Search

This paper investigates the performance of a network-coded cooperative (NCC) system in an underlay cognitive radio network (CRN). The primary network (PN) consists of a single transmitter-receiver pair, while the secondary network (SN) is composed of N sources, a single destination, and M decode-and-forward (DF) relays, employing network coding (NC) over non-binary Galois field. For the SN, a closed-form expression and an asymptotically tight end-to-end (E2E) outage probability (OP) are derived and the diversity order is quantified. Compared to the existing literature, the proposed CRN NCC has four main distinguishable features: i) it is applicable to general CRN NCC network settings with arbitrary number of sources and relays; ii) it considers general relay selection and independent and non-identically distributed (i.n.i.d.) Nakagami-m fading channels; iii) it accounts for maximum transmit power at the SN and assumes secondary-to-primary (S2P) and primary-to-secondary (P2S) interference links; and iv) it provides a generalization of previous works and includes existing results in the literature as special cases. Simulation results are further provided to confirm the correctness of our analysis.

This paper considers joint optimization of spectrum sensing, channel probing, and transmission power control for a single-channel secondary transmitter that operates with harvested energy from ambient sources. At each time slot, to maximize the expected secondary throughput, the transmitter needs to decide whether or not to perform the operations of spectrum sensing, channel probing, and transmission, according to energy status and channel fading status. First, we model this stochastic optimization problem as a two-stage continuous-state Markov decision process, with a sensing-and-probing stage and a transmit-power-control stage. We simplify this problem by a more useful after-state value function formulation. We then propose a reinforcement learning algorithm to learn the after-state value function from data samples when the statistical distributions of harvested energy and channel fading are unknown. Numerical results demonstrate learning characteristics and performance of the proposed algorithm.

Device-to-device (D2D) networks underlaying a millimeter-wave cellular network have great potential for capacity growth. Thus, it is important to characterize the outage of such a D2D link incorporating millimeter-wave propagation effects, user association rules, power control, and spatial randomness. To this end, we model the locations of cellular transmitters and receivers as homogeneous Poisson point processes and those of the D2D nodes as a Matern cluster process, and incorporate blockages due to random objects, sectored antenna patterns, log-distance path loss, and Nakagami- $m$ fading. Furthermore, we consider antenna gain inversion-based power control, and peak power constraints for D2D devices along with distinct path loss exponents and distinct fading severities for line-of-sight (LOS) and non-LOS scenarios. With the aid of stochastic geometry tools, we derive closed-form expressions of the moment generating function of the aggregate interference on a D2D receiver node and its outage probability for two transmitter–receiver association schemes— nearest association and LOS association. We finally show that the feasibility of millimeter-wave D2D communication relies heavily on the D2D cluster radii, peak power thresholds, and node densities. Furthermore, these parameters affect the performance of the desired link more than the interference and noise.

In this paper, we analyze the end-to-end (e2e) performance of a millimeter-wave (mmWave) multi-hop relay network. The relays in it are decode-and-forward (DF) type. As appropriate for mmWave bands, we incorporate path loss and blockages considering the links to be either line of sight (LOS) or non line of sight (NLOS). The links also experience Nakagami-m fading with different m-parameters for the LOS and NLOS states. We consider two scenarios, namely sparse and dense deployments. In the sparse case, the nodes (relays and the destination) are limited by additive noise only. We derive closed-form expressions for the distribution of equivalent e2e signal-to-noise-ratio (SNR), coverage probability, ergodic capacity, and symbol error rate (SER) for the three classes of digital modulation schemes, namely, binary phase shift keying (BPSK), differential BPSK (DBPSK), and square-quadrature amplitude modulation (QAM). In the dense case, the nodes are limited by interference only. Here, we consider two situations: 1) interference powers are independent and identically distributed (i.i.d.) and 2) they are independent but not identically distributed (i.n.i.d.). For the latter situation, closed-form analysis is exceedingly difficult. Therefore, we use the Welch-Satterthwaite Approximation for the sum of Gamma variables to derive the distribution of the total interference. For both situations, we derive the distribution of signal-to-interference ratio (SIR), coverage probability, ergodic capacity, and SERs for the DBPSK and BPSK. We study how these measures are affected by the number of hops. The accuracy of the analytical results is verified via Monte-Carlo simulation. We show that multi-hop relaying provides significant coverage improvements in blockage-prone mmWave networks.

High reliability and low latency are critical performance targets in the fifth-generation cellular networks. How does a full-duplex decode-forward relay fare in this context? To answer this question, we analyze the outage and (average) decoding-delay for both joint and sequential sliding window decoding. For comparison, we also analyze decoding delay of backward decoding and consider its existing outage analysis. In our analysis, we consider a block fading channel with full channel state information (CSI) availability at receivers and with limited CSI at transmitters and outage events at both relay and destination and channel variation over different blocks in sliding window decoding. Moreover, by analyzing the asymptotic performance at high SNR, we prove that both joint and sequential decoding achieve a full diversity order of two and derive the coding gain gaps between backward decoding and joint and sequential sliding window decoding. To see the benefits of full-duplex relaying, we also include the performance of half-duplex schemes and conclude that the preferred scheme depends on the rate, outage, and delay requirements for a specific service.

