Performance Analysis of System with Micro- and Macrodiversity Reception in Correlated Gamma Shadowed Rician Fading Channels

In this paper, the performance of wireless system employing microdiversity to mitigate the effects of short-term fading and macrodiversity to reduce long-term fading (shadowing) effects is studied. The system model assumes implementation of maximal-ratio combining (MRC) at the microlevel and selection combining (SC) at the macrolevel. The received signal envelope follows a Rician distribution and it also suffers gamma shadowing. Novel expressions for the probability density function (PDF), cumulative distribution function (CDF), and moment-generating function (MGF) of the output signal-to-noise ratio (SNR) are obtained. Several useful performance criteria, such as the moments of the output SNR and outage probability are analytically derived. Moreover, the average bit error probability (ABEP) for noncoherent binary differential phase-shift keying (BDPSK) is calculated using the MGF based approach while the ABEP for coherent binary phase-shift keying (BPSK) is studied by averaging the conditional bit error probability over the PDF. Numerical results are graphically presented to show the effects of various system parameters to the system performance, as well as the enhancement due to use of the combination of micro- and macrodiversity. Some of numerical results are complemented by equivalent computer simulated results which validate the accuracy of the proposed analysis. The agreement between the Rician-gamma and Rician-lognormal fading model is also established.     

Performance Analysis of Generic Amplify-and-Forward Cooperative Networks over Asymmetric Fading Channels

In this paper, we analyze the performance of multi-hop multi-branch amplify-and-forward (AF) networks over generalized fading channels. Using the moment generating function (MGF)-based approach, we develop general expressions for the outage probability and symbol-error rate (SER) performance of the system with maximal ratio combining (MRC) receiver. The MGF-based approach relies on numerical integration. To gain insights into system performance, we therefore investigate the asymptotic outage and SER performance of the system with MRC and selection combining (SC) receiver at the destination. In particular, we develop the asymptotic statistics of the end-to-end signal-to-noise ratio (SNR) of an AF multi-hop link. We further derive the cumulative density function of the sum of the individual end-to-end SNRs, received from different diversity paths for MRC receiver. We also study the power allocation problem in a multi-hop multi-branch system with MRC receiver. In generalized Gamma fading environments, we seek to find the power allocation strategy that maximizes the SNR at the destination subject to a total power constraint. By means of simulations, we validate our theoretical developments and verify the efficiency of our proposed power allocation in improving the received SNR compared to a generic cooperative system with no power allocation. We also conclude that our asymptotic expressions for the outage probability and SER match the simulations very well in medium-to-high-SNR regime.     

SER and outage of threshold-based hybrid selection/maximal-ratio combining over generalized fading channels

The average symbol-error rate and outage probability of threshold-based hybrid selection/maximal-ratio combining (T-HS/MRC) in generalized fading environments are analyzed. A T-HS/MRC combiner chooses the combined branches according to a predetermined normalized threshold and the strength of the instantaneous signal-to-noise ratio (SNR) of each branch. Therefore, the number of combined branches is a random variable, rather than a fixed number, as in conventional hybrid selection/maximal-ratio combining (H-S/MRC). Using the moment generating function method, a unified analysis of T-HS/MRC over various slow and frequency-nonselective fading channels is presented. Both independent, identically distributed and independent, nonidentically distributed diversity branches are considered. The derivation allows different M-ary linear modulation schemes. The theory is illustrated using coherent M-ary phase-shift keying in Nakagami-m fading as an example. It is shown that previous published results are incorrect.     

An MGF-based performance analysis of generalized selectioncombining over Rayleigh fading channels

Using the notion of the “spacing” between ordered exponential random variables, a performance analysis of the generalized selection combining (GSC) diversity scheme over Rayleigh fading channels is presented and compared with that of the conventional maximal-ratio combining and selection combining schemes. Starting with the moment generating function (MGF) of the GSC output signal-to-noise ratio (SNR), we derive closed-form expressions for the average combined SNR, outage probability, and average error probability of a wide variety of modulation schemes operating over independently, identically distributed (i.i.d.) diversity paths. Because of their simple form, these expressions readily allow numerical evaluation for cases of practical interest. The results are also extended to the case of non-i.i.d. diversity paths     

Performance analysis of coded communication systems on Nakagami fading channels with selection combining diversity

In this paper, we develop analytical tools for the performance analysis of coded, coherent communication systems on independent and identically distributed Nakagami-m fading channels with selection combining (SC) diversity. First, we derive an exact expression for the moment generation function (MGF) of the signal-to-noise ratio (SNR) of a code symbol at the output of the selection combiner. Next, based on Gauss-Chebyshev quadrature and Gauss-Laguerre quadrature rules, we propose a simple to compute, yet accurate, numerical solution for the pairwise error probability (PEP) of coded M-phase-shift keying (PSK) signals. Using the PEP expressions, we present the union bound-based bit-error performance of trellis-coded modulation schemes and turbo codes. Finally, we derive an exact expression for the computational cutoff rate of a coded system with M-PSK signaling and SC diversity, and show that the cutoff rate expression is a simple function of the MGF of the SNR at the output of the diversity combiner.     

