Modeling and analysis of cooperative spectrum sensing is an important aspect in cognitive radio systems. In this paper, the problem of energy detection (ED) of an unknown signal over Nakagami-$m$ fading is revisited. Specifically, an analytical expression for the local probability of detection is derived, while using the approach of ED at the individual secondary user (SU), a new fusion rule, based on the likelihood ratio test, is presented. The channels between the primary user to SUs and SUs to fusion center are considered to be independent Nakagami-$m$. The proposed fusion rule uses the channel statistics, instead of the instantaneous channel state information, and is based on the Neyman-Pearson criteria. Closed-form solutions for the system-level probability of detection and probability of false alarm are also derived. Furthermore, a closed-form expression for the optimal number of cooperative SUs, needed to minimize the total error rate, is presented. The usefulness of factor graph and sum-product-algorithm models for computing likelihoods, is also discussed to highlight its advantage, in terms of computational cost. The performance of the proposed schemes have been evaluated both by analysis and simulations. Results show that the proposed rules perform well over a wide range of the signal-to-noise ratio.
In this paper, we consider the downlink in a K-tier heterogeneous network in the presence of Nakagami-m fading and noise. For such a system, we derive closed-form approximations of coverage probability and average rate achievable. A piece-wise linear approximation is employed in obtaining the simplified expressions. The proposed results are verified numerically through simulations. A comparison with existing work shows that the proposed work is a good approximation.
An opportunistic DF-AF selection relaying scheme with maximal received signal-to-noise ratio (SNR) at the destination is investigated in this paper. The outage probability of the opportunistic DF-AF selection relaying scheme over Nakagami-m fading channels is analyzed, and a closed-form solution is obtained. We perform asymptotic analysis of the outage probability in high SNR domain. The coding gain and the diversity order are obtained. For the purpose of comparison, the asymptotic analysis of opportunistic AF scheme in Nakagami-m fading channels is also performed by using the Squeeze Theorem.…
The secrecy outage performance of wireless communication systems operating over spatially correlated composite fading channels is analyzed in this paper. We adopt a multiplicative composite channel model for both the legitimate communication link and the link between the eavesdropper and the legitimate transmitter, consisting of Nakagami-$m$ distributed small-scale fading and shadowing (large-scale fading) modeled by the Gamma distribution. We consider the realistic case where small-scale fading between the links is independent, but shadowing is arbitrarily correlated, and present novel analyt…
In this chapter, the authors present the performance of multi-antenna selective combining decode-and-forward (SC-DF) relay networks over independent and identically distributed (i.i.d) Nakagami-m fading channels. The outage probability, moment generation function, symbol error probability and average channel capacity are derived in closed-form using the Signal-to-Noise-Ratio (SNR) statistical characteristics. After that, the authors formulate the outage probability problem, optimize it with an approximated problem, and then solve it analytically. Finally, for comparison with analytical formula…
We present novel exact expressions and accurate closed-form approximations for the level crossing rate (LCR) and the average fade duration (AFD) of the double Nakagami-m random process. These results are then used to study the second order statistics of multiple input multiple output (MIMO) keyhole fading channels with space-time block coding. Numerical and computer simulation examples validate the accuracy of the presented mathematical analysis and show the tightness of the proposed approximations.
