiple-input multiple-output (MIMO) broadcast channel is proposed that allows simultaneous transmission to multiple users with limited feedback from each user. During a training phase, the base station modulates a training sequence on multiple sets of randomly chosen orthogonal beamforming vectors. Each user sends the index of the best beamforming vector and the corresponding signal-to-interference-plus-noise ratio for that set of orthogonal vectors back to the base station. The base station opportunistically determines the users and corresponding orthogonal vectors that maximize the sum capacity. Based on the capacity expressions, the optimal amount of training to maximize the sum capacity is derived as a function of the system parameters. The main advantage of the proposed system is that it provides throughput gains for the MIMO broadcast channel with a small feedback overhead, and provides these gains even with a small number of active users. Numerical simulations show that a 20% gain in sum capacity is achieved (for a small number of users) over conventional opportunistic space division multiple access, and a 100% gain (for a large number of users) over conventional opportunistic beamforming when the number of transmit antennas is four.

This paper addresses three issues in the field ofad hocnetwork capacity: the impact of (i) channel fading, (ii) channel inversion power control, and (iii) threshold–based scheduling on capacity. Channel inversion and threshold scheduling may be viewed as simple ways to exploit channel state information (CSI) without requiring cooperation across transmitters. We use thetransmission capacity(TC) as our metric, defined as the maximum spatial intensity of successful simultaneous transmissions subject to a constraint on the outage probability (OP). By assuming the nodes are located on the infinite plane according to a Poisson process, we are able to employ tools from stochastic geometry to obtain asymptotically tight bounds on the distribution of the signal-to-interference (SIR) level, yielding in turn tight bounds on the OP (relative to a given SIR threshold) and the TC. We demonstrate that in the absence of CSI, fading can significantly reduce the TC and somewhat surprisingly, channel inversion only makes matters worse. We develop a threshold-based transmission rule where transmitters are active only if the channel to their receiver is acceptably strong, obtain expressions for the optimal threshold, and show that this simple, fully distributed scheme can significantly reduce the effect of fading.

The transmission capacity (TC) of a wirelessad hocnetwork is defined as the maximum spatial intensity of successful transmissions such that the outage probability does not exceed some specified threshold. This work studies the improvement in TC obtainable with successive interference cancellation (SIC), an important receiver technique that has been shown to achieve the capacity of several classes of multiuser channels, but has not been carefully evaluated in the context ofad hocwireless networks. This paper develops closed-form upper bounds and easily computable lower bounds for the TC ofad hocnetworks with SIC receivers, for both perfect and imperfect SIC. The analysis applies to any multiuser receiver that cancels the$K$strongest interfering signals by a factor$z \in [0,1]$. In addition to providing the first closed-form capacity results for SIC inad hocnetworks, design-relevant insights are made possible. In particular, it is shown that SIC should be used with direct sequence spread spectrum. Also, any imperfections in the interference cancellation rapidly degrade its usefulness. More encouragingly, only a few—often just one—interfering nodes need to be canceled in order to get the vast majority of the available performance gain.

This paper proposes a power control strategy for the uplink of cellular MIMO spatial multiplexing systems, with a linear MMSE receiver applied at the base station and a single active user per time instant. A fixed per-stream SINR target is employed that allows guaranteed QoS for delay-sensitive applications. A straightforward application of single antenna power control is not possible in the MIMO context due to coordination between receive antennas and nonlinear dependence between interference and eigenspaces of the channel matrices. Two schemes are proposed to solve the problem. The first equally allocates power to all transmit antennas. Deriving an SINR lower bound based on an eigenvalue approximation of the composite interference, allows application of the conventional single antenna power control framework to solve this problem. To improve the feasibility performance, a second scheme is proposed that adaptively allocates power on the transmit antennas, where an iterative algorithm based on game theory is used to sequentially update each user's power distribution. The optimal solution with full channel knowledge, and a practical near-optimal solution requiring only partial channel knowledge, are both derived. Numerical results show that power control, compared to supposedly optimal waterfilling strategies, actually achieves higher throughput at the low SINRs typical in cellular systems, with significantly lower overhead and complexity. Due to its better exploitation of spatial diversity and reduced transmit power (and hence reduced interference), adaptive power allocation increases the achievable SINR by an order of magnitude over equal power allocation, resulting in far better coverage.

