Error probability performance of L-branch diversity reception ofMQAM in Rayleigh fading

New exact expressions involving hypergeometric functions are derived for the symbol-error rate (SER) of M-ary quadrature amplitude modulation (MQAM) for L branch diversity reception in Rayleigh fading and additive white Gaussian noise (AWGN). The diversity combining techniques considered are maximum ratio combining (MRC) and selection combining (SC). MRC with identical channels and dissimilar channels are analyzed     

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.     

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.     

Exact evaluation of maximal-ratio and equal-gain diversityreceivers for M-ary QAM on Nakagami fading channels

Exact integral expressions are derived for calculating the symbol-error rate (SER) of multilevel quadrature amplitude modulation (MQAM) in conjunction with L-fold antenna diversity on arbitrary Nakagami fading channel. Both maximal-ratio combining (MRC) (in independent and correlated fading) and equal-gain combining (EGC) predetection (in independent fading) diversity techniques have been considered. Exact closed-form SER expressions for two restricted Nakagami fading cases (MRC reception) are also derived. An exact analysis of EGC for MQAM has not been reported previously, despite its practical interest. Remarkably, the exact SER integrals can also be replaced by a finite-series approximation formula. A useful procedure for computing the confluent hypergeometric series is also presented     

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.     

MQAM和MPSK在Nakagami衰落信道中的BER性能

基于AWGN信道中MQAM和MPSK的BER性能的近似准确分析结果，本文导出并分析了MQAM和MPSK在Nakagami-m衰落信道中采用或不采用MRC分集时的BER性能。分析结果表明，在AWGN信道、瑞利衰落信道甚至莱斯衰落信道下，现有采用或不采用MRC分集的系统性能分析结果均可以作为本文分析结果的特例。     

Cognitive amplify‐and‐forward relay networks with beamforming under primary user power constraint over Nakagami‐m fading channels

In this paper, we analyze the performance of cognitive amplify‐and‐forward (AF) relay networks with beamforming under the peak interference power constraint of the primary user (PU). We focus on the scenario that beamforming is applied at the multi‐antenna secondary transmitter and receiver. Also, the secondary relay network operates in channel state information‐assisted AF mode, and the signals undergo independent Nakagami‐m fading. In particular, closed‐form expressions for the outage probability and symbol error rate (SER) of the considered network over Nakagami‐m fading are presented. More importantly, asymptotic closed‐form expressions for the outage probability and SER are derived. These tractable closed‐form expressions for the network performance readily enable us to evaluate and examine the impact of network parameters on the system performance. Specifically, the impact of the number of antennas, the fading severity parameters, the channel mean powers, and the peak interference power is addressed. The asymptotic analysis manifests that the peak interference power constraint imposed on the secondary relay network has no effect on the diversity gain. However, the coding gain is affected by the fading parameters of the links from the primary receiver to the secondary relay network. Copyright © 2012 John Wiley & Sons, Ltd.     

Performance of MRC Diversity Systems for the Detection of Signals with Nakagami Fading

Bit error rate (BER) is analyzed theoretically for diversity reception in Nakagami fading environment using anM-branch maximal ratio combiner (MRC). Coherent and incoherent reception of frequency shift keying (FSK) are considered, using the multiple branch diversity system for both identical and different diversity branch fading parameters. The effect of correlation is also considered for the dual diversity case. The results are extended to include coherent phase shift keying (CPSK) and differential phase shift keying (DPSK).     

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.     

Error Probabilities for MRC Diversity Reception of MDPSK in Slow Nakagami Fading

New closed form error probability expressions for M-arydifferential-phase-shift-keying (MDPSK) with maximal ratio combining (MRC)diversity reception in Nakagami fading, are derived. These expressions involveeasily computable Legendre polynomials and Associated Legendre functions. Bysetting the fading severity parameter m to unity, the new general errorprobability formula reduces to the known results for MDPSK systems in slowRayleigh fading. For binary DPSK, the bit error rate (BER) performance withMRC is compared with known results for selection diversity combining (SDC).It is shown that MRC is more effective than SDC in improving BER performancefor the Nakagami channels, as expected. We also discuss the ranges of thefading severity parameter and diversity order, within which the errorprobability expressions can be computed efficiently.     

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.     

相关MIMO Nakagami衰落信道上MQAM WCDMA系统的性能分析

使用矩生成函数(MGF)方法,推导相关MIMO Nakagami衰落信道上WCDMA系统下行链路中采用组合二维瑞克(2D RAKE)接收机和发送分集的M进制正交幅度调制(MQAM)的平均误符号率精确解析表达式.利用获得的解析表达式,研究天线阵结构(如发射天线和接收天线的数目、天线间的距离)和工作环境(如衰落系数、角度扩展、多径延迟轮廓等)对MQAM WCDMA系统性能的影响.     

Performance and diversity analysis of decode‐and‐forward cooperative system over Nakagami‐m fading channels

In this paper, we derive the upper bound of bit‐error rate (BER) performance and diversity gain for a decode‐and‐forward (DF) cooperative system. Either maximal‐ratio combining (MRC) or cooperative MRC (C‐MRC) is employed at the receiver in the presence of independent, non‐identical Nakagami‐m fading. Both analytical and simulation results show that C‐MRC takes advantage of spatial diversity more efficiently and thus achieves the same or better performance and diversity order as compared to MRC. Copyright © 2009 John Wiley & Sons, Ltd.     