In this paper, we analyze the symbol error rate (SER) of space-time network coding (STNC) in a distributed cooperative network over independent but not necessarily identically distributed (i.n.i.d.) Nakagami-$m$ fading channels. In this network, multiple sources communicate with a single destination with the assistance of multiple decode-and-forward (DF) relays. We first derive new exact closed-form expressions for the SER with $M$-ary phase shift-keying modulation ($M$-PSK) and $M$-ary quadrature amplitude modulation ($M$-QAM). We then derive new compact expressions for the asymptotic SER to …
This paper investigates the problem of power allocation for hybrid automatic repeat request (HARQ) schemes over time-correlated Nakagami-m fading channels under outage constraint. The presence of time correlation complicates the power allocation problem due to the involvement of multiple correlated fading channels. Under a general time-correlated Nakagami-m fading channel with exponential correlation, outage probabilities for three widely adopted HARQ schemes, including Type I HARQ, HARQ with chase combining (HARQ-CC) and HARQ with incremental redundancy (HARQ-IR), are first derived. With thes…
We present a novel relationship between the distribution of circular and non-circular complex Gaussian random variables. Specifically, we show that the distribution of the squared norm of a non-circular complex Gaussian random variable, usually referred to as squared Hoyt distribution, can be constructed from a conditional exponential distribution. From this fundamental connection we introduce a new approach, the Hoyt transform method, that allows to analyze the performance of a wireless link under Hoyt (Nakagami-q) fading in a very simple way. We illustrate that many performance metrics for H…
We consider Vertical Bell Laboratories Layered Space-Time (V-BLAST) systems in correlated multiple-input multiple-output (MIMO) Nakagami-m fading channels with equal power allocated to each transmit antenna and also we consider that the channel state information (CSI) is available only at the receiver. Now for practical application, study of the VBLAST MIMO system in correlated environment is necessary. In this paper, we present a detailed study of the channel capacity in correlated and uncorrelated channel condition and also validated the result with appropriate mathematical relation.
This letter provides closed-form expressions for the outage probability, the average level crossing rate (LCR) and the average fade duration (AFD) of a dual diversity selection combining (SC) system exposed to the combined influence of the cochannel interference (CCI) and the thermal noise (AWGN) in Nakagami fading channel. The branch selection is based on the desired signal power SC algorithm with all input signals assumed to be independent, while the powers of the desired signals in all diversity branches are mutually equal but distinct from the power of the interference signals. The analyti…
This paper studies the impact of co-channel interferences (CCIs) on the system performance of multi-hop amplify-and-forward (AF) relaying, in a simple and explicit way. For generality, the desired channels along consecutive relaying hops and the CCIs at all nodes are subject to Nakagami-$m$ fading with different shape factors. This study reveals that the diversity gain is determined only by the fading shape factor of the desired channels, regardless of the interference and the number of relaying hops. On the other hand, although the coding gain is in general a complex function of various syste…
In this paper, the energy efficiency of multihop relaying over Nakagami-$m$ fading channels is investigated. The "consumption factor" is used as a metric to evaluate the energy efficiency, and it is derived in closed-form for both amplify-and-forward and decode-and-forward relaying. Then, based on the obtained expressions, we propose a power allocation strategy maximizing the consumption factor. In addition, two sub-optimal, low complexity, power allocation algorithms are proposed and analyzed, and the obtained power allocation schemes are compared, in terms of energy efficiency as well as oth…
We report the similarity between the Nakagami-m fading distribution and the three Gaussian ensembles of random matrix theory. We provide a brief review of random matrix theory and wireless fading. We show that the Nakagami-m distribution serves as mapping between the three ensembles. The statistics of the wireless fading amplitude, as modeled by Nakagami-m distribution, provide a rare example of a classically chaotic system that exhibits a transition between the Gaussian orthogonal, Gaussian unitary, and Gaussian symplectic ensembles of random matrix theory.
