Forward Error Correction (FEC) is used ubiquitously in the communication pipeline. We explore noncooperative decoding where we aim to recover the code rate of a linear block code. We present a metric to characterize the quality of the code rate recovery which uses any rank based estimation technique. We derive a closed form expression for this metric in terms of the algorithmic and the environmental parameters and assert that it should be low for good recovery. We use this metric to derive an expression for a better code rate estimate in high noise conditions and compare it with existing estimates. Finally we validate the derived expression for the metric and the improved performance in the code rate estimate by simulating the recovery of a Low Density Parity Check (LDPC) code. This also enables us to derive the optimal algorithmic parameters for recovery.

G networks aim to support the ambitious use cases outlined in the ITU IMT 2030 vision document. These use cases demand inherent support for precise localization and accurate sensing capabilities, necessitating advancements in angle, time, and phase measurement capabilities in the present networks and devices. The positioning and sensing requirements of $\mathbf{6 G}$ networks can be met by systems that support extreme massive MIMO, wide bandwidth, improved link budgets, and enhanced signal processing for positioning methods. This work proposes an angle-based position estimation method in a massive MIMOOFDM system capable of achieving centimeter-level positioning accuracy within the hardware and computational constraints. The method provides improved performance for both downlink angle of departure (DL-AoD) and uplink angle of arrival (ULAoA) techniques. Additionally, the proposed method satisfies the key performance indicators (KPIs) of 20 cm and 3 m positioning accuracy for the 90 percentile of user equipment (UEs) for outdoor and indoor factory scenarios respectively as required by releases 16 and 17 specifications of 3GPP. Furthermore, it outperforms traditional iterative algorithms (such as gradient descent and Newton-Raphson) by more than $2 \times$ in terms of 90 percentile positioning accuracy, while incurring three to four orders lower computational complexity and 50 percent lower memory complexity.

Massive MIMO antennas in cellular systems help support a large number of users in the same time-frequency resource and provide significant array gain for uplink reception. However, channel estimation in such large antenna systems can be tricky, not only since pilot assignment for multiple users is challenging, but also because the pilot overhead especially for rapidly changing channels can diminish the system throughput significantly. A pilotless transceiver where the receiver can perform blind demodulation can solve these issues and boost system throughput by eliminating the need for pilots in channel estimation. In this paper, we propose an iterative matrix decomposition algorithm for the blind demodulation of massive MIMO OFDM signals. This new decomposition technique provides estimates of both the user symbols and the user channel in the frequency domain simultaneously (to a scaling factor) without any pilots. Simulation results demonstrate that the lack of pilots does not affect the error performance of the proposed algorithm when compared to maximal-ratio-combining (MRC) with pilot-based channel estimation across a wide range of signal strengths.

Massive MIMO opens up attractive possibilities for next generation wireless systems with its large number of antennas offering spatial diversity and multiplexing gain. However, the fronthaul link that connects a massive MIMO Remote Radio Head (RRH) and carries IQ samples to the Baseband Unit (BBU) of the base station can throttle the network capacity/speed if appropriate data compression techniques are not applied. In this paper, we propose an iterative technique for fronthaul load reduction in the uplink for massive MIMO systems that utilizes the convolution structure of the received signals. We use an alternating minimisation algorithm for blind deconvolution of the received data matrix that provides compression ratios of 30-50. In addition, the technique presented here can be used for blind decoding of OFDM signals in massive MIMO systems.

In this work, we analyze the maximum number of wireless transmitters (nodes) that can be scheduled subject to interference constraints across the nodes. Given a set of nodes, the problem reduces to finding the maximum cardinality of a subset that can concurrently transmit without violating interference constraints. The resulting packing problem is a binary optimization problem, which is NP hard. We propose a semi-definite (SDP) relaxation for the NP hard problem and discuss the algorithm and the quality of the relaxation by providing approximation ratios for the relaxation.

