Performance analysis of maximum ratio combining with imperfect channel estimation in the presence of cochannel interferences

In this paper, we analyze the performance of maximum ratio combining (MRC) systems with imperfect channel estimation in the presence of cochannel interference (CCI) with an arbitrary power interference-to-noise ratio (INR). The maximum combining weights are the imperfect estimates of the desired user's fading channel coefficients and are assumed to be complex Gaussian distributed. The quantified measure for estimation error is the correlation coefficient between the true fading channel coefficients and their estimates. Exact closedform expressions are derived for the probability density function (pdf) of the signal-to-interference-plus-noise ratio (SINR), as well as performance metrics including outage probability and the average symbol error probability (ASEP) for some modulation formats. Simulation results demonstrate the accuracy of our theoretic analysis.     

M-ary NCFSK with S+N selection combining in Rician fading

The performances of general M-ary and binary orthogonal noncoherent frequency-shift keying signal-plus-noise (S+N) receiver structures in slow, flat Rician fading channels are examined. The fading on the diversity branches is assumed to be independent, but not necessarily identically distributed. For each receiver, a symbol-error probability expression is derived as a single integral with finite integration limits. Extensive Monte Carlo simulation results are presented to validate the analytical expressions. The results indicate that, unlike previously published results, the performance of S+N selection combining (SC) is not always superior to that of classical SC in fading and is dependent on the value of the signal-to-noise ratio (SNR), the modulation order, the diversity order, the multipath intensity profile, and the fading parameter. It is further shown that increasing the number of diversity branches in a S+N SC receiver does not necessarily decrease the probability of error if the system is operating in the low-SNR region. The performances of S+N SC schemes are also compared with the performances of equal-gain combining and square-law combining receivers.     

A new closed-form of ASEP and channel capacity with MRC and selection combining over Inverse Gaussian shadowing

This paper analyse and investigate the performance of communication system with maximal ratio combining (MRC) and selection combining (SC) over Inverse Gaussian (IG) fading distribution. All formats of coherent and non-coherent modulation schemes are considered and novel analytical expressions of average symbol error probability (ASEP) with diversity are derived. Gamma and IG fading distributions are popularly used as a mathematically less complex solution to lognormal in the open literature. Hence, we provide a comparative analysis between IG and gamma fading with the aim to provide a quantitative measure of the difference between the two distributions in the context of ASEP. Moreover, the novel closed-form expressions of channel capacity under transmission schemes such as optimal rate adaptation (ORA) and channel inversion fixed rate (CIFR) are derived and analysed with MRC and SC diversity over IG fading. The analytical results have been validated with the Monte Carlo simulations and the exact numerical results.     

Predetection Switched Combining in Correlated Rician Fading

The performance of dual-branch predetection switch-and-stay combining (SSC) in correlated Rician fading is considered in conjunction with several modulation formats. Analytical expressions are derived for the average symbol error rate (SER) of predetection SSC in correlated Rician fading. Switching thresholds that minimize the average SER are obtained. The impact of fading factor and the fading correlation on the performance of predetection SSC is studied. Analytical expressions for the output average signal-to-noise ratio (SNR) and the outage probability are derived. The validity of the analytical expressions are verified using Monte Carlo simulation.     

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.     

Effect of Channel Estimation Errors on M -QAM With MRC and EGC in Nakagami Fading Channels

We study the effect of imperfect channel estimation (ICE) on the error probability performance of M-level quadrature amplitude modulation ( M-QAM) with maximal-ratio combining and equal-gain combining diversity formats in Nakagami fading channels. We provide a novel formulation of the bit-error rate (BER) of M-QAM with ICE in terms of the signal constellation-dependent effective signal-to-noise ratios (SNRs) or amplitudes, which allows us to derive the general, accurate, and easy-to-evaluate BER formulas for square and rectangular diversity M-QAM with channel estimation errors. Our result shows that the performance loss caused by ICE may be manifested by the signal decision space distortion and a scaling of the effective SNR. Using our analytical result, we evaluate the performance of M-QAM with pilot-symbol assisted modulation and present some insightful findings     

Optimal diversity combining based on linear estimation of rician fading channels

Optimal receiver diversity combining employing linear channel estimation is examined. Based on the statistical properties of least-squares (LS) and minimum mean square error (MMSE) channel estimation, an optimal diversity receiver for wireless systems employing practical linear channel estimation on Rician fading channels is proposed. The new receiver structure includes the conventional maximal ratio combining receiver as a special case. Exact analytical expressions for the symbol error rates (SERs) of LS and MMSE channel estimation aided optimal diversity combining are derived. It is shown that, if an optimal detector is used, an MPSK wireless system with MMSE channel estimation has the same SER when the MMSE channel estimation is replaced by LS estimation. This is an interesting counterexample to the common perception that channel estimation with smaller mean square error leads to smaller SER. Extensive simulation results validate the theoretical results.     