This paper analyzes the performance of cooperative hybrid automatic repeat request with incremental redundancy (HARQ-IR) and proposes a new approach of outage probability approximation for performance analysis. A general time-correlated Nakagami fading channel covering fast fading and Rayleigh fading as special cases is considered here. An efficient inverse moment matching method is proposed to approximate the outage probability in closed-form. The effect of approximation degree is theoretically analyzed to ease its selection. Moreover, diversity order of cooperative HARQ-IR is analyzed. It is…
Non-orthogonal multiple access (NOMA) has attracted great recent attention due to its high spectral efficiency. Besides, NOMA can be easily implemented in physical layer, thus its interplays with other psychical layer techniques have been analyzed widely by researches. Cooperative NOMA schemes are the most investigated among these interplays. However, these studies mostly analyze cooperative NOMA schemes in terms of achievable rate and outage probability whereas bit error probability (BEP) for those systems has not been studied well although it is one of the most important performance metrics.…
Recently, spatial stochastic models based on determinantal point processes (DPP) are studied as promising models for analysis of cellular wireless networks. Indeed, the DPPs can express the repulsive nature of the macro base station (BS) configuration observed in a real cellular network and have many desirable mathematical properties to analyze the network performance. However, almost all the prior works on the DPP based models assume the Rayleigh fading while the spatial models based on Poisson point processes have been developed to allow arbitrary distributions of fading/shadowing propagatio…
Now-a-days, intense research is going on two-hop wireless link under different fading conditions with its remedial measures. In this paper work, a two-hop link under three different conditions is considered: (i) MIMO on both hops, (ii) MISO in first hop and SIMO in second hop and finally (iii) SIMO in first hop and MISO in second hop. The three models used here give the flexibility of using STBC (Space Time Block Coding) and combining scheme on any of the source to relay (S- R) and relay to destination (R-D) link. Even incorporation of Transmitting Antenna Selection (TAS) is possible on any li…
In this paper, we consider an overlay cognitive radio network, in which a secondary transmitter (ST) is willing to relay the information of a primary transmitter toward a primary receiver. In return, ST can access the licensed band to send its own information superimposed with the primary signal to a secondary receiver. The power-limited ST uses a power splitting protocol to harvest energy from its received signal to increase its transmit power. We analyze the performance of the primary and the secondary systems under independent Nakagami-m fading by deriving their corresponding outage probabi…
An ad hoc network with a finite spatial extent and number of nodes or mobiles is analyzed. The mobile locations may be drawn from any spatial distribution, and interference-avoidance protocols or protection against physical collisions among the mobiles may be modeled by placing an exclusion zone around each radio. The channel model accounts for the path loss, Nakagami fading, and shadowing of each received signal. The Nakagami m-parameter can vary among the mobiles, taking any positive value for each of the interference signals and any positive integer value for the desired signal. The analysi…
In the next few years, the development of wireless communication systems propel the world into a fully connected society where the Machine-type Communications (MTC) plays a substantial role as key enabler in the future cellular systems. MTC is categorized into mMTC and uMTC, where mMTC provides the connectivity to massive number of devices while uMTC is related to low latency and ultra-high reliability of the wireless communications. This paper studies uMTC with incremental relaying technique, where the source and relay collaborate to transfer the message to a destination. In this paper, we co…
In this paper, outage performance of hybrid automatic repeat request with incremental redundancy (HARQ-IR) is analyzed. Unlike prior analyses, time-correlated Nakagami-$m$ fading channel is considered. The outage analysis thus involves the probability distribution analysis of a product of multiple correlated shifted Gamma random variables and is more challenging than prior analyses. Based on the finding of the conditional independence of the received signal-to-noise ratios (SNRs), the outage probability is exactly derived by using conditional Mellin transform. Specifically, the outage probabil…
This paper addresses the problem of rate selection for the cooperative hybrid automatic repeat request with chase combination (HARQ-CC) system, where time correlated Nakagami-m fading channels are considered. To deal with this problem, the closed-form cumulative distribution function (CDF) for the combine SNRs through maximal ratio combining (MRC) is first derived as a generalized Fox's $\bar H$ function. By using this result, outage probability and delay-limited throughput (DLT) are derived in closed forms, which then enables the rate selection for maximum DLT. These analytical results are va…
This paper considers the analysis and optimization of a frequency-hopping ad hoc network with a finite number of mobiles and finite spatial extent. The mobiles communicate using coded continuous-phase frequency-shift keying (CPFSK) modulation. The performance of the system is a function of the number of hopping channels, the rate of the error-correction code, and the modulation index used by the CPFSK modulation. For a given channel model and density of mobiles, these parameters are jointly optimized by maximizing the (modulation-constrained) transmission capacity, which is a measure of the sp…