Time selective sampling is capable of eliminating strong interference signals without requiring a high linearity receiver front-end. This can be used to implement a full-duplex transceiver front-end by sampling the weak received signal at the zero-crossings of the strong transmitted signal. In this work, we propose a circuit technique to directly sample the received RF signal at the antenna port by exploiting implicit voltage-to-delay conversion occurring in a full-duplex system. The sampler is implemented in a 65 nm CMOS process, and simulation results show a sensitivity of -67 dBm in the presence of a +5.5 dBm Tx signal. The received signal has a 10 MHz bandwidth, and the overall receiver consumes 33.2 mW from a 1.2 V power supply.

We propose distributed scheduling algorithms that guarantee a constant fraction of the maximum throughput for typical wireless topologies, and have O(1) delay and complexity in the network size. Our algorithms resolve collisions among pairs of conflicting nodes by assigning a master-slave hierarchy. When the master-slave hierarchy is chosen randomly, our algorithm matches the throughput performance of the maximal scheduling policies, with a complexity and delay that do not scale with network size. When the master-slave hierarchy is chosen based on the network topology, the throughput performance of our algorithm is characterized by a parameter of the conflict graph called the master-interference degree. For commonly used conflict graph topologies, our results lead to the best known throughput guarantees among the algorithms that have O(1) delay and complexity. Numerical results indicate that our algorithms out-perform the existing O(1) complexity algorithms like Q-CSMA.

In this paper, we derive the data-aided error vector magnitude (EVM) in an interference limited system when both the desired channel and interferers experience independent and nonidentically distributed κ-μ shadowed fading. Then, it is analytically shown that the EVM is equal to the square root of number of interferers when the desired channel and interferers do not experience fading. Furthermore, the EVM is derived in the presence of interference and noise, when the desired channel experiences κ-μ shadowed fading and the interferers experience independent and identical Nakagami fading. Moreover, using the properties of the special functions, the derived EVM expressions are also simplified for various special cases.

The coverage probability of a user in a mmwave system depends on the availability of line-of- sight paths or reflected paths from any base station. Many prior works modelled blockages using random shape theory and analyzed the SIR distribution with and without interference. While, it is intuitive that the reflected paths do not significantly contribute to the coverage (because of longer path lengths), there are no works which provide a model and study the coverage with reflections. In this paper, we model and analyze the impact of reflectors using stochastic geometry. We observe that the reflectors have very little impact on the coverage probability.

Device-to-device (D2D) communication is expected to increase the coverage probability by coexisting along with the conventional cellular systems in 5G technology. As the user equipments are often held closer to the human body, D2D links experience shadowing modelled by the κ-μ shadowed fading model. Though the cellular links do not experience κ-μ shadowed fading, the same is assumed here as it generalizes many popular fading distributions such as Rayleigh, Rician, Nakagami, κ-μ, η-μ, Hoyt etc. Thus the above assumption makes the results obtained here generic. We show that by neglecting shadowing in the D2D link, coverage probability of D2D user is overestimated at low SIR thresholds and under-estimated at high SIR thresholds. Though cellular links are interfered with by the D2D links, we observe that there is negligible impact on cellular coverage probability due to any change of fading parameters in the D2D links. Also, when all the links are Rayleigh faded, the D2D distance below which D2D mode is preferred to cellular mode of communication is obtained analytically.

We consider a carrier sense multiple access (CSMA)-based scheduling algorithm for a single-hop wireless network under a realistic signal-to-interference-plus-noise ratio model for the interference. We propose two local optimization-based approximation algorithms to efficiently estimate certain attempt rate parameters of CSMA called fugacities. It is known that adaptive CSMA can achieve throughput optimality by sampling feasible schedules from a Gibbs distribution, with appropriate fugacities. Unfortunately, obtaining these optimal fugacities is an NP-hard problem. Furthermore, the existing adaptive CSMA algorithms use a stochastic gradient descent-based method, which usually entails an impractically slow (exponential in the size of the network) convergence to the optimal fugacities. To address this issue, we first propose an algorithm to estimate the fugacities, that can support a given set of desired service rates. The convergence rate and the complexity of this algorithm are independent of the network size, and depend only on the neighborhood size of a link. Furthermore, we show that the proposed algorithm corresponds exactly to performing the well-known Bethe approximation to the underlying Gibbs distribution. Then, we propose another local algorithm to estimate the optimal fugacities under a utility maximization framework, and characterize its accuracy. Numerical results indicate that the proposed methods have a good degree of accuracy, and achieve extremely fast convergence to near-optimal fugacities, and often outperform the convergence rate of the stochastic gradient descent by a few orders of magnitude.