Distributed antenna systems (DAS) have been widely implemented in state-of-the art cellular communication systems to cover dead spots. Recent academic studies have shown that in addition to coverage improvements, DAS can also have potential advantages such as reduced power and increased system capacity in a single cell environment. This paper analytically quantifies downlink capacity of multicell DAS for two different transmission strategies: selection diversity (where just one or two of the distributed antennas are used) and blanket transmission (where all antennas in the cell broadcast data). Simple repeaters are a special case of our analysis. A generalized information theoretic analysis is provided to illuminate the fundamental limits of such systems in the cellular context. The results show that DAS reduces other-cell interference in a multicell environment and hence significantly improves capacity (by about 2x), with particularly large improvements for users near cell boundaries. Less obviously, from a communication theory standpoint, it is shown that selection diversity is preferable to blanket transmission in terms of achievable ergodic capacity. For blanket transmission, we show that the optimal transmission strategy is just phase steering due to the per antenna module power constraints in DAS

Even though spatial multiplexing provides a significant spectral efficiency advantage in a single point-to-point noise- limited link, recent studies have shown that this advantage can be lost in cellular MIMO systems unless extra diversity is provided. Spread spectrum is a likely candidate for the extra diversity because spread spectrum can simultaneously provide frequency diversity and robustness to interference. This paper investigates the effectiveness of spatial multiplexing in the forward link of cellular MIMO-CDMA systems with linear receivers. Through the development of new closed-form results on outage probability and capacity for MIMO-CDMA, we show that even MIMO-CDMA loses the spatial multiplexing gain in a cellular context. These results indicate that a practical cellular MIMO system, which will be interference-limited and have a low-complexity receiver, requires new study on techniques to efficiently reduce the impact of the other-cell interference. The developed analytical framework can be used for evaluating other techniques.

Direct Sequence Code Division Multiple Access (DS-CDMA) receivers typically use Maximal Ratio Combining (MRC) to favorably combine the energies of distinct multipath components from diversity branches. In previous research, compromising assumptions have been made to simplify the analysis, including a Gaussian approximation for interference or constant equal cross correlations. However, these assumptions corrupt the analysis especially in certain operating conditions such as a relatively small number of users, which is particularly relevant for modern CDMA systems that carry data. The contribution of this paper is to provide a general framework for accurately analyzing the performance of the diversity receiver in CDMA systems without these compromising approximations. From the analytical and numerical results, it is: shown that the developed framework provides higher accuracy than previous approaches.

In ad hoc networks, it may be helpful to suppress transmissions by nodes around the desired receiver in order to increase the likelihood of successful communication. This paper introduces the concept of a guard zone, defined as the region around each receiver where interfering transmissions are inhibited. Using stochastic geometry, the guard zone size that maximizes the transmission capacity for spread spectrum ad hoc networks is derived - narrowband transmission (spreading gain of unity) is a special case. A large guard zone naturally decreases the interference, but at the cost of inefficient spatial reuse. The derived results provide insight into the design of contention resolution algorithms by quantifying the optimal tradeoff between interference and spatial reuse in terms of the system parameters. A capacity increase relative to random access (ALOHA) in the range of 2 - 100 fold is demonstrated through an optimal guard zone; the capacity increase depending primarily on the required outage probability, as higher required QoS increasingly rewards scheduling. Compared to the ubiquitous carrier sense multiple access (CSMA) which essentially implements a guard zone around the transmitter rather than the receiver - we observe a capacity increase on the order of 30 - 100%

The sum capacity of a Gaussian broadcast MIMO channel can be achieved with dirty paper coding (DPC). However, algorithms that approach the DPC sum capacity do not appear viable in the forseeable future, which motivates lower complexity interference suppression techniques. Block diagonalization (BD) is a linear preceding technique for downlink multiuser MIMO systems. With perfect channel knowledge at the transmitter, BD can eliminate other users' interference at each receiver. In this paper, we study the sum capacity of BD with and without receive antenna selection. We analytically compare BD without receive antenna selection to DPC for a set of given channels. It is shown that (1) if the user channels are orthogonal to each other, then BD achieves the same sum capacity as DPC; (2) if the user channels lie in the same subspace, then the gain of DPC over BD can be upper bounded by the minimum of the number of transmit and receive antennas. These observations also hold for BD with receive antenna selection. Further, we study the ergodic sum capacity of BD with and without receive antenna selection in a Rayleigh fading channel. Simulations show that BD can achieve a significant part of the total throughput of DPC. An upper bound on the ergodic sum capacity gain of DPC over BD is proposed for easy estimation of the gap between the sum capacity of DPC and BD without receive antenna selection.

