Performance of M-MRC receivers over TWDP fading channels

An expression of characteristic function of signal-to-noise ratio (SNR) for two waves with diffused power (TWDP) fading channel is derived. Using this expression, the expression for the probability density function (PDF) of the output SNR of maximal ratio combining (MRC) receiver is obtained. Expressions for the performance matrix of MRC receiver over TWDP fading channels are also deduced. PDF based approach is followed to derive expressions of outage probability and average symbol error rate for coherent and non-coherent m-ary modulation schemes. Effects of the number of branches M and the fading parameters K and Δ on the system performance are studied. The results obtained are verified by Monte Carlo simulation.     

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.     

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.     

Higher Order Capacity Statistics of Diversity Receivers

A statistical analysis for the channel capacity (CC) for several diversity receivers under optimal rate adaptation with constant transmit power is provided. Independent but not necessarily identically distributed Nakagami-m fading channels are considered. Specifically, the moments of the CC at the output of selection combining, maximal-ratio combining, and switched and stay combining are obtained, assuming integer-order fading parameters, while for the Rayleigh model the moments of the CC at the output of equal-gain combining and generalized-selection combining are derived in closed form. Using these formulas, a new performance criterion, namely as fading figure (FF) as well as the variance, skewness, and kurtosis, are studied. Our findings show that the FF improves with an increase of the signal-to-noise ratio (SNR), the fading parameters, and/or the diversity order. Also, unlike to the variance of the error probability, the variance of the CC is a monotonic function of the average input SNR.     

莱斯多径衰落信道下OFDM系统的容量方差分析

方差是系统容量的一个重要参数,可以用来估计通信系统的中断容量。该文研究了正交频分复用（OFDM）系统在莱斯衰落信道下的容量方差。首先该文建立了多径莱斯信道的模型并且定义了多径莱斯信道的莱斯因子,基于此信道模型推出了一个OFDM系统容量方差新的数学表达式,此表达式以OFDM系统的子载波数、信噪比、信道的多径时延等为参数。基于此表达式,计算机仿真和数值计算研究了信噪比、多径数目、莱斯因子对OFDM系统容量方差的影响。结果表明:计算机仿真和数值计算基本吻合,验证了所推导数学表达式的正确性;系统容量方差与信噪比成正比,与莱斯因子和信道的多径数目成反比。另外,该文以积分的形式给出了任意两个相关莱斯随机变量的联合概率密度函数。      

MIMO-OFDM系统无线衰落信道容量分析

推导了MIMO-OFDM系统在衰落信道下的各态历经容量、最优发送策略、使用等功率分配时的容量上界以及相对于单天线OFDM系统的容量增益。结果表明：天线数和平均接收信噪比是决定MIMO-OFDM系统信道容量的关键因素。天线数越多或者接收信噪比越大,信道的容量越大,信道容量几乎不受多径时延扩展的影响。慢衰落信道下的最大信道容量可以使用空-频两维注水算法得到,当接收信噪比足够大时,最大信道容量也可以用平均分配发送功率的方法逼近。     

Performance of Single and Multichannel Coherent Reception under Rician Fading

In the present work, simple closed-form series solutions for the average error rate of several coherent modulation schemes such as, binary phase shift keying (BPSK), binary frequency shift keying (BFSK), differential binary phase shift keying (DBPSK), quadrature phase shift keying (QPSK), offset-QPSK, minimum shift keying (MSK), and square M-ary quadrature amplitude modulation (M-QAM), operating over frequency non-selective slow Rician fading channel and corrupted by additive white Gaussian noise (AWGN) are derived. Further, to improve the link quality, receiver antenna space diversity is considered, where multiple independent and identically distributed (i.i.d.) as well as uncorrelated signal replicas are combined before successive demodulation. The proposed linear predetection combiner follows optimum maximal ratio combining (MRC) algorithm. Starting from a novel unified expression of conditional error probability the error rates are analysed using probability density function (pdf) based approach. The derived end expressions, consisting of rapidly converging infinite series summations of Gauss hypergeometric function, are accurate, free from any numerical integration and general enough, as it encompasses as special situations, some cases of non-diversity, non-fading AWGN and Rayleigh fading. Symbol or, bit error probabilities (SEP/BEP) are graphically displayed against signal to noise ratio (SNR) per bit per channel for all the digital modulation schemes stated above with different values of diversity order L and varying values of the channel specular-to-scatter ratio or, the Rician parameter K, as found from the measured statistics of mobile and indoor wireless channels. In addition, to examine the dependence of error rate performance of M-QAM on the constellation size M, numerical results are plotted for various values of M. Selected simulation results are also provided to verify the analytical deductions. The series solutions presented in current text realize a trade-off between precision and complexity and offers valuable insight into the performance evaluation over a fading channel in a unified manner.     

Fading Margin Analysis for Asynchronous CDMA Systems

In this paper, a detailed theoretical analysis of fading margin in an asynchronous code division multiple access (A-CDMA) system is discussed. Rayleigh and Rician frequency-selective slowly fading channels are considered. Probability distribution and density functions of the probability of error are derived for Rayleigh and Rician fading channels. The fluctuations in the channel capacity are proved to be directly proportional to the signal-to-noise ratio (SNR) variations. Fading margin is calculated for both Rayleigh and Rician fading channels as a function of the probability of error specification and the probability of unsatisfactory operation.     