The complexity and uncertainty inherent in large cellular networks make the acquisition of location and channel information of all but perhaps a few neighboring network nodes (base stations (BSs)) difficult for a given user. Therefore, a cell association policy must operate with sparse information. Thus, the serving BS is proposed to be the one that provides the highest instantaneous signal-to-interference ratio (SIR) from among all BSs providing average received signal power exceeding a predetermined minimum. This policy is evaluated for the downlink of single-tier (homogeneous) and two-tier (heterogeneous) networks, and for the latter, the key advantage of the proposed policy is its capability to enable traffic offloading. Two methods to determine the minimum average signal power are given. Coverage probabilities and average rates of mobile stations in coverage are derived, accounting for path loss, multipath fading, and random locations of BSs in each tier. Analysis is verified by Monte Carlo simulations. We observe that the instantaneous SIR and average received signal power of a few BSs are sufficient to achieve the coverage corresponding to the highest SIR association, which in general requires instantaneous SIR information of a larger subset of a network. We also observe that in a two-tier network, the effect of strong interference from high-power BSs, such as macro BSs, can be limited by proper choice of minimum average received signal power for low-power BSs.

For spectrum sensing in cognitive radio networks, the IEEE 802.22 standard requires the detection of primary signals with a signal-to-noise ratio (SNR) as low as −20 dB and receiver sensitivity as low as −116 dBm. Under such low-SNR levels, the performance of a conventional energy detector is analyzed in this paper. The analysis includes novel expressions for missed-detection probability and area under the receiver operating characteristic (ROC) curve. Thus, a unified framework covering fading channels, square-law diversity combining, and cooperative spectrum-sensing scenarios is developed. The detection threshold is optimized to minimize the total error rate subject to bounded false-alarm and missed-detection probabilities, which outperforms traditional detection threshold selection. Numerical results and Monte Carlo simulation results with the IEEE 802.22 sensing requirements are provided and discussed.

Although the approximations based on the central limit theorem (CLT) for the detection probability $(P_d)$ of the energy detector and of its more generalized cousin, the $p$ -norm detector, are accurate for large sample sizes, their accuracy is poor otherwise. A recent work has addressed this problem by developing a cube-of-Gaussian approximation (CGA). However, CGA may not be the only option and thus this letter investigates five other classical approximations for deriving $P_d$ . They tightly match the exact values even for few samples and thus are more accurate than CLT. These approximations have been unnoticed in the signal detection research community and this letter aims at making them known to a wider audience. Because the range of their potential applications could be diverse, to demonstrate their utility, we derive a novel expression for the area under the receiver operating characteristic curve of the $p$ -norm detector.

Missed-detection probability expressions for energy detectors often involve infinite series and do not provide quick insights into the effects of operating conditions. To overcome these limitations, we develop novel asymptotic analyses by proposing an approximate probability density function (PDF) of a random variable $\beta$ , which, in general, can characterize fading channels in diverse operating conditions. The coefficients of the proposed approximate PDF of $\beta$ are obtained by matching the coefficients of the approximate PDF's series expansion (or coefficients of the approximate PDF's moment generating function (MGF)) with those of the exact PDF (or MGF) of $\beta$ . By using the proposed approximation, a unified closed-form asymptotic missed-detection probability is derived. Its usefulness is then demonstrated for fading channels without and with antenna diversity, for cooperative detection, and in co-channel interference. For each case, the sensing gain, which reveals the effect of the operating conditions on the detection performance, is determined explicitly. Furthermore, the asymptotic complementary area under the receiver operating characteristic curve, an alternative performance metric, is derived, and found to reveal the sensing gain. Numerical results verify the accuracy of our derived asymptotic expressions over a wider signal-to-noise ratio (SNR) range compared to the existing asymptotic solution, which is accurate only for high SNRs.

We analyse the end-to-end (E2E) outage probabilities (OPs) of zero-forcing beamforming and maximal-ratio-transmission/combining (ZFB-MRT/MRC) for an underlay network, which consists of a single-antenna fixed-gain amplify-and-forward (AF) two-way relay and two multi-antenna terminals. Assuming both path loss effects and small-scale fading and considering both secondary-to-primary (S2P) and primary-to-secondary (P2S) interferences, the exact and asymptotic E2E OPs are derived.

In cellular networks, each mobile station adjusts its power level under control of its base station, i.e., through uplink transmit power control, which is essential to reach desired signal-to-interference-plus-noise ratio (SINR) at the base station and to limit inter-cell interference. The optimal levels of transmit power in a network depend on path loss, shadowing, and multipath fading, as well as the network configuration. However, since path loss is distance dependent and the cell association distances are correlated due to the cell association policies, the performance analysis of the uplink transmit power control is very complicated. Consequently, the impact of a specific power control algorithm on network performance is hard to quantify. In this paper, we analyze three uplink transmit power control schemes. We assume the standard power-law path loss and composite Rayleigh-lognormal fading. Using stochastic geometry tools, we derive the cumulative distribution function and the probability density function of the uplink transmit power and the resulting network coverage probability. It is shown that the coverage is highly dependent on the severity of shadowing, the power control scheme, and its parameters, but invariant of the density of deployment of base stations when the shadowing is mild and power control is fractional. At low SINRs, compensation of both path loss and shadowing improves the coverage. However, at high SINRs, compensating for path loss only improves coverage. Increase in the severity of shadowing significantly reduces the coverage.