The fundamental problem in the design of a fullduplex radio is the cancellation of the self-interference (SI) signal generated by the transmitter. Current techniques for suppressing SI rely on generating a copy of the SI signal and subtracting it partly in the radio frequency (RF) and digital domains. A critical step in replicating the self-interference is the estimation of the multipath channel through which the transmitted signal propagates to the antenna. Since there is no prior model on the number of multipath reflections, current techniques assume a tap delay line filter (in the RF and digital domain) with a large number of taps, and estimate the taps in the analog and the digital domain. In this paper, using a linearization technique, we show that the self-interference channel in an indoor environment can be effectively modeled as H(f ) = C0- C1f in the frequency domain. Thus, the effective self-interference channel can be represented by two parameters C0and C1, irrespective of the multipath environment. We also provide experimental evidence to verify the above channel model and propose novel low-complexity designs for self-interference cancellation.

With the successful demonstration of in-band full-duplex (IBFD) transceivers, a new research dimension has been added to wireless networks. This paper proposes a use case of this capability for IBFD self-backhauling heterogeneous networks (HetNets). IBFD self-backhauling in a HetNet refers to IBFD-enabled small cells backhauling themselves with macro cells over the wireless channel. Owing to their IBFD capability, the small cells simultaneously communicate over the access and backhaul links, using the same frequency band. The idea is doubly advantageous, as it obviates the need for fiber backhauling small cells every hundred meters and allows the access spectrum to be reused for backhauling at no extra cost. This paper considers the case of a two-tier cellular network with IBFD-enabled small cells, wirelessly backhauling themselves with conventional macro cells. For clear exposition, the case considered is that of the Frequency Division Duplexing (FDD) network, where within access and backhaul links, the downlink (DL) and uplink are frequency duplexed (f1 , f2 respectively), while the total frequency spectrum used at access and backhaul (f1+f2 ) is the same. Analytical expressions for coverage and average DL rate in such a network are derived using tools from the field of stochastic geometry. It is shown that DL rate in such networks could be close to double that of a conventional TDD/FDD self-backhauling network, at the expense of reduced coverage due to higher interference in IBFD networks. For the proposed IBFD network, the conflicting aspects of increased interference on one side and high spectral efficiency on the other are captured into a mathematical model. The mathematical model introduces an end-to-end joint analysis of backhaul (or fronthaul) and access links, in contrast to the largely available access-centric studies.

Cloud radio networks coordinate transmission among base stations (BSs) to reduce the interference effects, particularly for the cell-edge users. In this paper, we analyze the performance of a cloud network with static clustering where geographically close BSs form a cloud network of cooperating BSs. Due to finite cooperation, the interference in a practical cloud radio cannot be removed, and in this paper, the distance-based interference is taken into account in the analysis. In particular, we consider centralized zero forcing equalizer and dirty paper precoding for canceling the interference. Bounds are developed on the signal-to-interference ratio distribution and achievable rate with full and limited channel feedback from the cluster users. The adverse effect of finite clusters on the achievable rate is quantified. We show that the number of cooperating BSs is more crucial than the cluster area when full channel state information from the cluster is available for precoding. Also, we study the impact of limiting the channel state information on the achievable rate. We show that even with a practically feasible feedback of about five to six channel states from each user, significant gain in mean rate and cell edge rate compared with conventional cellular systems can be obtained.