CDF and MGF based analysis over Rayleigh TWDP shadowed fading channel for indoor communication

Recently, the two-wave with diffuse power (TWDP) distribution has been extensively used to model the shadowing in multipath-faded/shadowed indoor environment. In this article, novel expressions for joint moments, mean, second moment, variance and cumulative distribution function for Rayleigh TWDP shadowed fading model are derived. By using the derived expression of mean and variance, the expression for amount of fading is obtained. Also, the outage probability, moment generating function and average bit error rate (ABER) for various modulation schemes namely binary phase shift keying (BPSK), binary frequency shift keying (BFSK), minimum shift keying (MSK), differentially coherent phase shift keying (DCPSK) and non-coherent frequency shift keying (NCFSK) are calculated. The derived expressions for cumulative distribution function, outage probability and ABER are presented in analytical format and have been numerically evaluated. Moreover, the numerical results of ABER using MSK and DPSK modulation schemes is compare with results of Rayleigh Gamma composite fading model. The study shows that better outage probability (0.01) is observed at 40dB average signal to noise ratio (SNR) with 5dB lowest threshold SNR, however, at higher threshold SNR (>5dB) with fixed average SNR (40dB), poor outage probability performance are obtained. Further, at higher shadowing (10dB), for fixed average SNR (15dB), minimum error probability (10^?4) is observe, while at lower shadowing (less than 10dB), higher error probability (greater than 10^?4) is observed that represents poor BER performance.     

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.     

SER Performance of Amplify-and-Forward Cooperative Diversity Over Asymmetric Fading Channels

In this paper, the performance of amplify-and-forward (AF) cooperative diversity is analyzed over asymmetric fading channels. The source–relay and the relay–destination links experience Rayleigh fading while the source–destination link is subject to generalized Gamma fading. First, the probability density function (PDF) and the moment generating function (MGF) of the source–relay–destination link and the MGF of the source–destination link are derived. Then, the symbol error rate (SER) is determined based on the MGF of the total end-to-end signal-to-noise ratio (SNR). Moreover, the SER performance of N-relay assisted AF cooperative diversity is illustrated for M-ary phase shift keying (M-PSK) and M-ary quadrature amplitude modulation (M-QAM). Based on the derived MGF expressions, the numerical results are obtained by varying the modulation types and channel parameters for different scenarios.     

New closed-form expressions for SNR estimates of Nakagami fading channels by the method of moments

Method of moments has been a parameter estimation technique appropriate to calculate signal-to-noise ratio (SNR) estimates in fading channel models in which an optimal technique like maximum likelihood estimation is not mathematically tractable. In this article, the ratio of the second moment squared to the fourth moment of the received signal envelope is considered to calculate an exact expression for the SNR estimate in Nakagami-m fading channel for M-QAM and \(\theta \)-MQAM modulations as well as expressions to evaluate the variance and the mean of the estimate. The paper presents two useful contributions for SNR estimation theory on Nakagami fading. Besides the exact algebraic expression for the estimate for a generalized QAM modulation scheme, its performance is evaluated through a statistical linearization argument.     

On the asymptotic capacity of stationary Gaussian fading channels

We consider a peak-power-limited single-antenna flat complex-Gaussian fading channel where the receiver and transmitter, while fully cognizant of the distribution of the fading process, have no knowledge of its realization. Upper and lower bounds on channel capacity are derived, with special emphasis on tightness in the high signal-to-noise ratio (SNR) regime. Necessary and sufficient conditions (in terms of the autocorrelation of the fading process) are derived for capacity to grow double-logarithmically in the SNR. For cases in which capacity increases logarithmically in the SNR, we provide an expression for the "pre-log", i.e., for the asymptotic ratio between channel capacity and the logarithm of the SNR. This ratio is given by the Lebesgue measure of the set of harmonics where the spectral density of the fading process is zero. We finally demonstrate that the asymptotic dependence of channel capacity on the SNR need not be limited to logarithmic or double-logarithmic behaviors. We exhibit power spectra for which capacity grows as a fractional power of the logarithm of the SNR     

Performance Analysis of the Double-Antenna SDC System Over <Emphasis Type="Italic">N</Emphasis>-Nakagami Fading Channels

The performance of the double-antenna switched diversity combining (SDC) system over N-Nakagami fading channels is investigated in this paper. Based on the method of the probability density function of the signal-to-noise ratio, the exact expressions for the channel capacity and average symbol error probability (ASEP) are derived. Then the channel capacity and ASEP performance under different conditions is evaluated through numerical simulations to verify the analysis. The simulation results showed that the performance of the double-antenna SDC system is improved with the fading coefficient increased, but the level of improvement is declined as the number of cascaded components increased.     