Millimeter wave communication is a promising concept for the fifth generation (5G) of cellular wireless networks due to the large available bandwidth while device to device (D2D) communication among nearby devices which saves network resources is also gaining attention. As such, D2D networks underlaying millimeter wave cellular systems hold massive potential. However, the performance of such a D2D network incorporating spatial randomness and power control has not yet been characterized. To fill this knowledge gap, we develop a comprehensive analysis of the performance of a D2D receiver. To this end, we model cellular transmitters and receivers as homogeneous Poisson point processes and the D2D network as a Matern cluster process, and incorporate blockages due to random objects, sectored antenna patterns, log-distance path loss, and Nakagami-m fading. Furthermore, we consider path loss and antenna gain inversion based power control, and peak power constraints for D2D devices along with distinct path loss exponents and fading severities for line-of-sight and non-line-of-sight scenarios. With the aid of stochastic geometry tools, we derive closed-form expressions of the moment generating function of the aggregate interference experienced by a D2D receiver and its outage probability. We finally show that the feasibility of millimeter wave D2D communication relies heavily on the D2D cluster radii, peak power thresholds, and node densities.

Performance analysis of the p-norm detector to date has been limited to ad hoc approximations, nonfading channels, and Rayleigh fading. To overcome these limitations, we develop several analytical/numerical solutions for detection probability P d and false alarm probability P f , which are necessary to specify the receiver operating characteristic (ROC) curves of the p-norm detector. First, for nonfading channels (additive white Gaussian noise (AWGN) only), the moment-generating function (mgf) of the decision variable is derived in two forms: 1) closed form for even integer p and 2) series form for arbitrary p. To evaluate P d and P f , a numerical method utilizing the Talbot inversion is developed for case 1, and an infinite series expansion with convergence acceleration based on the e-algorithm is derived for case 2. As an alternative to mgf-based analysis, a Laguerre polynomial series is also used to derive new P d and P f approximations. Second, series-form mgf-based P d expressions are derived for κ-μ and α-μ fading channels. Third, for antenna diversity reception, new p-law combining (pLC) and p-law selection (pLS) schemes are proposed. The performance of these combiners with the p-norm detector is derived for Nakagami-m fading and is compared with that of the classical maximal ratio combining (MRC) and selection combining (SC). Interestingly, both pLC and pLS perform similarly to SC at low signal-to-noise ratio (SNR) but outperform it at relatively high SNR, with pLC performing closer to the optimal MRC. Numerical results are presented to verify the derived results and to provide further insights.

We investigate the outage and decoding-delay performances for full-duplex (FD) decode-forward (DF) relaying with backward and sliding window decoding. In our analysis, we consider a block fading channel with full channel state information (CSI) availability at receivers and with limited CSI at transmitters. For backward decoding where the destination starts decoding from the last transmission block, we derive the average block decoding delay. For sliding window decoding, we analyze both joint and sequential decoding where the destination utilizes two received blocks either simultaneously or sequentially to decode the source data. We then derive their average block decoding delays and outage performances by considering channel variation over two transmission blocks and outage events at both the relay and the destination. When comparing FD relaying with backward decoding and half-duplex (HD) transmission, numerical results show that joint sliding-window decoding is the preferred choice in terms of complexity, decoding delay and outage performances.

We derive uniform approximations (UAs) for typical performance measures such as error probability, outage probability and capacity of wireless transmissions over flat fading channels impaired by noise. Uniform refers to the fact that these approximations are accurate over the whole range (low to high) of signal-to-noise ratio (SNR) values. First, the high-SNR results of Wang and Giannakis are generalized and unified for an arbitrary performance measure. Second, we develop a Mellin-transform-based procedure to construct low- and high-SNR asymptotics of error probability or outage. Specifically, these asymptotics are related to the left- and right-sided poles of a Mellin product with respect to its fundamental strip. Third, by using multiple low-SNR terms and a single high-SNR term, UAs for the error probability of coherent modulation are constructed for Rayleigh fading, maximal-ratio-combining (MRC), selection-combining (SC), dual hop relaying, and co-channel interference. UAs are also developed for the error probability of single- and multi-channel differential modulation, the product of two Q functions, and the miss probability of energy detection. By using a single low-SNR term and multiple high-SNR terms, the outage probability UA is also developed. Finally, since the capacity measure is not an exponentially decaying function, we derive a UA for an intermediate function which is based on the moment-generating function (MGF) and ultimately, the resulting approximation for the capacity.

This paper introduces the fundamentals of generalized singular value decomposition (GSVD) beamforming: a noniterative beamforming technique based on GSVD for the two-user multiple-input-multiple-output (MIMO) downlink. The numbers of private/common channels produced by GSVD beamforming and transmit power normalization are investigated; the channel gains under Rayleigh fading are characterized exactly for configurations that involve only common channels. Moreover, symbol error rates (SERs) are presented for elementary multicasting and two-way relaying applications; the performance distinctions of the private/common channels and the effect of channel-estimation errors and asymmetries in channel fading are highlighted thereby.

The aggregate interference caused on a primary receiver by Cognitive Radio (CR) nodes distrbuted uniformly in an annular region around it is investigated, assuming Rayleigh fading and path loss. By approximating the aggregate interference with that caused by the nearest CR interferer, the exact analytical moment generating function for the nearest interferer is derived for cases of no power control and distance based power control. The outage probability based on the approximation is derived, which is a tight lower bound under certain conditions.

