Low Earth Orbit (LEO) nano-satellites can provide uplink connectivity for large numbers of distributed Internet of Things (IoT) sensing devices. To achieve a target Quality-of-Service (QoS), devices must send packets multiple times, due to collisions. This paper characterises the achievable set of terminal QoS targets, and determines the optimal uplink packet attempt rates. We show that QoS target feasibility is determined by the solution of a linear program (LP), and that the solution gives the optimal packet attempt rates. We show that the QoS targets can be modified using the shadow prices from the LP, to obtain feasibility. We show that our LP based approach can support greater than 30% more ground sensor terminals, compared to existing schemes.

This paper considers multiuser millimeter wave (mmWave) MIMO communication systems where both the base station (BS) and the user equipments (UEs) use analog beamforming (BF). We propose a beam acquisition approach to find the best directions for the narrow beams, required to achieve BS-UE links above a minimum signal-to-noise ratio (SNR) threshold. The multiple UEs first select their beams simultaneously, based on signals transmitted from the BS on wide training beams. The BS then switches to a beam acquisition mode in order to select the best beam direction for each UE, based on training signals the UEs send on the uplink. We propose a novel parallel beam acquisition scheme for this uplink phase. We also propose a user rejection policy, in which weak UEs that do not satisfy a target SNR threshold, equivalent to a certain bit error rate, are rejected. To do so, we derive the posterior probability that a BS beam has a resultant SNR below the target SNR threshold. We also propose a generalized likelihood ratio test (GLRT) to reduce the computational burden. We derive closed-form error probability expressions for the proposed GLRT approach, and examine the trade-off between the beam acquisition time and accuracy in selecting the beams. We show that the beam acquisition time of our proposed approach is as low as 3% of existing approaches.

This paper analyses the data message success rate for Internet of Things (IoT) sensing devices communicating over Low Earth Orbit (LEO) satellite links. We present an analytical framework for optimizing multi-objective multi-packet reception on the uplink. We present an analytical result for the probability of message success for a given ground terminal, and present an analytical result for the overall probability of message success, averaged across all terminals.

This paper considers millimeter-wave (mmWave) networks with hybrid beamforming communications, where base stations have a limited number of radio frequency (RF) chains. The base stations have overlapping coverage to overcome blockage issues in both downlink and uplink transmission. We propose a user association (UA) scheme that minimizes the time required for clearing data traffic of users in the coverage area. We formulate the UA problem as a time allocation problem, allocating time to user-base station links. We provide an innovative two-stage approach to solve this problem. Stage one optimizes a time fraction allocation for user-base station links. Then these time fractions are distributed across the RF chains at each base station using a fully distributed algorithm. Stage two then schedules the user-base station links, provably solving the UA minimum clearing time problem. We then characterize the achievability of any set of target user rates. Numerical results show that our proposed UA scheme achieves significantly reduced clearing times in comparison to baseline schemes.

This paper presents an efficient practical Zak-OTFS modulation implementation using time and frequency windowing methods. We present two general classes of delay-Doppler (DD) twisted convolution (TC) filters (Type-1 and Type-2), and show that they can be realized by time and frequency windowing functions. We then propose practical methods to generate time domain Zak-OTFS signals, for actual transmission, using the windowing functions. For Type-1, the signals are generated using an interpolation filter. For Type-2, they are generated using a form of precoded OFDM. We show that this allows a wide variety of pulse shapes to be implemented in practice for Zak-OTFS modulation. This was not previously possible. We also show that the Type-2 signals are more spectrally efficient than their Type-1 counterparts. Finally, we compare the channel predictability of the two implementations.

This paper designs energy-efficient trajectories for unmanned aerial vehicles (UAVs) harvesting data sequentially from distributed ground nodes. We propose a novel optimization framework for path planning, based on dynamic programming. We develop an optimum backward-forward algorithm that jointly optimizes the hovering locations for each ground node, and the visiting order to those locations. Our algorithm minimizes the total energy consumption of the UAV over its trajectory. Our framework is compatible with various probabilistic wireless communication channel models, and can also be applied to different cost functions, including minimising the total flying time, and allowing for bi-directional communications. We also develop a lower complexity algorithm that approximates the optimum UAV trajectory by decomposing the original problem into two sub-problems, and iterating back and forth between the two. This alternating algorithm has polynomial time complexity, and we show that it produces a near-optimum UAV trajectory, with as little deviation as 5% to 15% from the average energy consumption of the optimum algorithm.

This paper provides capacity results for multi-user mm-wave hybrid-beamforming, and presents optimal joint beam allocation and user scheduling algorithms. We characterize the downlink capacity of a practical system with quantized analog beamforming code-books under the constraint that users cannot be scheduled at the same time if they are closer together than a beam width in angle. We show that the capacity region is determined by a small number of linear inequality constraints. We also present capacity-achieving scheduling algorithms that provide beam allocations guaranteeing that user rate requirements are met within each resource block. In particular, we propose “sand-filling” algorithms that are provably optimal and which have linear complexity. Intuitively, our schemes can be viewed in terms of filling containers with coloured sand, in such a way that the colours at any given height do not conflict with the colours in the other containers at the same height, where the containers represent the RF chains (i.e. the beamforming resources), and the coloured sand represents the users (and their rate requirements). We show a numerical example where the capacity of our scheme is 82% higher than a traditional resource partitioning scheme.

This paper develops a beam direction optimization framework for next-generation GEO satellite networks. The objective is to meet traffic demands at user locations. Given beam-pointing directions, the downlink of the GEO satellite is a vector broadcast channel that consists of a single transmitter and multiple distributed ground users. We characterize the downlink channel matrix for the multibeam satellite network by using an array factor formula for uniform planar arrays. We obtain a necessary and sufficient condition dependent on the downlink channel matrix to provision traffic demands by meeting given SINR targets at user locations. Utilizing the necessary and sufficient conditions, we formulate a joint beam direction and power optimization problem to attain target SINRs which uses minimum total power. Our results demonstrate that analog beamforming with optimized beam shifts can achieve an SINR gain of 8 dB when compared to analog beamforming without beam direction optimization. It also offers a spatial multiplexing advantage of 90 km by enabling simultaneous provisioning of user locations in close proximity within the same frequency band. When compared to hybrid beamforming, our scheme can achieve an SINR gain of 2 dB.

This paper proposes an efficient 3D deployment approach for multiple UAV base stations, to maximize the probability of connections for users spread over a wide area. We consider covering a circular region, such as might apply in a disaster scenario affecting a city centre where terrestrial base stations have become inoperable. We compare two approaches to deploying UAVs. One is a regular triangular arrangement of UAVs and the other is an optimized circle packing arrangement. We start by considering a flying height optimized for a single UAV. We then show that both approaches can be improved by varying the height and flying locations of the UAVs, to expand the overall desired coverage area and overlap the individual UAV coverage areas. We show that the simple regular triangular arrangement can obtain superior connectivity compared to the circle packing approach, with significantly lower complexity.

In this paper, we consider a millimeter wave network deployed to cover an urban street. Each base station (BS) employs hybrid beamforming with a limited number of radio frequency (RF) chains. Its link to any user equipment (UE) is prone to being blocked by vehicles and pedestrians moving along the street. We propose a Round Robin (RR) access protocol with proactive cell switching in which each UE switches its connection to the least loaded line of sight BS at the end of its RR transmission frame or any time when its link is blocked. We compare the UE connectivity performance of the proposed protocol to the conventional cellular network association protocols and the RR protocols which switch only when the link is blocked. Our results reveal the impacts of different system parameters (i.e. the number of BSs, the number of RF chains, the length of RR transmission frame) on the performance of the protocol, and the importance of cell switching in dealing with load balancing as well as blockage

This paper presents a new distributed slot reservation frame-work for joint resource allocation and flow control in mmWave IAB networks. We derive the Dynamic Slot Reservation (DSR) algorithm from a novel approach to solve a minimum clearing time linear program in a completely distributed manner. The algorithm to solve this problem, the Static Slot Reservation (SSR) algorithm, is also a contribution of the paper. We compare the delay performance of the DSR algorithm with a well known optimal, centralized algorithm, the joint-MWM algorithm, for a realistic IAB network scenario of multi-hop flows. We show that flows that traverse several links have significantly lower delays under DSR than under the joint-MWM algorithm. This paper also provides an instantaneous rate control policy for IAB networks which changes flow rates based on the number of flows at each node in the network. The flow rates under this policy are the same as the steady-state flow rates achieved by the DSR algorithm. We prove that the proposed flow control policy provides stability for all flow arrival rate vectors that are achievable by any flow control policy. This paper provides distributed admission control policies to provide rate and/or latency guarantees to flows under dynamic scenarios with stochastic flow arrivals and changing access link rates.

