Abstract This paper presents an exact statistical analysis for the best relay location in a random two‐way relay network whose channels are subject to multi‐slope path loss and Rayleigh fading. In this network, relays are distributed randomly as a two‐dimensional Poisson point process, and the best relay is selected according to a max–min criterion. The midpoint between the two sources is adopted as a reference point and the relays are indexed such that the closer to the reference point, the smaller is the index. An exact analytical expression is derived for the probability that the th nearest relay to the reference point is the best relay. Then, a detailed statistical analysis for the location of the best relay with respect to the reference point is presented. In each case, a low‐complexity approximation is also derived and its accuracy is verified by numerical simulation. The proposed analysis demonstrates the counter‐intuitive fact that the best relay in a random two‐way relay network is quite unlikely to be located on, or very close to the reference point. Numerical results also suggest that the proposed analysis can be used to restrict the search region for finding the best relay.

Small cells are regarded as a promising solution for improving the coverage and spectral efficiency of the fifth generation (5G) cellular networks. Small cell networks utilize low transmission power levels and thus, are appropriate for deploying full-duplex (FD) technology. In this paper, a hybrid full/half duplex (FD/HD) small cell network exploiting fractional frequency reuse (FFR) and fractional power control (FPC) for interference mitigation is considered. Theoretical expressions for the coverage probability and the average sum-rate in uplink and downlink directions are derived for systems that make use of conventional frequency reuse, hard FFR, and soft FFR. The impact of various system parameters, such as power control parameter, small base station (SBS) density, and self-interference cancellation (SIC) parameters on system performance are investigated. The numerical experiments show that SBSs tend to operate in FD mode for large values of SBS density and SIC level. Also, interestingly, the optimal sum-rate is achieved when all SBSs operate either in FD or in HD mode. Finally, it is observed that exploiting FFR techniques in FD networks making use of FPC, significantly improves downlink coverage probability.

In massive MIMO wiretap settings, the base station can significantly suppress eavesdroppers by narrow beamforming toward legitimate terminals. Numerical investigations show that by this approach, secrecy is obtained at no significant cost. We call this property of massive MIMO systems "secrecy for free" and show that it not only holds when all the transmit antennas at the base station are employed, but also when only a single antenna is set active. Using linear precoding, the information leakage to the eavesdroppers can be sufficiently diminished, when the total number of available transmit antennas at the base station grows large, even when only a fixed number of them are selected. This result indicates that passive eavesdropping has no significant impact on massive MIMO systems, regardless of the number of active transmit antennas.

In this paper, we study the impacts of transmit antenna selection on the secrecy performance of massive MIMO systems. We consider a wiretap setting in which a fixed number of transmit antennas are selected and then confidential messages are transmitted over them to a multi-antenna legitimate receiver while being overheard by a multi-antenna eavesdropper. For this setup, we derive an accurate approximation of the instantaneous secrecy rate. Using this approximation, it is shown that in some wiretap settings under antenna selection the growth in the number of active antennas enhances the secrecy performance of the system up to some optimal number and degrades it when this optimal number is surpassed. This observation demonstrates that antenna selection in some massive MIMO settings not only reduces the RF-complexity, but also enhances the secrecy performance. We then consider various scenarios and derive the optimal number of active antennas analytically using our large-system approximation. Numerical investigations show an accurate match between simulations and the analytic results.

Antenna selection is an effective means to address the cost and complexity issues in massive MIMO systems. This paper studies the performance limits of massive MIMO systems under practical antenna selection algorithms. A massive MIMO system is considered in which the transmitter employs only a fixed-size subset of the available antennas with the strongest channel gains. For this setup, the input-output mutual information of the system is shown to be well-approximated by a normal random variable when the number of transmit antennas is large. The mean of this random variable grows proportional to the number of antennas and its variance vanishes in the large-system limit. This behavior of the mutual information generalizes the well-known channel hardening property in massive MIMO systems to the cases with antenna selection. Our investigations show that 90% of the ergodic rate achieved by full antenna selection can be achieved by selecting less than 30% of the transmit antennas. Using large-system analysis, we drive an analytical expression for the number of selected antennas that maximizes the energy efficiency. This number is also derived for the case where a certain fraction of the totally achievable rate is aimed to be achieved. Our numerical investigations demonstrate a close match between the analytical and simulation results even for scenarios with not-so-large dimensions.