This paper investigates the aggregate interference on a primary user caused by a random number of cognitive radio transmitters distributed in a finite ring. A composite model involving path loss, Rayleigh fading, and shadowing is considered. The exact closed-form moment generating function and an accurate approximation are derived. The aggregate interference is shown to be accurately approximated by a Gamma distribution. The exact outage and an asymptotic approximation are derived.

A new class of approximations for the bit error rate (BER), the symbol error rate (SER), and the outage of wireless digital communication systems impaired by fading and noise is derived. As compared to conventional high signal-to-noise ratio (SNR) approximations [1], these new approximations are better by an order of magnitude in the high SNR regime and retain their accuracy for a wider range of SNRs. They require the first two terms of the Taylor expansion of the channel probability density function (PDF). The resulting approximations for two diversity combiners, multiple-antenna eigenmode transmission and several important modulation schemes are developed.

Two new transmit/receive (Tx/Rx) antenna selection strategies are proposed and analyzed for two-way multiple-input multiple-output (MIMO) amplify-and-forward (AF) relay networks. These two strategies select the best transmit and receive antennas at the two sources and the relay based on (i) minimizing the overall outage probability and (ii) maximizing the sum-rate. The performance of these selection strategies is quantified by deriving the overall outage probability, its high SNR approximation and the diversity order providing valuable insights into practical system-designs. Importantly, multiple relay and multiple user two-way relay network set-ups are also treated by proposing and analyzing (i) joint relay and antenna selection strategies, and (ii) joint user, relay and antenna selection strategies, respectively. Interestingly, our outage probability results reveal that the joint relay and antenna selection strategies achieve significant diversity and array gains over those of their single relay counterparts. In fact, the diversity orders of individual relayed-branches accumulate to yield the overall diversity of the multi-relay networks. For example, at 10-2 outage probability, the dual-antenna relay provides a 14 dB gain over a single-antenna relay, and having two dual-antenna relays improves the gain by another 5 dB. Moreover, the performance degradation due to practical transmission impairments (i) feedback delays, (ii) spatially-correlated fading and (iii) non-identically distributed fading is quantified. Impact of channel prediction to circumvent outdated channel state information for antenna selection due to feedback delay is also studied. All the derivations are validated through Monte-Carlo simulations.

In the presence of the primary user's interference, the outage probability of a dual-hop decode-and-forward (DF) cognitive relay network (CRN) over Rayleigh fading channels is investigated. We first derive the exact expression for the outage probability, using which the impact of different system parameters on the outage performance is presented in the asymptotic regimes. In addition, the asymptotic outage probability is also derived in the high signal-to-noise ratio (SNR) regime.

This paper considers the analytical performance of primary users (PUs) subject to interference due to secondary users (SU) in an underlay cognitive radio system over Rayleigh fading. In particular, we focus on a more general spatial configuration where the interfered PU, not only located at the center of the cell, is having a protective region which is free of SUs and the SUs are distributed over a finite area in contrast to the commonly used infinite area assumption. We first characterize the statistical properties of the aggregate interference at the PU due to SUs, by deriving new exact closed form expressions for the moment generating function, cumulants, first, second and third moments and first order expansions of the cumulative distribution functions corresponding to propagation scenarios with path loss factors, two and four. We then investigate the PU performance by presenting new analytical expressions for the outage probability, amount of fading as well as the diversity order and coding gain. Our results indicate that the PU can achieve the full diversity gain given a non-zero protective region around the PU.

A comprehensive performance analysis framework for dual-hop multiple-input multiple-output (MIMO) amplify-and-forward (AF) relay networks with hop-by-hop beamforming (i.e. both source and relay perform beamforming) is presented. The system performance degradation due to practical transmission impairments (i) feedback delays, (ii) channel estimation errors and (iii) spatially-correlated fading is quantified. To this end, closed-form expressions for the cumulative distribution function of the end-to-end signal-to-noise ratio, its moment generating function, the outage probability, and the average bit error rate (BER) are derived. The asymptotic high SNR approximations of the outage probability and average BER are derived to obtain valuable system-design insights such as the diversity order and array gain. In order to illustrate the usefulness of our analysis, four applications, which employ dual-hop MIMO relaying with hop-by-hop beamforming, are also presented and analyzed. Furthermore, our analyses are validated through Monte-Carlo simulations.

The use of space time block codes (STBCs) over frequency selective multipath multiple-input multiple-output (MIMO) channels is investigated in combination with spatial multipath resolution (SMR) [1], a novel spatial signal processing technique proposed by the authors for mitigating inter-symbol interference. Neither STBC nor SMR requires transmit channel state information. This fact, along with SMR not requiring any modification to the transmitter, makes the MIMO STBC-SMR hybrid effective. Numerical results are presented, illustrating how the scheme fares under the Alamouti STBC scheme, and highlighting the advantage of adaptive SMR - i.e., adapting the number of multipaths resolved based on the channel state. A practical multipath MIMO channel based on the IEEE 802.15.3c NLOS (CM4) model is used for simulation.