We find that placing each pilot tone in an equally spaced manner according to the conventional placement scheme is not suitable for doubly selective channel estimation. In this paper, we propose an efficient pilot tone placement scheme enabling accurate channel estimation in OFDM systems regardless of time variations of a channel. Since the number of channel impulse response taps to be estimated is typically much greater than the number of pilot tones, linear minimum mean square error (LMMSE) estimation schemes for time-invariant channels cannot be straightforwardly extended to doubly selective channel estimation. To overcome this problem, we propose an accurate LMMSE channel estimator that exploits a small number of pilot tones located according to the derived pilot placement. To achieve performance close to the LMMSE estimator but with lower complexity, an approximate LMMSE (ALMMSE) channel estimator is also proposed. Finally, we propose a novel iterative ALMMSE channel estimator that achieves better performance than the LMMSE and ALMMSE estimators, while having complexity in between the two.

Power control is an important technique for interference management in interference-limited multiuser communication systems. In this paper, we propose a novel multidimensional power control technique for the uplink of cellular MIMO systems. Similar to prior single antenna power control work, we employ a fixed SINR target that allows guaranteed quality-of-service for delay-sensitive data applications. The proposed power control scheme is a more general technique because it incorporates single antenna, orthogonal multi-carrier, and utility-based power control schemes as special cases. Two approaches are proposed, the first where each user's power is equally allocated to its antenna array, in the second the allocation is adaptive. The optimal solution with full channel knowledge, and a practical near-optimal solution requiring only partial channel knowledge, are both derived. Numerical results show that power control actually achieves higher throughput a.t the low SINRs typical in cellular systems, compared to supposedly optimal water-filling strategies, with lower overhead and complexity. In the higher SINR ranges, iterative water-filling indeed slightly outperforms adaptive power allocation. Due to its better exploitation of spatial diversity and reduced transmit power (and hence reduced other-cell interference), adaptive power allocation increases the achievable SINR by an order of magnitude over equal power allocation, resulting in far better coverage.

In wireless networks where all users have different channel characteristics and service classes, it is challenging to design an adaptive scheduler to support quality of service (QoS). Some fraction of multiuser diversity gain, which offers significant capacity increase, should be sacrificed to meet certain QoS targets. We present an opportunistic scheduling scheme under resource-sharing constraints. The scheduler solves the weighted fairness by diverting a fraction of resources from surplus users to underserved users. Given the average received signal-to-noise ratios (SNR) of users and resource-sharing constraints, the capacity of the proposed scheduler is analyzed over Rayleigh fading channels. Degree of weighted fairness for various scheduling schemes is also provided. Numerical results illustrate that while sacrificing a fraction of the achievable total capacity the proposed scheduler provides perfect weighted fairness.

In this paper, a novel transmission technique for the multiple-input multiple-output (MIMO) broadcast channel is proposed that allows simultaneous transmission to multiple users under a limited feedback requirement. During a training phase, the base station modulates a training sequence on multiple sets of randomly generated orthogonal beamforming vectors. Then, based on the users' feedback, the base station opportunistically selects the users and corresponding orthogonal vectors that maximize the sum capacity. From theoretical analysis, the optimal amount of training to maximize the sum capacity is derived as a function of the system parameters. The main advantage of the proposed system is that it provides throughput gains for the MIMO broadcast channel with a small feedback overhead, and provides these gains even with a small number of active users. Numerical simulations show that a 20% gain in sum capacity is achieved (for a small number of users) over conventional opportunistic space division multiple access, and a 100% gain (for a large number of users) over conventional opportunistic beamforming.

A novel method based on Markov chain theory is proposed for analyzing the effect of feedback delay on a transmit beamforming system with limited feedback. Using this method, the ergodic capacity with delayed feedback of channel state information is derived. The capacity gain with respect to the case of no feedback is shown to decrease at least exponentially with the feedback delay. From these results, useful design guidelines can be derived for choosing system parameters including the vehicular speed and the tolerable feedback delay.

A novel method is proposed for reducing the feedback rate of a transmit beamforming system with feedback of quantized channel state information. Specifically, the channel is modeled as a Markov chain and the feedback bits are compressed by truncating the Markov chain transition probabilities. Using the proposed method, the feedback rate can be compressed by more than 100% without degrading the system performance.