This paper considers the implementation of compressive sensing (CS) approaches for beam alignment (BA) in multiuser millimeter wave (mmWave) MIMO systems. We particularly consider wideband time-varying channels in the practical low SNR regime. We examine two different time scales for beam-switching in the BA training phase at both the base station (BS) and the user equipment (UE). We also compare different time scales for running the CS algorithm at the UE, with their corresponding overhead and complexity. We propose an overarching trial-based protocol that re- initializes the BA process at particular times. We also propose a new approach to designing the CS sensing matrix (SM), based on a deterministic construction. Rows of our proposed SM are Kronecker product decomposable, making it ideal for the BA problem. We show that when block-based beam switching is employed in combination with running the CS algorithm Every Epoch (CS-EE), our proposed SM gives superior performance compared to the other approaches. Moreover, our proposed overarching trial-based protocol enhances the performance even further. We also show that running the CS algorithm Every Block (CS-EB) outperforms CS-EE at the cost of higher complexity and overhead.

We consider the stability region of a mmWave integrated access and backhaul (IAB) network with stochastic arrivals and time-varying link rates. In the scheduling of links, we consider a limit on the number of RF chains, and the half-duplex constraint which occurs due to the wireless backhaul links. We characterize the stability region, and propose a back-pressure policy for the IAB network under the RF chains and half-duplex constraints. To implement the back-pressure policy, it is required to compute the maximum weighted schedule, which is a complex problem in general. For the IAB network, we present a distributed message passing scheme to compute the maximum weighted schedule, with almost linear complexity. We also investigate a class of local scheduling policies for the IAB network, which have a smaller stability region in general, but require no message passing. We characterize the stability region for the local class, and show that it is same as the global stability region, if the link rates are un-varying. We provide a bound on the gap between local and global regions when the links are time varying. We propose a local max-weight algorithm which achieves the stability region for the local class, and we present numerical results.

This paper jointly optimizes the flying location and wireless communication transmit power for an unmanned aerial vehicle (UAV) conducting covert operations. This is motivated by application scenarios such as military ground surveillance from airborne platforms, where it is vital for a UAV’s signal transmission to be undetectable by those within the surveillance region. Specifically, we maximize the communication quality to a legitimate receiver, who is also a ground-user but outside the surveillance region, under specific constraints on communication covertness, maximum transmit power, and the UAV’s physical location related to the required surveillance quality. We provide an explicit solution to the optimization problem for one of the most practical constraint combinations. For other constraint combinations, we determine feasible regions for flight, that can then be searched to establish the UAV’s optimal location. In many cases, the 2-dimensional optimal location is achieved by a 1-dimensional search. We discuss two heuristic approaches to UAV placement, and show that in some cases they are able to achieve close to optimal, but that in other cases significant gains can be achieved by employing our developed solutions.

Millimetre wave (mmWave) beam tracking is a challenging task because tracking algorithms are required to provide consistent high accuracy with low probability of loss of track and minimal overhead. To meet these requirements, we propose in this article a new cost-effective analog beam tracking framework namely Adaptive Tracking with Stochastic Control (ATSC). Under this framework, beam direction updates are made using a novel mechanism based on measurements taken from only two beam directions perturbed from the current data beam. To achieve high tracking accuracy and reliability, we provide a systematic approach to jointly optimise the algorithm parameters. The complete framework includes a method for adapting the tracking rate together with a criterion for realignment (perceived loss of track). ATSC adapts the amount of tracking overhead that matches well to the mobility level, without incurring frequent loss of track, as verified by an extensive set of experiments under both representative statistical channel models as well as realistic urban scenarios simulated by ray-tracing software. In particular, numerical results show that ATSC can track dominant channel directions with high accuracy for vehicles moving at 72 km/hour in complicated urban scenarios, with an overhead of less than 1%.

In this paper, we propose an adaptive beam search algorithm for the initial alignment of millimetre-Wave beams. The proposed algorithm works by gradually deactivating beams that are unlikely the best beam from a pre-synthesised codebook to save overhead, based on a Bayesian probability criterion with a uniform improper prior. The beam deactivations can be implemented with low-complexity operations that require computing a low-degree polynomial or a search through a look-up table. The proposed algorithm does not require prior knowledge of channel statistics or signal to noise ratios (SNRs) to optimise the amount of searching time, and uses a suitable amount of time to achieve satisfactory beam search accuracy in different SNRs and fading scenarios. Numerical results confirm that the proposed algorithm can adapt to a wide range of channels with a fixed algorithm parameter, and can achieve better balance between beam search overhead and accuracy than non-adaptive approaches with fixed overhead.

Millimeter wave (mmWave) multiple-input multiple-output (MIMO) communication systems with a large number of antennas are power hungry when using conventional high-resolution analog-to-digital/digital-to-analog converters (A/Ds). To reduce the power consumption of mmWave MIMO systems, existing studies have considered hybrid structures with a reduced number of high-resolution or low-resolution A/Ds at either the transmitter or the receiver side. In this paper, we propose and investigate a multi-user hybrid architecture with low-resolution A/Ds equipped at both the transmitter and the receivers. To mitigate the impact of utilizing low-resolution A/Ds at the transceivers, we propose a novel data transmission scheme, which exploits a weighted phased-array to synthesize the beamforming matrix in the analog domain so as to mitigate inter-user interference. Under the scheme proposed, we derive the achievable rate and the energy efficiency to establish guidelines on the optimal resolution choice of A/Ds for hybrid mmWave systems. For a typical total transmit power at the BS, e.g., 30 dBm, the proposed scheme with 5~6-bit A/Ds can significantly improve the energy efficiency by as much as 100% over that of the conventional hybrid MIMO architecture with high-resolution A/Ds (10-bit A/Ds), without significant degradation in data rate performance.

In this article, we consider joint optimization of user association and resource allocation in three tier HetNets. We formulate the objective of minimizing the resources required to clear a given set of files, as a linear program. We show that the optimal user association is determined by a rate-biasing rule, where a bias value is associated with each BS. We show that each rate-bias value crucially only takes values from a finite set which we characterize. We present a complete analytical solution along with new structural results. Using these results, we present efficient distributed algorithms for optimal control of three tier HetNets. The method involves a 1D search for a resource variable at the macro-level, and 2D search at the pico-level for a resource variable and a bias value. We apply our results to a variety of hierarchical network examples.

Millimeter Wave (mmWave) communications rely on highly directional beams to combat severe propagation loss. In this paper, an adaptive beam search algorithm based on spatial scanning, called Iterative Deactivation and Beam Shifting (IDBS), is proposed for mmWave beam alignment. IDBS does not require advance information such as the Signal-to-Noise Ratio (SNR) and channel statistics, and matches the training overhead to the unknown SNR to achieve satisfactory performance. The algorithm works by gradually deactivating beams using a Bayesian probability criterion based on a uniform improper prior, where beam deactivation can be implemented with low-complexity operations that require computing a low-degree polynomial or a search through a look-up table. Numerical results confirm that IDBS adapts to different propagation scenarios such as line-of-sight and non-line-of-sight and to different SNRs. It can achieve better tradeoffs between training overhead and beam alignment accuracy than existing non-adaptive algorithms that have fixed training overheads.

Swift and accurate alignment of transmitter (Tx) and receiver (Rx) beams is one of the fundamental design challenges to support directional transmission in millimeter-wave cellular communications. In this paper, we propose a new Optimized Two-Stage Search (OTSS) algorithm for Tx-Rx beam alignment via beam training. In contrast to one-shot exhaustive search, OTSS judiciously divides the training energy budget into two stages. In the first stage, OTSS explores and trains all candidate Tx-Rx beam pairs and then discards a set of less favorable pairs learned from the measured received signal. In the second stage, OTSS takes an extra measurement for each of the remaining pairs and combines with the previous measurement to determine the best one. For OTSS, we derive fundamental bounds on its misalignment probability under a single-path channel model with ideal codebooks and establish a guideline on its optimized parameter choices. Numerical results have confirmed the advantage of OTSS over the state-of-the-art baselines.

While Gaussian signalling is assumed in many studies on covert communications, its optimality has not been carefully investigated. In this work, we examine this optimality by considering the approach of upper bounding D(p0(y)∥p1(y)) as the covert communication constraint, where D(p0(y)∥p1(y)) is the Kullback-Leibler divergence from p0(y) to p1(y), p0(y) and p1(y) are the likelihood functions of the observation y at the warden under the null hypothesis (no covert transmission) and alternative hypothesis (a covert transmission occurs), respectively. Considering additive white Gaussian noise at both the receiver and the warden, we prove that Gaussian signalling is not optimal in terms of maximizing the mutual information of transmitted and received signals for covert communications with D(p0(y)∥p1(y)) ≤ 2ϵ2as the constraint. We also explicitly show a skew-normal signalling can outperform Gaussian signalling in terms of achieving higher mutual information subject to the same covertness constraint D(p0(y)∥p1(y)) ≤ 2ϵ2.