This letter analyzes the performance of energy- detection-based spectrum sensing in a cognitive radio (CR) possessing multiple correlated antennas when the channel from the primary user (PU) to the CR is Nakagami-m faded. The probability of detection of the CR by employing square law combining (SLC) is derived by using the MGF-based approach. Special cases of equally correlated, exponentially correlated and a linear array of 2, 3 and 4 arbitrarily correlated antennas are treated. Numerical and simulation results are used to quantify the detector performance as a function of antenna correlation across the branches, number of antennas, fading severity and the time-bandwidth product.

For a multiple antenna land mobile satellite (LMS) communication system with a terrestrial relay node, the system performance when channel state information (CSI) is not available at the source and the relay is analyzed. The system employs orthogonal space time block code (OSTBC) encoding with fixed gain amplify and forward (AF) relaying. The moment generating function (MGF) and first and second moments of the signal-to-noise ratio (SNR) at the destination are derived in exact closed form. The average symbol error rate (SER) and the amount of fading (AoF) of the system are also derived.

Wireless multiple-input multiple-output (MIMO) terminals with a large number of antennas are becoming a reality, increasing the spatial spatial degree of freedoms (DoFs) available at the terminals. This paper proposes exploiting the excess spatial DoFs available at the receiver for spatial multipath resolution. A rake-receiver structure, whose fingers are implemented through spatial signal processing, is introduced for that. The joint computation of beamforming matrices for the transmitter and each receiver finger to achieve single-carrier eigenmode transmission over a multipath MIMO channel is developed. Numerical results on the error performance are provided for a practical multipath MIMO channel based on the IEEE 802.15.3c NLOS (CM4) model.

SUMMARY To assess the performance of maximum-likelihood (ML) based Nakagami m parameter estimators, current methods rely on Monte Carlo simulation. In order to enable the analytical performance evaluation of ML-based m parameter estimators, we study the statistical properties of a parameter Δ, which is defined as the log-ratio of the arithmetic mean to the geometric mean for Nakagami-m fading power. Closed-form expressions are derived for the probability density function (PDF) of Δ. It is found that for large sample size, the PDF of Δ can be well approximated by a two-parameter Gamma PDF.

Composite fading (i.e., multipath fading and shadowing together) has increasingly been analyzed by means of the K channel and related models. Nevertheless, these models do have computational and analytical difficulties. Motivated by this context, we propose a mixture gamma (MG) distribution for the signal-to-noise ratio (SNR) of wireless channels. Not only is it a more accurate model for composite fading, but is also a versatile approximation for any fading SNR. As this distribution consists of N (≥ 1) component gamma distributions, we show how its parameters can be determined by using probability density function (PDF) or moment generating function (MGF) matching. We demonstrate the accuracy of the MG model by computing the mean square error (MSE) or the Kullback-Leibler (KL) divergence or by comparing the moments. With this model, performance metrics such as the average channel capacity, the outage probability, the symbol error rate (SER), and the detection capability of an energy detector are readily derived.

The performance of three transmit antenna selection (TAS) strategies for dual-hop multiple-input-multiple-output (MIMO) ideal channel-assisted amplify-and-forward (AF) relay networks is analyzed. All channel fades are assumed to be Nakagami-m (integer m) fading. The source, relay, and destination are MIMO terminals. The optimal TAS and two suboptimal TAS strategies are considered. Since direct analysis of the end-to-end signal-to-noise ratio (e2e SNR) of the optimal TAS is intractable, a lower bound of the e2e SNR is derived. Its cumulative distribution function and the moment generating function (mgf) are derived and used to obtain the upper bounds of the outage probability and the average symbol error rate (SER). For the two suboptimal TAS strategies, we derive the exact mgfs of the e2e SNR and obtain accurate and efficient closed-form approximations for the outage probability and the average SER. The asymptotic outage probability and the average SER, which are exact in high SNR, are also derived, and they provide valuable insights into the system design parameters, such as diversity order and array gain. The exact outage probability, average SER, and their high SNR approximations are also derived for the optimal TAS when the direct path is ignored. The impact of outdated channel state information (CSI) on the performance of TAS is also studied. Specifically, the amount of performance degradation due to feedback delays is studied by deriving the asymptotic outage probability and the average SER and thereby quantifying the reduction of diversity order and array gain. Numerical and Monte Carlo simulation results are provided to analyze the system performance and verify the accuracy of our analysis.

A comprehensive performance analysis of the energy detector over fading channels with single antenna reception or with antenna diversity reception is developed. For the no-diversity case and for the maximal ratio combining (MRC) diversity case, with either Nakagami-m or Rician fading, expressions for the probability of detection are derived by using the moment generating function (MGF) method and probability density function (PDF) method. The former, which avoids some difficulties of the latter, uses a contour integral representation of the Marcum-Q function. For the equal gain combining (EGC) diversity case, with Nakagami-m fading, expressions for the probability of detection are derived for the cases L =2,3,4 and L >; 4, where L is the number of diversity branches. For the selection combining (SC) diversity, with Nakagami-m fading, expressions for the probability of detection are derived for the cases L =2 and L >; 2. A discussion on the comparison between MGF and PDF methods is presented. We also derive several series truncation error bounds that allow series termination with a finite number of terms for a given figure of accuracy. These results help quantify and understand the achievable improvement in the energy detector's performance with diversity reception. Numerical and simulation results are also provided.

