Average bit error probability performance of intelligent reflecting surface-aided wireless communications over Hoyt fading

In this article, the performance of a wireless communication system with an intelligent reflecting surface (IRS) panel installed between the transmitter and receiver is studied. The channel is considered to be the Hoyt faded and additive white Gaussian noise. Closed-form expressions for average bit error probability (ABEP) for both coherent Gray-coded rectangular quadrature amplitude modulation and non-coherent modulation schemes are presented. We apply the moment-generating function-based method for the derivation. In addition, asymptotic ABEP expressions are also obtained. Using asymptotic ABEP expressions, we obtained diversity order which is a function of the number of IRS elements. The effect of the number of IRS elements and fading parameters on the ABEP is studied. The ABEP performance improves with an increase in the number of reflecting elements but degrades with an increase in the fading severity. The accuracy of each analytical ABEP expression is verified by the simulation of the system considered herewith.     

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 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.     

Effect of bit-to-bit dependence on packet error rate using asynchronous DS-CDMA for mobile packet radio networks

The probability of packet success for asynchronous direct sequence code division multiple access (DS-CDMA) over the multipath fading channel is investigated under different fading conditions and for different cases. We studied the bit-to-bit dependence caused by the multipath fading and by the multiple access interference (MAI) originating from the chip and phase offsets between the desired and interfering signals. We investigated the effect of using the Gaussian versus the improved Gaussian process on the computation of probability of packet success as well as the effect of the bit-to-bit dependence within a packet. The improved Gaussian approximation provides more accurate values for the probability of bit error for any number of simultaneous users, while it also allows us to incorporate the effects of bit-to-bit dependence into the calculations of the probability of packet success.This paper was presented in part at the 17th Biennial Symposium on Communiations, Kingston, June 1994. This work was supported by a strategic grant (STR-0100720) from the Natural Sciences and Engineering Research Council (NSERC) of Canada.     

Simplified approximations to the average of some useful forms of Gaussian Q functions with MRC diversity reception over Nakagami-q and Rician fading channels and their applications

In this paper, using an accurate exponential based approximation on the Gaussian Q function, the simplified novel approximations to the average of some useful forms of Gaussian Q functions, with maximal-ratio combining (MRC) diversity reception, over independent but not necessarily identical Nakagami-q (Hoyt) and Rician fading channels are proposed. The results proved to be useful in accurate estimation of the symbol error probability (SEP) for various digital modulation schemes like cross-QAM, triangular-QAM (TQAM), rectangular-QAM and square-QAM (SQAM), over the same fading statistics. Asymptotic expressions of the proposed approximations are also derived in this paper. Various simulation results are provided to verify the accuracy and significance of the proposed work.     

Performances of 16QAM with fading compensation and postdetection diversity reception in satellite mobile channels

This paper studies the effects of N-branch postdetection selection diversity reception, where N = 1, 2, 3 or 4, incorporated with fading compensation on a digital satellite mobile system. The digital satellite mobile system transmits a pilot-symbol-aided 16-ary quadrature-amplitude modulated (PSA-16QAM) signal over the Rician channels. A selection method that makes use of the pilot symbols to select one of the N branches in the diversity reception system for signal detection, and a novel PSA technique that makes use of both the pilot symbols and data symbols for fading compensation, are proposed. Computer simulation tests are used to assess the effects of the proposed techniques on bit-error rate performances (BER) of the PSA-16QAM system in the presence of additive white Gaussian noise (AWGN) or co-channel interference (CCI) in the Rician faded channels. When frequency diversity is used, PSA-16QAM with 2-branch and 4-branch diversity reception occupies about the same bandwidths as quaternary phase-shift-keying (QPSK) without using diversity and with 2-branch diversity, respectively, yet achieving the same capacity. Thus, simulation tests on the BER performances of a QPSK system without diversity and with 2-branch diversity are also carried out and the results are used to determine the preferred system arrangements. © 1997 John Wiley & Sons, Ltd.     

Generalized solution to symbol error probability integral containing over different fading models

This paper presents a generalized solution to the symbol error probability (SEP) integral containing the product of two Gaussian Q‐functions . Numerical integration technique is first used to approximate the polar form of as a sum of exponentials. This approximation is then used to derive a closed‐form solution to the related SEP integral. Due to the exponential nature of the approximation, solution to the integral is expressed in terms of moment generating function (MGF) of a fading distribution. Therefore, the solution to integral exists for all fading distributions which have well‐defined MGF. The mathematical complexity of the proposed solution is directly proportional to the complexity of MGF expression. For most of the fading models, the corresponding MGF involves power or exponential functions, which guarantees algebraic simplicity of the proposed solution. Further, this generalized solution is used to evaluate the SEP of various modulation schemes over different fading channels. Various computer simulations run in MATLAB for wide range of scenarios confirm the accuracy of the proposed approximation and solution.     