We address the critical problem of hiding unmanned aerial vehicles (UAV) for wireless transmissions by the emerging covert communication technology, since in military surveillance scenarios the disclosure of a UAV's location information may lead to an attack. Specifically, we jointly optimize the UAV's transmit power and height in order to maximize the communication quality to a legitimate receiver subject to a covertness constraint, a maximum transmit power constraint, and a lower bound and an upper bound on the UAV's height. To this end, we first derive the UAV's optimal height for maximizing the legitimate communication quality without any constraint and then we address this problem under constraints in particular the covertness constraint. Our solution explicitly shows the impact of these constraints and reveals the tradeoff among the legitimate communication quality, covertness requirement, and surveillance cost. For example, our examination demonstrates that the legitimate communication quality increases with the surveillance cost represented by the quality of the camera used for conducting surveillance.

Swift and accurate alignment of transmitter (Tx) and receiver (Rx) beams is a fundamental design challenge to enable the reliable outdoor millimeter-wave communications. In this paper, we propose a new optimized two-stage search (OTSS) algorithm for Tx–Rx beam alignment via spatial scanning. In contrast to one-shot exhaustive search, the OTSS judiciously divides the training energy budget into two stages. In the first stage, OTSS explores and trains all candidate beam pairs and, then, eliminates a set of less favorable pairs learned from the received signal profile. In the second stage, OTSS takes an extra measurement for the each of the survived pairs and combines with the previous measurement to determine the best one. For the OTSS, we derive an upper bound on its misalignment probability, under a single-path channel model with training codebooks having an ideal beam pattern. We also characterize the decay rate function of the upper bound with respect to the training budget and further derive the optimal design parameters of OTSS that maximize the decay rate. OTSS is proved to asymptotically outperform the state-of-the-art beam alignment algorithms and is numerically shown to achieve better performance with limited training budget and practically synthesized beams.

In this paper, we examine the optimality of Gaussian signalling for covert communications with an upper bound on D(p1||p0) or D(p0||p1) as the covertness constraint, where D(p1||p0) and D(p0||p1) are different due to the asymmetry of Kullback-Leibler divergence, p0(y) and p1(y) are the likelihood functions of the observation y at the warden under the null hypothesis (no covert transmission) and alternative hypothesis (a covert transmission occurs), respectively. Considering additive white Gaussian noise at both the receiver and the warden, we prove that the Gaussian signalling is optimal in terms of maximizing the mutual information of transmitted and received signals for covert communications with an upper bound on D(p1||p0) as the constraint. More interestingly, we also prove that the Gaussian signalling is not optimal for covert communications with an upper bound on D(p0||p1) as the constraint, for which as we explicitly show skew-normal signalling can outperform the Gaussian signalling in terms of achieving higher mutual information. Finally, we prove that, for Gaussian signalling, an upper bound on D(p1||p0) is a tighter covertness constraint in that it leads to lower mutual information than the same upper bound on D(p0||p1), by proving D(p0||p1) ≤ D(p1||p0).

We formulate a linear programming problem to find the minimum clearing time in HetNets. Although this program is NP hard in general, we consider particular topologies that arise in HetNets, including a two cell HetNet and a linear chain of HetNets, both with wireless backhaul, and we provide an efficient, greedy algorithm that provably solves the minimum clearing time problem for these networks. We show how this algorithm can be applied to jointly optimize the ABS time across multiple macros in a HetNet, and we demonstrate capacity gains of the algorithm, compared to standard approaches to Inter Cell Interference Coordination. This paper provides insight into how to manage interference in presence of more than one macro, and how to efficiently operate wireless backhaul in HetNets.

We propose a beamforming technique for the multicell downlink of a multicarrier code division multiple access (MC-CDMA) system with sparse signatures. We propose a distributed beamforming algorithm using the sum-product algorithm. The distributed beamforming algorithm converges very quickly to the centralized beamforming solution, minimizing the delay associated with computation of the transmit vector. The complexity of distributed beamforming depends on the number of base stations (BSs) that are in range of each user, not on the size of the entire network.

In millimeter wave cellular communication, fast and reliable beam alignment via beam training is crucial to harvest sufficient beamforming gain for the subsequent data transmission. In this paper, we establish fundamental limits in beam-alignment performance under both the exhaustive search and the hierarchical search that adopts multi-resolution beamforming codebooks, accounting for time-domain training overhead. Specifically, we derive lower and upper bounds on the probability of misalignment for an arbitrary level in the hierarchical search, based on a single-path channel model. Using the method of large deviations, we characterize the decay rate functions of both bounds and show that the bounds coincide as the training sequence length goes large. We go on to characterize the asymptotic misalignment probability of both the hierarchical and exhaustive search, and show that the latter asymptotically outperforms the former, subject to the same training overhead and codebook resolution. We show via numerical results that this relative performance behavior holds in the non-asymptotic regime. Moreover, the exhaustive search is shown to achieve significantly higher worst case spectrum efficiency than the hierarchical search, when the pre-beamforming signal-to-noise ratio (SNR) is relatively low. This paper hence implies that the exhaustive search is more effective for users situated further from base stations, as they tend to have low SNR.

In this paper, we develop an analytical framework for the initial access (also known as base station (BS) discovery) in a millimeter-wave communication system and propose an effective strategy for transmitting the reference signals (RSs) used for BS discovery. Specifically, by formulating the problem of BS discovery at user equipments (UEs) as hypothesis tests, we derive a detector based on the generalized likelihood ratio test and characterize the statistical behavior of the detector. The theoretical results obtained allow analysis of the impact of key system parameters on the performance of BS discovery, and show that RS transmission with narrow beams may not be helpful in improving the overall BS discovery performance due to the cost of spatial scanning. Using the method of large deviations, we identify the desirable beam pattern that minimizes the average miss-discovery probability of UEs within a targeted detectable region. We then propose to transmit the RS with sequential scanning, using a pre-designed codebook with narrow and/or wide beams to approximate the desirable patterns. The proposed design allows flexible choices of the codebook sizes and the associated beam widths to better approximate the desirable patterns. Numerical results demonstrate the effectiveness of the proposed method.

Heterogenous wireless networks (Hetnets) provide a powerful approach to meet the massive growth in traffic demands, but also impose a significant challenge on backhaul. Caching at small base stations (BSs) and wireless small cell backhaul have been proposed as attractive solutions to address this new challenge. In this paper, we consider the optimal caching and user association to minimize the total time to satisfy the average demands in cached-enabled Hetnets with wireless backhaul. We formulate this problem as a mixed discrete- continuous optimization for given bandwidth and cache resources. First, we characterize the structure of the optimal solution. Specifically, we show that the optimal caching is to store the most popular files at each pico BS, and the optimal user association has a threshold form. We also obtain the closed-form optimal solution in the homogenous scenario of pico cells. Then, we analyze the impact of bandwidth and cache resources on the minimum total time to satisfy the average demands. Finally, using numerical simulations, we verify the analytical results.

Using stochastic geometry, downlink (DL) coverage probability in slot-based two-tier heterogeneous cellular networks (HCNs) is studied. Two traffic patterns namely slotted-asynchronous and exponential-interarrival are introduced to capture user activity, and the DL coverage probability based on max-SINR association is derived. In contrast to many works, the transmission slots of base stations (BS) are not synchronous. This causes a packet transmitted in one slot to experience varying levels of interference during the time slot interval. The SINR statistical distribution during one slot is derived for both traffic patterns. The numerical results are presented to illustrate the analytical ones. The comparison between asynchronous and conventional synchronous HCNs is provided to illustrate the asynchronous effect on DL performance. It is shown that to meet high coverage requirements, synchronizing slots from different BSs help to boost the coverage performance. Furthermore, it is shown that densifying networks with low-power BSs improves coverage performance and the improvement is more pronounced at higher path-loss exponents.

Coordinated scheduling/beamforming (CS/CB) is a cost-effective coordinated multipoint (CoMP) transmission paradigm that has been incorporated in the recent long-term evolution cellular standard. In this paper, we study CS/CB with the aim of developing low-complexity multicell coordinated user scheduling policies. We focus on a class of multicell interfering broadcast networks in which base stations have only local data and local channel state information, but each has sufficient antennas to serve multiple users using zero-forcing beamforming. The coordination problem is formulated as finding scheduling decisions across the cells such that the network sum rate is maximized. Starting from the two-cell model, we uncover the structure for a good scheduling decision, which in turn leads to the definition of two distributed scheduling policies of differing complexity and intercell coordination. Asymptotic theoretical bounds on the average sum rate are derived to predict the performance of the policies proposed. We extend to some example networks containing more than two cells and develop network-wide coordination policies. Numerical results confirm the effectiveness of the proposed policies and shed light on practical coordinated system design.

This work introduces a novel cooperation framework that allows mobile service providers (MSPs) to offload traffic onto each other so that temporarily unused spectrum/resources of cellular bands can be opportunistically harvested. Specifically, through traffic offloading, MSPs aim to maximize their profit while maintaining their QoS commitment. For that purpose, we model the strategic cooperation between MSPs as a stochastic Markov game in which the dynamics of MSPs' resources and user behaviors are captured by an underlying Markov decision process. We prove that the game is irreducible and admits a Nash Equilibrium at which all MSPs benefit from traffic offloading. A practical algorithm that uses only local information to govern traffic offloading at MSPs is then developed. Numerical simulations show that by designing appropriate profit sharing contracts, this algorithm can achieve almost the same performance as that of a socially optimal solution.