In this paper, channel estimation and training sequence design are considered for amplify-and-forward (AF)-based two-way relay networks (TWRNs) in a time-selective fading environment. A new complex-exponential basis expansion model (CE-BEM) is proposed to represent the mobile-to-mobile time-varying channels. To estimate such channels, a novel pilot symbol-aided transmission scheme is developed such that a low complex linear approach can estimate the BEM coefficients of the convoluted channels. More essentially, two algorithms are designed to extract the BEM coefficients of the individual channels. The optimal training parameters, including the number of the pilot symbols, the placement of the pilot symbols, and the power allocation to the pilot symbols, are derived by minimizing the channel mean-square error (MSE). The selections of the system parameters are thoroughly discussed in order to guide practical system design. Finally, extensive numerical results are provided to corroborate the proposed studies.

A new class of upper bounds on the end-to-end signal-to-noise ratio (SNR) of channel-assisted amplify-and-forward (AF) multi-hop (N ≥ 2) relay networks is presented. It is the half-harmonic mean of the minimum of the first P ≥ 0 hop SNRs and the minimum of the remaining N-P hop SNRs. The parameter P varies between 0 to N and may be chosen to provide the tightest bound. The closed-form cumulative distribution function and moment generating function are derived for independent and non-identically distributed Rayleigh fading and for independent and identically distributed Nakagami-m fading, where m is an integer. The resulting outage probability and the average symbol error rate bounds are asymptotically-exact. The asymptotic-exactness holds for any 0 ≤ P ≤ N. As applications, two cases of multi-hop multi-branch relay networks (i) the best branch selection and (ii) maximal ratio combining reception are treated. Numerical results are provided to verify the comparative performance against the existing bounds.

This paper analyzes the performance of an energy detector over wireless channels with composite multipath fading and shadowing effects. These effects are modeled by using the K and K_G channel models. Closed-form average detection probabilities are derived for both K and K_G channel models for the no-diversity reception case. A simple approximation is also derived for large values of energy threshold in the energy detector. The analysis is then extended to cases with diversity receptions including maximal ratio combining (MRC) and selection combining (SC). Analytical results are verified by Monte Carlo simulation and by numerical methods. Receiver operating characteristic (ROC) curves are presented for different degrees of multipath fading and shadowing. Finally, the Rayleigh-lognormal distribution and the K distribution are numerically compared, and the validity of the K channel model for representing the impact of shadowing on the performance of energy detection is affirmed.

We present a general two-parameter received signal-to-noise ratio (SNR) model for two-hop amplify-and-forward (AF) relaying. It encompasses AF schemes that select the relay gain as the reciprocal of a linear combination of the channel gain and the noise power of the incoming link, including all channel-noise-assisted, channel-assisted, and blind relay schemes. Moreover, the model is flexible enough to represent independent source and relay power allocations. A unified performance analysis is then developed for AF relaying over independent but nonidentically distributed Nakagami-m faded links, where m is an integer. Exact analytical expressions are derived for the cumulative-distribution function (cdf), probability density function (pdf), and moment-generating function (mgf) of the received SNR. Monte Carlo simulation results are provided to verify the results.

A simple figure of merit to describe the performance of an energy detector is desirable. The area under the receiver operating characteristic (ROC) curve, denoted (AUC), is such a measure, which varies between 1/2 and 1. If the detector's performance is no better than flipping a coin, then the AUC is 1/2 , and it increases to one as the detector performance improves. However, in the wireless literature, the AUC measure has gone unnoticed. In this paper, to address this gap, we comprehensively analyze the AUC of an energy detector with no-diversity reception and with several popular diversity schemes. The channel model is assumed to be Nakagami-m fading. First, the average AUC is derived for the case of no-diversity reception. Second, the average AUC is derived for diversity reception cases including maximal ratio combining (MRC), square-law combining (SLC) and selection combining (SC). Further, for Rayleigh fading channels, the impacts of channel estimation errors and fading correlations are analyzed. High SNR (signal-to-noise ratio) approximations and the detection diversity gain are also derived. The analytical results are verified by numerical computations and by Monte-Carlo simulations.

Receive antenna selection for unitary space-time modulation (USTM) over semi-correlated Ricean fading channels is analyzed (this work generalizes that of Ma and Tepedelenlio-glu for the independent and identically distributed (i.i.d.) Rayleigh fading case). The antenna selection rule is that the receive antennas with the largest signal powers are chosen. For single antenna selection, we derive the maximum likelihood decoding for the correlated Ricean case. We also derive the Chernoff bound on the pairwise error probability for the high signal to- noise ratio (SNR) region and obtain the coding gain and diversity order. Our results show that even when there are transmitter side correlations and a line of sight component, receive antenna selection with USTM preserves the full diversity order if the USTM constellation is of full rank. We also give an approximation to the distribution function of a quadratic form of non-zero mean complex Gaussian variates (from Nabar et al.) at the high SNR region. Based on this approximation, a closed-form expression for the coding gain is also obtained and compared with that of the i.i.d. Rayleigh case. We also analyze the case of multiple receive antenna selection and derive the coding gain and diversity order. We show that USTM constellations, which have been proposed for the i.i.d. Rayleigh channel, can be used with the correlated Ricean channel as well.

This paper analyzes the performance of multiple-input-multiple-output (MIMO) systems with transmit and receive antenna selection (T-RAS). The average bit error rate (BER) and the average symbol error rate (SER) are derived by utilizing the characteristic function (CF) of the joint output signal-to-noise ratios (SNRs). Our approach can be used over not only independent but also arbitrary correlated channels. For the sake of brevity, this paper focuses on Nakagami-m fading channels. The simulation results are provided to validate the numerical calculations.

