Serial relaying communications over generalized‐gamma fading channels

In this paper, a study on the end‐to‐end performance of multi‐hop non‐regenerative relaying networks over independent generalized‐gamma (GG) fading channels is presented. Using an upper bound for the end‐to‐end signal‐to‐noise ratio (SNR), novel closed‐form expressions for the probability density function, the moments, and the moments‐generating function of the end‐to‐end SNR are presented. Based on these derived formulas, lower bounds for the outage and the average bit error probability (ABEP) are derived in closed form. Special attention is given to the low‐ and high‐SNR regions having practical interest as well as to the Nakagami fading scenario. Moreover, the performance of the considered system when employing adaptive square‐quadrature amplitude modulation is further analyzed in terms of the average spectral efficiency, the bit error outage, and the ABEP. Computer simulation results verify the tightness and the accuracy of the proposed bounds. Copyright © 2011 John Wiley & Sons, Ltd.     

Cross‐layer design for MIMO systems over spatially correlated and keyhole Nakagami‐m fading channels

Cross‐layer design is a generic designation for a set of efficient adaptive transmission schemes, across multiple layers of the protocol stack, that are aimed at enhancing the spectral efficiency and increasing the transmission reliability of wireless communication systems. In this paper, one such cross‐layer design scheme that combines physical layer adaptive modulation and coding (AMC) with link layer truncated automatic repeat request (T‐ARQ) is proposed for multiple‐input multiple‐output (MIMO) systems employing orthogonal space‐‐time block coding (OSTBC). The performance of the proposed cross‐layer design is evaluated in terms of achievable average spectral efficiency (ASE), average packet loss rate (PLR) and outage probability, for which analytical expressions are derived, considering transmission over two types of MIMO fading channels, namely, spatially correlated Nakagami‐m fading channels and keyhole Nakagami‐m fading channels. Furthermore, the effects of the maximum number of ARQ retransmissions, numbers of transmit and receive antennas, Nakagami fading parameter and spatial correlation parameters, are studied and discussed based on numerical results and comparisons. Copyright © 2009 John Wiley & Sons, Ltd.     

SEP calculations for coherent M‐ary FSK in different fading channels with MRC diversity

In this paper, the authors derive symbol error probability (SEP) expressions for coherent M‐ary frequency shift keying (MFSK) modulation schemes in multipath fading channels. The multipath or small‐scale fading process is assumed to be slow and frequency non‐selective. In addition, the channel is also subjected to the usual degradation caused by the additive white Gaussian noise (AWGN). Different small‐scale fading statistics such as Rayleigh, Rician (Nakagami‐n), Hoyt (Nakagami‐q), and Nakagami‐m have been considered to portray diverse wireless environments. Further, to mitigate fading effects through space diversity, the receiver front‐end is assumed to be equipped with multiple antennas. Independent and identically distributed (IID) as well as uncorrelated signal replicas received through all these antennas are combined with a linear combiner before successive demodulation. As the detection is coherent in nature and thus involves phase estimation, optimum phase‐coherent combining algorithms, such as predetection maximal ratio combining (MRC), may be used without any added complexity to the receiver. In the current text, utilizing the alternate expressions for integer powers (1≤n≤4) of Gaussian Q function, SEP values of coherent MFSK are obtained through moment generating function (MGF) approach for all the fading models (with or without MRC diversity) described above. The derived end expressions are composed of finite range integrals, which can be numerically computed with ease, dispenses with the need of individual expressions for different M, and gives exact values up to M=5. When the constellation size becomes bigger (M≥6), the same SEP expressions provide a quite realistic approximation, much tighter than the bounds found in previous literatures. Error probabilities are graphically displayed for each fading model with different values of constellation size M, diversity order L, and for corresponding fading parameters (K, q, or m). To validate the proposed approximation method extensive Monte‐Carlo simulations were also performed, which show a close match with the analytical results deduced in the paper. Both these theoretical and simulation results offer valuable insight to assess the efficacy of relatively less studied coherent MFSK in the context of the optimum modulation choice in wireless communication. Copyright © 2010 John Wiley & Sons, Ltd.     