In this paper, the performance of a promising technology for the next generation wireless communications, non-orthogonal multiple access (NOMA), is investigated. In particular, the bit error rate (BER) performance of downlink NOMA systems over Nakagami-m flat fading channels, is presented. Under various conditions and scenarios, the exact BER of downlink NOMA systems considering successive interference cancellation (SIC) is derived. The transmitted signals are randomly generated from quadrature phase shift keying (QPSK) and two NOMA systems are considered; two users' and three users' systems. …
In this paper, we investigate the error performance of the protograph (LDPC) codes over Nakagami-$m$ fading relay channels. We first calculate the decoding thresholds of the protograph codes over such channels with different fading depths (i.e., different values of $m$) by exploiting the modified protograph extrinsic information transfer (PEXIT) algorithm. Furthermore, based on the PEXIT analysis and using Gaussian approximation, we derive the bit-error-rate (BER) expressions for the error-free (EF) relaying protocol and decode-and-forward (DF) relaying protocol. We finally compare the thresho…
The research presents a procedure of the closed-form average bit error rate evaluation for wireless communication systems in the presence of multipath fading. A generalization of the classical moment generating function is applied, and a connection between the Hankel-type contour-integral representation of the Marcum Q-function and Gauss Q-function is obtained and applied to the analytic derivation of the quadrature amplitude modulated signal average bit error rate in the presence of Nakagami-m fading. The correctness of the obtained solution was verified, and its computational efficiency (in …
This letter investigates the uplink outage performance of intelligent reflecting surface (IRS)-assisted non-orthogonal multiple access (NOMA). We consider the general case where all users have both direct and reflection links, and all links undergo Nakagami-m fading. We approximate the received powers of the NOMA users as Gamma random variables via moments matching. This allows for tractable expressions of the outage under interference cancellation (IC), while being flexible in modeling various propagation environments. Our analysis shows that under certain conditions, the presence of an IRS m…
Reconfigurable intelligent surfaces (RISs) have sparked a renewed interest in the research community envisioning future wireless communication networks. In this study, we analyzed the performance of RIS-enabled non-orthogonal multiple access (NOMA) based device-to-device (D2D) wireless communication system, where the RIS is partitioned to serve a pair of D2D users. Specifically, closed-form expressions are derived for the upper and lower limits of spectral efficiency (SE) and energy efficiency (EE). In addition, the performance of the proposed NOMA-based system is also compared with its orthog…
There are several cases in wireless communications theory where the statistics of the sum of independent or correlated Nakagami-m random variables (RVs) is necessary to be known. However, a closed-form solution to the distribution of this sum does not exist when the number of constituent RVs exceeds two, even for the special case of Rayleigh fading. In this paper, we present an efficient closed-form approximation for the distribution of the sum of arbitrary correlated Nakagami-m envelopes with identical and integer fading parameters. The distribution becomes exact for maximal correlation, whil…
NOMA is as a strong candidate for the Future Radio Access Network (FRA) due to its potential to support massive connectivity and high spectral efficiency. However, the most important drawback of NOMA is the error during Successive Interference Canceller (SIC) is implemented because of the inter-user interferences. In this paper, we derive closed-form exact Bit-Error Rate expressions for Downlink(DL) NOMA over Nakagami-m fading channels in the presence of SIC errors. The derived expressions are validated by the computer simulations. It is shown that the m parameter still represents the diversit…
This paper studies the application of cooperative techniques for non-orthogonal multiple access (NOMA). More particularly, the fixed gain amplify-and-forward (AF) relaying with NOMA is investigated over Nakagami-$m$ fading channels. Two scenarios are considered insightfully. 1) The first scenario is that the base station (BS) intends to communicate with multiple users through the assistance of AF relaying, where the direct links are existent between the BS and users; and 2) The second scenario is that the AF relaying is inexistent between the BS and users. To characterize the performance of th…
The performance of $L$-branch scan-and-wait combining (SWC) reception systems over arbitrarily correlated and not necessarily identically distributed Nakagami-$m$ fading channels is analyzed and evaluated. Firstly, a fast convergent infinite series representation for the SWC output signal-noise ratio (SNR) is presented. This expression is used to obtain analytical expressions in the form of infinite series for the average error probability performance of various modulation schemes for integer values of $m$ as well as the average number of paths estimation and average waiting time (AWT) of $L$-…
In a cooperative spectrum sharing (CSS) protocol, two wireless systems operate over the same frequency band albeit with different priorities. The secondary (or cognitive) system which has a lower priority, helps the higher priority primary system to achieve its target rate by acting as a relay and allocating a fraction of its power to forward the primary signal. The secondary system in return is benefited by transmitting its own data on primary system's spectrum. In this paper, we have analyzed the performance of multiple antenna cooperative spectrum sharing protocol under Nakagami-m Fading. C…