Unified analysis of EGC diversity over Weibull fading channels

In this paper, the performance analysis based on PDF approach of an L ‐branch equal gain combiner (EGC) over independent and not necessarily identical Weibull fading channels is presented. Several closed‐form approximate expressions are derived in terms of only one Fox H‐function as PDF, cumulative distribution function, and moments of the EGC output Signal‐to‐noise ratio (SNR), outage probability, amount of fading, channel capacity, and the average symbol error rate for various digital modulation schemes. All results are illustrated and verified by simulations using computer algebra systems.     

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.     

A simple method to approximate the probability of error for equal gain combiner over independent fading channels

Using the Beaulieu series, the probability of error for equal gain combiner over independent fading channels can be formulated in the form of an infinite series. The computation of the coefficients of this series needs complicated integrations over fading envelope distribution. In this paper, a new approximation method is developed for the computation of the required coefficients of the error probability series, which needs only mean and variance of the fading envelope. Hence, the purposed method eliminates the need for complicated integrations while computing the required coefficients. This feature provides an interesting flexibility for our developed method, so that it can be used as a unified method for performance analysis of equal gain combiner over various independent fading channels, especially where the required integrations have no closed‐form solutions. To present an application for the proposed approximation method, the fading channel is modeled by three‐parameter generalized Gamma distribution (GG3), which is a generic model that covers many well‐known channel models for both multipath and shadow fading. The presented numerical results show good accuracy as well as low computational complexity of the presented method. Copyright © 2007 John Wiley & Sons, Ltd.     

Comments on “Average LCR and AFD for SC diversity over correlated Weibull fading channels”

In a recent paper, two formulae for the average level crossing rate and fade duration at the output of dual-branch selection diversity receivers have been derived. In this short communication, some previously published works including results being in a more general setting are reviewed and compared.     

Performance of DSWC diversity system using suboptimum adaptive switching threshold in independent and correlated nakagami‐m fading channels

The use of dual switched combining (DSWC) diversity reception scheme, for combating the detrimental effects of fading on digital transmissions, is popular due to its simpler implementation. The performance of switched diversity strategy is dependent on the selection of the switching threshold. But, for the analysis and design of the DSWC diversity system, the closed form analytical solution for optimum adaptive switching threshold is not possible for most of the modulation schemes in correlated fading environment. This letter presents an approximate, but simple and closed form, generic expression for adaptive switching threshold, called in this case as suboptimum adaptive switching threshold, in independent and correlated Nakagami‐m fading channels for a wide range of binary and M‐ary modulation schemes. It is shown that the average symbol error rate (ASER) performance obtained using this suboptimum adaptive switching threshold is almost same as obtained using optimum adaptive switching threshold. Copyright © 2005 John Wiley & Sons, Ltd.     

Performance analysis of equal-gain diversity receivers over generalized Gamma fading channels

Generalized Gamma (GG) distribution is a generic model that covers many well-known fading distributions as special cases. This paper deals with the performance analysis of L-branch equal gain combining (EGC) receivers operating over GG fading channels. For these receivers and by using convergent infinite series approach, the probability of error (P_e) can be formulated in the form of an infinite series. The coefficients of P_e series can be derived by calculating complicated integrations over the fading envelope distribution. In this paper, it is shown that the required integrations for the case of GG distribution have a complex closed-form in terms of Meijer's G function, and then, a new approximation method is developed for computation of them. The proposed method only needs mean and variance of the fading envelope; hence it has low complexity and eliminates the need for calculation of complex functions. The presented numerical examples show that the developed method can approximate the required parameters and also the individual coefficients accurately and this accuracy increases with the increase of L. The proposed method is applied to analyze the probability of error performance of the L-branch EGC receiver with both coherent phase shift keying (CPSK) and frequency shift keying (CFSK) modulation schemes under different GG channel conditions. Also the effect of gain unbalance between diversity branches on the probability of error is investigated.     

Outage probability and channel capacity for the Nth best relay selection AF relaying over INID Rayleigh fading channels

Cooperative diversity systems have recently been proposed as a way to form virtual antenna schemes without utilizing collocated multiple antennas. In this paper, we consider the Nth best opportunistic amplify‐and‐forward (AF) cooperative diversity systems. The AF type can be regarded as one on the basis of modified channel state information. Wireless channels between any pair of nodes (i.e., direct and dual hop links) are assumed quasi‐static independent and nonidentically distributed (INID) Rayleigh fading. The best opportunistic AF (OAF) scheme requires two phases of transmission. During the first phase, the source node transmits a signal to all relays and the destination. In the second phase, the best relay is only selected on the basis of highest signal‐to‐noise ratio (SNR) scheme to forward the source signal to the destination. Therefore, the indirect link (i.e., source‐selected relay destination) can give the highest received SNR. However, the best relay selection cannot be available so that we might choose the second, third, or generally the Nth best relay. In this paper, we derive the approximated outage probability and channel capacity for the Nth best OAF relay systems over INID Rayleigh fading channels. At first, the indirect link's received SNR is approximated as harmonic mean upper bound. With this information, we obtain the given relay's Nth best selection probability as the closed form. Finally, both outage probability and channel capacity are derived as the closed forms. Simulation results are finally presented to validate the analysis. Copyright © 2011 John Wiley & Sons, Ltd.     