Generation of bivariate Nakagami‐m fading envelopes with arbitrary not necessary identical fading parameters

In this paper, a generation procedure of two correlated Nakagami‐m random variables for arbitrary fading parameters values (not necessary identical) is described. For the generation of two correlated Nakagami‐m samples, the proposed method uses the generalized Rice distribution, which appears in the conditional distribution of two correlated Nakagami‐m variables. This procedure can be applied to simulate diversity systems such as selection combiners, equal‐gain combiners, and maximal‐ratio combiners as well as multiple‐input multiple‐output (MIMO) receiver systems, in Nakagami‐m channels. Copyright © 2006 John Wiley & Sons, Ltd.     

Performance analysis of cooperative network over Nakagami and Rician fading channels

This paper presents an analysis on the performance of single‐relay and multiple fixed‐relay cooperative network. The relay nodes operate in amplify‐and‐forward (AF) mode and transmit the signal through orthogonal channels. We consider maximal‐ratio combining at the destination to get the spatial diversity by adding the received signals coherently. The closed‐form moment‐generating function (MGF) for the total equivalent signal‐to‐noise ratio (SNR) is derived. The exact expressions of symbol‐error rate, outage capacity, and outage probability are obtained using the closed‐form MGF for single‐relay and multiple‐relay cooperative network with M‐ary phase shift keying (M‐PSK) and M‐ary quadrature amplitude modulation (M‐QAM) over independent and non‐identical Nakagami‐m channels and Rician fading channels. The approximated closed‐form expression of ergodic capacity is derived for both Nakagami‐m and Rician fading channels. The performance of the system is analyzed at various relay locations. The theoretical results are then compared with the simulation results obtained for binary PSK, quadrature PSK, and 16‐QAM modulation schemes to verify the analysis. Here, the expressions derived can be easily and more efficiently used to compute the performance parameters than doing Monte Carlo simulations. It is shown that cooperation is significant only for low K values for Rician by plotting cooperation gain versus K. The results show that the cooperative network performs best when the relay is located in the middle of source to destination link, at lower SNR values, and the performance of the system is worst if the relay is located closer to the source than to the destination. Copyright © 2013 John Wiley & Sons, Ltd.     

Outage Probability of Decode‐and‐Forward Relaying Systems with Efficient Partial Relay Selection in Nakagami Fading Channels

Recently, efficient partial relay selection (e‐PRS) was proposed as an enhanced version of PRS. In comparing e‐PRS, PRS, and the best relay selection (BRS), there is a tradeoff between complexity and performance; that is, the complexity for PRS, e‐PRS, and BRS is low to high, respectively, but vice versa for performance. In this paper, we study the outage probability for e‐PRS in decode‐and‐forward (DF) relaying systems over non‐identical Nakagami‐m fading channels, where the fading parameter m is an integer. In particular, we provide closed‐form expressions of the exact outage probability and asymptotic outage probability for e‐PRS in DF relaying systems. Numerical results show that e‐PRS achieves similar outage performance to that of BRS for a low or medium signal‐to‐noise ratio, a high fading parameter, a small number of relays, and a large difference between the average channel powers for the first and the second hops.     

BER performance of MQAM with L‐branch MRC diversity reception over correlated Nakagami‐m fading channels

Exact and closed form generalized expressions for bit error rate (BER) of M‐ary quadrature amplitude modulation (MQAM) with L‐branch maximal ratio combining (MRC) space diversity reception in fading channels are derived and analyzed. The fading channels are modeled as identical but correlated frequency‐nonselective slow Nakagami‐m fading channels corrupted by additive white Gaussian noise (AWGN). Analytical results obtained are in terms of few finite range integrals with an integrand composed of elementary functions. Because of their simple form, these analytical results readily allow numerical evaluation in cases of practical interest. The results are also general enough to include Nakagami‐m fading channels with and without correlation, no diversity system, Rayleigh fading channels with and without correlation, and AWGN as special cases. The numerical results for the case of 16QAM are shown graphically and also in tabular form in order to examine the effects of fading severity, order of diversity, and branch correlation on the BER performance. The two correlation models considered are constant correlation model and exponential correlation model. One may be interested to know how the BER of MQAM is related to symbol error rate (SER) of MQAM. Therefore, the BER results obtained in this paper are also compared with that obtained directly from the SER. It is expected that the analytical results presented in this paper will provide a convenient tool for design and analysis of a radio communication system with space diversity reception in uncorrelated and correlated fading environment. Copyright © 2002 John Wiley & Sons, Ltd.     