In this paper, we propose a novel cooperative scheme to enhance the performance of multiple-access (MA) differential-chaos-shift-keying (DCSK) systems. We provide the bit-error-rate (BER) performance and throughput analyses for the new system with a decode-and-forward (DF) protocol over Nakagami-$m$ fading channels. Our simulated results not only show that this system significantly improves the BER performance as compared to the existing DCSK non-cooperative (DCSK-NC) system and the multiple-input multiple-output DCSK (MIMO-DCSK) system, but also verify the theoretical analyses. Furthermore, w…
Utilizing relaying techniques to improve performance of wireless systems is a promising avenue. However, it is crucial to understand what type of relaying schemes should be used for achieving different performance objectives under realistic fading conditions. In this paper, we present a general framework for modelling and evaluating the performance of relaying schemes based on the decode-and-forward (DF) protocol over independent and not necessarily identically distributed (INID) Nakagami-m fading channels. In particular, we present closed-form expressions for the statistics of the instantaneo…
Random matrix model for the Nakagami-q (Hoyt) fading in multiple-input multiple-output (MIMO) communication channels with arbitrary number of transmitting and receiving antennas is considered. The joint probability density for the eigenvalues of H†H (or HH†), where H is the channel matrix, is shown to correspond to the Laguerre crossover ensemble of random matrices and is given in terms of a Pfaffian. Exact expression for the marginal density of eigenvalues is obtained as a series consisting of associated Laguerre polynomials. This is used to study the effect of fading on the Shannon channel c…
We study the potential employment of improper Gaussian signaling (IGS) in full-duplex relaying (FDR) with non-negligible residual self-interference (RSI) under Nakagami- m fading. IGS is recently shown to outperform traditional proper Gaussian signaling (PGS) in several interference-limited settings. In this work, IGS is employed as an attempt to alleviate RSI. We use two performance metrics, namely, the outage probability and the ergodic rate. First, we provide upper and lower bounds for the system performance in terms of the relay transmit power and circularity coefficient, a measure of the …
In this paper, we study vehicular communications (VCs) at intersections, in the presence of interference over Nakagami-m fading channels. The interference are originated from vehicles located on two perpendicular roads. We derive the outage probability, and closed forms are obtained. The outage probability is derived when the destination is on the road (vehicle, cyclist, pedestrian) or outside the road (base station, road side unit). We compare the performance of line of sight (LOS) scenarios and non-line of sight (NLOS) scenarios, and show that NLOS scenarios offer better performance than LOS…
Despite being ubiquitous in practice, the performance of maximal-ratio combining (MRC) in the presence of interference is not well understood. Because the interference received at each antenna originates from the same set of interferers, but partially de-correlates over the fading channel, it possesses a complex correlation structure. This work develops a realistic analytic model that accurately accounts for the interference correlation using stochastic geometry. Modeling interference by a Poisson shot noise process with independent Nakagami fading, we derive the link success probability for d…
Chaotic Communications have drawn a great deal of attention to the wireless communication industry and research due to its limitless meritorious features, including excellent anti-fading and anti-intercept capabilities and jamming resistance exempli gratia. Differential Chaos Shift Keying (DCSK) is of particular interest due to its low-complexity and low-power and many attractive properties. However, most of the DCSK studies reported in the literature considered the additive white Gaussian noise environment in non-cooperative scenarios. Moreover, the analytical derivations and evaluation of th…
The probability density function (PDF) and cumulative distribution function of the sum of L independent but not necessarily identically distributed Gamma variates, applicable to the output statistics of maximal ratio combining (MRC) receiver operating over Nakagami-m fading channels or in other words to the statistical analysis of the scenario where the sum of squared Nakagami-m distributions are user-of-interest, is presented in closed-form in terms of well-known Meijer's G function and easily computable Fox's H-bar function for integer valued and non-integer valued m fading parameters. Furth…
In this paper, we obtain asymptotic expressions for the ergodic capacity of the keyhole multiple-input multiple-output (MIMO) channel at low signal-to-noise ratio (SNR) in independent and identically distributed Nakagami-$m$ fading conditions with perfect channel state information at the transmitter and receiver. We show that the low-SNR capacity of this keyhole MIMO channel scales proportionally as $\frac{\textrm{SNR}}{4} \log^2 \left(1/{\textrm{SNR}}\right)$. Our main contribution is to identify a surprising result that the low-SNR capacity of the MIMO fading channel increases in the presenc…
In this correspondence, we propose a tight lower bound to the outage probability of discrete-input Nakagami-m block-fading channels. The approach permits an efficient method for numerical evaluation of the bound, providing an additional tool for system design. The optimal rate-diversity trade-off for the Nakagami-m block-fading channel is also derived and a tight upper bound is obtained for the optimal coding gain constant.