In this paper, we consider cellular networks with the base station locations modeled by a Poisson point process. However, unlike earlier works, we consider the cases of no fading and partial fading and analyze the asymptotic behavior of the distribution of the downlink signal-to-interference ratio (SIR) of a typical user. This non-fading case has been elusive since the standard Laplace trick cannot be used. We provide the asymptotics of the SIR distribution FSIR(θ) = P(SIR <; θ) as θ → 0 for the cases of no-fading and partial fading, where only the interfering base stations are subject to fading. We also introduce a new point process-the squared relative distance process-that facilitates the asymptotic analysis of the SIR and expedites simulations.

Recent successful demonstrations of radios for in-band full-duplex (IBFD) wireless systems offer interesting network-level case studies. The impact of such a capability on a cellular network as a whole is an open research area. IBFD self-backhauling for small cells is one interesting use case of such a capability proposed in this paper. It refers to the use of same frequency band for backhaul and access links, simultaneously. The advantage of IBFD self-backhauling is twofold - efficient reuse of channel resources along with convenient wireless back-hauling of dense small-cells without having to lay down fiber links every hundred meters. This work considers the case of a two-tier cellular network with IBFD-enabled small cells, wirelessly self-backhauling themselves with conventional macro cells. Analytical expressions for coverage and average downlink (DL) rate in such a network are derived using tools from the field of stochastic geometry. It is shown that DL rate in such networks could be close to double that of conventional time-division/frequency-division duplexed self-backhauling networks, at the expense of lower coverage due to increased interference. The interplay between increased interference on one side and high spectral efficiency on the other is captured through a mathematical model. Moreover, the proposed analysis is done jointly for backhaul (or fronthaul) and access links, in contrast to the largely available access-centric analyses.

It has recently been observed that the SIR distributions of a variety of cellular network models and transmission techniques look very similar in shape. As a result, they are well approximated by a simple horizontal shift (or gain) of the distribution of the most tractable model, the Poisson point process (PPP). To study and explain this behavior, this paper focuses on general single-tier network models with nearest-base station association and studies the asymptotic gain both at 0 and at infinity. We show that the gain at 0 is determined by the so-called mean interference-to-signal ratio (MISR) between the PPP and the network model under consideration, while the gain at infinity is determined by the expected fading-to-interference ratio (EFIR). The analysis of the MISR is based on a novel type of point process, the so-called relative distance process, which is a one-dimensional point process on the unit interval [0,1] that fully determines the SIR. A comparison of the gains at 0 and infinity shows that the gain at 0 indeed provides an excellent approximation for the entire SIR distribution. Moreover, the gain is mostly a function of the network geometry and barely depends on the path loss exponent and the fading. The results are illustrated using several examples of repulsive point processes.

It has recently been observed that the SIR distributions of a variety of cellular network models and transmission techniques look very similar in shape. As a result, they are well approximated by a simple horizontal shift of the distribution of the most tractable model, the Poisson point process. This paper makes a first step towards explaining this remarkable property by showing that the asymptotics of the SIR distribution near 0 and near infinity can only differ by a constant.

Motivated by recent high bandwidth communication systems, Inter-Symbol Interference (ISI) channels with 1-bit quantized output are considered under an average-power-constrained continuous input. While the exact capacity is difficult to characterize, an approximation that matches with the exact channel output up to a probability of error is provided. The approximation does not have additive noise, but constrains the channel output (without noise) to be above a threshold in absolute value. The capacity under the approximation is computed using methods involving standard Gibbs distributions. Markovian achievable schemes approaching the approximate capacity are provided. The methods used over the approximate ISI channel result in ideas for practical coding schemes for ISI channels with 1-bit output quantization.