Performance of joint transmit and receive antenna selection in dual hop amplify‐and‐forward relay network over Nakagami‐m fading channels

In this paper, performance of joint transmit and receive antenna selection in each hop of dual hop amplify‐and‐forward relay network is analyzed over flat and asymmetric Nakagami‐m fading channels. In the network, source, relay, and destination are equipped with multiple antennas. By considering relay location, we derive exact closed‐form cumulative distribution function, moment generating function, moments of end‐to‐end signal‐to‐noise ratio and closed form symbol error probability expressions for fixed and channel state information‐based relay gains. We also derive the asymptotical outage probability and symbol error probability expressions to obtain diversity order and array gain of the network. Analytical results are validated by the Monte Carlo simulations. Copyright © 2012 John Wiley & Sons, Ltd.     

Exact analysis of maximal ratio transmission-based decode-and-forward relaying with arbitrary number of co-channel interferers

This paper analyzes the performance of maximal ratio transmission (MRT)-based cooperative communication system over Nakagami- $m$ fading channels in the existence of co-channel interference which is becoming a critical factor since the limited spectrum bands are shared by growing number of devices. In particular, a dual-hop decode-and-forward relaying is investigated when multiple interferers affect the relay and the destination nodes. Firstly, the cumulative distribution function (CDF) and the probability density function (PDF) of the signal-to-interference-plus-noise ratio (SINR) are derived. Then, the exact expressions for the outage probability (OP), average bit error probability (ABEP), and ergodic capacity are obtained. Furthermore, asymptotic expressions for OP and ABEP are provided to find the diversity and coding gains. Finally, simulation results are presented to validate our theoretical findings.     

Performance analysis of Alamouti scheme with transmit antenna selection in non‐identical Nakagami‐m fading channels

In this paper, error performances of multiple‐input multiple‐output systems that employ Alamouti‐coded transmission with transmit antenna selection are examined for binary phase‐shift keying, binary frequency‐shift keying, M‐ary phase‐shift keying, and M‐ary quadrature amplitude‐modulation signals in independent but non‐identically distributed flat Nakagami‐m fading channels. Exact symbol error rate expressions are derived by using the moment‐generating function‐based analysis method. Upper bound expressions have been obtained in order to examine the asymptotic diversity order of transmit antenna selection/Alamouti scheme. Also, outage probability analysis of investigated systems has been given in order to examine the system capacity. Monte Carlo simulations have validated the analytical symbol error rate performance results. Copyright © 2011 John Wiley & Sons, Ltd.     

Impact of transmission techniques in asymmetric RF/FSO system over Nakagami‐m and gamma‐gamma fading channels with pointing errors

In this paper, the performance of transmission techniques on the fixed‐gain amplify‐and‐forward–based asymmetric radio frequency/free space optical (RF/FSO) communication system is studied. The RF link and FSO link are, respectively, modeled by the Nakagami‐m and Gamma‐Gamma fading channels under the effect of zero boresight and non‐zero boresight pointing errors subject to heterodyne detection. Maximum ratio transmission (MRT) and orthogonal space‐time block coding (OSTBC) techniques are the transmission scenarios considered at the system source while selection combining is used for reception at the relay and destination for the signal detection. Moreover, a unified cumulative density distribution (CDF) of end‐to‐end signal‐to‐noise ratio is derived for the system. By utilizing this channel statistical CDF, the closed‐form expressions for the outage probability and average bit error rate for the M‐ary phase shift keying modulation are then obtained for the system. The analysis presented illustrates that both the atmospheric turbulence and pointing error significantly degrade the system performance. Based on this, the MRT transmission technique offers a better performance compared with the OSTBC techniques under the same system conditions. The accuracy of the analytical results is verified by Monte‐Carlo simulations.     