This paper studies the impact of transmit antenna selection on the secrecy performance of massive MIMO wiretap channels. We consider a scenario in which a multi-antenna transmitter selects a subset of transmit antennas with the strongest channel gains. Confidential messages are then transmitted to a multi-antenna legitimate receiver while the channel is being overheard by a multi-antenna eavesdropper. For this setup, we approximate the distribution of the instantaneous secrecy rate in the large-system limit. The approximation enables us to investigate the optimal number of selected antennas which maximizes the asymptotic secrecy throughput of the system. We show that increasing the number of selected antennas enhances the secrecy performance of the system up to some optimal value, and that further growth in the number of selected antennas has a destructive effect. Using the large-system approximation, we obtain the optimal number of selected antennas analytically for various scenarios. Our numerical investigations show an accurate match between simulations and the analytic results even for not so large dimensions.

Consider a fading Gaussian MIMO channel with Nttransmit and Nrreceive antennas. The transmitter selects Ltantennas corresponding to the strongest channels. For this setup, we study the distribution of the input-output mutual information when Ntgrows large. We show that, for any Nrand Lt, the distribution of the input-output mutual information is accurately approximated by a Gaussian distribution whose mean grows large and whose variance converges to zero. Our analysis depicts that, in the large limit, the gap between the expectation of the mutual information and its corresponding upper bound, derived by applying Jensen's inequality, converges to a constant which only depends on Nrand Lt. The result extends the scope of channel hardening to the general case of antenna selection with multiple receive and selected transmit antennas. Although the analyses are given for the large-system limit, our numerical investigations indicate the robustness of the approximated distribution even when the number of antennas is not large.

The throughput performance of a random cooperative medium access control (CoopMAC) network in the presence of shadowing and path loss is considered. The nodes are assumed to be distributed as a homogeneous two‐dimensional Poisson point process with constant intensity. The helpers are divided into several tiers each having a distinct operating region and a distinct cooperative throughput. Then, the conditions under which a helper in a particular tier can improve the transmission rate between a given pair of nodes are examined. Based on these conditions, an exact analytical expression is derived for the average cooperative throughput of a Poisson CoopMAC network that is subject to path loss and shadowing. The expression is then used to investigate the effects of shadowing, intensity of helpers and distance between source and destination nodes on the average cooperative throughput of the network.

The cooperative medium access control (CoopMAC) protocol in the presence of randomly distributed nodes and shadowing is considered. The nodes are assumed to be distributed according to a homogeneous 2-D Poisson point process. A new scheme is proposed for helper selection and throughput performance analysis, which depends on the shadowing parameters as well as the distribution of helpers. In the proposed protocol, the potential helpers are divided into several tiers based on their cooperative transmission rate in a way that the lower the tier index, the higher its priority. When there are several helpers of the same tier, the helper that is less affected by shadowing is chosen for cooperation. The helper tiers are classified into five different classes according to their operating regions. Then, upper and lower bounds are derived for the average cooperative throughput of the proposed CoopMAC scheme by using this classification. It is observed that the proposed scheme readily outperforms the conventional CoopMAC protocol in having larger average throughput. It is also seen that the cooperative throughput of the proposed scheme approaches the upper bound when the density of nodes increases.

The problem of multiband cooperative spectrum sensing with imperfect reporting channels is considered. It is assumed that the secondary users (SUs) make use of an energy detection scheme to sense a number of frequency subbands (assigned to primary users) and report their sensing results to a fusion centre through noisy channels. Exact expressions for the opportunistic throughput, false alarm and missed detection probabilities are derived in terms of the overall sensing‐plus‐reporting time, sensing subintervals, reporting subintervals and decision thresholds for each SU in each subband. Then, an optimisation problem is formulated that aims to maximise the opportunistic throughput of the cognitive radio network so as to maintain the interference incident on the primary network below a given level. The constraints of the optimisation problem are shown to be non‐convex and the conditions under which these constraints become convex are examined. It is also shown that the objective function of the problem is non‐convex and two suboptimal techniques are introduced to effectively solve the problem using the algorithms developed for solving convex optimisation problems.

Random wireless networks with finite number of nodes distributed uniformly in a square-shaped finite region are considered. The transmission channels are assumed to experience Nakagami-m fading. A closed-form expression for the cumulative distribution function (CDF) of the interference power imposed on two randomly-located communicating nodes is derived. In contrast to most of the existing literature, the receiving node is not necessarily required to be located at the center of the network region. Two packet traffic patterns, viz., slotted-synchronous and slotted-asynchronous are considered and closed-form expressions for the CDF of the interference is obtained for each traffic pattern. Computer simulation illustrates the validity of the theoretical analyses.