Pilot symbols reduce the transmit energy for data symbols per orthogonal frequency division multiplexing (OFDM) symbol under a fixed total transmit power constraint, while they facilitate channel estimation. In this paper, we investigate the effect of the pilot-to-data power ratio (PDPR) on symbol error rate (SER) and spectral efficiency of multiple-input multiple- output (MIMO) OFDM systems with adaptive modulation and a linear receiver. We derive the optimal PDPR to minimize the average SER of multilevel quadrature amplitude modulation (M- QAM) MIMO-OFDM systems. Wishart matrix analysis can be used to analyze the effect of channel estimation error on the average SER performance of the M-QAM spatial multiplexing MIMO-OFDM systems with zero-forcing (ZF) receiver. By using the optimal PDPR in the MIMO-OFDM system with adaptive modulation, about 2.5dB gain can be obtained. It is quite practical to use the results to design the PDPR for typical cases, since there is a fairly broad range of PDPR which minimizes the SER.

We provide closed form upper and lower bounds on the distribution of the signal to interference ratio (SIR) seen by a typical receiver in an ad hoc network where transmitter locations form a Poisson process. The aggregate co-channel interference in such a network is known to be a power law shot noise process and the distribution is known to be symmetric stable; we will show the same is true of the SIR. Stable distributions are unwieldy in that there is no closed form expression for their PDF and CDF; this is the motivation behind seeking simple bounds on the SIR. We consider a broad class of channel models that have a deterministic, distance dependent path-loss component and a random, distance-independent component. This class of channel models includes lognormal shadowing, Rayleigh fading, the Nakagami model, and others. We show that the lower bound on SIR is tight and that the upper bound has a bounded error that depends on the path loss exponent but not on the random channel variation. Numerical plots of the SIR distribution for a variety of common channel models are provided to illustrate the bounds. The bounds are useful for computing common network performance metrics like outage probability and BER.

Multiple antenna wireless systems with feedback of quantized channel information, called "limited feedback” systems, are attractive choices for improving the quality of downlink (DL) transmission. Most work in this area use the block-fading channel model where the DL channel is assumed constant in each block and different blocks uncorrelated. In this paper, we consider limited feedback for a temporally correlated DL channel. Markov models are introduced for characterizing the temporal correlation and probability distribution of the DL channel. Using the Markov models, average feedback rates are derived. Numerical results show that the feedback rates are proportional to the Doppler frequency.

This paper develops an improved and generalized analytical model for time-hopping ultra-wideband (UWB) systems. In particular, the important effects of multiple access, multipath channels, and imperfect power control are incorporated in the analysis, whereas in prior work they were often neglected. Biterror probability is derived for two different modulation schemes: time-hopping spread-spectrum with pulse position modulation (TH-PPM) and time-hopping spread-spectrum with binary phase shift keying (TH-BPSK). Invariant of the channel model, number of users, or power control error, it is found that binary antipodal modulation has superior performance to PPM. The developed model and analytical framework is quite general and can be adapted to the analysis of future impulse radio piconet systems.

Scheduling algorithms in ad hoc networks allow nodes to share the wireless channel so that concurrent transmissions can be decoded successfully. On one hand, the scheduling needs to be efficient to maximize the spatial reuse and minimize retransmissions due to collisions. But on the other hand, due to the very nature of uncentralized wireless networks, the scheduling algorithm needs to be easily implementable in a distributed fashion with little, if any, coordination with other nodes in the network. The goal of this paper is to propose and evaluate a simple scheduling technique based on receiver guard zones. In particular, using stochastic geometry, we show that a near-optimal guard zone can easily be realized in a distributed manner, and that this has about a 2 - 100x increase in capacity as compared to an ALOHA network; the capacity increase depending primarily on the required outage probability E, as lower E tolerances increasingly reward scheduling. By implementing guard zone-based scheduling, we show that the attained performance is about 70 - 80% of a well-known near-optimal (and practically infeasible) centralized scheme.

As an alternative to traditional static frequency reuse patterns, this paper investigates cooperatively scheduling among neighboring base stations in a cellular multiple antenna system, where each cell adopts dirty paper coding. It is shown that cooperatively scheduled transmission can achieve almost the same amount of interference reduction as conventional frequency reuse and achieve an extra capacity gain. We analytically quantify the capacity gain of cooperatively scheduled transmission over conventional frequency reuse in an Mttimes Mrdirty paper coded MIMO system. The theoretical analysis of this paper also provides an altered view of multiuser diversity in the context of a multi-cell system. Because the positions of the users are important in a multi-cell system, we find that the gain is O(radiclog K), from selecting the maximum of a compound lognormal-exponential distribution, whereas multiuser diversity capacity gain has been previously known to grow as O(log log K), from selecting the maximum of K exponentially-distributed powers

