Asymptotic analysis of multi‐branch EGC and SC over equally correlated Rician channels

Closed‐form asymptotic expressions for bit error rate and outage probability are derived for multi‐branch equal gain combining and selection combining receiver diversity over equally correlated Rician channels. Numerical results indicate that these analytical solutions can provide accurate estimation of bit error rate and outage probability in large signal‐to‐noise ratio regimes. The analytical results reveal some important insights into the performance characteristics of equal gain combining and selection combining diversity operating over equally correlated Rician fading channels. Copyright © 2013 John Wiley & Sons, Ltd.     

Performance evaluation of generalized selection diversity systems over Nakagami‐m fading channels

The generalized selection combining (GSC) scheme that adaptively combines a subset of M strongest paths out of L available diversity paths finds applications in several wideband receivers and broadband wireless communications. In this paper, exact closed‐form expressions for the moment generating function (MGF), the probability density function (PDF) and the cumulative density function (CDF) of the GSC(M, L) output signal‐to‐noise ratio (SNR) in independent and identically distributed (i.i.d) Nakagami‐m fading channels are derived while the fading index is a positive integer. These expressions hold for any M and L and provide a comprehensive framework for performance analysis including the derivation of closed‐form formulas for the average symbol error probability (ASEP) of a broad class of binary and M‐ary modulations, mean combined SNR and the outage probability of GSC(M, L) receiver structures. When the Nakagami‐m fading index is not an integer, the MGF of GSC(M, L) output SNR is derived as an (M − 1)‐fold infinite series. With this MGF, analytical expressions for both the outage probability and error rates can be readily obtained. An easily programmable recursive solution of the MGF of GSC(M, L) output SNR is also outlined for both the positive integer and noninteger fading severity index cases. Copyright © 2002 John Wiley & Sons, Ltd.     

Performance analysis of a variable‐gain amplify‐and‐forward relayed mixed RF‐FSO system

In this work, an amplify‐and‐forward variable‐gain relayed mixed RF‐FSO system is studied. The considered dual‐hop system consists of a radio frequency (RF) link followed by a free space optical (FSO) channel. The RF link is affected by short‐term multipath fading and long‐term shadowing effects and is assumed to follow the generalized‐K fading distribution that approximates accurately several important distributions often used to model communication channels. The FSO channel experiences fading caused by atmospheric turbulence that is modeled by the gamma‐gamma distribution characterizing moderate and strong turbulence conditions. The FSO channel also suffers path loss and pointing error induced misalignment fading. The performance of the considered system is analyzed under the collective influence of distribution shaping parameters, pointing errors that result in misalignment fading, atmospheric turbulence, and path loss. The moment‐generating function of the Signal power to noise power ratio measured end‐to‐end for this system is derived. The cumulative distribution function for the Signal power to noise power ratio present between the source and destination receiver is also evaluated. Further, we investigate the error and outage performance and the average channel capacity for this system. The analytical expressions in closed form for the outage probability, symbol and bit error rate considering different modulation schemes and channel capacity are also derived. The mathematical expressions obtained are also demonstrated by numerical plots.     

Performance analysis of AF OFDM system using multiple relay in presence of nonlinear‐PA over inid Nakagami‐m fading

In this paper, performance of an orthogonal frequency division multiplexing–based variable‐gain amplify and forward cooperative system using multiple relay with relay selection is analyzed over independent but not necessarily identically distributed frequency selective Nakagami‐m fading channels. For the analysis, nonlinear power amplifier is considered at the relay, and selection combining is adopted at destination node. Closed‐form expressions of the outage probability for various threshold signal‐to‐noise ratio (SNR) values and average symbol error rate for M‐ary quadrature amplitude modulation techniques are derived for the considered system. Further, the outage probability analysis is performed in high SNR regime to obtain the diversity order. Furthermore, impact of different fading parameters, multiple relay, and nonlinear power amplifier is highlighted on the outage probability and asymptotic outage probability for various threshold SNRs and on the average symbol error rate for various quadrature amplitude modulation constellations. The derived analytical expressions are generalized for various fading environments while considering the integer‐valued fading parameters. Finally, all the analytical results are verified through the Monte Carlo simulations for various SNR levels and system configurations.     

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.     

On the Performance Analysis of Digital Modulations in Generalized-K Fading Channels

In this paper we present novel expressions for several performance metrics of communication systems operating over a composite fading environment modelled by the generalized-K distribution. Initially, for a generalized-K fading channel with arbitrary values for the small and large-scale fading parameters we derive a closed-form expression for the moment generating function (MGF) of the received signal-to-noise ratio (SNR) and utilize it to obtain the exact average symbol error probability for a variety of digital modulations using the MGF based approach. Then, for integer values of the small-scale fading parameter, we derive a novel closed-form expression for the cumulative distribution function of the received SNR, which is then used to obtain closed-form expressions for the outage probability, the average bit error probability of various digital modulations, and the ergodic capacity of the generalized-K fading channel.     