Performance analysis of three-branch selection combining over arbitrarily correlated Rayleigh-fading channels

The recent literature has thoroughly treated two-branch selection combining (SC) over correlated Rayleigh fading and three-branch SC over exponentially correlated Rayleigh fading. However, a long-standing open problem involves the three-branch SC performance over arbitrarily correlated Rayleigh fading. We solve this problem completely by deriving new infinite series expressions for the cumulative distribution function, the probability density function, and the moment generating function (mgf) of the three-branch SC output signal-to-noise ratio (SNR). The output mgf can be used to derive the average symbol-error rate for any two-dimensional digital modulations. The outage probability and the higher moments of the SC output SNR are also derived. These analytical results are canonical, in that the three-branch SC performance is now completely solved for arbitrary correlation. Some previous results are shown to be special cases of our new results.     

Performance of RCPC codes with soft-decision decoding overNakagami-m fading channels

The analytical upper bounds on the pairwise error probability of rate compatible punctured convolutional (RCPC) codes, using coherent BPSK signals over slow frequency nonselective Nakagami-m fading channels with AWGN, are evaluated. With perfect channel state information (CSI) assumption, we use a direct integral with the Nakagami-m probability density function to obtain a closed form upper bound. For the case without CSI, we find an approximated upper bound for the high SNR cases and the approximation can be justified for signal to noise ratio (SNR) E _s/N₀ ≫ 1.5 dB     

Performance Evaluation of Space–Time Block Codes Over Keyhole Weibull Fading Channels

It is well known that degenerate channel phenomena known as keyholes may significantly reduce the capacity of multiple-input and multiple-output (mimo) channels. Keyhole mimo channels were predicted theoretically and also observed experimentally. In this paper, a novel method of analyzing the performance of keyhole mimo channels is proposed. The proposed method is based on the assumption that the received signal at the keyhole encompasses an arbitrary number of multipath components and the propagation environment is such that the resulting signal is observed as a non-linear function of the modulus of the sum of these components. Based on this assumption, we initially introduce the double Weibull fading model, constructed by the product of two independent Weibull distributed fading envelopes. Closed-form expressions for its moments-generating function, probability density function, cumulative distribution function, and moments are also derived. Based on these formulas, we analytically evaluate the performance of a 2 × 2 mimo space–time block-coding (stbc) system, where performance metrics such as the average symbol error probability for several modulation schemes, outage probability, amount of fading and ergodic capacity are given in closed form. Various performance evaluation results are presented in order to verify the proposed analysis.

平坦衰落环境中多输入多输出系统衰落相关与信道容量研究

为分析模型物理参数和天线排列方式对多输入多输出系统信道容量的影响,提出了一种平坦衰落环境中信道容量的研究方法。该方法基于接收均匀圆阵和均匀线阵分别构建了蕴含模型物理参数的相关矩阵,并利用Wishart分布的性质推导了信道容量上下限。该方法回避了求取衰落相关矩阵特征值的概率密度函数,降低了运算量;可被推广到多天线-频分复用系统。仿真结果表明,天线间距较小时,采用均匀圆阵比均匀线阵的系统信道容量要高;天线间距增大到一定程度后,系统信道容量达到饱和。散射角越大,信道容量的增长速率越快且采用均匀线阵比均匀圆阵系统的信道容量高。接收信噪比较大时,平均信道容量上下限基本接近其实际值。     

A comprehensive performance analysis of relay-aided CDMA communications over dissimilar fading channels

In this paper, bit error probability (BEP), outage probability (OP) and channel capacity (CC) of direct-sequence code-division multiple access systems with amplify-and-forward relaying are presented for different fading scenarios. In the first scenario, the source-destination link is assumed to experience Rayleigh fading while it is subject to Nakagami-m fading in the second scenario. The source-relay and relay-destination channels are considered to have Nakagami-m fading conditions in two scenarios. First, analytical expressions for the end-to-end probability density function (PDF) are derived by using the convolution integral. Then, BEP, OP and CC are obtained based on these PDFs in terms of infinite series. Truncation error analyses are presented for different parameter values in order to show that truncation error arising from the infinite series is negligible. Simple and easy-to-compute asymptotic expressions are also introduced for BEP and OP in order to simplify the performance analysis in high signal-to-noise ratio region. Simulation results are provided to show the accuracy of the proposed approximate and asymptotic expressions.     

Capacity and error probability performance analysis for MIMO MC DS-CDMA system in η–μ fading environment

In this paper, we investigate the effect of multiple input multiple output (MIMO) systems on the performance of the multicarrier direct sequence code division multiple access (MC DS-CDMA) system operating over independent identically distributed (i.i.d) η–μ flat fading environment in terms of average error probability and average channel capacity. We derive the instantaneous signal to interference noise ratio (SINR) at the output of the receiver. Hence, based on moment generating function (MGF) approach, we obtain the probability density function (PDF) of the instantaneous SINR. Closed form expressions of average error probabilities for the system are developed and expressed in Appell's and Lauriccella's hypergeometric functions. Furthermore, we achieve exact expression of average channel capacity for the system. Finally, we validate our results using Monte Carlo simulation technique and also compare with those already available in the literature.