Error Rate of Quadrature Subbranch Hybrid Selection/ Maximal-Ratio Combining in Rayleigh Fading

The symbol-error rate (SER) of a quadrature subbranch hybrid selection/maximal-ratio combining (QBHS/MRC) scheme for 1-D modulations in Rayleigh fading is examined. At the receiver, N diversity branches are split into 2N in-phase and quadrature subbranches. Traditional hybrid selection/maximal-ratio combining (H-S/MRC) is then applied over the 2N subbranches. M-ary pulse amplitude modulation, including coherent binary phase-shift keying, with QBHS/MRC is studied. The SER performances of QBHS/MRC and H-S/MRC are compared. Results show that QBHS/MRC systems outperform traditional H-S/MRC systems     

Performance of M-PSK with GSC and EGC with Gaussian weighting errors

Using a moment-generating function (MGF)-based approach, we study the performance of M-ary phase-shift keying (M-PSK) with generalized selection combining (GSC) and equal gain combining (EGC) in fading channels (including Rayleigh, Rician, Nakagami-m, and Nakagami-q fading) with independent and identically distributed (i.i.d) branches. Analytical expressions for the error and outage probabilities, the signal-to-noise-ratio (SNR) statistics, and the channel capacity of M-PSK diversity receivers are derived, taking into account the effects of Gaussian weighting errors and all relevant system and channel parameters. Unlike the case of perfect channel-state information (CSI), the outage probability for the case of imperfect channel estimation (ICE) is not only a function of the normalized SNR with respect to the SNR threshold, but also a function of the operating SNR itself. The SNR loss of the M-PSK GSC and EGC receivers due to ICE and the relation between the receiver input and output SNRs for ICE are derived. Our results show that, even with ICE, GSC and EGC are effective in improving the output SNR and significantly reduce the error floor and the channel-capacity loss caused by ICE.     

Analysis of hybrid selection/maximal-ratio combining in correlated Nakagami fading

We present an analysis of a hybrid selection/maximal-ratio combining diversity system over an evenly correlated slow frequency-nonselective Nakagami fading channel, where the correlation coefficient between any pair of the diversity branch gain amplitudes is the same, and all average branch signal-to-noise ratios (SNRs) are equal. In this system, the L branches with the largest instantaneous SNR out of N available branches are selected and combined using maximal-ratio combining. From the joint characteristic function (cf) of the instantaneous branch SNRs, we obtain an expression for the cf of the combiner output SNR as a series of elementary cfs. The expression can be conveniently used to obtain the symbol error probability of coherent detection of different M-ary modulation schemes. We illustrate our methodology using M-ary phase-shift keying as an example.     

Outage probability of multi-hop MIMO relaying with transmit antenna selection and ideal relay gain over rayleigh fading channels

We present a study on the outage probability of multi-hop wireless communication systems with multiple-input multiple-output (MIMO) link based on the transmit antenna selection and the maximal-ratio combining (MRC) at the receiver. A nonregenerative system (NS) is investigated with an ideal amplifying gain. MIMO channels are assumed in uncorrelated Rayleigh fading.We derive a moment generating function (MGF) of the reciprocal of the end-to-end signal-to-noise ratio (SNR) and obtain a closed-form approximation on the outage probability through the numerical inversion of a Laplace transform. Numerical results show that the presented outage is exactly matched with the outage probability when assuming the ideal relay gain. For more practical gains, the result is shown to be a lowerbound that gets tight at high average SNR as well as for a small number of hops and/or of antennas. We also compare the outage probabilities of nonregenerative MIMO relaying with a regenerative counterpart for multiple hops.     