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.     

Average probability of packet error with diversity reception over arbitrarily correlated fading channels

Closed form expressions for the average probability of packet error (PPE) are presented for no diversity, maximum ratio combining (MRC), selection combining (SC) and switch and stay combining (SSC) diversity schemes. The average PPE for the no diversity case is obtained in two alternative expressions assuming arbitrarily correlated Nakagami and Rician fading channels. For the MRC case, L diversity branches are considered and the channel samples are assumed to follow Nakagami distribution and to be arbitrarily correlated in both time and space. For the SC diversity scheme with L diversity branches, two bounds on the average PPE are derived for both slow and fast fading channels. The average PPE in this case is obtained in an infinite integral form for Nakagami channels while it is reduced to a closed form expression for the Rayleigh case. The average PPE is also derived in the case of SSC diversity with dual branches for both slow and fast Rayleigh fading channels. The new formulas are applicable for all modulation schemes where the conditional probability of error has an exponential dependence on the signal‐to‐noise ratio. The average PPE is then used to obtain a modified expression for the throughput for network protocols. In general, the diversity gain exhibits a little diminishing effect as the number of diversity branches increases. In addition, the system is found to be more sensitive to the space correlation than to the time correlation. The effects of different system parameters and diversity schemes are studied and discussed. Specific figures about the system performance are also provided. Copyright © 2004 John Wiley & Sons, Ltd.     

Exact BER for M-QAM with MRC and Imperfect Channel Estimation in Rician Fading Channels

In this paper, we study the effect of imperfect channel estimation (ICE) on the performance of M-level quadrature amplitude modulation (M-QAM) with maximum ratio combining (MRC) and pilot-symbol assisted modulation (PSAM) in generalized Rician fading channels. By expressing the bit error rate (BER) of MRC diversity M-QAM in terms of the distribution of new decision variables, we derive novel, exact, and easy-to-evaluate BER expressions for diversity M-QAM with channel estimation errors. Our results include versatile system and fading channel parameters (e.g., arbitrary spatial and temporal correlation patterns among the diversity branches), and are valid for arbitrary linear channel estimators and square and rectangular M -QAM with different constellation sizes. In addition, we evaluate the performance of minimum mean-squared error (MMSE)- and sinc-interpolator-based channel estimators with PSAM, and provide some new insights into the performance of M-QAM with PSAM in generalized fading channels     

Performance of MFSK signals with postdetection square-law diversity combining in arbitrarily correlated Nakagami-m fading channels

This letter presents an analysis of the error probability for noncoherent orthogonal multiple frequency-shift keying (MFSK) signals with postdetection square-law combining (SLC) when the signals transmitted over additive white Gaussian noise (AWGN) and slow frequency-nonselective arbitrarily correlated Nakagami-m fading channels. New exact expressions in a onefold integral for the probability of error of MFSK signals with postdetection square-law diversity combining operating in AWGN channel as well as in arbitrarily correlated Nakagami-m fading channels are derived. The effects of arbitrarily values of fading severity parameter m and the arbitrarily correlation between the L diversity channels are considered. The derived expressions can be easily computed, and hence, can be usefully exploited in the performance evaluation of digital mobile radio systems.     

Performance analysis of multibranch switched diversity systems

We investigate the performance of multibranch switched diversity systems. Specifically, we first derive generic formulas for the cumulative distribution function, probability density function, and moment-generating function of the combined signal power for both switch-and-stay combining (SSC) and switch-and-examine combining (SEC) schemes. We then capitalize on these expressions to obtain closed-form expressions for the outage probability and average error rate for various practical communication scenarios of interest. As a byproduct of our analysis we prove that for SSC with identically distributed and uniformly correlated branches, increasing the number of branches to more than two does not improve the performance, but the performance can be different in the case the branches are not identically distributed and/or not uniformly correlated. We also show that, in general, the SEC performance improves with additional branches. The mathematical formalism is illustrated with a number of selected numerical examples.     

Symbol error probability of two-dimensional signaling in Ricean fading with imperfect channel estimation

In this paper, a general analytical framework is developed for calculating the symbol error rate of two-dimensional (2-D) signaling in Ricean fading with imperfect channel estimation. We show that in the presence of channel estimation errors, the symbol error rate of arbitrary 2-D signaling in Ricean fading can be expressed as a two-fold proper integral with finite integration limits, which is suitable for numerical evaluation. This new analysis is applicable to any channel estimation scheme where the estimated and the actual channel gains are jointly complex-Gaussian. System parameters related to specific channel estimation schemes are optimized and the effect of Doppler frequency shift in the channel line-of-sight component on the error performance is investigated using our analysis.     