Performance of the combining received differential encoding transmit diversity with imperfect carrier recovery over correlated Nakagami fading channels

A differential detection scheme for transmit diversity was proposed by Tarokh, which can achieve full diversity order without the requirement to estimate the channel state at the receiver. This paper investigates the potential of using multiple receive antennas for differential space time coded MPSK signals over correlated Nakagami fading channels. We also investigate the effect of the carrier frequency offset (CFO) and channel correlation on its performance and present some results on its maximal tolerable frequency offsets for different MPSK signals. The results have shown that the differential encoding transmit diversity is very robust to the CFO and channel correlation. Copyright © 2004 John Wiley & Sons, Ltd.     

OFDM-MQAM在相关Nakagami-m衰落信道上的性能分析

本文研究频率选择性相关Nakagami衰落信道上采用最大比合并(MRC)分集接收的正交频分多路复用M进制正交幅度调制(OFDM-MQAM)系统.使用矩生成函数(MGF)方法和高斯超几何函数、Appell超几何函数或Lauricella函数,推导任意衰落参数频率选择性相关Nakagami衰落信道上MRC分集接收的OFDM-MQAM系统的误符号率(SER)性能,获得了OFDM-MQAM误符号率的一个新的解析表达式.数值计算结果阐明了多径路径数、Nakagami衰落参数和信道脉冲响应抽头间的相关系数对OFDM-MQAM误符号率性能的影响.     

Performance analysis of dual switched diversity over correlated Weibull fading channels with co‐channel interference

This paper studies the performance of switch and stay combining (SSC) diversity in the presence of co‐channel interference over correlated Weibull fading channels. SSC diversity based on signal‐to‐interference ratio (SIR) is a low‐complexity and a very efficient technique that reduces fading and co‐channel interference influence. New closed‐form expressions for the probability density function and cumulative distribution function of the output SIR's are derived. These formulas are used in a detailed analysis of the average output SIR and outage probability. The influence of fading severity and correlation coefficient on the optimum switching threshold and system performance is investigated. Monte Carlo simulations are performed to verify obtained theoretical results and determine average bit error rate in detecting binary phase‐shift keying (BPSK), differential BPSK and quadrature amplitude modulation signals. Copyright © 2011 John Wiley & Sons, Ltd.     

Outage probability and error rate analysis of full duplex relay in asymmetric fading channels

Full duplex (FD) technique has evolved as a viable solution to address the spectrum scarce issue. It has gained research interest for its potential to double the wireless link capacity and enhance spectral efficiency (SE). In this paper, the end-to-end performance of an amplify-and-forward full duplex relay(FDR) in asymmetric Rayleigh–Rician fading channels is explored, unlike the other works that assume symmetric fading conditions in both the links. The asymmetric or mixed fading channels properly model the realistic communication scenarios like satellite/terrestrial wireless communication systems. In this work, we consider that the source-relay link experiences Rayleigh fading and the relay-destination link experiences Rician fading. The novel exact and lower bound closed form analytical expressions for outage probability (OP) and bit error rate (BER) for the considered FD system are derived. Moreover, the effect of severity of fading and the amount of residual self-interference (RSI) on the performance of FDR are also studied. In addition, MC simulations are carried out to validate the results. It is observed that the performance metrics, OP and BER, are highly dependent on the severity of fading and the amount of RSI. Furthermore, it is found that typically at the SNR of 10 dB, an improvement of approximately 27.6% in OP is obtained. Also, our work offers appreciable SNR gain, for example, for a BER of 10⁻², an SNR improvement of around 11 dB is achieved. These findings have been compared with the mixed Rayleigh–Rician fading channel conditions considering only half duplex(HD) mode. These parameter metrics are helpful in analyzing the performance of FD in various communication scenarios such as LoS/NLoS conditions and hence pave the way for more realistic FDR.     

Exact error probability of Orthogonal Space-Time Block Codes over flat fading channels

Space time block coding is a modulation scheme recently discovered for the transmit an- tenna diversity to combat the effects of wireless fading channels. Using the equivalent Single-Input Single-Output (SISO) model, this paper presents closed-form expressions for the exact Symbol Error Rate (SER) and Bit Error Rate (BER) of Orthogonal Space-Time Block Codes (OSTBCs) with M-ary Phase-Shift Keying (MPSK) and M-ary Quadrature Amplitude Modulation (MQAM) over flat un- correlated Nakagami-m and Ricean fading channels.     

空间分集相关信道中信号误比特率研究

系统的分集情况对系统的影响是很大的。这里我们研究了空间分集对系统性能的影响。本文推导了在空间分集的情况下非相干检测 FSK信号的误比特率 ,并利用了多径信道的衰落相关性模型 ,通过计算机模拟的方法具体研究了空间分集中天线的距离和散射体分布对的非相干检测 FSK信号误比特率的影响。