A new approach in fairness is proposed by using a probabilistic relay assignment strategy for cooperative communication systems. In this approach, relays are allocated to sources based on a probabilistic relay assignment function, which is characterised by the outage probability. To examine the proposed relay assignment strategy, an exact expression for the outage probability of an opportunistic coded cooperation diversity system is derived. It is assumed that the relays in this system are distributed according to a two‐dimensional homogeneous Poisson point process, and the transmission channels undergo Rayleigh fading as well as path loss. It is observed that the proposed strategy reduces the number of requests for using the relays and, thus, utilises the relays more efficiently. Furthermore, compared to the conventional opportunistic relay assignment strategy, the total power consumed by the relays decreases, while the quality of service requirements are still satisfied.

Multiaccess interference (MAI)-plus-noise whitening for detecting impulse radio ultra-wide bandwidth (IR-UWB) signals transmitted over ideal free-space and the IEEE 802.15.3a channels is considered. IR-UWB signals are very sparse in time and, thus, MAI-plus-noise whitening cannot introduce intersymbol interference (ISI) in IR-UWB systems operating on an ideal free-space channel. In addition, ISI in UWB multipath fading channels can be eliminated by a proper choice of the frame duration. An analytical expression for the signal-to-interference-plus-noise ratio (SINR) of IR-UWB systems after MAI-plus-noise whitening is derived and the SINR improvement due to whitening is investigated. It is shown that whitening can improve the performance of a variety of the well-known IR-UWB receivers, viz., soft-limiting, P-order metric, optimal, and the conventional matched filter receivers. It is also observed that MAI-plus-noise whitening can improve the overall SINR of the system and, thus, decrease the complexity of Rake receivers through reducing the number of their processing branches.

The performance of opportunistic relaying in a dual-hop amplify-and-forward relay network where the relaying nodes are distributed according to a homogeneous two-dimensional Poisson point process with fixed density is analyzed. Largely ignored in the literature, this assumption leads to more realistic results, as in a typical practical scenario neither the number of relays nor their distances from the source and destination are known. An exact expression for the outage probability of this cooperative system for general fading environments and different types of relaying is derived. The expression is then {simplified under an assumption that the radius of the relay deployment region is sufficiently large}, and specialized to additive white Gaussian noise (no fading), Rayleigh fading and severe (half-Gaussian) fading environments. Simple and tight upper and lower bounds on the outage probability are also derived. Simulation results validate the theoretical analyses and verify the accuracies of the proposed bounds.

An exact expression for the outage probability of opportunistic relaying in a dual-hop amplify-and-forward relay network is derived for general fading environments and the case where the source and destination nodes make use of directional antennas. The relaying nodes are assumed to be distributed according to a homogeneous two-dimensional Poisson point process with fixed density. This assumption is of great practical importance as in a typical practical scenario, the number of relays as well as their distances from the source and destination are random. It is observed that under some circumstances, a directional antenna at the source may permit more efficient deployment of the relay network than the case where an omnidirectional antenna is used.

The Nakagami-0.5 distribution is an important special case of the Nakagami distribution as it represents a worst case fading scenario. This scenario is of particular significance for wireless applications with high quality of service requirements. The bit error probability (BEP) performances of three basic diversity combining schemes in Nakagami-0.5 fading are considered. It is shown that the error rate performances of dual branch equal gain and selection combining (SC) diversity are identical regardless of modulation format. It is also shown that L-branch maximal ratio combining diversity in Nakagami-0.5 fading has the same BEP performance as single branch reception in Nakagami-L/2 fading with L times the transmission power of each branch. A useful upper bound for the BEP of L-branch SC diversity in Nakagami-0.5 fading is also derived. The performance degradation for the worst case Nakagami-0.5 fading relative to Rayleigh fading can be as much as 24.6 dB for a dual-diversity receiver at target BEP of 10-6. The additional resources required to restore a specified performance level, as increased channel signal-to-noise ratio and as number of additional diversity branches, are quantified. It is concluded that worst case Nakagami channels can result in dramatically poorer performance than Rayleigh channels, making proper system design and evaluation essential to achieve a required transmission quality.

Multiple-symbol differential detection (MSDD) of differentially encoded phase-shift keying (PSK) signals in the presence of random frequency variation and additive white Gaussian noise is studied. It is shown that frequency variation distorts the transmitted signal through attenuating its amplitude and introducing a time-varying phase shift to the information symbols. A double differential PSK (DDPSK) modulation scheme is then introduced and a MSDD for detecting DDPSK signals in the presence of frequency offset is proposed. It is shown that the proposed receiver is robust to the distortions caused by the random frequency variation. A lower bound on the error probability of the proposed MSDD receiver is also derived and compared to that of an autocorrelation demodulator for the case where the observation interval approaches infinity.