Nakagami衰落上DE-QPSK在联合收发分集下的性能分析

利用高斯Q函数的高阶次幂在最大比合并（MRC）分集接收瑞利衰落信道上统计平均的结果,推导了Nakagami 衰落信道上采用组合发射选择合并（SC）/接收 MRC 天线分集的相干检测差分编码四相相移键控（DE-QPSK）的平均误符号率（ASER）精确表达式。利用高斯Q函数的近似表达式和矩生成函数（MGF）方法,推导了Nakagami衰落信道上采用组合SC/MRC天线分集的相干检测DE-QPSK 的ASER近似表达式。通过数值计算和仿真,验证了DE-QPSK的ASER精确表达式的正确性以及近似表达式的准确性。利用精确表达式和近似表达式可研究收发天线数目和衰落参数对DE-QPSK的ASER性能的影响,为实际SC/MRC天线分集方案的设计提供了理论指导。     

Error analysis of generalized selection combining over relay channel

Cooperative communication is a recently popular concept which allows single-antenna devices to benefit from spatial diversity. The performance analysis of cooperative communication using generalized selection combining (GSC) over independent not necessarily identically distributed Nakagami-m fading channels is presented and compared with that of the conventional maximal ratio combining (MRC) and selection combining (SC) schemes. With the aid of Padé approximants theory, new closed-form expression is derived for the moment-generating function (MGF) of the GSC output signal-to-noise ratio (SNR). MGF is an important tool for researching the system performance. In this paper, the average bit-error probability is accurately approximated using the well-known MGF approach. Numerical results show that the proposed mathematical analysis is accurate and that for the more severe fading cases, the GSC receivers are closer to the optimum MRC receivers.     

Analysis of Transmit Antenna Selection/Maximal-Ratio Combining in Rayleigh Fading Channels

In this paper, we investigate a multiple-input-multiple-output (MIMO) scheme combining transmit antenna selection and receiver maximal-ratio combining (the TAS/MRC scheme). In this scheme, a single transmit antenna, which maximizes the total received signal power at the receiver, is selected for uncoded transmission. The closed-form outage probability of the system with transmit antenna selection is presented. The bit error rate (BER) of the TAS/MRC scheme is derived for binary phase-shift keying (BPSK) in flat Rayleigh fading channels. The BER analysis demonstrates that the TAS/MRC scheme can achieve a full diversity order at high signal-to-noise ratios (SNRs), as if all the transmit antennas were used. The average SNR gain of the TAS/MRC is quantified and compared with those of uncoded receiver MRC and space-time block codes (STBCs). The analytical results are verified by simulation. It is shown that the TAS/MRC scheme outperforms some more complex space-time codes of the same spectral efficiency. The cost of the improved performance is a low-rate feedback channel. We also show that channel estimation errors based on pilot symbols have no impact on the diversity order over quasi-static fading channels.     

信道预测联合收发分集的正交信号误码性能

为解决采用最小均方误差(MMSE)信道预测的发射天线选择(TASP)/接收天线最大比合并(MRC)的无线通信系统设计问题,利用抛物柱面函数以及高斯Q函数的近似表达式和矩生成函数(MGF)法,分别推导了瑞利块衰落信道上采用TASP/MRC天线分集的相干检测M进制正交和双正交信号的平均误符号率(ASER)精确表达式以及正交信号ASER的近似表达式.数值计算和仿真结果验证了采用TASP/MRC和相干检测的正交/双正交ASER精确表达式的正确性以及正交信号ASER近似表达式的准确性.上述M进制正交/双正交信号ASER精确或近似表达式,可用于设计采用相干检测M进制正交和双正交信号的TASP/MRC天线分集系统,并能够快速地确定收发天线数和信道预测器级数等参数,避免耗时的计算机仿真.     

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.     

Diversity reception over generalized-K (KG) fading channels

A detailed performance analysis for the most important diversity receivers operating over a composite fading channel modeled by the generalized-K (Kg) distribution is presented. The Kg distribution has been recently considered as a generic and versatile distribution for the accurate modeling of a great variety of short term fading in conjunction with long term fading (shadowing) channel conditions. For this relatively new composite fading model, expressions for important statistical metrics of maximal ratio combining (MRC), equal gain combining (EGC), selection combining (SC) and switch and stay combining (SSC) diversity receivers are derived. Using these expressions and by considering independent but not necessarily identical distributed fading channel conditions, performance criteria, such as average output signal-to-noise ratio, amount of fading and outage probability are obtained in closed form. Moreover, following the moments generating function (MGF) based approach for MRC and SSC receivers, and the Pade approximants method for SC and EGC receivers, the average bit error probability is studied. The proposed mathematical analysis is complemented by various performance evaluation results which demonstrate the accuracy of the theoretical approach.     