Generalized spatial modulation (GSM) is a variant of spatial modulation (SM) which offers enhanced spectral efficiency with a moderate increase in signal processing complexity. This paper proposes a novel compressive sensing (CS) aided detection algorithm which offers better performance than traditional CS based detection algorithms. In contrast to widely considered frequency-flat channel models, we have adopted frequency-selective wireless channel models to account for high data-rate applications. Our proposed algorithm offers superior performance over traditional CS based algorithms even in the presence of channel estimation errors. Numerical experiments are conducted to investigate the mathematical analysis under different suppositions on channel state information. Normalized mean-square error (NMSE) and bit-error rate (BER) versus signal-to-noise (SNR) curves are studied to investigate the performance under different detection algorithms.

Heterogeneous wireless networks (HetNets) provide a means to increase network capacity by introducing small cells and adopting a layered architecture. HetNets allocate resources flexibly through time sharing and cell range expansion/contraction allowing a wide range of possible schedulers. In this paper, we define the capacity of a HetNet down link in terms of the maximum number of downloads per second, which can be achieved for a given offered traffic density. Given this definition we show that the capacity is determined via the solution to a continuous linear program (LP). If the solution is smaller than 1 then there is a scheduler such that the number of mobiles in the network has ergodic properties with finite mean waiting time. If the solution is greater than 1 then no such scheduler exists. These results have clear implications for network planning. The above results continue to hold if a more general class of schedulers is considered.

We investigate a joint user association and resource allocation problem in a three-tier heterogeneous network. Orthogonal resource allocation among different tiers is assumed. The problem is formulated as minimizing the total resources required to satisfy given user traffic demands. We first examine the structure of the optimal solution for this convex optimization problem and show that the optimal user association and hence resource allocation is determined by a bias value on the data rate offered by each base station. We then develop distributed algorithms based on the dual ascent method in determining the optimal rate bias for each BS. Numerical experiments demonstrate that the developed algorithms converge fast and produce close-to-optimal solutions. It is also shown that under cross-tier orthogonal resource allocation, the three-tier deployment provides significant performance improvement over a two-tier deployment, using the same set of base stations in each case.

We introduce a novel Multi-Carrier Code Division Multiple Access (MC-CDMA) system, where random sparse signatures are deployed in the frequency domain. Data symbols transmitted from base station (BS) to mobile stations (MSs) are drawn from discrete finite alphabets, such as M-QAM constellations. Transmitter-based precoding is introduced so as to allow simple despreading followed by single-user detection at MSs. A power-efficient non-linear precoding optimization problem is formulated by imposing minimum Symbol Error Probability (SEP) targets at MSs. We first elaborate on how to translate the SEP targets into exact constraint regions on noiseless received components at MSs. With relaxation on the exact regions, a tractable convex problem is obtained. A dual-decomposition-based algorithm is then developed to accommodate parallel processors to perform precoding calculation. The signature sparsity turns out to be vital to reduce interprocessor communication overhead and computational complexity for pre-coding. The scheme proposed offers considerable transmit power reduction compared with the conventional zero-forcing precoder.

We investigate a coordinated scheduling problem in a two-cell network where in each cell, two users are scheduled for simultaneous communication. Zero-forcing (ZF) beamforming is employed at each base station to suppress both intra- and inter-cell interference. The coordinated scheduling/beamforming problem is formulated as finding proper scheduling decisions and hence beamformers across the network such that a weighted sum-throughput is maximized. We propose three distributed scheduling policies that only require local data and local channel state information at each cell, and consume much less computation and communication overhead than the global optimization approach via exhaustive search. The proposed policies illustrate the complexity-performance tradeoff for the coordinated system. Nevertheless, numerical results show that at all levels of complexity, the proposed policies perform close to the global optimization approach with ZF beamforming and outperform the scheme with matched filtering beamforming even with global coordination.

Energy efficiency and quality-of-service (QoS) have been two key considerations in the design of modern multi-user communication systems. In this paper, we study optimal rate control over the multiple-access channel to minimize the sum transmission energy under general QoS constraints. We model the data flows and QoS constraints using a cumulative curves methodology and formulate the optimization problem as a continuous-time control problem. We analyze the optimality properties and show that the optimization problem has a dynamic programming (DP) structure induced by successive interference cancellation (SIC). Based on the DP structure, we propose a low-complexity solution, which is amenable to an appealing graphical visualization and has the same order of complexity as the single user energy minimization problem. We bound the energy gap between the low-complexity solution and the optimal solution, and show that the energy gap diminishes to zero in the symmetric high SNR regime.

Stability properties for optimum utility based scheduling algorithms in wireless Heterogeneous Networks (Hetnets) is investigated. Utility based schedulers are modelled as a Markov process which is shown not only to have ergodic properties but also certain finite moments, depending on the algorithm choice. The same properties adhere to periodic versions of these schedulers.

We consider a coordinated multiuser scheduling problem for a multicell mutually interfering broadcast network. In particular, we focus on a two-cell cluster, where both base stations have only local data and local channel state information, but each has sufficient number of antennas to serve multiple homogeneous users under a full zero-forcing beamforming transmission. The scheduling problem is formulated as finding proper scheduled users and hence beamformers across the cells such that the sum rate is maximized. We uncover the structure for a good scheduling decision, which in turn motivates three distributed coordinated scheduling policies of different levels of complexity. For the simplest policy, we derive a lower bound on the expected achievable sum rate. It is shown in the large user population limit, the simplest policy suffices to preserve the best possible multiplexing gain and multiuser diversity gain for the model studied, but it does induce a pairing loss on the sum rate due to the limited coordination between cells.

We are concerned with the throughput of a full-duplex (FD) MIMO network. Unlike conventional half-duplex (HD) MIMO, two wireless devices of a bidirectional FD-MIMO link have freedom of selecting which antennas/RF-chains to transmit or receive before tuning their radiation patterns to maximize the link's throughput. The freedom in configuring the function of available RF-chains, resulting in various FD-MIMO transmission modes, is referred to asFD-MIMO freedomthat is shown to significantly improve the spectral efficiency of a given link. For a given RF-chain/antenna selection of a set of FD-MIMO links, we end up with a non-convex throughput maximization problem of a heterogeneous MIMO network. We design both centralized (using the augmented Lagrange function) and distributed algorithm (using a hierarchical game and pricing) to solve the problem for its locally optimal solutions. Comparing the achieved throughput of the FD-MIMO network, averaged over all obtained locally optimal solutions, with that when FD-MIMO nodes choose to operate in an HD mode, we find the HD mode surprisingly outperforms the FD mode. This trend is also observed when exploring all possible communication modes of a small size FD-MIMO network.

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.

The Wyner interference network is a popular model used in research on cellular networks due to its simplicity and analytical tractability. In this paper, the optimal power allocation strategies in symmetric one- and two-sided Wyner models are investigated. We determine a sufficient condition for binary power control (BPC) to be optimal that can be applied to the one-sided symmetric model. We consider binary power schemes for the symmetric two-sided Wyner network. Using a method of grouping links and performing a piecewise comparison of the group rates, we are able to determine the optimal power policy that maximizes the network sum rate. The result of the optimization can be expressed as follows for both types of networks: When the interfering channel gain √ϵ is small, it is optimal (in the class of binary schemes) to have all links on; otherwise, alternate links are switched off to remove interference. We characterize the critical values of ϵ where the transitions occur.

The deployment of pico cells to cover traffic hot spots within the footprint of a macro cell provides a powerful approach to meet the massive growth in traffic demands fueled by smartphones and bandwidth-hungry applications. Joint optimization of resource allocation and user association is of critical importance to achieve the maximum capacity benefits in such heterogeneous network deployments (HetNets). We first examine the problem of minimizing the amount of resources required to satisfy given traffic demands. We characterize the structure of the optimal solution, and identify a simple optimality condition in terms of the physical transmission rates of the edge users between the macro cell and the various pico cells. We further demonstrate how these structural properties can be leveraged in designing a distributed online algorithm for achieving a max-min fair throughput allocation across all users. Numerical experiments are presented to illustrate the results.

This work studies a novel power-efficient precoder design problem for a linear cellular array with base station (BS) cooperation: data symbols intended for mobile stations (MSs) are drawn from discrete finite alphabets, precoding is performed among BSs to produce appropriate signals transmitted over the channel, symbol-by-symbol detection is performed at each MS, and a minimum Symbol Error Probability (SEP) for detection is introduced as the Quality-of-Service (QoS) metric at each MS. With regular constellations such as 16-QAM deployed as system data inputs, the SEP constraints are formulated and characterized by a set of convex relaxations on the received signals. A convex power optimization problem is then formulated subject to the SEP constraints. By the primal-dual decomposition approach, a distributed algorithm is developed to solve the problem in which only local communication among BSs is required. Our scheme is shown to significantly outperform linear zero-forcing precoder in terms of transmit power consumption.