The problem of transmitter pulse-shaping design for suppressing multiple access interference in bandlimited multiaccess communication systems is considered. The design is laid out in such a way that the transmitter-receiver (T-R) combination maximizes the signal-to-interference-plus-noise ratio (SINR). It is shown that the optimum transmitter filter is composed of a sum of two sinc functions with different gains and bandwidths. An exact expression for the output SINR of the proposed T-R combinations is derived and compared to that of the conventional matched filter (CMF) receiver with a root raised-cosine transmitter filter. The SINRs of the proposed T-R pairs and the CMF receiver in the presence of timing error are also analyzed and accurate expressions for them are derived.

The problem of cochannel interference (CCI) suppression using a noise-plus-interference whitening matched filter (WMF) is addressed. Binary phase-shift keying modulated transmission over a Nakagami-m fading channel is considered in a bandlimited microcellular wireless system. It is shown that the signal-to-interference-plus-noise ratio (SINR) of the WMF can not exceed that of the conventional matched filter (CMF) receiver for synchronous CCI, but in the asynchronous channel, CCI whitening can be used to improve receiver performance. The SINR-maximizing filter (SINRMF) in an asynchronous channel is derived and shown to be composed of a WMF followed by a discrete time filter. The SINRs of the WMF and SINRMF receivers are analytically evaluated for a standard raised-cosine (RC) and a Beaulieu-Tan-Damen pulse. It is shown that for the RC pulse, the WMF can achieve a SINR gain as large as 1.76 dB over the CMF receiver provided that the transmission is free of intersymbol interference (ISI). The SINR of the ISI-impaired system is also evaluated and the conditions under which this system can achieve close to ISI-free SINR are studied. The SINR is evaluated for the SINRMF and it is shown that this filter can restore much of the SINR loss incurred due to ISI introduced by the WMF.

The problem of cochannel interference mitigation using interference-plus-noise whitening receiver design in the presence of intersymbol interference (ISI) is considered. The effect of ISI on the signal-to-interference-plus-noise ratio (SINR) of the interference whitening receiver is examined. Then, two methods are proposed to maximize the SINR without introducing ISI. In the first method, the transmitter and receiver filters are designed to maximize the SINR while their overall spectrum maintains a given Nyquist spectrum to avoid ISI. In the second method, the transmitter filter is assumed to be fixed and only the receiver filter is designed to achieve maximum SINR without introducing ISI. The SINR of the ISI-free SINR-maximizing filter is then analytically compared with that of the conventional matched filter receiver and the interference whitening receiver. Numerical results are presented for the cases when standard raised-cosine and Beaulieu-Tan-Damen pulses are used in the system.

Two multiuser combining receiver structures for space diversity reception of a signal distorted by cochannel interference and additive white Gaussian noise are derived. The desired and interfering signals are assumed to be binary phase- shift keying modulated and Rayleigh-faded. The first receiver concurrently minimizes the error probability for all users and is composed of a bank of maximal ratio combiners (MRC's) followed by a maximum-likelihood detector. In the second receiver, the error probability is minimized only for the desired user and it is shown that the receiver comprises an MRC bank followed by a likelihood ratio tester that picks the globally best hypothesis. Simulation results illustrate the superiority of the proposed detection strategies over a receiver which makes use of optimum combining, especially for small values of signal-to- interference power ratios.

The detection of a binary phase-shift keying signal distorted by like-modulated cochannel interference and noise using a noise-plus-interference whitening matched filter (WMF) is considered. The interfering signals are assumed to be independent and Rayleigh-faded. It is shown that in a synchronous channel, the signal-to-interference-plus-noise ratio (SINR) at the output of a WMF can not exceed that of the conventional matched filter (CMF) receiver. It is observed that in a synchronous channel, an interference WMF degrades the performance both through decreasing the SINR and introducing intersymbol interference (ISI). In contrast, in an asynchronous channel an optimal WMF can improve the SINR relative to the CMF receiver. It is shown that for a standard raised-cosine pulse the maximum achievable SINR gain over the CMF receiver is 1.76 dB. The SINR of the WMF receiver in asynchronous CCI is also evaluated for the case when a linear equalizer is used to mitigate the ISI caused by the WMF.