Bit error rate for rectangular QAM with arbitrary constellation mapping in Nakagami‐m channels

We present closed‐form expressions for the bit error rate (BER) of rectangular quadrature amplitude modulation (QAM) in Nakagami‐m fading channels. The presented formulas, which are valid for arbitrary bits‐to‐symbols mapping, thus may be used when non‐Gray mapping is employed, are particularly useful in the low signal‐to‐noise ratio (SNR) range and/or for small values of the parameter m. The advantage of the proposed expressions over the known bounding techniques is illustrated through numerical simulations. Copyright © 2006 John Wiley & Sons, Ltd.     

Enhanced switch combining for spatial diversity with a switch window over correlated Nakagami‐m fading channels

On the basis of a mixture of the selection combining and switch‐and‐stay combining schemes, the enhanced switch combining (ESC) scheme is proposed for antenna diversity over multiple correlated Nakagami‐m fading channels, where a switch window with upper and lower switch thresholds are used. Compared with the existing select‐and‐stay combining or switch with post‐examining, the ESC scheme reduces simultaneous multiantenna observations and hence saves processing time and energy from multibranch observations, while achieving matched receiver performance. Thus, ESC also has better performance than switch‐and‐examine combining (SEC). To assess the reduction of simultaneous observations, a dual‐observation rate is defined. Moreover, the ESC unifies some well‐known switch‐based combining schemes (for example selection combining, switch‐and‐stay combining, or SEC) in the sense that, by adjusting switch thresholds, these combining schemes become different special cases of ESC. The CDF, PDF, and moment generating function of the combined signal‐to‐noise ratio for ESC are derived for general fading channels. Then, the outage probability and the average BER of different binary modulations over correlated Nakagami‐m fading channels are evaluated. Numerical results from analysis and simulation are presented to demonstrate ESC performance. Copyright © 2012 John Wiley & Sons, Ltd.     

Performance analysis of hybrid transmit antenna selection/maximal‐ratio transmission in Nakagami‐m fading channels

Hybrid diversity systems have been of great importance because they provide better diversity orders and robustness to the fading effects of wireless communication systems. This paper focuses on the performance analysis of multiple‐input gle‐output systems that employ combined transmit antenna selection (TAS)/maximal‐ratio transmission (MRT) techniques (i.e., hybrid TAS/MRT). The probability density function, the moment generating function and the n ^th order moments of the output signal‐to‐noise ratio of the investigated diversity scheme are derived for independent identically distributed flat Nakagami‐m fading channels. The system capacity of the hybrid TAS/MRT scheme is examined from the outage probability perspective. Exact bit/symbol error rate (BER/SER) expressions for binary frequency shift keying, M‐ary phase shift keying and square M‐ary quadrature amplitude modulation signals are derived by using the moment generating function‐based analysis method. By deriving the upper bounds for BER/SER expressions, it is also shown that the investigated systems achieve full diversity orders at high signal‐to‐noise ratios. Also, by Monte Carlo simulations, analytical performance results are validated and the effect of feedback delay, channel estimation error and feedback quantization error on BER/SER performances are examined. Copyright © 2011 John Wiley & Sons, Ltd.     

Performance of wireless multihop communications systems with cooperative diversity over fading channels

We present closed‐form bounds for the performance of wireless multihop communications systems with cooperative diversity over Nakagami‐m fading channels. The end‐to‐end signal‐to‐noise ratio is formulated and upper bounded by using the inequality between harmonic and geometric means of positive random variables. Closed‐form expression is derived for the moment‐generating function and is used to obtain lower bounds for the average error probability. Numerical results are compared with computer simulations showing the tightness of the proposed bounds. Copyright © 2007 John Wiley & Sons, Ltd.     