The sum capacity of a Gaussian broadcast MIMO channel can be achieved with Dirty Paper Coding (DPC). Deploying DPC in real-time systems is, however, impractical. Block Diagonalization (BD) is an alternative precoding technique for downlink multiuser MIMO systems, which can eliminate inter-user interference at each receiver, at the expense of suboptimal sum capacity vs. DPC. In this paper, we study the sum capacity loss of BD for a fixed channel. We show that 1) if the user channels are orthogonal to each other, then BD achieves the complete sum capacity; and 2) if the user channels lie in a common row vector space, then the gain of DPC over BD can be bounded by the minimum of the number of transmit and receive antennas and the number of users. We also compare the ergodic sum capacity of DPC with that of BD in a Rayleigh fading channel. Simulations show that BD can achieve a significant part of the total throughput of DPC. An upper bound on the ergodic sum capacity gain of DPC over BD is derived, which can be evaluated with a few numerical integrations. With this bound, we can easily estimate how far away BD is from being optimal in terms of ergodic sum capacity, which is useful in directing practical system designs.

Improving downlink CDMA capacity has been an area of intensive research for the past decade, especially as the downlink has become the capacity limiting link. Multi-antenna technologies are an obvious candidate for increasing the downlink capacity, but successfully decoding spatially multiplexed signals is very challenging in an interference-limited environment, such as that of CDMA cellular systems. In this paper, a simple and novel MIMO-CDMA system design is developed, in which users are assigned to a transmit antenna either without regard to channel knowledge (static) or based on antenna selection feedback bits (dynamic). These proposed antenna partitioning techniques have a minimal increase in complexity and require only small changes to existing CDMA standards. The outage probability and capacity of the proposed systems are derived and it is shown that they outperform conventional CDMA systems regardless of the number of antennas or antenna partitioning technique.

New unified linear preceding and decoding techniques are presented in this paper, which are suitable for block transmission systems such as orthogonal frequency division multiplexing (OFDM) systems, synchronous code division multiple access (CDMA) systems, single carrier systems and multiple-input-multiple-output (MIMO) systems. First, a linear precoder that achieves minimum symbol-error-rate (MSER) is proposed and analyzed. Motivated by the fact that the conventional and the MSER precoders achieve a diversity order of one, a new method of applying linear preceding over subchannels, named multichannel precoding (MP), is developed to exploit the diversity gain. It is shown that even if a suboptimal linear decoder is used, MP improves the SER performance significantly. Given the block and linear nature of the linearly preceded system, lattice decoding is a suitable and efficient method for optimally detecting data symbols. Some analytical results are presented for the linearly preceded system with lattice decoding. The SER performance of different linearly preceded systems are also compared numerically.

Orthogonal frequency division multiplexing (OFDM) can be used with a multiple-input multiple-output (MIMO) system to improve communication quality and capacity. Pilot-symbol-aided or decision-directed channel estimation must be used to track channel variations in MIMO-OFDM systems. While pilot symbols facilitate channel estimation, they reduce the transmit energy for data symbols under a fixed total transmit power constraint. We analyze the effects of pilot-symbol-aided channel estimation on the lower bound of the capacity and derive the optimal pilot-to-data power ratio (PDPR) in MIMO-OFDM systems with three different types of pilot patterns: independent, scattered, and orthogonal. The result implies that implementing the optimal PDPR in an actual MIMO-OFDM system should prove relatively straightforward, since there is a surprisingly broad range of PDPR values over which near optimal capacity is achieved.

The motivation of this paper is to find the class of channels that provides the largest capacity with both the transmit power constraint and channel Frobenius norm constraints. We study both the point-to-point case and the broadcast case. For point-to-point MIMO channels, the optimal channels must have T* equal singular values, where T* is dependent on the available transmit power and the channel Frobenius norm. This result agrees with the previous work by Chiurtu et al. For multiuser broadcast channels, we obtain an upper bound on the sum capacity. We also show that the bound is asymptotically tight for high SNR when all user channels have the same Frobenius norm constraint and N/sub t/ /spl ges/ KN/sub r/, where N/sub t/ and N/sub r/ are the numbers of transmit and receive antennas and K is the number of users.