Nakagami-m衰落信道下固定增益中继系统性能分析

 在Nakagami-m衰落信道下,分析了两跳固定增益放大转发中继通信系统的性能.首先采用基于概率密度函数(PDF)的性能分析法推导了无协作分集时系统的中断概率和平均误符号率(ASER)的闭合表达式,然后采用基于矩生成函数(MGF)的方法推导了有协作分集时系统的中断概率和ASER表达式以及接收信噪比的n阶矩的闭合表达式.仿真结果显示,所推导的闭合表达式与数值仿真结果吻合良好,协作分集和较大的m值可提升系统性能,中继前后两跳的信道质量对系统性能的影响并不相同.     

Analysis of hybrid selection/maximal-ratio diversity combiners withGaussian errors

The paper examines the impact of Gaussian distributed weighting errors (in the channel gain estimates used for coherent combination) on both the output statistics of a hybrid selection/maximal-ratio (SC/MRC) receiver and the degradation of the average symbol-error rate (ASER) performance as compared with the ideal case. New expressions are derived for the probability density function, cumulative distribution function and moment generating function (MGF) of the coherent hybrid SC/MRC combiner output signal-to-noise ratio (SNR). The MGF is then used to derive exact, closed-form, ASER expressions for binary and M-ary modulations in conjunction a nonideal hybrid SC/MRC receiver in a Rayleigh fading environment. Results for both selection combining (SC) and maximal-ratio combining (MRC) are obtained as limiting cases. Additionally, the effect of the weighting errors on both the outage rate of error probability and the average combined SNR is investigated. These analytical results provide insights into the tradeoff between diversity gain and combination losses, in concert with increasing orders of diversity branches in an energy-sharing communication system     

Switching rate and receiver performance of binary modulations with the selection‐and‐stay combining over independent and correlated Nakagami‐m fading channels

The dual‐branch selection‐and‐stay combining (SSTC) is analyzed for diversity reception on independent and correlated Nakagami‐m fading channels, where the conventional selection combining (SC) is employed only at the switching instance, and the receiver uses the selected branch till its signal‐to‐noise ratio (SNR) estimation is lower than a preset threshold. In this combining scheme, the receiver only needs to continuously estimate the SNR of the single selected branch. For the performance analysis of SSTC, the switching rate and the average bit error rates (BERs) of different binary coherent and non‐coherent modulations are evaluated. Numerical results based on the analysis and simulations are illustrated. According to the analysis and numerical results, the SSTC outperforms the existing switch‐and‐stay combining in the senses of the average BER and switching rate. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

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.     

Unified performance analysis of maximal‐ratio combining for spectrum sharing systems with antenna correlation

A comprehensive analytical framework of a spectrum sharing system, in which secondary receiver (SR) is equipped with multiple antennas, is presented over Rayleigh fading channels. The impact of spatial fading correlation on the performance of spectrum sharing system with maximal‐ratio combining at the SR is investigated. In particular, we explicitly derive the CDF and moment generating function of the end‐to‐end signal‐to‐noise ratio by assuming a correlation model with arbitrary eigenvalue multiplicities at the SR. On the basis of these results, we conduct an evaluation of secondary system performance in terms of the outage probability, the average symbol error probability, and the ergodic capacity. All analytical results are verified by Monte Carlo simulations. Furthermore, to obtain an insight of system performance, the asymptotic analysis is studied to obtain the diversity gain and the coding gain in the peak transmit power dominated region. Our results show that the diversity gain is unaffected by antenna correlation whereas the coding gain is degraded. Copyright © 2013 John Wiley & Sons, Ltd.     

Performance analysis of selective combining decode‐and‐forward relay networks over Nakagami‐n and Nakagami‐q fading channels

In this paper, we present the performance of selective combining decode‐and‐forward relay networks in independent and non‐identically distributed Nakagami‐n and Nakagami‐q fading channels by using the best–worse and the decoding‐set approaches. 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, we analyze the outage probability at high SNRs, and then, we optimize it. Beside the optimum method, we have proposed a sub‐optimum adaptive method. Also, we derive the outage probability for the selection‐combining case with the direct link between the source and the destination. Finally, for comparison with analytical formulas, we perform some Monte‐Carlo simulations. Copyright © 2012 John Wiley & Sons, Ltd.     

The effect of Gaussian error in selection diversity combiners

Selection diversity combining (SDC) is one of the simplest and most commonly implemented diversity mechanism for mitigating the detrimental effects of deep fades experienced on wireless channels. While SDC improves the mean combined signal‐to‐noise ratio (SNR) over that of a single branch with increasing diversity order, its main advantage is the reduction of the probability of deep fades. The effect of Gaussian errors in the branch gain estimates on the SDC receiver performance is investigated by deriving new closed‐form expressions for the probability density function, cumulative distribution function and the moment generating function of the combiner output SNR statistic. Mathematical expressions for quantifying the degradation in the mean combined SNR, outage probability and the average symbol error rate of a broad class of binary and multilevel modulation schemes owing to imperfect branch SNR estimates in Rayleigh fading are also derived. It is shown that combiner errors affect the mean combined SNR negligibly in comparison to their effect on the deep fades. Copyright © 2001 John Wiley & Sons, Ltd.     