The deployment of pico cells to cover traffic hot spots within the footprint of a macro cell provides a powerful approach to meet the massive growth in traffic demands fueled by smartphones and bandwidth-hungry applications. Joint optimization of resource allocation and user association is of critical importance to achieve the maximal capacity benefits in such heterogeneous network deployments (HetNets). We specifically examine the problem of maximizing the aggregate throughput utility of the various users. We characterize the structure of the optimal solution, and identify a simple optimality condition in terms of the transmission rates of the edge users between the macro cell and the various pico cells. Exploiting the structural properties, we develop distributed online algorithms for the broad class of alpha-fair utility functions, which includes several common fairness notions. Numerical experiments are presented to illustrate the results.

This paper considers base station (BS) cooperation in the form of coordinated beamforming, focusing on min-max fairness in the power usage subject to target SINR constraints at each single-antenna user. We show that the optimal beamforming strategies have an interesting nested zero-forcing structure. In the asymptotic regime where the number of antennas at each BS and that of users in each cell both grow large with their ratio tending to a finite constant, the dimensionality of the optimization problem that needs to be solved is greatly reduced, and only knowledge of statistics is required to solve it. The optimal solution is characterized in general, and an algorithm is proposed that converges to the optimal transmit parameters, for feasible SINR targets. For the two cell case, a simple single parameter characterization is obtained. These asymptotic results provide insights into the average performance, as well as simple but efficient beamforming strategies for the finite system case. In particular, the asymptotically optimal beamformers only require the BSs to have local instantaneous channel state information; the remaining parameters of the beamformers can be calculated using channel statistics, thereby reducing the channel state information estimation and signaling overhead.

A Rayleigh fading spatially correlated broadcast setting with$M = 2$antennas at the transmitter and two users (each with a single antenna) is considered. It is assumed that the users have perfect channel information about their links, whereas the transmitter has only statistical information of each user's link (covariance matrix of the vector channel). A low-complexity linear beamforming strategy that allocates equal power and one spatial eigenmode to each user is employed at the transmitter. Beamforming vectors on the Grassmann manifold that depend only on statistical information are to be designed at the transmitter to maximize the ergodic sum-rate delivered to the two users. Toward this goal, the beamforming vectors are first fixed and a closed-form expression is obtained for the ergodic sum-rate in terms of the covariance matrices of the links. This expression is nonconvex in the beamforming vectors ensuring that the classical Lagrange multiplier technique is not applicable. Despite this difficulty, the optimal solution to this problem is shown to be the same as the solution to the maximization of an appropriately defined average signal-to-interference and noise ratio metric for each user. This solution is the dominant generalized eigenvector of a pair of positive-definite matrices where the first matrix is the covariance matrix of the forward link and the second is an appropriately designed “effective” interference covariance matrix. In this sense, our work is a generalization of optimal signalling along the dominant eigenmode of the transmit covariance matrix in the single-user case. Finally, the ergodic sum-rate for the general broadcast setting with$M$antennas at the transmitter and$M$-users (each with a single antenna) is obtained in terms of the covariance matrices of the links and the beamforming vectors.

This paper considers the optimum single cell power control maximizing the aggregate (uplink) communication rate of the cell when there are peak power constraints at mobile users, and a low-complexity data decoder (without successive decoding) at the base station. It is shown that the optimum power allocation is binary, which means that links are either “on” or “off.” By exploiting further structure of the optimum binary power allocation, a simple polynomial-time algorithm for finding the optimum transmission power allocation is proposed, together with a reduced complexity near-optimal heuristic algorithm. Sufficient conditions under which channel-state aware time division multiple access (TDMA) maximizes the aggregate communication rate are established. In a numerical study, we compare and contrast the performance achieved by the optimum binary power-control policy with other suboptimum policies and the throughput capacity achievable via successive decoding. It is observed that two dominant modes of communication arise, wideband or TDMA, and that successive decoding achieves better sum-rates only under near perfect interference cancellation efficiency. In this paper, we exploit the theory of majorization to obtain the aforementioned results. In the final part of this paper, we do so to solve power-control problems in the areas of femtocells and cognitive radio and find that, again, optimal solutions have a binary (or almost binary) character.

This paper considers maximizing the network-wide minimum supported rate in the downlink of a two-cell system, where each base station (BS) is endowed with multiple antennas. This is done for different levels of cell cooperation. At one extreme, we consider single cell processing where the BS is oblivious to the interference it is creating at the other cell. At the other extreme, we consider full cooperative macroscopic beamforming. In between, we consider coordinated beamforming, which takes account of inter-cell interference, but does not require full cooperation between the BSs. We combine elements of Lagrangian duality and large system analysis to obtain limiting SINRs and bit-rates, allowing comparison between the considered schemes. The main contributions of the paper are theorems which provide concise formulas for optimal transmit power, beamforming vectors, and achieved signal to interference and noise ratio (SINR) for the considered schemes. The formulas obtained are valid for the limit in which the number of users per cell, K, and the number of antennas per base station, N, tend to infinity, with fixed ratio β = K/N. These theorems also provide expressions for the effective bandwidths occupied by users, and the effective interference caused in the adjacent cell, which allow direct comparisons between the considered schemes.

This paper considers the optimum single cell power-control maximizing the aggregate (uplink) communication rate of the cell when there are peak power constraints at mobile users, and a low-complexity data decoder (without successive decoding) at the base station. It is shown, via the theory of majorization, that the optimum power allocation is binary, which means links are either “on” or “off”. By exploiting further structure of the optimum binary power allocation, a simple polynomial-time algorithm for finding the optimum transmission power allocation is proposed. Sufficient conditions under which channel-state aware time-division-multiple-access (TDMA) maximizes the aggregate communication rate are established. Finally, a simulation study is performed and it is observed that two dominant modes of communication arise, wideband or TDMA. The heuristic algorithm that chooses the best of these two modes is observed to be extremely close to optimal.

This paper considers base station (BS) cooperation in the form of coordinated beamforming, focusing on min-max fairness in the power usage subject to target SINR constraints. We show that the optimal beamforming strategies have an interesting nested zero-forcing structure. We then consider the asymptotic regime where the number of antennas at each BS and the number of users in each cell both grow large with their ratio tending to a finite constant. The limiting optimal beamformer structure is characterized in terms of the solution of a convex optimization problem. The dimensionality of this optimization problem is constant, as opposed to the problem of solving for the exactly optimal beamformer, and only knowledge of statistics is required to solve it. These asymptotic results provide insights into the average performance, as well as simple but efficient strategies for the finite system case. In particular, the optimal beamforming strategy from the large systems analysis only requires the base stations to have local instantaneous channel state information; the remaining parameters of the beamformer can be calculated using channel statistics which can easily be shared amongst the base stations.

Binary power control has been shown to be optimal in a variety of network conditions. In the context of sumrate maximisation in interference networks, our main result states that the optimal power policy for a link is binary if it only interferes with one other link in the network. Examples of networks which have at least one link with this attribute include the two-link interference channel (IC), the one-sided Wyner network and the many-to-one interference channel. Previous works have fully characterised the optimal power scheme for the two-link IC and they agree with our results. For the one-sided Wyner network, our main result leads to a problem which is tractable and can be solved using dynamic programming methods.

In a Wyner model each link only interferes with links adjacent to it. We consider the problem of finding the optimal power allocation which maximizes the sum-rate of such a network. Each link has a maximum power constraint and the power allocation is assumed to be time and frequency flat. In the case of 3- and 4-link Wyner models, we show that the optimal power schemes are in fact binary, i.e. a link is either switched off or turned on at full power. The problem is then extended to larger-sized Wyner models by limiting to optimal binary power schemes. Interesting phase transitions are observed as the interference cross-gain, ε, traverses various thresholds.

In this paper, we propose a method for user selection and channel estimation using compressed sensing. In particular, we consider a multiple-input multiple-output (MIMO) downlink broadcast scenario. We establish that full channel state information (and not just channel quality) for each self-selecting user can be obtained at the base-station via compressed sensing with no increase in overhead for the uplink feedback channel. We demonstrate the new method as a medium access technique for MIMO downlink broadcast with transmitter precoding and linear receiver processing.

The focus of this work is on the two user interference channel with two antennas at each transmitter and a single antenna at both users. We assume that both the transmitters use a linear beamforming scheme for signaling and the users treat interference as noise. The links are assumed to be spatially correlated and the focus is on understanding the structure of the beamforming vectors that maximize the average sum-rate as a function of the statistics of all the channels and the SNR level at both the transmitters. Building on recent work that studies Pareto optimality in a similar context, we show that (from the class of linear beamforming schemes) a rank-1 beamformer is always optimal when both the transmitters are of low-SNR. In general, the rank of the optimal beamforming matrix is a complicated function of the SNRs and channel statistics. Nevertheless, it is shown that the high-SNR optimal rank-1 beamformer is the generalized eigenvector of the two links as seen from each transmitter.