This paper characterizes the performance of cellular networks employing multiple antenna open-loop spatial multiplexing (SM) techniques. We use a stochastic geometric framework to model distance depended inter cell interference. Using this framework, we analyze the coverage and rate using two linear receivers, namely, partial zero-forcing (PZF) and minimum-mean-square-estimation (MMSE) receivers. Analytical expressions are obtained for coverage and rate distribution that are suitable for fast numerical computation. In the case of the PZF receiver, we show that it is not optimal to utilize all the receive antenna for canceling interference. With α as the path loss exponent, Nttransmit antenna, Nrreceive antenna, we show that Nt⌈(1-2/α) (Nr/Nt-1/2)⌉ receive antennas for interference cancellation and the remaining antennas for signal enhancement (array gain). For both PZF and MMSE receivers, we observe that increasing the number of data streams provides an improvement in the mean data rate with diminishing returns. Also transmitting Nrstreams is not optimal in terms of the mean sum rate. We observe that increasing the SM rate with a PZF receiver always degrades the cell edge data rate while the performance with MMSE receiver is nearly independent of the SM rate.

In this paper, we analyze the downlink of a multi-antenna heterogeneous cellular network with distance-dependent interference. In particular, we consider open-loop spatial multiplexing (SM) with minimum mean-square estimation (MMSE) receiver for suppressing self-interference as well as other cell interference. Coverage probability and rate distribution are obtained with biased user association rule and inter-cell interference. The results show that using full rate SM at the macro base stations (BSs) degrades the data rate for a large percentage of cell-edge users compared to a low rate SM transmission. Therefore, the cell edge data rate can be improved substantially by reducing the SM rate at the macro BSs while maintaining full SM rate at the pico BSs. The loss in mean spectrum efficiency (SE) caused by the SM rate reduction is shown to be acceptable for the cases of interest.

In cellular networks, cell size reduction is an important technique for improving the spectral reuse and achieving higher data rates. In addition, it results in power savings as it leads to a decrease in transmit power. However, it is not clear if the transmit power can be indefinitely decreased with the cell sizes. In this paper, we analyze the impact of transmit power reduction (cell size reduction) on the performance of the network. More precisely, we obtain a lower bound on the transmit power such that a minimum coverage and a minimum data rate can be guaranteed. We then analyze the area power consumption metric, which denotes the total power consumed per unit area. Under the constraints of target coverage and target data rate, the area power consumption is minimized and the optimal base station density is obtained. For a path loss exponent α > 4, we observe the existence of a minimum cell size below which shrinking the cell would result in an overall increase of power. However, for α ≤ 4, there exists no such optimal cell-size, as the area power consumption increases with base station density.

Design of tunable multi-band time delay elements based on frequency translation is presented. The proposed topology exhibits time delay of multiple periods of the RF carrier. Two possible implementations of the proposed idea are presented and simulation results are shown for one such implementation. The implemented circuit exhibits an envelope delay of 2.5 ns with the RF carrier delay tunable from 0° to 360° in 45° steps in the 2.4 GHz ISM band.

In cellular networks, all base stations (BSs) do not continuously transmit i.e., the BSs transmit only when their queues are non-empty. This implies that the system resources are only partially loaded, and the dynamics of such a network differs significantly from that of a fully-loaded system. The coverage probability in a fully- and partially-loaded cellular network is analysed. We consider a regular spatial arrangement of base stations, and obtain the coverage probability in the presence of interference. More specifically, expressions for coverage probability are obtained for square and hexagonal lattices with full and partial loading. The coverage probability is obtained using properties of lattice sums which were first used in physics to analyse potentials in crystal structures.

In this paper we consider a multi-user spatial multiplexing (SM) cellular network, where Ntstreams are transmitted to Ntusers in the cell. Specifically, we obtain the coverage and rate expressions for a system employing zero-forcing (ZF) receiver. Compared to single stream transmission (SST), it is interesting to see that SM degrades the rate for a notable percentage of users. For the case of two and four receiver antennas, the increase in mean rate of SM is modest compared to single stream transmission (SST) while SST provides a gain over SM for cell edge users.