An analytical expression for the bit-error rate (BER) of an individually optimal receiver in a two-user synchronous channel is derived. The desired signal is a binary phase-shift keying (BPSK) signal corrupted by a like-modulated interference and additive white Gaussian noise (AWGN). The BER expression decomposes into the probability of error of BPSK in AWGN plus an interference term which tends to zero when either the interferer power or the interferer signal correlation with the desired signal approaches zero

An exact expression for the bit error rate of a synchronous maximum-likelihood receiver used to detect a bandlimited binary phase-shift keying (BPSK) signal in the presence of a similar BPSK signal, additive white Gaussian noise and imperfect carrier phase recovery is derived. The users are assumed to employ pulse-shaping filters whose impulse responses satisfy Nyquist's first criterion. The receiver's error probability is compared with that of the perfect phase recovery case to show its sensitivity to carrier phase errors. It is shown that the receiver is more robust to carrier phase mismatch at high signal-to-interference ratios (SIR's) than low SIR's

An exact expression for the bit error probability of a maximum-likelihood receiver used to detect two bandlimited binary phase-shift keying signals in a synchronous additive white Gaussian noise channel in the presence of carrier phase recovery errors is derived. The users employ pulse-shaping filters whose impulse responses satisfy Nyquist's first criterion for zero intersymbol interference. The receiver's error probability is compared with that of the perfect phase recovery case for various values of signal-to-interference ratio (SIR) to show its sensitivity to carrier phase errors. It is shown that the receiver is more robust to carrier phase mismatch at large values of SIR than at small values of SIR.

A new and intuitive expression for the bit error probability (BEP) of a two-user synchronous jointly optimum receiver in an additive white Gaussian noise (AWGN) channel is derived. The desired and interfering users are assumed to use binary phase-shift keying (BPSK) modulation. The new expression decomposes into the BEP of BPSK in AWGN plus a term due to the interference. It is shown that the term due to interference vanishes when the interference power or its correlation with the desired signal tends to zero.

The exact bit error rate (BER) of a synchronous individually optimal receiver (IOR) used to detect a binary phase-shift keying (BPSK) signal distorted by a like-modulated signal and additive white Gaussian noise (AWGN) is derived. It is shown that the BER expression decomposes into the probability of error of BPSK in AWGN plus an interference term. It is observed that as the noise decreases the IOR performance approaches the performance of a single cochannel interferer jointly optimal receiver.

The conventional multiple-symbol differential detection (MSDD) of differential phase-shift keying (DPSK) signals is studied in the presence of frequency offset. It is shown that in the case of nonzero frequency offset, the performance of the conventional MSDD receiver degrades by increasing the number of observed samples. A double DPSK (DDPSK) modulation scheme is then introduced and it is shown that in the presence of nonzero frequency offset, an MSDD receiver with DDPSK modulation outperforms a conventional MSDD receiver with DPSK modulation, when both receivers use a large number of received samples. Examples lead to a conjecture that the performance of an optimum MSDD receiver with DDPSK modulation and an infinite number of received samples, approaches that of a conventional DPSK demodulator with two received samples.

A synchronized per survivor processing (PSP) maximum likelihood sequence detection (MLSD) receiver is presented for a fast frequency-selective Rayleigh fading channel and large carrier frequency offset. It is shown that, by incorporating the synchronization parameters (the timing error, carrier frequency and phase offsets) into the channel-impulse response (CIR) and modifying the resulting state-space model by a differential approach, the time-varying carrier frequency offset can be effectively tracked using a simple least mean square (LMS) estimator. New criteria are proposed based on the smoothness of the estimated channel derivatives. New criteria are proposed based on this fact that, for smoothly time-varying CIR and frequency offset, the magnitude of the CIR time derivative compared with the magnitude of CIR should be very small. It is illustrated that the new criteria and the conventional mean square error (MSE) are complementary.

This paper presents a maximum likelihood sequence detection (MLSD) receiver which performs joint data detection, channel equalization and synchronization over a fast frequency-selective Rayleigh fading channel. An optimal per-survivor processing (PSP) technique is employed which is a combination of statistical channel modeling and differential Kalman filter. It is shown that by incorporating the synchronization parameters into the channel impulse response and modification of the resulting state space model by a differential approach, frequency synchronization can be achieved by a simple adaptive algorithm in addition to data detection and channel estimation. It is also shown that by applying the so called approach, the differential Kalman filter could be simplified to a simple LMS estimator without any considerable lack in performance.