In this paper, the effectiveness of spatial multiplexing in the forward link of cellular CDMA systems with linear (i.e. low complexity) receivers is investigated. General MIMO systems without spreading are a special case of our analysis when the spreading gain is unity. Through the development of new closed-form results on outage probability and capacity for MIMO-CDMA, we show that cellular MIMO outage capacity is severely degraded by the enhancement of other-cell interference by the linear spatial receiver, and that a large number of transmit and receive antennas is required to simply break even with a SISO system. The results indicate that for practical cellular MIMO systems, which will be interference-limited and have low complexity receivers, future research is required on feasible methods for reducing the impact of other-cell interference. The framework presented in this paper can be used for future analysis of multicell MIMO systems.

A novel blind widely linear (WL) minimum output energy (MOE) algorithm is proposed for the CDMA receiver. Whereas the conventional WL algorithms are only applicable to real-valued modulation, the proposed receiver is applicable to complex-valued modulation. The blind WL-MOE filter is analyzed, and the convergence properties of an adaptive implementation are derived. Simulation results confirm that the proposed algorithm has higher steady-state SINR and faster convergence speed than the conventional MOE algorithm but cannot outperform the conventional WL-MOE due to severer constraints.

In this paper, upper and lower bounds on the transmission capacity of spread-spectrum (SS) wireless ad hoc networks are derived. We define transmission capacity as the product of the maximum density of successful transmissions multiplied by their data rate, given an outage constraint. Assuming that the nodes are randomly distributed in space according to a Poisson point process, we derive upper and lower bounds for frequency hopping (FH-CDMA) and direct sequence (DS-CDMA) SS networks, which incorporate traditional modulation types (no spreading) as a special case. These bounds cleanly summarize how ad hoc network capacity is affected by the outage probability, spreading factor, transmission power, target signal-to-noise ratio (SNR), and other system parameters. Using these bounds, it can be shown that FH-CDMA obtains a higher transmission capacity than DS-CDMA on the order of M/sup 1-2//spl alpha//, where M is the spreading factor and /spl alpha/>2 is the path loss exponent. A tangential contribution is an (apparently) novel technique for obtaining tight bounds on tail probabilities of additive functionals of homogeneous Poisson point processes.

Successive interference cancellation (SIC) is a technique for increasing the capacity of cellular code-division multiple-access (CDMA) systems. To be successful, SIC systems require a specific distribution of the users' received powers, especially in the inevitable event of imperfect interference cancellation. This apparent complication of standard CDMA power control has been frequently cited as a major drawback of SIC. In this paper, it is shown that surprisingly, these "complications" come with no additional complexity. It is shown that 1-bit UP/DOWN power control-like that used in commercial systems-monotonically converges to the optimal power distribution for SIC with cancellation error. The convergence is proven to within a discrete step-size in both signal-to-noise plus interference ratio and power. Additionally, the algorithm is applicable to multipath and fading channels and can overcome channel estimation error with a standard outer power control loop.

In this letter, the performance for the delay diversity receiver is analyzed in asynchronous code division multiple access (CDMA) channels. The outage probability and the bit error probability of the delay diversity receiver are accurately derived and compared with those of the conventional diversity receiver. From the analytical and numerical results, it is confirmed that the delay diversity receiver achieves a remarkable diversity gain with reasonable cost and complexity in asynchronous CDMA channels. Specifically, for roughly the same hardware complexity, the delay diversity receiver achieves nearly twice the diversity order of the conventional receiver.

Multiuser orthogonal frequency division multiplexing (MU-OFDM) is a promising technique for achieving high downlink capacities in future cellular and wireless local area network (LAN) systems. The sum capacity of MU-OFDM is maximized when each subchannel is assigned to the user with the best channel-to-noise ratio for that subchannel, with power subsequently distributed by water-filling. However, fairness among the users cannot generally be achieved with such a scheme. In this paper, a set of proportional fairness constraints is imposed to assure that each user can achieve a required data rate, as in a system with quality of service guarantees. Since the optimal solution to the constrained fairness problem is extremely computationally complex to obtain, a low-complexity suboptimal algorithm that separates subchannel allocation and power allocation is proposed. In the proposed algorithm, subchannel allocation is first performed by assuming an equal power distribution. An optimal power allocation algorithm then maximizes the sum capacity while maintaining proportional fairness. The proposed algorithm is shown to achieve about 95% of the optimal capacity in a two-user system, while reducing the complexity from exponential to linear in the number of subchannels. It is also shown that with the proposed resource allocation algorithm, the sum capacity is distributed more fairly and flexibly among users than the sum capacity maximization method.