The orders of magnitude increase in projected demand for wireless cellular data require drastic increases in spatial reuse, with picocells with diameters of the order of 100-200 m supplementing existing macrocells whose diameters are of the order of kilometers. In this paper, we observe that the nature of interference changes fundamentally as we shrink cell size, with near line of sight interference from neighboring picocells seeing significantly smaller path loss exponents than interference in macrocellular environments. Using a propagation model proposed by Franceschetti, which compactly models increased interference in small cells, we show that the network capacity does not scale linearly with the reduction in cell size with standard frequency reuse strategies. Rather, more sophisticated resource sharing strategies based on beamforming and base station cooperation are required to realize the potential of small cells in providing high spectral efficiencies and quasi-deterministic guarantees on availability. Numerical results justifying these conclusions include Chernoff bounds on outage probability for random base station deployment (according to a spatial Poisson process), and simulations for deployment in a regular grid.

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

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

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

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

In orthogonal frequency division multiple access downlink, the signal-to-interference-noise ratio (SINR) of every subband at each user is estimated with the aid of pilots and the channel quality (some function of SINR's) is fed back to the base station (BS). This information is utilized by the BS for downlink scheduling. However, the SINR of the bands at each user are correlated due to the common interfering BSs. In this paper, we obtain the order statistics of band SINR's by considering the the co-channel interference and taking the correlations of interference across the bands into consideration. The order statistics are then used to analyse a best-m band feedback scheme, in which every users reports the index of their best-m bands to the BS. The BS utilizes this information and does greedy allocation of the bands to the users. We observe that utilizing the partial ordering of SINR's for channel allocation provides substantial gains over random allocation of bands to the users even in the presence of interference.

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

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

We consider a two-hop cellular system in which the mobile nodes help the base station by relaying information to the dead spots. While two-hop cellular schemes have been analyzed previously, the distribution of the node locations has not been explicitly taken into account. In this paper, we model the base station locations deterministically and the mobile stations by a point process on the plane. The node with the best channel to the destination that received information in the first hop acts as a relay to the destination (selection cooperation), and we obtain the success probability of this two-hop scheme, accounting for the interference from all other cells. We use tools from stochastic geometry and point process theory to analyze this two-hop opportunistic relaying scheme. Besides the results obtained, a main contribution of the paper is to introduce a mathematical framework that can be used to analyze arbitrary relaying schemes.

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

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

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

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

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

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

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

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

Outage probabilities in wireless networks depend on various factors: the node distribution, the MAC scheme, and the models for path loss, fading, and transmission success. In prior work on outage characterization for networks with randomly placed nodes, most of the emphasis was put on networks whose nodes are Poisson-distributed and where ALOHA is used as the MAC protocol. In this paper, we provide a general framework for the analysis of outage probabilities in the high-reliability regime. The outage probability characterization is based on two parameters: the intrinsic spatial contention γ of the network, introduced by Haenggi in a previous work, and the coordination level achieved by the MAC as measured by the interference scaling exponent κ introduced in this paper. We study outage probabilities under the signal-to-interference ratio (SIR) model, Rayleigh fading, and power-law path loss and explain how the two parameters depend on the network model. The main result is that the outage probability approaches γηκas the density of interferers η goes to zero, and that κ assumes values in the range 1 ≤ κ ≤ α/2 for all practical MAC protocols, where α is the path-loss exponent. This asymptotic expression is valid for all motion-invariant point processes. We suggest a novel and complete taxonomy of MAC protocols based mainly on the value of κ. Finally, our findings suggest a conjecture that bounds the outage probability for all interferer densities.

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

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

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

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

Superposition coding is a well-known capacity-achieving coding scheme for stochastically degraded broadcast channels. Although well-studied in theory, it is important to understand issues that arise when implementing this scheme in a practical setting. In this paper, we present a software-radio based design of a superposition coding system on the GNU Radio platform with the Universal Software Radio Peripheral acting as the transceiver frontend. We also study the packet error performance and discuss some issues that arise in its implementation.