Several time-division multiple-access (TDMA) cooperative wireless relay protocols and their performances have recently been developed by Nabar, Bolcskei, and Kneubuhler. Their work, however, is limited to an upper bound-based performance analysis for Rayleigh fading. We thus provide an exact analysis of two of their protocols in single-relay and multiple-relay networks over independent identically distributed (i.i.d.) Nakagami-m fading channels. Our analysis is focused on an Alamouti-coded system with two-stage protocols, fixed-gain amplify-and-forward (AF) relays, and maximal ratio combiner (MRC) reception. The performance metrics are the capacity, the diversity order, and the symbol error rate (SER). The closed-form moment-generating function (MGF) of the total end-to-end signal-to-noise ratio (SNR) is derived. The MGF is then used to derive the diversity order and the SER of M-ary phase-shift keying (M-PSK) and M-ary quadrature amplitude modulation (M -QAM). It is found that the end-to-end SNR for relaying with orthogonal channels is higher than that of nonorthogonal relay channels. The diversity order of a multiple-relay network (n relays) in a Nakagami-m environment is shown to be (n + 1)m. The closed-form SER expressions for relay-destination links with high SNRs and static relay-destination links are derived. Numerical and simulation results are provided to verify the analysis.

This paper presents linear and nonlinear precoding design for error-rate improvement in orthogonal space-time block-coded (OSTBC) multiple-input-multiple-output (MIMO) orthogonal frequency-division-multiplexed (OFDM) downlink, where both the conditional mean of the channel gain matrix and the channel gain covariance matrix may be available at the transmitter. The conditional means of the channel matrix are derived for a general transmit-antenna-correlated frequency-selective fading MIMO channel with estimation errors and feedback delay. Mean-feedback linear precoding and nonlinear Tomlinson-Harashima precoding (THP) are developed to maximize the signal-to-noise power ratio (SNR). The intuition that when the mean feedback becomes accurate the mean-feedback precoding outperforms covariance precoding is confirmed. Dual-mode precoding is also proposed, in which the novel mean-feedback precoding or covariance precoding is adaptively chosen at the receiver. The precoding-mode switching metric is the maximized SNR, which is an indicator of the error rate. The receiver calculates its metric, selects the mode that achieves a higher SNR, and decides whether mean feedback is necessary. Our proposed precoders (both mean feedback and adaptive) significantly reduce the system error rate. Nonlinear precoding is shown to outperform linear precoding. Adaptive precoding outperforms both mean-feedback precoding and covariance precoding if individually applied in OSTBC OFDM.

The cumulative distribution function (cdf) of a sum of correlated or even independent lognormal random variables (RVs), which is of wide interest in wireless communications, remains unsolved despite long standing efforts. Several cdf approximations are thus widely used. This letter derives bounds for the cdf of a sum of 2 or 3 arbitrarily correlated lognormal RVs and of a sum of any number of equally-correlated lognormal RVs. The bounds are single-fold integrals of readily computable functions and extend previously known bounds for independent lognormal summands. An improved set of bounds are also derived which are expressed as 2-fold integrals. For correlated lognormal fading channels, new expressions are derived for the moments of the output SNR and amount of fading for maximal ratio combining (MRC), selection combining (SC) and equal gain combining (EGC) and outage probability expressions for SC.

This letter considers multiple symbol differential detection for multiple-antenna systems over flat Ricean-fading channels when partial channel state information (CSI) is available at the transmitter. Using the maximum likelihood (ML) principle, and assuming perfect knowledge of the channel mean, we derive the optimal multiple symbol detection (MSD) rule for diagonal differential unitary space-time modulation (DUSTM). This rule is used to develop a sphere decoding bound intersection detector (SD-BID) with low complexity. A suboptimal MSD based decision feedback DD (DF-DD) algorithm is also derived. The simulation results show that our proposed MSD algorithms reduce the error floor of conventional differential detection and that the computational complexity of these new algorithms is reasonably low.

Spectrum sensing performance of a cognitive radio (CR) deploying the traditional energy detector (ED) degrades in the presence of random network interference where both the number and locations of the interferers are random, thus preventing correct detection of primary user (PU) in the band of interest. However, it is not clear how the ED performance in such random network interference can be improved. Moreover, the previous studies do not consider complete modeling of the wireless environment including the cumulative effects of path-loss, fading and random network interference. We thus take these effects into account and investigate the performance of the p-norm detector, which offers the flexibility of adapting p to the operating conditions (as against fixed p = 2 for ED). Such adaptability yields remarkable performance gains over ED (say, 15% gain even at 10 dB lower (than that for ED) PU signal powers). Further, cooperative spectrum sensing with multiple CRs yields additional performance gains (say, 30% better performance at optimal cooperative detection threshold) compared to single CR based sensing even under the cumulative effects of path-loss, fading and random network interference.