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.     

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.     

Second‐order statistics of system with N‐branch microdiversity and L‐branch macrodiversity operating over gamma shadowed Nakagami‐m fading channels

The problem concerning short‐term fading and long‐term fading (shadowing) and their deleterious effects on wireless systems performance has been in focus for a long time. In this paper, motivated by the results of propagation measurements in land‐mobile and indoor‐mobile systems, and by the fact that gamma distribution can describe shadowing reliably, Nakagami‐m distribution is used to model the signal envelope and gamma distribution is used to model the average signal power. Receive diversity with maximal‐ratio combining and selection combining is implemented at the microlevel and macrolevel, respectively. The general case is explored, which assumes that microdiversity and macrodiversity are provided through arbitrary number of channels. Because shadowing has larger correlation distance than short‐term fading, correlated macrodiversity channels are studied. This paper investigates the dynamics of the received signal. A novel rapidly converging infinite‐series expression for average level crossing rate and average fade duration are obtained. Numerical results are graphically presented to examine the impact of fading severity, shadowing severity, number of diversity branches at the microlevel, number of base stations and correlation between base stations to the system's performance. Computer simulations are also performed to verify the validity and the accuracy of proposed theoretical analysis. Copyright © 2012 John Wiley & Sons, Ltd.     

Quadrature space shift keying performance with dual‐hop AF relay over mixed fading

Quadrature space shift keying (QSSK) modulation combined with cooperative relaying improves the reliability in communication and enhances the overall spectral efficiency. Here, QSSK scheme is analyzed for multiple‐input multiple‐output (MIMO) wireless communication system with dual‐hop amplify‐and‐forward (AF) relaying systems over asymmetric mixed Rayleigh/Rician and symmetric Nakagami‐m/Nakagami‐m fading channels. Analytical expressions for cumulative distribution function (CDF) of the end‐to‐end signal‐to‐noise ratio are derived and used to evaluate the average bit error probability (ABEP) of QSSK modulation in mixed asymmetric and symmetric fading channels. The obtained ABEP expression is in the form of Whittaker function, which can be numerically evaluated using its numerical or series representation. Numerical and simulation results are presented to illustrate the impact of fading parameters on the system performance.     

An Exact Error Probability Analysis of OFDM Systems with Frequency Offset

In this paper, we derive exact closed form bit error rate (BER) or symbol error rate (SER) expressions for orthogonal frequency division multiplexing (OFDM) systems with carrier frequency offset (CFO). We consider the performance of an OFDM system subject to CFO error in additive white Gaussian noise (AWGN), frequency flat and frequency selective Rayleigh fading channels. The BER/ SER performances of BPSK and QPSK modulation schemes are analyzed for AWGN and frequency-flat Rayleigh fading channels while BPSK is considered for frequency-selective Rayleigh fading channels. Our results can easily be reduced to the respective analytical error rate expressions for the OFDM systems without CFO error. Furthermore, the simulation results are provided to verify the accuracy of the new error rate expressions.     

BER of Differentially Detected π/4-DQPSK with Selection Combining in Nakagami-m Fading

Nakagami’s m distribution is a versatile statistical model to characterize small-scale multipath fading in wireless channels. On the other hand, selection combining (SC) is a widely practiced diversity technique to mitigate the detrimental effects of multipath fading. Thus, when SC is applied over Nakagami fading channel, the error performance improvement for any given modulation format is of considerable interest. Since the last decade, π/4-shifted differential quadrature phase shift keying (π/4-DQPSK) modulation has attracted much attention as it is used for high-capacity code division multiple access (CDMA) based digital cellular systems. One of the major reasons behind this is the provision for differential detection which allows production of low complexity mobile units. In this paper, we present analytical expressions for bit error rate (BER) of π/4-DQPSK modulation with L-branch SC diversity in Nakagami-m fading channels perturbed by additive white Gaussian noise (AWGN). The derived end expressions are in closed form and contain finite series of Gaussian hypergeometric function. This makes evaluation of error rates much more straightforward compared to earlier approaches that required single or even double numerical integration. Some special instances such as the nondiversity case and Rayleigh fading case are also investigated and plotted along with the main findings. For different fading parameter (m) values and for different diversity orders (L), simulated results are shown to be in excellent agreement with the derived analytical results. All the results are, however, limited to integer values of fading severity parameter m.     

Analysis of SER of MIMO‐MRC systems with imperfect channel estimation in the presence of non‐Rayleigh CCIs

In this paper, we study the average symbol error rate (SER) for a multiple input multiple output (MIMO) maximal ratio combining (MRC) system with Rayleigh fading desired signal in the presence of non‐Rayleigh fading co‐channel interferers (CCIs) and additive white Gaussian noise (AWGN). To simulate the actual environments of wireless transmission, we assume that the transceiver only obtains imperfect channel estimation (ICE). For the cases of Nakagami and Rician fading CCIs, analytic expressions for the SER have been derived approximately by introducing the modified signal‐to‐interference and noise power ratio (SINR) that can be obtained by averaging the CCI term in the original SINR over the distribution of ICE of intended user. These formulas can provide important reference of design of MIMO diversity systems. Numerical simulations verify the effectiveness of these formulas. Copyright © 2010 John Wiley & Sons, Ltd.