A spatially correlated broadcast setting with M antennas at the base station and M users (each with a single antenna) is considered. We assume that the users have perfect channel information about their links and the base station has only statistical information about each user's link. The base station employs a linear beamforming strategy with one spatial eigen-mode allocated to each user. The goal of this work is to understand the structure of the beamforming vectors that maximize the ergodic sum-rate achieved by treating interference as noise. In the M = 2 case, we first fix the beamforming vectors and compute the ergodic sum-rate in closed-form as a function of the channel statistics. We then show that the optimal beamforming vectors are the dominant generalized eigenvectors of the covariance matrices of the two links. It is difficult to obtain intuition on the structure of the optimal beamforming vectors for M > 2 due to the complicated nature of the sum-rate expression. Nevertheless, in the case of asymptotic M, we show that the optimal beamforming vectors have to satisfy a set of fixed-point equations.

This paper presents an overview of the theory and currently known techniques for multi-cell MIMO (multiple input multiple output) cooperation in wireless networks. In dense networks where interference emerges as the key capacity-limiting factor, multi-cell cooperation can dramatically improve the system performance. Remarkably, such techniques literally exploit inter-cell interference by allowing the user data to be jointly processed by several interfering base stations, thus mimicking the benefits of a large virtual MIMO array. Multi-cell MIMO cooperation concepts are examined from different perspectives, including an examination of the fundamental information-theoretic limits, a review of the coding and signal processing algorithmic developments, and, going beyond that, consideration of very practical issues related to scalability and system-level integration. A few promising and quite fundamental research avenues are also suggested.

The one tutorial paper and eight contributed papers in this special issue focus on cooperative communications in MIMO cellular networks.

We consider the power optimization problem of maximizing the sum rate of a symmetric network of interfering links in Gaussian noise. All transmitters have an average transmit power constraint, the same for all transmitters. This problem has application to DSL, as well as wireless networks. We solve this nonconvex problem by indentifying some underlying convex structure. In particular, we characterize the maximum sum rate of the network, and show that there are essentially two possible states at the optimal solution depending on the cross-gain (√ε) between the links, and/or the average power constraint: the first is a wideband (WB) state, in which all links interfere with each other, and the second is a frequency division multiplexing (FDM) state, in which all links operate in orthogonal frequency bands. The FDM state is optimal if the cross-gain between the links is above 1/√2. If √ε <; 1/√2, then FDM is still optimal provided the SNR of the links is sufficiently high. With √ε <; 1/√2, the WB state occurs when the SNR is low, but as we increase the SNR from low to high, there is a smooth transition from the WB state to the FDM state: For intermediate SNR values, the optimal configuration is a mixture, with some fraction of the bandwidth in the WB state, and the other fraction in the FDM state. We also consider an alternative formulation in which the power is mandated to be frequency flat. In this formulation, the optimal configuration is either all links at full power, or just one link at full power. In this setting, there is an abrupt phase transition between these two states.

We consider the power optimization problem of maximizing the sum rate of a symmetric network of interfering links in Gaussian noise. All transmitters have an average transmit power constraint, the same for all transmitters. We solve this nonconvex problem by indentifying some underlying convex structure. In particular, we characterize the maximum sum rate of the network, and show that there are essentially two possible states at the optimal solution depending on the cross-gain (radicisin) between the links, and/or the average power constraint: the first is a wideband (WB) state , in which all links interfere with each other, and the second is a frequency division multiplexing (FDM) state, in which all links operate in orthogonal frequency bands. The FDM state is optimal if the cross-gain between the links is above 1/radic2. If isin < 1/2, then FDM is still optimal provided the average power of the links is sufficiently high. With e < 1/2, the WB state occurs when the average power level is low (relative to the noise and the cross-gain factor), but as we increase the average power level from low to high, there is a smooth transition from the WB state to the FDM state: For intermediate average power levels, the optimal configuration is a mixture, with some fraction of the bandwidth in the WB state, and the other fraction in the FDM state. This work has applications to DSL, as well as to wireless networks.

We analyze the asymptotic performance of sparse signal recovery from noisy measurements. In particular, we generalize some of the existing results for the Gaussian case to sub-Gaussian and other ensembles. An achievable result is presented for the linear sparsity regime. A converse on the number of required measurements in the sub-linear regime is also presented, which cover many of the widely used measurement ensembles. Our converse idea makes use of a correspondence between compressed sensing ideas and compound channels in information theory.

We propose a novel access technique for cellular downlink resource sharing. In particular, a distributed self-selection procedure is combined with the technique of compressed sensing to identify a set of users who are getting simultaneous access to the downlink broadcast channel. The performance of the proposed method is analyzed, and its suitability as an alternate access mechanism is argued.

This paper considers the problem of minimizing outage probabilities in the downlink of a multiuser, multicell orthogonal frequency division multiple access (OFDMA) cellular network with frequency selective fading, imperfect channel state information, and frequency hopping. The task is to determine the allocation of powers and subcarriers for users to ensure that the user outage probabilities are as low as possible. We formulate a min-max outage probability problem and solve it under the constraint that the transmit power spectrum at each base station is flat. In particular, we obtain a subchannel allocation algorithm that has complexityO(LlogL) inL, the number of users in the cell. We also consider suboptimal but implementable approaches with and without the flat transmit power spectrum constraint. We conclude that the flat transmit spectrum approach has merit, and warrants further study.

We take a cross-layer design approach to study rate control in multihop wireless networks. Due to the lossy nature of wireless links, the data rate of a given flow becomes smaller and smaller along its routing path. As a result, the data rate received successfully at the destination node (the effective rate) is typically lower than the transmission rate at the source node (the injection rate). In light of this observation, we treat each flow as a "leaky-pipe" flow and introduce the notion of "effective utility" associated with the effective rate (not the injection rate) of each flow. We then explore rate control through effective network utility maximization (ENUM) in this study. Two network models are studied in this paper: (1) ENUM with link outage constraints with a maximum error rate at each link; (2) ENUM with path outage constraints where there exists an end-to-end outage requirement for each flow. For both models, we explicitly take into account the "thinning" feature of data flows and devise distributed hop-by-hop rate control algorithms accordingly. Our numerical examples corroborate that higher effective network utility and better fairness can be achieved by the ENUM algorithms than the standard NUM.

Due to multi-path fading and co-channel interference, wireless links are lossy in nature. As a result, the data rate of a given flow becomes "thinner and thinner" along its routing path, and the data rate received successfully at the destination node (theeffectiverate) is typically lower than the transmission rate at the source node (theinjectionrate). In light of this observation, each flow is treated as a "leaky-pipe" model in this study. Moreover, we introduce the notion of "effective utility" associated with the effective rate (not the injection rate) for each flow, and explore rate control mechanisms through effective network utility maximization (ENUM). We focus on two network models: (1) ENUM with link outage constraints with a maximum error rate at each link; (2) ENUM with path outage constraints where there exists an end-to-end outage requirement for each flow. For both problems, we explicitly take into account the "thinning" feature of data flows and devise distributed hop-by-hop rate control algorithms accordingly. Our numerical examples corroborate that higher effective network utility and better fairness among effective flow rates can be achieved by the ENUM algorithms than the standard NUM.

In this paper, we consider multicell processing on the downlink of a cellular network to accomplish ldquomacrodiversityrdquo transmit beamforming. The particular downlink beamformer structure we consider allows a recasting of the downlink beamforming problem as a virtual linear mean square error (LMMSE) estimation problem. We exploit the structure of the channel and develop distributed beamforming algorithms using local message passing between neighboring base stations. For 1-D networks, we use the Kalman smoothing framework to obtain a forward-backward beamforming algorithm. We also propose a limited extent version of this algorithm that shows that the delay need not grow with the size of the network in practice. For 2-D cellular networks, we remodel the network as a factor graph and present a distributed beamforming algorithm based on the sum-product algorithm. Despite the presence of loops in the factor graph, the algorithm produces optimal results if convergence occurs.

This paper investigates the interaction between end-to-end flow control and medium access control (MAC)-layer scheduling on wireless links. We consider a wireless network with multiple users receiving information from a common access point; each user suffers fading and a scheduler allocates the channel based on channel quality but is subject to fairness and latency considerations. We show that the fairness property of the scheduler is compromised by the transport-layer flow control of transmission control protocol (TCP) New Reno. We provide a receiver-side control algorithm, CLAMP, that remedies this situation. CLAMP works at a receiver to control a TCP sender by setting the TCP receiver's advertised window limit, and this allows the scheduler to allocate bandwidth fairly between the users.

This paper considers the problem of joint detection in the uplink of cellular multiaccess networks with base-station cooperation. Distributed multiuser detection algorithms with local message passing among neighbor base stations are proposed and compared in terms of computational complexity required in the base stations, the amount of serial communications among them, error rate performance, and convergence speed. The algorithms based on the belief propagation algorithm result in complexity and delay per base station which do not grow as the network size increases. In addition, it is observed that these algorithms have near single-user error rate performance for the fading channels considered. Thus it is illustrated that using the belief propagation algorithm, it is possible to have full frequency re-use and achieve near-optimal performance with moderate computational complexity and a limited amount of message passing between base stations of adjacent cells.