Motivated by practical considerations in the design of low-complexity receiver structures for wideband cellular code division multiple access, millimeter wave, and ultrawideband communications, the study on the generalized selection combining (GSC) receiver that adaptively combines a subset of M "strongest" paths out of L available paths has intensified over the past few years. This paper derives concise analytical expressions for the moment generating function (MGF) of the GSC(M,L) output signal-to-noise ratio when the fading statistics are independent and identically distributed. The novelty of this mathematical framework in computing the MGF relies on the fact that it allows all common multipath fading channel models (Rayleigh, Rician, Nakagami-m, and Nakagami-q) to be treated in a unified sense. It also leads to a much more computationally efficient formula than those available in the literature and is valid for any combinations of M and L values. Using these newly derived MGFs, a unified error probability analysis for many coherent and noncoherent digital-modulation/detection schemes in a myriad of fading environments was provided

Imperfect channel estimation (ICE) can severely degrade the bit error rate (BER) of digital modulations with maximum ratio combining (MRC) diversity reception. The resulting performance analysis problem in its most general setting has not been addressed before. In this paper, the effect of ICE on the BER of an arbitrary square/rectangular Gray-coded quadratic amplitude modulation (QAM) in generalized Ricean fading channels when MRC reception is employed is analyzed. A general expression for the bit error probability of an arbitrary square/rectangular QAM scheme is first derived. This general formula requires a number of conditional probabilities, which is derived in closed form for independent and nonidentically distributed (i.n.d.) Rayleigh-fading channels with MRC and ICE. An efficient numerical method is also presented to compute the conditional probabilities for i.n.d. and correlated Ricean fading. In addition, extensive Monte Carlo simulations that agree excellently with the analytical results are presented

The effect of imperfect channel estimation (CE) on the performance of pilot-symbol-assisted modulation (PSAM) and MRC Rake reception over time- or frequency-selective fading channels with either a uniform power delay profile (UPDP) or a nonuniform power delay profile (NPDP) is investigated. For time-selective channels, a Wiener filter or linear minimum mean square error (LMMSE) filter for CE is considered, and a closed-form asymptotic expression for the mean square error (MSE) when the number of pilots used for CE approaches infinity is derived. In high signal-to-noise ratio (SNR), the MSE becomes independent of the channel Doppler spectrum. A characteristic function method is used to derive new closed-form expressions for the bit error rate (BER) of Rake receivers in UPDP and NPDP channels. The results are extended to two-dimensional (2-D) Rake receivers. The pilot-symbol spacing and pilot-to-data power ratio are optimized by minimizing the BER. For UPDP channels, elegant results are obtained in the asymptotic case. Furthermore, robust spacing design criteria are derived for the maximum Doppler frequency.

Performance analysis of the energy detector (ED) in fading channels has received enormous attention recently. However, averaging the generalized Marcum-Q function over fading statistics often results in complicated special functions and/or infinite series based expressions. Motivated by the need for simple expressions without compromising the accuracy, we propose a new representation for the probability density function (PDF) of the fading channel gain. This representation is then used to derive simple, unified expression for asymptotic miss-detection probability in closed-form. The derived expression is evaluated for several fading channels and antenna diversity schemes. Numerical results reveal its high accuracy over a wide range of signal-to-noise-ratio (SNR) (as low as 0 dB) unlike the existing asymptotic expression which is accurate only for high SNR regime (say, SNR ≥ 20 dB).

Moments of the multibranch equal gain combiner (EGC) output signal-to-noise ratio (SNR) are only known for independent fading channels or exponentially correlated Nakagami-m fading channels. In this paper, we derive the moments of the EGC output SNR in equally correlated Rayleigh, Rician, and Nakagami-m fading channels. Our moment expressions can be used to evaluate the outage and the average error rate as well as purely moments-based measures such as the average output SNR and the amount of fading as functions of the fading correlation. Numerical results that illustrate the effect of fading correlation on the distribution of the EGC output SNR are also provided.

The study on generalized selection combining (GSC(N,L)) diversity systems that adaptively combines a subset of N paths with the highest instantaneous signal-to-noise ratios (SNRs) out of L available diversity paths has both theoretical and practical importance in the design of low-complexity receiver structures for cellular wideband CDMA, indoor millimeter-wave and ultra-wideband communications. This paper presents a novel mathematical framework to tackle the problem at hand by deriving a single integral expression for the moment generating function (mgf) of the GSC(N,L) output SNR when the L resolvable multipaths are independent with nonidentical fading statistics. The mgf is then used to unify the performance evaluation of a broad range of digital modulation/detection schemes in practical wireless channels.

Signal fading is a ubiquitous problem in mobile and wireless communications. In digital systems, fading results in bit errors, and evaluating the average error rate under fairly general fading models and multichannel reception is often required. Predominantly to date, most researchers perform the averaging using the probability density function method or the moment generating function (MGF) method. This paper presents a third method, called the characteristic function (CHF) method, for calculating the average error rates and outage performance of a broad class of coherent, differentially coherent, and noncoherent communication systems, with or without diversity reception, in a myriad of fading environments. Unlike the MGF technique, the proposed CHF method (based on Parseval's theorem) enables us to unify the average error-rate analysis of different modulation formats and all commonly used predetection diversity techniques (i.e., maximal-ratio combining, equal-gain combining, selection diversity, and switched diversity) within a single common framework. The CHF method also lends itself to the averaging of the conditional error probability involving the complementary incomplete Gamma function and the confluent hypergeometric function over fading amplitudes, which heretofore resisted to a simple form. As an aside, we show some previous results as special cases of our unified framework.