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

We consider a time-slotted two-hop wireless system in which the sources transmit to the relays in the even time slots (first hop) and the relays forward the packets to the destinations in the odd time slots (second hop). Each source may connect to multiple relays in the first hop. In the presence of interference and without tight coordination of the relays, it is not clear which relays should transmit the packet. We propose four decentralized methods of relay selection, some based on location information and others based on the received signal strength (RSS).We provide a complete analytical characterization of these methods using tools from stochastic geometry. We use simulation results to compare these methods in terms of end-to-end success probability.

In a wireless network, the set of transmitting nodes changes frequently because of the MAC scheduler and the traffic load. Analyzing the connectivity of such a network using static graphs would lead to pessimistic performance results. In this paper, we consider an ad hoc network with half-duplex radios that uses multihop routing and slotted ALOHA for the network MAC contention and introduce a random dynamic multi-digraph to model its connectivity. We first provide analytical results about the degree distribution of the graph. Next, defining the path formation time as the minimum time required for a causal path to form between the source and destination on the dynamic graph, we derive the distributional properties of the connection delay using techniques from first-passage percolation and epidemic processes.We show that the delay scales linearly with the distance and provide asymptotic results (with respect to time) for the positions of the nodes which are able to receive information from a transmitter located at the origin. We also provide simulation results to support the theoretical results.

In the analysis of large random wireless networks, the underlying node distribution is almost ubiquitously assumed to be the homogeneous Poisson point process. In this paper, the node locations are assumed to form aPoissonclusterprocesson the plane. We derive the distributional properties of the interference and provide upper and lower bounds for its distribution. We consider the probability of successful transmission in an interference-limited channel when fading is modeled as Rayleigh. We provide a numerically integrable expression for the outage probability and closed-form upper and lower bounds. We show that when the transmitter-receiver distance is large, the success probability is greater than that of a Poisson arrangement. These results characterize the performance of the system under geographical or MAC-induced clustering. We obtain the maximum intensity of transmitting nodes for a given outage constraint, i.e., the transmission capacity (of this spatial arrangement) and show that it is equal to that of a Poisson arrangement of nodes. For the analysis, techniques from stochastic geometry are used, in particular the probability generating functional of Poisson cluster processes, the Palm characterization of Poisson cluster processes, and the Campbell-Mecke theorem.

The multihop spatial reuse Aloha (MSR-Aloha) protocol was recently introduced by Baccelli et aL, where each transmitter selects the receiver among its feasible next hops that maximizes the forward progress of the head of line packet towards its final destination. They identify the optimal medium access probability (MAP) that maximizes the spatial density of progress, defined as the product of the spatial intensity of attempted transmissions times the average per-hop progress of each packet towards its destination. We propose a variant called longest edge routing where each transmitter selects its longest feasible edge, and then identifies a packet in its backlog whose next hop is the associated receiver. The main contribution of this work (and of Baccelli et aL) is the use of stochastic geometry to identify the optimal MAP and the corresponding optimal spatial density of progress.

In this paper we derive the tail properties of interference for any stationary and isotropic spatial distribution of transmitting nodes. Previously the properties of interference were known only when the nodes are distributed as a homogeneous Poisson point process on the plane. We show the effect of a singular path loss model on the tail distribution of the interference. When the path loss function has a singularity at the origin, the interference is shown to be a heavy-tailed distribution under very mild conditions. When the path loss is bounded, the distribution of the interference is predominantly dictated by the fading. We also provide asymptotically tight upper and lower bounds on the CDF of the interference, and discuss the effectiveness of using a Gaussian approximation for modelling the interference.

The transport capacity of a dense ad hoc network with n nodes scales like radicn. We show that the transport capacity divided by radicn approaches a non-random limit with probability one when the nodes are i.i.d. distributed on the unit square. We prove that the transport capacity under the protocol model is a subadditive Euclidean functional and use the machinery of subadditive functions in the spirit of Steele to show the existence of the limit.

We consider a hybrid wireless network, in which the low-power nodes collect data and pass it to the data aggregation nodes (base stations). The low-power nodes are assumed to form a Poisson point process and communicate to the base stations using spread spectrum. We derive bounds to the probability of sensor node isolation, when the base stations are arranged randomly or in a regular fashion.