Frequency planning is a common intercell interference (ICI) management strategy in narrowband cellular networks. In this paper, we consider an alternative approach that allows full frequency reuse in every cell and deploys a network-wide linear minimum mean square error (LMMSE) receiver as the front-end processor to suppress ICI. Assuming equal transmit power for all users, we compare the achievable rate of the LMMSE receiver in the information-theoretic sense against the rates achieved by two different frequency reuse schemes, namely the conventional reuse scheme with single-cell processing and a reuse scheme that allows interference-free processing of signals from adjacent cells. We first compare the performance under a fixed path-gain model and then extend to a random fading model.

In this paper, derivatives of mutual information for a general linear Gaussian vector channel are considered. We consider two applications. First, it is shown how the corresponding gradient relates to the minimum mean squared error (MMSE) estimator and its error matrix. Secondly, we determine the directional derivative of mutual information and use this geometrically intuitive concept to characterize the capacity-achieving input distribution of the above channel subject to certain power constraints. The well-known water-filling solution is revisited and obtained as a special case. Also for shaping constraints on the maximum and the Euclidean norm of mean powers explicit solutions are derived. Moreover, uncorrected sum power constraints are considered. The optimum input can here always be achieved by linear precoding.

We consider a cellular network where base stations can cooperate to determine the signals to be transmitted on the downlink. Using a particular downlink beamformer structure, we recast our downlink beamforming problem as a virtual linear minimum mean square error (LMMSE) estimation problem. Based on this virtual set up, we remodel the network as a factor graph with loops and present a simple distributed cooperative scheme for base stations based on the sum-product algorithm. We study the condition for convergence for the distributed algorithm and demonstrate its performance via simulations.

In this correspondence, we determine the optimal power allocation to antennas in a Gaussian vector channel subject to lscrp-norm constrained eigenvalues. Optimal solutions are characterized by using directional derivatives of the mutual information. As the central result, the optimal power assignment is obtained as the level crossing points of a set of simple monotone functions. The well-known water-filling principle for sum power constraints is retrieved as the limiting case p=1. A nested Newton type algorithm is given for finding numerical solutions

This paper considers the problem of joint detection in the uplink of cellular multiaccess networks with base-station cooperation. Distributed multiuser detection algorithms with local passing among neighbor base stations are proposed and compared in terms of computational complexity required in the base stations, the amount of serial communications among them, error rate performance, and convergence speed. The algorithms based on the belief propagation algorithm result in complexity and delay per base station which do not grow as the network size increases. In addition, it is observed that these algorithms have near single user error rate performance for the fading channels considered. Thus it is illustrated that using the belief propagation algorithm, it is possible to use non-orthogonal signaling and still achieve near single user performance with moderate computational complexity and a limited amount of message passing between base stations of adjacent cells.

We provide scaling results for the sum capacity of the multi-access, uplink channel in a flat fading environment, when there is interference from other cells. We consider a scaling regime where the number of antennas per user remains fixed but the number of antennas at the base station and the number of users in each cell grow large together. We characterize the asymptotic behaviour of the spectral efficiencies in each cell, in three scenarios: 1) single cell processing with full frequency reuse 2) single cell processing, with frequency re-use partitioning of adjacent cells and 3) base station cooperative decoding (macro-diversity). It is shown that base station cooperation provides very significant gains in spectral efficiency over single cell processing.

In the present paper, we consider the problem of joint bandwidth (subcarriers) and power allocation for the downlink of a multi-user multi-cell OFDM cellular network. This resource allocation problem is formulated as a power minimization problem, subject to meeting the target rates of all users in the network. We develop a distributed solution to find the globally optimal allocation which determines the subcarrier and power allocation dynamically. In addition, we investigate the impact of reducing the complexity by reducing the number of degrees of freedom available in the optimization. In particular, we consider a static bandwidth allocation scheme, and a static power allocation scheme. The numerical results show that the penalty on network performance due to the reduction in the available degrees of freedom is not significant.

Scaling results for the sum capacity of the multiple access, uplink channel are provided for a flat-fading environment, with multiple-input-multiple-output (MIMO) links, when there is interference from other cells. The classical MIMO scaling regime is considered in which the number of antennas per user and per base station grow large together. Utilizing the known characterizations of the limiting eigenvalue distributions of large random matrices, the asymptotic behavior of the sum capacity of the system is characterized for an architecture in which the base stations cooperate in the joint decoding process of all users (macrodiversity). This asymptotic sum capacity is compared with that of the conventional scenario in which the base stations only decode the users in their cells. For the case of base station cooperation, an interesting "resource pooling" phenomenon is observed: in some cases, the limiting performance of a macrodiversity multiuser network has the same asymptotic behavior as that of a single-user MIMO link with an equivalent amount of pooled received power. This resource pooling phenomenon allows us to derive an elegant closed-form expression for the sum capacity of a new version of Wyner's classical model of a cellular network, in which MIMO links are incorporated into the model.

We consider a cellular network where base stations can cooperate to determine the signals to be transmitted on the downlink. In such a scenario, it would be possible to use "macroscopic" transmit beamforming to improve system performance. The downlink beamformer of interest is generalised from some transmit beamformers that have been shown to meet various optimality criteria in the literature. The particular downlink beamformer structure enables us to recast our downlink beamforming problem as a virtual LMMSE estimation problem. Based on this virtual set up, we exploit the structure of the channel and develop distributed beamforming algorithms using local message passing between neighbouring base stations. Two algorithms are outlined, both of which are based on the Kalman smoothing framework. The first algorithm is a forward-backward algorithm that produces optimal performance, but it has the disadvantage of a delay that grows linearly with array size. The second algorithm, which is a limited extent algorithm, solves the delay problem by using only local information

In ad-hoc networks, the optimal hop size is a trade-off between the transmission errors and the number of hops required. This paper investigates the optimal hop size and transmission strategy in networks with overlaid base stations. The objective is to maximize the minimum throughput any user achieves, excluding traffic that it relays. The optimum depends on the routing algorithm used, and a specific receiver-based algorithm is proposed. Optimal parameters are derived using a simplified model, and are shown by simulation to out-perform systems with the optimal position-invariant hop size. For this choice of objective, improvement is obtained by using one hop size for the base station and another for relays.

We consider the problem of multiuser detection in cellular networks. In particular, we present a distributed forward-backward algorithm with local message passing for efficient implementation of the linear minimum mean square error (LMMSE) receiver, for a simple model of a 1D cellular system. The distributed algorithm is based on the well-known interpretation of Kalman smoothing as a linear combination of the forward and backward filtered estimates. We also show that near-optimal performance can be achieved by only relying on information from a local linear segment of the entire array. This results in a limited extent distributed algorithm that greatly reduces processing delay, especially for large networks, yet with little loss in performance.

We derive the Linear Minimum Mean Square Error (LMMSE) receiver for Wyner's model of a linear cellular array. By exploiting the special structure of the channel model, we obtain explicit Mean Square Error (MSE) expressions and information capacity formulae for both finite-sized as well as infinite-sized linear cellular arrays. We show that the performance of an individual user becomes insensitive to the array size for large array sizes and that the proportion of users achieving almost the same performance converges to one, as the array size tends to infinity. The effects of intercell interference and noise on the performance of each user are also investigated.

Distributed decoding in the uplink of a rectangular planar cellular array with local message passing is considered. Two algorithms are proposed and compared: a BCJR-type algorithm applied to linear subgraphs, and belief propagation applied to the 2D graph of the cellular array.

The paper presents an improved version of CLAMP, a system that controls the behavior of TCP to enhance the performance of wireless access points. It only requires modifications to be made to the access network, and is totally compatible with TCP senders. We demonstrate its performance by simulation, and provide insight into the stability of the algorithm via analysis.

Wireless local area networks (WLANS) (1997) allow the transmission of bursty data traffic over fading, wireless links. We formulate and analyze a simple model of controlled ALOHA in a Rayleigh fading environment. We consider the application of a one bit per slot feedback control algorithm, from (Sylvie Ghez, et al., 1989), and propose a new algorithm involving higher rates of feedback per slot. Our algorithm is based on an optimization framework, which enables one to determine the desired rate of feedback, and we demonstrate the effectiveness of our algorithm in improving delay performance as compared to the 1-bit feedback algorithm.

The paper presents a solution for providing differentiated capacity allocation in an access network. The system is based on CLAMP (curtailing the large TCP advertised window to maximize performance), an algorithm that can differentiate between flows sharing the same FIFO queue. The system is suitable for access networks, such as those based on DSL and HFC modems and wireless LAN access points. The deployment of CLAMP is completely contained within the access network; no changes to the remainder of the network are required. CLAMP provides the opportunity to enforce local policies on TCP flows that originate from sources distributed globally. The performance of CLAMP is verified by both simulation and analysis.