Multiuser spatial multiplexing uses precoding to support multiple users in multi-antenna wireless channels. In this paper, two transmit diversity techniques are proposed that use extra transmit antennas to obtain additional diversity. In one solution, an eigenmode selection technique is proposed to achieve higher diversity gain by optimally matching the data streams to eigenmodes with superior channel conditions. In the other solution, a multiuser antenna selection algorithm is proposed that achieves good performance with fewer RF chains and lower system cost. Selection criteria for single-user spatial multiplexing are extended to the multiuser scenario in the context of unitary downlink precoding, and a novel selection algorithm that is near optimal in terms of symbol error rate (SER) is proposed. Simulation results show dramatic SNR reductions of 6-10 dB at an uncoded SER of 10/sup -3/ with only one extra antenna.

The paper provides a general framework for accurately analyzing the bit error probability of the maximal ratio combining (MRC) diversity receiver in CDMA systems. In previous research on MRC receivers for direct sequence code division multiple access (DS-CDMA), compromising assumptions have been made to simplify the analysis, including a Gaussian approximation for interference or constant equal cross correlations. These assumptions can produce inaccurate results, especially when the number of users is small or when the diversity order is high, as will increasingly be the case in high-rate CDMA systems. We derive a novel closed-form bit error probability expression without these assumptions and verify through simulations that this new framework is highly accurate.

In this paper, the performance of the delay diversity receiver is analyzed in asynchronous CDMA channels. The outage probability and the bit error probability of the delay diversity receiver are accurately derived and compared with those of the conventional diversity receiver. From the analytical and numerical results, it is confirmed that the delay diversity receiver achieves a remarkable diversity gain with reasonable cost and complexity in asynchronous CDMA channels. Specifically, for roughly the same hardware complexity, the delay diversity receiver achieves nearly twice the diversity order of the conventional receiver.

In ad hoc networks, it is necessary to suppress transmissions by nodes around the desired receiver in order to achieve successful communication. This minimum separation, the critical radius, has important implications on carrier sensing and other MAC-level protocols. Previously, the critical radius has not been well understood. The critical radius is investigated in CDMA ad hoc networks, with non-spread spectrum ad hoc networks being a special case where the spreading gain is unity. It is shown that the size of this exclusion zone has a large impact on the transmission capacity of ad hoc networks, and an optimal critical radius is found using stochastic geometry.

We compare the capacities achieved by space-time water-filling and spatial water-filling for MIMO fading channels. Both the effects of fast fading and shadowing are considered. It is found that for Rayleigh fast fading MIMO channels, the spectral efficiency per antenna achieved by one-dimensional spatial water-filling is close to two-dimensional space-time water-filling. However, with log-normal shadowing, space-time water-filling achieves significantly higher capacity per antenna than spatial water-filling at low to moderate SNR regimes. Furthermore, space-time water-filling has lower computational complexity than spatial water-filling. It is also shown that space-time water-filling requires a priori knowledge of the channel gain distribution, and for Rayleigh channels with log-normal shadowing, the spectral efficiency advantage over spatial water-filling comes with an increased channel outage probability.

Upper and lower bounds on the transmission capacity of direct-sequence CDMA wireless ad hoc networks are derived. The transmission capacity is a stochastic measure of the allowable number of transmissions per unit area, and is a generalization of previous measures of ad hoc network capacity. Successive interference cancellation (SIC) is attractive for DS-CDMA ad hoc networks since the dominant nearby interferers can be cancelled. Our closed-form results cleanly summarize the dependence of ad hoc network capacity on pathloss, spreading, outage probability, and interference cancellation accuracy. Other multiple access schemes, such as CSMA and DS-CDMA without SIC, are special cases. Perfect interference cancellation increases transmission capacity by nearly two orders of magnitude. Furthermore, cancelling just the strongest interferer generally gives the majority of the capacity gain, so the latency and complexity cost of SIC should be negligible.

Space-time block codes (STBC) are powerful techniques to achieve full spatial diversity in Rayleigh fading channels with low decoding complexity. When channel state information is available to the transmitter, space-time block codes can be improved through the use of a transmit precoder chosen based in part on the current channel state. We investigate the downlink transmission of an Alamouti space-time block coded multiuser wireless system in which complete channel knowledge is available to the base transceiver station. A novel unitary precoder is proposed that, with enough antennas, can effectively precancel co-channel interference at each mobile user thus enabling simple single user space-time block decoding. It is shown that excess transmit antennas, beyond the minimum required for precancellation, can he used to further improve the diversity performance through careful selection of the precoding matrix. Though the derivation assumes perfect channel state information, the impact of estimation error is investigated by deriving a lower bound on the signal to interference plus noise ratio. Monte Carlo simulations show that our proposed downlink precoder can effectively cancel the interference between mobiles, while still providing good diversity performance.