Performance analysis of two‐hop decode‐amplify‐forward relayed system in different fading conditions

Recent advances in the field of wireless communication have proven the importance of diversity in combating channel fading and improving the bit error rates (BERs). In this report, a dual‐hop decode‐amplify‐forward (DAF) transmission system over Nakagami‐m fading channel is studied. The DAF relay system is a hybrid of decode‐and‐forward and amplify‐and‐forward relay systems that shows the benefits of both decode‐and‐forward and amplify‐and‐forward relay systems and is also called hybrid relay system or hybrid DAF relay system. Signal‐to‐noise ratios and BERs for various system models with varying number of transmit and receive antennas have been discussed. The diversity is achieved in two ways: firstly, by the use of relay and secondly, by the use of multiple antennas at both the transmitter and the receiver. Dual‐hop relaying gives better trunking efficiency and with single antenna at the relay site acquisition and antenna structures are much less expensive. The variations in the performance levels when the relay is moved to different locations within the line of sight of the transmitter and the receiver have also been analyzed. BERs with respect to variations in the fading parameter ‘m’ have also been presented and discussed. Copyright © 2013 John Wiley & Sons, Ltd.     

Combined orthogonal physical‐layer network coding over fading two‐way relay channels

This paper proposes a new physical‐layer network coding (PNC) scheme, named combined orthogonal PNC (COPNC), for fading two‐way relay channels. The scheme is based on orthogonal PNC (OPNC). In the scheme, the two source nodes employ orthogonal carriers, and the relay node makes an orthogonal combining of the two information bits rather than exclusive or (XOR), which is employed in most PNC schemes. The paper also analyzes the bit error rate (BER) performance of PNC, OPNC, and COPNC for Rayleigh fading model. Simulation results for Rayleigh and Nakagami‐m fading channels show that COPNC can provide outstanding BER performance compared with PNC and OPNC, especially when the uplink channel conditions are asymmetric. The results in Nakagami‐m channels also imply that COPNC will provide higher BER gain with more severe fading depth. Potential works about COPNC are also presented in this paper. Copyright © 2013 John Wiley & Sons, Ltd.     

Outage Probability of Opportunistic Amplify‐and‐Forward Relaying in Nakagami‐m Fading Channels

We address the outage performance for the opportunistic amplify‐and‐forward relaying strategies under Nakagami‐m fading channels. A closed‐form expression for the outage probability is derived. Simulation results verify our theoretical solutions.     

Secrecy outage probability of inter‐vehicular cognitive radio networks

Herein, we consider an underlay cognitive radio network (CRN) where mobile secondary user wishes to transmit a confidential information to the secondary destination in the presence of an illegitimate eavesdropper which is trying to steal the classified message signal. The proposed scenario can be viable for a secondary safety task force working with a primary regiment, which wishes to transmit the confidential information to the commander while an eavesdropper is trying to intercept the classified information. In the analysis, two novel power allocation methods are considered by assuming perfect and limited feedback channels of the primary network, and for both methods, exact and asymptotic expressions of secrecy outage probability (SOP) are derived for N*Nakagami‐m fading channels which are used to model fading channels such as mobile‐to‐mobile/vehicle‐to‐vehicle communication systems where the nodes are moving into a rich scattering environment. We further verified our analytic results through Monte‐Carlo simulations. It is shown from the numerical results that the cascading degree of the channels has a worsening effect on the secrecy outage performance of the CRN systems.     

An evolutionary spectrum approach to modeling non‐stationary fading channels

To evaluate mobile communication systems, it is important to develop accurate and concise fading channel models. However, fading encountered in mobile communication is usually non‐stationary, and the existing methods can only model quasi‐stationary or piecewise‐stationary fading instead of general non‐stationary fading. To address this, this paper proposes an evolutionary spectrum (ES)‐based approach to modeling non‐stationary fading channels. Our ES approach is more general than the existing piecewise‐stationary models and is capable of characterizing a general non‐stationary fading channel that has an arbitrary ES (or time‐varying power spectral density); our ES approach is parsimonious and is also able to generate stationary fading processes. As an example, we show how to apply our ES approach to generating stationary and non‐stationary correlated Nakagami‐m fading channel processes. Simulation results show that the ES of the channel gain process produced by our ES‐based channel model agrees well with the user‐specified ES, indicating the accuracy of our ES‐based channel model. Copyright © 2011 John Wiley & Sons, Ltd.