In this paper, the minimal base-station density for a code-division multiple-access (CDMA) cellular radio network is determined such that the outage probability does not exceed a certain threshold. Base stations are assumed to be located on a regular triangular grid of minimum distance d, while mobiles are randomly distributed according to a two-dimensional Poisson point pattern. Each mobile may be connected to, at most, one of four surrounding base stations, effectively connecting and applying power control to the one with least attenuation. Thus, we model the use of macroscopic selection diversity. We obtain a normal approximation to the total interference power at a reference base station for a correlated log-normal shadowing law. The base station distance we obtain is proportional to the inverse of the square root of the traffic intensity, and we obtain the constant of proportionality, which is itself a function of the minimum acceptable carrier-to-interference (C/I) ratio and the maximum tolerable outage probability. Our formula for this distance can be used in network planning and design.

Performance comparisons are provided for different receivers in a time-slotted mobile network designed to carry delay-insensitive traffic. We show that even with one user per timeslot, capacity gains are achieved from some degree of spreading and multiuser detection against no-spreading and also against spreading plus matched filtering. Our results suggest that frequency partitioning between cells may be superior still, for the scenario considered in the present paper. However, our results also suggest that with optimal scheduling of users (not included in our model) full frequency reuse and no spreading may be optimal, but this issue requires further study.

We present a model for characterising the behaviour of the buffer at a base station router when TCP flow control is used in combination with a link layer retransmission protocol over a cellular wireless link. We show how our model can be used to predict packet latency, optimally dimension the buffer, and tune TCP to ensure maximum utilisation of the link, for specific wireless channel conditions. Finally we verify the model with simulation results obtained using the NS-2 simulator.

We investigate performance improvements through TCP window size optimisation achievable when TCP Reno is used over a highly heterogeneous network, such as an 802.11b wireless LAN or a GPRS-based internet connection. Initially, our modelling focuses on a constant rate, buffered access link, based on a loss-less wireless channel and with a bandwidth at least one order of magnitude less than its fixed-network continuation into the core. We implement the model guidelines on wireless LAN and GPRS access links, confirming that TCP throughput can be increased by optimising the TCP receiver window size to the link characteristics, and more significantly, that there exists a broad range of near-optimal awnd values.

We investigate the problem of reverse link resource allocation in a multi-class cellular network with specific network quality of service guarantees. Using maximum outage thresholds and outage probabilities, we approximate an acceptance region of feasible spatial intensity functions by a single linear constraint.

Much of the performance analysis on multiuser receivers for direct-sequence code-division multiple-access (CDMA) systems is focused on worst case near-far scenarios. The user capacity of power-controlled networks with multiuser receivers are less well-understood. Tse and Hanly (see ibid., vol.45, p.541-657, 1999) have shown that under some conditions, the user capacity of an uplink power-controlled CDMA cell for several important linear receivers can be very simply characterized via a notion of effective bandwidth. We show that these results extend to the case of antenna arrays. We consider a CDMA system consisting of users transmitting to an antenna array with a multiuser receiver, and obtain the limiting signal-to-interference (SIR) performance in a large system using random spreading sequences. Using this result, we show that the SIR requirements of all the users can be met if and only if the sum of the effective bandwidths of the users is less than the total number of degrees of freedom in the system. The effective bandwidth of a user depends only on its own requirement. Our results show that the total number of degrees of freedom of the whole system is the product of the spreading gain and the number of antennas. In the case when the fading distributions to the antennas are identical, we show that a curious phenomenon of "resource pooling" arises: the multiantenna system behaves like a system with only one antenna but with the processing gain the product of the processing gain of the original system and the number of antennas, and the received power of each user the sum of the received powers at the individual antennas.

We investigate the notion of "congestion" in spread spectrum wireless networks, such as those employing direct-sequence code-division multiple access. We find "congestion" to be multidimensional in nature, but two features emerge: (1) when congestion occurs, transmit powers and cell site interference levels increase and (2) capacity constraints are approached. Among other measures, we focus on a particular measure, /spl lambda/, which is immediately of interest, since /spl lambda/<1 is the condition for network feasibility. We relate /spl lambda/ both to the "power warfare" that arises as "capacity limits" are approached, and to the level of traffic in the network, where we consider traffic in regions ranging from local (single cells) to global (the whole network).

Multiuser receivers improve the performance of spread-spectrum and antenna-array systems by exploiting the structure of the multiaccess interference when demodulating the signal of a user. Much of the previous work on the performance analysis of multiuser receivers has focused on their ability to reject worst case interference. Their performance in a power-controlled network and the resulting user capacity are less well-understood. We show that in a large system with each user using random spreading sequences, the limiting interference effects under several linear multiuser receivers can be decoupled, such that each interferer can be ascribed a level of effective interference that it provides to the user to be demodulated. Applying these results to the uplink of a single power-controlled cell, we derive an effective bandwidth characterization of the user capacity: the signal-to-interference requirements of all the users can be met if and only if the sum of the effective bandwidths of the users is less than the total number of degrees of freedom in the system. The effective bandwidth of a user depends only on its own SIR requirement, and simple expressions are derived for three linear receivers: the conventional matched filter, the decorrelator, and the MMSE receiver. The effective bandwidths under the three receivers serve as a basis for performance comparison.

To meet the increasing capacity demand on wireless networks there have been intense efforts in the past decade on developing multiuser receiver structures which mitigate the interference between users in spread-spectrum and antenna array systems. While much of the research is performed at the physical layer, the capacity of networks with multiuser receivers and the associated resource allocation problems are less well-understood. We show that under some conditions, the capacity of a single cell for several important receivers can be very simply characterized via a notion of effective bandwidth: the QoS requirements of all the users can be met if and only if the sum of the effective bandwidths of the users is less than the total number of degrees of freedom in the system. The number of degrees of freedom is the processing gain in a spread-spectrum system and the number of antenna elements in an antenna array. The effective bandwidth of a user depends only on its own QoS requirement, expressed in terms of the desired signal-to-interference ratio. It is hoped that such an abstraction of resource requirement will help in bridging the resource allocation problems at the networking layer and multiuser techniques at the physical layer.

For pt.I see ibid., vol.44, no.7, p.2796-815 (1998). In multiaccess wireless systems, dynamic allocation of resources such as transmit power, bandwidths, and rates is an important means to deal with the time-varying nature of the environment. We consider the problem of optimal resource allocation from an information-theoretic point of view. We focus on the multiaccess fading channel with Gaussian noise, and define two notions of capacity depending on whether the traffic is delay-sensitive or not. In the present paper, we introduce a notion of delay-limited capacity which is the maximum rate achievable with delay independent of how slow the fading is. We characterize the delay-limited capacity region of the multiaccess fading channel and the associated optimal resource allocation schemes. We show that successive decoding is optimal, and the optimal decoding order and power allocation can be found explicitly as a function of the fading states; this is a consequence of an underlying polymatroid structure that we exploit.

In multiaccess wireless systems, dynamic allocation of resources such as transmit power, bandwidths, and rates is an important means to deal with the time-varying nature of the environment. We consider the problem of optimal resource allocation from an information-theoretic point of view. We focus on the multiaccess fading channel with Gaussian noise, and define two notions of capacity depending on whether the traffic is delay-sensitive or not. We characterize the throughput capacity region which contains the long-term achievable rates through the time-varying channel. We show that each point on the boundary of the region can be achieved by successive decoding. Moreover, the optimal rate and power allocations in each fading state can be explicitly obtained in a greedy manner. The solution can be viewed as the generalization of the water-filling construction for single-user channels to multiaccess channels with arbitrary number of users, and exploits the underlying polymatroid structure of the capacity region.

What is the capacity of the uplink of a radio network of receivers? We consider a spread spectrum model in which each user is decoded by all the receivers in the network (macrodiversity). We use a carrier-to-interference performance criterion that we derive from Shannon theory; each user must find the right transmitter power level to satisfy its carrier-to interference constraint. Satisfying this requirement for all users is equivalent to solving a fixed point problem. We use this power control problem to derive the network capacity region and find that the feasibility of a configuration of users is independent of their positions in the network; each user can be assigned a bandwidth that is independent of the user's position in the network. Our capacity region is an upper bound over all schemes that treat the interference of other users as pure noise. To show that the capacity can be realized in practice, we propose a decentralized power adaptation algorithm and prove global convergence to the fixed point via a monotonicity argument.

There is much current interest in spread spectrum wireless mobile communications and in particular the issue of spread spectrum wireless capacity. We characterize spread spectrum cellular capacity and provide a combined power control, cell-site selection algorithm that enables this capacity to be achieved. The algorithm adapts users' transmitter power levels and switches them between cell-sites, and it is shown that the algorithm converges to an allocation of users to cells that is optimal in the sense that interference is minimized. The algorithm is decentralized, and can be considered as a mechanism for cell-site diversity and handover. We provide numerical examples to show how effectively the algorithm relieves local network congestion, by switching users in a heavily congested cell to adjacent, less congested cells.>