Performance analysis of multi-antenna relay networks with imperfect channel estimation

In this paper, we present the performance of multi-antenna selective combining decode-and-forward (SC-DF) relay networks over independent but non-identical Nakagami-m fading channels with imperfect channel estimation. The outage probability, moment generating function (MGF) and symbol error probability (SEP) will be derived in closed-form using the SNR statistical characteristics. To make the analysis trackable, we have derived the MGF and SEP for integer values of fading severity, m. Also, to make the relations more simple, we develop high signal to noise ratio (SNR) analysis for the performance metrics of our system. Subsequently, we propose optimal and adaptive power allocation algorithms along with the equal power allocation method. Finally, for comparison with analytical formulas, we perform some Monte-Carlo simulations.     

Performance analysis of dual MRC receiver in correlated hoyt fading channels

Performance of a dual maximal ratio combining receiver has been analyzed in correlated Hoyt fading channels. Analytical expressions for the probability density function of the receiver output signal-to-noise ratio (SNR), average SNR, outage probability and average bit error rate performance for binary, coherent and non-coherent modulations have been presented. Numerical results show that for coherent phase shit-keying and differential phase shift-keying modulations, to achieve an ABER of 10^?7, the required excess SNR is relatively small for correlation coefficient (?) less than 0.5 than it is for ? ≫ 0.5.     

Signaling constellations for fading channels

The performance of various coherent 8-ary and 16-ary modulations in additive white Gaussian noise (AWGN) and slowly fading channels are analyzed. New expressions for the exact symbol error rates (SER) in fading with diversity combining are derived for any two-dimensional signaling format having polygonal decision boundaries. Maximal ratio combining, equal gain combining, and selection combining are considered. The SER formulas obtained make it possible for the first time to optimize parameters of various constellations precisely and to determine,which constellation has the lowest probability of error. For example, a star constellation such as that specified in the CCITT V.29 standard can be improved by adjusting the amplitude ratios of the points in the constellation to save about 0.63 dB power in AWGN without sacrificing the phase error tolerance, while maintaining the same error rate. The sensitivity of each constellation to phase error is presented and comparisons are made. Six 8-ary signal sets and 11 16-ary signal sets are examined using the new symbol error probability formulas to determine best signal sets for fading channels     

N-m衰落下双跳多中继协作通信系统的性能分析

An exact average symbol error rate analysis for the distributed dual-hop relay cooperative network with multiple relays in a Nakagami-m fading environment is presented. In the derivation of the moment generation function of receiver Signal-to-Noise Ratio(SNR), the sectional integral method is used, instead of the cumulative density function method which is ordinarily used by the deduction of the outage probability of S-R-D link. The accurate symbol error rate of a dual-hop relay cooperative network is obtained with the closed-form Moment Genoration Function (MGF) expression. The correctness of the symbol error rate is verified through numerical simulations and is compared with other analytical methods. These deductions clearly show that the distributed cooperative diversity network presented has strong superiorities in overcoming severe fading and can achieve full diversity order.     

Performance of Non-coherent MFSK with Selection and Switched Diversity Over Hoyt Fading Channel

A closed-form expression of cumulative distribution function (CDF) of the instantaneous signal to noise ratio (SNR) in Hoyt fading channel is derived. This CDF and associated formulas are then used to find out the error probability of non-coherent M-ary frequency shift keying with multichannel reception. Simple finite-range integral expression for the symbol error probability (SEP) with selection diversity is found through CDF method. Next, closed-form expressions of moment generating functions (MGF) are presented for the switched diversity case and SEP values are calculated using the derived MGFs. Some other performance parameters like, outage probability and average SNR with switched diversity, are provided. In addition, analytic frameworks are presented for calculation of optimum switching thresholds that ensure minimum outage probability or minimum SEP. The analysis is quite general in the sense that it covers switch and stay combining and Rayleigh fading as special cases.     

Performance comparison of dual‐hop hybrid decode‐or‐amplify‐forward relay schemes for M‐ary quadrature amplitude modulation burst transmission over Rayleigh fading channels

This paper shows the analytical performance expressions of M‐ary quadrature amplitude modulation burst symbol transmission for hybrid decode‐or‐amplify‐forward (HDAF) relay schemes over quasi‐static Rayleigh‐fading channels. First, we derive the probability density function of the received instantaneous signal‐to‐noise ratio as the simplified form, which is related to all the possible occurrence probabilities of error‐events for M‐ary quadrature amplitude modulation burst transmission. On the basis of the derived probability density function, we express average bit error probability, average symbol error probability, and average burst error rate as closed forms, which can be also applied to both amplify‐and‐forward and adaptive decode‐and‐forward (ADF) schemes. The analysis and simulation results show that HDAF scheme for burst transmission can achieve the performance of ADF scheme with symbol‐by‐symbol transmission, which is the achievable lower bound. Furthermore, the outage probability, the normalized channel capacity, and the goodput performance are also derived as closed forms. The analysis shows the superiority of HDAF scheme to ADF scheme. Comparison with simulations confirms that the derived analytical expressions are accurate over all signal‐to‐noise ratio regions and for different numbers of relays and modulation orders.