A novel multi-code multicarrier code division multiple access (MC-MC-CDMA) system is proposed and analyzed in a frequency selective fading channel. By allowing each user to transmit multiple orthogonal codes, the proposed MC-MC-CDMA system can support various data rates, as required by next generation standards, and achieve spreading gain in the time domain. Multicarrier CDMA provides robustness to multipath and spreading in the frequency domain. The bit error rate of the system is analytically derived in frequency selective fading, with Gaussian noise and multiple access interference. The results show that the proposed MC-MC-CDMA system clearly outperforms both single-code multicarrier CDMA (MC-CDMA) and single-carrier multi-code CDMA in a fixed bandwidth allocation. This indicates that MC-MC-CDMA should be seriously considered for next generation cellular systems.

A high capacity, low complexity, and robust system design for a successive interference cancellation (SIC) system is developed and analyzed. Multicarrier code-division multiple access (MC-CDMA) is used to suppress multipath and to overcome the multipath channel estimation problem in single-carrier SIC systems. In addition, an optimal power control algorithm for MC-CDMA with SIC is derived, allowing analytical bit-error rate expressions to be found for an uncoded system. Low-rate forward error-correcting codes are then added to the system to achieve robustness. It is found that the capacity of the coded system approaches the additive white Gaussian noise capacity for SIC, even in a fading multipath channel with channel estimation error. This indicates that MC-CDMA is very attractive for systems employing SIC.

Multiuser orthogonal frequency division multiplexing (MU-OFDM) is a promising technique for achieving high downlink capacities in future cellular systems. A key issue in MU-OFDM is the allocation of the OFDM subcarriers and power among users sharing the channel. Previous allocation algorithms cannot ensure fairness in advance. In this paper, a proportional rate adaptive resource allocation method for MU-OFDM is proposed. Subcarrier and power allocation are carried out sequentially to reduce the complexity, and an optimal power allocation procedure is derived, through which proportional fairness is achieved. Simulation results show that this low-complexity MU-OFDM system achieves double the capacity of a fixed time division approach to OFDM multiple access, and also has higher capacity than previously derived suboptimal power distribution schemes.

Successive interference cancellation, in conjunction with orthogonal convolutional codes, has been shown to approach the Shannon capacity for an additive white Gaussian noise channel. However, this requires highly accurate estimates for the amplitude and phase of each user's signal. We derive an optimal power control strategy specifically designed to maximize the overall capacity under the constraint of a high degree of estimation error. This power control strategy presents a general formula of which other power control algorithms are special cases. Even with estimation error as high as 50%, capacity can be approximately doubled relative to not using interference cancellation. In addition, when properly applied to multicell mobile networks, this power control scheme can reduce the handset transmit power, and therefore other-cell interference, by more than an order of magnitude.

This paper proposes and analyzes an iterative power control scheme for use with successive interference cancellation (SIC) in the presence of cancellation errors. SIC is shown by Andrews and Meng (see IEEE Transactions On Wireless Communications, Oct. 2001), to increase the capacity of cellular CDMA systems significantly, even if the signal cancellation is imperfect due to estimation errors. However, an important complication of SIC relative to conventional CDMA receivers is that a specific non-uniform distribution of powers must be assigned to the users in order for the system to function robustly. This paper proposes a simple up/down distributed iterative power control scheme for DS-CDMA systems employing SIC. We analyze its feasibility region and prove that it converges to close to the optimum solution even in the presence of estimation errors. The total received power is shown to be a reliable metric for admission control. This analysis considers both multi-rate CDMA where each user has a different target signal-to-interference-and-noise ratio (SINR), and asynchronous power control where user power updates occur asynchronously.

Successive interference cancellation (SIC), in conjunction with orthogonal convolutional codes, has been shown to approach the Shannon capacity for an AWGN channel. However, multi-cell fading wireless channels induce error in the amplitude and phase estimates required to perform perfect cancellation of the interference. By combining SIC with a previously developed power control algorithm, we show that other-cell interference and transmit power can be reduced by an order of magnitude or more relative to a conventional (IS-95 style) CDMA system. In addition, even as estimation error becomes large, the capacity is more than doubled over systems without interference cancellation or those that employ SIC without optimum power control.