Outage probability analysis of multiple intelligent reflecting surface-assisted single-input single-output system with switched diversity

In this paper, we have presented the outage probability analysis of multiple intelligent reflecting surface (IRS)-assisted single-input-single-output (SISO) system with switched diversity schemes. The switched diversity is simpler than the selection combining diversity technique, which can help in reducing the channel estimation overhead. There are two main types of switch diversity schemes, namely, switch and stay combining (SSC) and switch and examine combining (SEC). We consider a SISO wireless scenario in which a single transmitting antenna is sending its message to the receiving antenna with the aid of multiple IRS panels. This communication scenario will arise as a typical application of uplink scenario for future 6G wireless systems. The outage probability (OP) expressions for dual-IRS-panel-aided SSC system and multiple-IRS-panel-aided SEC system are analyzed, respectively, over Rician fading channels. We derive tight approximate OP expressions in closed form for a large number of IRS elements. Further, we derive a simple asymptotic OP for studying diversity order and coding gain. The OP performance with respect to each system parameter is thoroughly explored. Several numerical OP results are presented with corresponding simulated OP results to validate the accuracy of the presented analytical analysis.     

Turbo码在最大比合并分集接收系统中的性能分析

该文提出了turbo码在最大比合并分集接收无线通信系统中纠错性能的联合上界。基于误差积分函数的简化计算式,推导了分集接收的多路信道分别具有不同衰落特性时,成对差错概率的精确表达式。以瑞利衰落信道为例,对采用turbo码的分集接收无线系统的性能进行了数值计算和仿真。结果表明:turbo码纠错性能联合上界数值计算式与仿真结果一致,可普遍用于信道衰落统计特性各不相同的分集接收系统。     

采用两条支路分集接收的相关瑞利衰落信道容量

本文研究采用两条支路最大比合并(MRC)或选择合并(SC)分集接收的相关瑞利衰落信道理论容量推导恒定发射功率自适应M进制正交幅度调制(M-QAM)的频谱效率,并将它们与独立同分布瑞利信道理论容量进行比较,其结果对收发信机之间无视距分量路径、接收机上分集天线之间的距离小于半个波长的无线通信系统设计具有指导作用.     

A simple bit error probability analysis for square QAM in rayleigh fading with channel estimation

A new approach is presented for analyzing the bit error probability (BEP) of square, multilevel, quadrature amplitude modulation over a nonselective Rayleigh fading channel, with imperfect channel estimation employing pilot-symbolassisted- modulation. It is much simpler and more powerful than those in the literature, and the average BEP is obtained by calculating the BEP for each individual bit. The results are given in simple, exact, closed-form expressions that do not require any numerical integration. These expressions show explicitly the behavior of the BEP as a function of various system parameters. Three channel estimation schemes are investigated. It is shown that existing channel estimation schemes using sinc interpolation and Gaussian interpolation can be improved.     

Effect of Channel Estimation Error on Bit Error Probability in OFDM Systems over Rayleigh and Ricean Fading Channels

A characteristic function-based method is used to derive closed-form bit error probability (BEP) expressions for orthogonal frequency-division multiplexing (OFDM) systems in the presence of channel estimation error over frequency-selective Rayleigh fading channels and frequency-selective Ricean fading channels. Both single channel reception and diversity reception with maximal ratio combining (MRC) are examined. The BEP expressions are shown to be sums of several conditional probability functions which can be calculated by using proper complex Gaussian random variable theory and a characteristic function method. The closed-form BEP expressions can be used to accurately investigate the bit error rate performance degradation caused by channel estimation error under different wireless channel environment models. The performances of two interpolation methods, a sine interpolator with Hamming windowing and a Wiener interpolator, are compared.     

有信道估计误差MIMO MRC系统性能研究

利用维希特随机矩阵理论和矩生成函数方法,推导了有信道估计误差的独立瑞利衰落信道上采用多输入多输出（MIMO）最大比合并（MRC）天线分集方案的矩形M进制正交幅度调制（MQAM）的平均误符号率（SER）解析表达式。数值计算结果阐明了信道估计误差和收发天线数对矩形MQAM调制MIMO MRC系统误码性能的影响。     

MMSE diversity combining for wide-band digital cellular radio

A study of minimum mean-square error (MMSE) diversity combining for wide-band digital cellular radio, designed to combat intersymbol interference (ISI) caused by frequency selective fading is outlined. The systems analyzed use binary phase-shift keying (BPSK), quarternary phase-shift keying (QPSK) or 16-level quadrature amplitude modulation (16-QAM) with cosine rolloff spectral shaping, and space diversity with selection, maximal ratio or MMSE combining. A set of performance curves is presented for selected combining schemes showing the influence of the following system parameters: the diversity order (1 to 4); the cosine rolloff factor; the power delay spectrum (with its associated delay spread); the signal-to-interference ratio; and the number of modulation levels (2, 4 and 16)