Vehicle-to-everything (V2X) connectivity in 5G-and-beyond communication networks supports the futuristic intelligent transportation system (ITS) by allowing vehicles to intelligently connect with everything. The advent of reconfigurable intelligent surfaces (RISs) has led to realizing the true potential of V2X communication. In this work, we propose a dual RIS-based vehicle-to-infrastructure (V2I) communication scheme. Following that, the performance of the proposed communication scheme is evaluated in terms of deriving the closed-form expressions for outage probability, spectral efficiency an…
Stochastic geometry (SG) has been widely accepted as a fundamental tool for modeling and analyzing cellular networks. However, the fading models used with SG analysis are mainly confined to the simplistic Rayleigh fading, which is extended to the Nakagami-m fading in some special cases. However, neither the Rayleigh nor the Nakagami-m accounts for dominant specular components (DSCs) which may appear in realistic fading channels. In this paper, we present a tractable model for cellular networks with generalized two-ray (GTR) fading channel. The GTR fading explicitly accounts for two DSCs in add…
Examining the effect of imperfect transmit antenna selection (TAS) caused by the feedback link errors on the performance of hybrid TAS/space-time block coding (STBC) with selection combining (SC) (i.e., joint transmit and receive antenna selection (TRAS)/STBC) and TAS/STBC (with receive maximal-ratio combining (MRC)-like combining structure) over Nakagami-m fading channels is the main objective of this paper. Under ideal channel estimation and delay-free feedback assumptions, statistical expressions and several performance metrics related to the post-processing signal-to-noise ratio (SNR) are …
In this paper, we study power allocation strategies for a fixed-gain amplify-and-forward relay network employing multiple relays. We consider two optimization problems for the relay network: 1) optimal power allocation to maximize the end-to-end signal-to-noise ratio (SNR) and 2) minimizing the total consumed power while maintaining the end-to-end SNR over a threshold value. We investigate these two problems for two relaying protocols of all-participate relaying and selective relaying and multiple cases of available channel state information (CSI) at the relays. We show that the SNR maximizati…
Consider $n$ source-destination pairs randomly located in a shared wireless medium, resulting in interference between different transmissions. All wireless links are modeled by independently and identically distributed (i.i.d.) random variables, indicating that the dominant channel effect is the random fading phenomenon. We characterize the throughput of one-hop communication in such network. First, we present a closed-form expression for throughput scaling of a heuristic strategy, for a completely general channel power distribution. This heuristic strategy is based on activating the source-de…
Backscatter communication (BackCom) has been emerging as a prospective candidate in tackling lifetime management problems for massively deployed Internet-of-Things devices, which suffer from battery-related issues, i.e., replacements, charging, and recycling. This passive sensing approach allows a backscatter sensor node (BSN) to transmit information by reflecting the incident signal from a carrier emitter without initiating its transmission. To multiplex multiple BSNs, power-domain non-orthogonal multiple access (NOMA), which is a prime candidate for multiple access in beyond 5G systems, is f…
Device-to-device (D2D) communications are now considered as an integral part of future 5G networks which will enable direct communication between user equipment (UE) without unnecessary routing via the network infrastructure. This architecture will result in higher throughputs than conventional cellular networks, but with the increased potential for co-channel interference induced by randomly located cellular and D2D UEs. The physical channels which constitute D2D communications can be expected to be complex in nature, experiencing both line-of-sight (LOS) and non-LOS (NLOS) conditions across …