Performance of cooperative diversity using Equal Gain Combining (EGC) over Nakagami-m fading channels

Cooperative diversity is a promising technology for future wireless networks. In this paper, we derive exact closed-form expressions for the average bit error rate (BER) and outage probability (Pout) for differential equal gain combining (EGC) in cooperative diversity networks. The considered network uses amplify-and-forward relaying over independent non-identical Nakagami-m fading channels. The performance metrics (BER and Pout) are derived using the moment generating function (MGF) method. Furthermore, we found (in terms of MGF) the SNR moments, the average signal-to-noise ratio (SNR) and amount of fading. Numerical results show that the differential EGC can bene?t from the path-loss reduction and outperform the traditional multiple-input single output (MISO) system. Also, numerical results show that the performance of the differential EGC is comparable to the maximum ratio combining (MRC) performance.     

Performance analysis of QAM in amplify-and-forward cooperative communication networks over Rayleigh fading channels

Performance analysis of quadrature amplitude modulation (QAM) schemes for cooperative amplify-and-forward (AF) dual-hop relaying system over independent and identically distributed (i.i.d.) Rayleigh fading channels are presented in this paper. Specifically, we derive closed-form lower-bound expressions of average symbol error rate (ASER) for general order rectangular QAM (RQAM) and cross QAM (XQAM) using well-known moment generating function (MGF) based approach with maximal ratio combining (MRC) scheme. Further, using best relay selection scheme (BRS), we also derive an ASER expression for XQAM. Numerical and simulated results are compared to validate the correctness of derived expressions. Furthermore, comparative analysis of RQAM and XQAM schemes is discussed which confirms that XQAM is better alternative over RQAM for transmission of odd number of bits per symbol for the considered system model. We also compare the ASER performance for MRC and BRS schemes in terms of SNR gain using different XQAM constellations. Moreover, the impact of system parameters on ASER is also highlighted.     

Performance of dual maximal ratio combining diversity in nonidentical correlated Weibull fading channels using Pade/spl acute/ approximation

In this letter, we evaluate the performance of the dual-branch maximal ratio combining (MRC) diversity scheme in nonidentical correlated Weibull fading channels with arbitrary parameters. We first use the Pade/spl acute/ approximation (PA) to find closed-form rational expressions for the moment generating function (MGF) of the output signal-to-noise ratio (SNR) of the MRC receiver. Different performance measures, such as the outage probability and the average symbol-error rate for different linear modulations, are then presented using the well-known MGF approach. Furthermore, the effect of the input SNRs unbalancing, the severity of fading, and the degree of correlation on the system performance are also studied. Our results are validated by comparing them with computer simulations, and we show that the PA technique is indeed a convenient tool for such performance evaluation studies.     

Virtual branch analysis of symbol error probability for hybridselection/maximal-ratio combining in Rayleigh fading

We derive analytical expressions for the symbol error probability (SEP) for a hybrid selection/maximal-ratio combining (H-S/MRC) diversity system in multipath-fading wireless environments. With H-S/MRC, L out of N diversity branches are selected and combined using maximal-ratio combining (MRC). We consider coherent detection of M-ary phase-shift keying (MPSK) and quadrature amplitude modulation (MQAM) using H-S/MRC for the case of independent Rayleigh fading with equal signal-to-noise ratio averaged over the fading. The proposed problem is made analytically tractable by transforming the ordered physical diversity branches, which are correlated, into independent and identically distributed (i.i.d.) “virtual branches,” which results in a simple derivation of the SEP for arbitrary L and N. We further obtain a canonical structure for the SEP of H-S/MRC as a weighted sum of the elementary SEPs, which are the SEPs using MRC with i.i.d. diversity branches in Rayleigh fading, or equivalently the SEPs of the nondiversity (single-branch) system in Nakagami fading, whose closed-form expressions are well-known. We present numerical examples illustrating that H-S/MRC, even with L≪N, can achieve a performance close to that of N-branch MRC     

Equal-gain and maximal-ratio combining over nonidentical Weibull fading channels

We study the performance of L-branch equal-gain combining (EGC) and maximal-ratio combining (MRC) receivers operating over nonidentical Weibull-fading channels. Closed-form expressions are derived for the moments of the signal-to-noise ratio (SNR) at the output of the combiner and significant performance criteria, for both independent and correlative fading, such as average output SNR, amount of fading and spectral efficiency at the low power regime, are studied. We also evaluate the outage and the average symbol error probability (ASEP) for several coherent and noncoherent modulation schemes, using a closed-form expression for the moment-generating function (mgf) of the output SNR for MRC receivers and the Pade/spl acute/ approximation to the mgf for EGC receivers. The ASEP of dual-branch EGC and MRC receivers is also obtained in correlative fading. The proposed mathematical analysis is complimented by various numerical results, which point out the effects of fading severity and correlation on the overall system performance. Computer simulations are also performed to verify the validity and the accuracy of the proposed theoretical approach.