Level Crossing Rate and Average Fade Duration of EGC Systems With Cochannel Interference in Rayleigh Fading

Both the first-order signal statistics (e.g., the outage probability) and the second-order signal statistics [e.g., the average level crossing rate (LCR) and the average fade duration (AFD)] are important design criteria and performance measures for wireless communication systems, including the equal gain combining (EGC) systems in the presence of the cochannel interference (CCI). Although the analytical expressions for the outage probability of the coherent EGC systems are exposed to CCI and various fading channels are already known, the respective expressions for the average LCR and the AFD are not available in the literature. This paper presents such analytical expressions for the Rayleigh fading channel, which are obtained by utilizing a novel analytical approach that does not require the explicit expression for the joint probability density function (pdf) of the instantaneous output signal-to-interference ratio and its time derivative. Applying the characteristic function method and the Beaulieu series, we determined the average LCR and the AFD at the output of an interference-limited EGC system with an arbitrary diversity order and an arbitrary number of cochannel interferers in the form of an infinite integral and infinite series. For the dual diversity case, the respective expressions are derived in closed forms in terms of the gamma and beta functions.     

Error Performance of DQPSK with EGC Diversity Reception over Fading Channels

This paper derives the average bit error probability (BEP) of differential quaternary phase shift keying (DQPSK) with postdetection equal gain combining (EGC) diversity reception over independent and arbitrarily correlated fading channels. First, using the associated Legendre functions, the average BEP of DQPSK is analyzed over independent Rayleigh, Nakagami-m, and Rician fading channels. Finite-series closed-form expressions for the average BEP of DQPSK over L-branch independent Rayleigh and Nakagami-m fading channels (for integer Lm) are presented. Besides, a finite-series closed-form expression is given for the average BEP of differential binary phase shift keying (DBPSK) with EGC over independent Rician fading channels. Second, an alternative approach is propounded to study the performance of DQPSK over arbitrarily correlated Nakagami-m and Rician fading channels. Relatively simple BEP expressions in terms of a finite sum of a finite-range integral are proposed. Moreover, the penalty in signal to noise ratio (SNR) due to arbitrarily correlated channel fading is also investigated. Finally, the accuracy of the results is verified by computer simulation.     

常见分集合并系统的性能分析

在移动通信中,分集技术是一种最有效的抗衰落技术。本文对3种常见的线性合并分集技术进行简要分析,给出它们的基带表示和合并器输出信噪比的概率密度函数(pdf),由此给出它们的合并增益。针对系统采用MPSK调制的情况,对瑞利衰落信道的3种合并分集系统的比特误码率(BER)性能进行理论研究,分别给出选择性合并(SC)和最大比率合并(MRC)系统的理论比特误码率表达式;对于等增益合并(EGC)分集,给出了一种近似的EGC系统的输出信噪比的pdf,由此导出EGC的一种近似的BER表达式,由蒙特卡罗仿真结果可以看出此近似的BER数值结果是准确的。数值结果显示:MRC性能最好,EGC性能稍差,而SC性能较差。文中给出的分析方法对于实际分集系统的理论研究具有普遍的指导意义。     

Closed-Form Analysis of Equal-Gain Diversity in Wireless Radio Networks

This paper deals with the performance of predetection equal-gain combining (EGC) receivers operating over multipath fading plus cochannel interference (CCI) and additive white Gaussian noise channels. The desired components of the received signals are considered to experience independent but not-necessarily identically distributed Nakagami-m fading, while the interferers are subject to independent Rayleigh fading. The analysis is not only limited to equal average fading power interferers, but the case of interferers with distinct average powers is also examined. By following the coherent interference power calculation, novel closed-form expressions for the moments of the EGC output signal-to-interference-plus-noise ratio (SINR) are derived, which are being used to study the performance of the average output SINR. Furthermore, by assuming an interference-limited fading scenario, novel closed-form union performance bounds are derived. More specifically, tight upper bounds for the outage and average symbol error probability for several constant envelope modulation schemes, and lower bounds for the Shannon average spectral efficiency, are provided. Numerical results demonstrate the effect of the number of interferers, the number of the receiver branches, and the severity of fading on the EGC receiver performance. Computer simulations have been also performed to verify the tightness of the proposed bounds and the correctness of the mathematical analysis. It is shown that the performance of cellular radio systems in the uplink is degraded mainly from the first-tier CCI of the adjacent cells     

Error rates of DPSK systems with MIMO EGC diversity reception over Rayleigh fading channels

This paper analyzes the average bit error probability (BEP) of the differential binary and quaternary phase-shift keying (DBPSK and DQPSK respectively) with multiple-input multiple-output (MIMO) systems employing postdetection equal gain combining (MIMO EGC) diversity reception over Rayleigh fading channels. Finite closed-form expressions for the average BEP of DBPSK and DQPSK are presented. Two approaches are introduced to analyze the error rate of DQPSK. The proposed structure for the differential phase-shift keying (DPSK) with MIMO EGC provides a reduced-complexity and low-cost receiver for MIMO systems compared to the coherent phase-shift keying system (PSK) with MIMO employing maximal ratio combining (MIMO MRC) diversity reception. Finally, a useful procedure for computing the associated Legendre functions of the second kind with half-odd-integer order and arbitrarily degree is presented.     

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 system with selection combining over correlated Weibull fading channels in the presence of cochannel interference

Selection diversity based on the signal to interference ratio (SIR) is a very efficient technique that reduces fading and channel interference influence. In this paper, system performances of selection combining and correlated Weibull channels are analyzed. Fading between the diversity branches and between interferers is correlated and Weibull distributed. Very useful closed-form expressions are obtained for the output SIR's probability density function (PDF) and cumulative distribution function which is main contribution of this paper. Outage probability, the average output SIR, and the average error probability for coherent, noncoherent modulation are derived. Numerical results presented in this paper point out the effects of fading severity and correlation on the system performances.     

Closed-form analysis of dual-diversity equal-gain combining over Rayleigh fading channels

Starting with a new expression for the probability density function of the signal-to-noise ratio at the output of dual-diversity equal-gain combining (EGC) over Rayleigh channels, we provide closed-form expressions for the average bit and symbol error rate of M-ary phase-shift keying signals. Numerical examples indicate that EGC maintains a good diversity gain as long as the degree of unbalance is not very low but suffers a sharp and significant degradation when the degree of unbalance approaches zero.     

Performance Analysis of Land Mobile Satellite Communication Systems with Equal-Gain Combining over Shadowed-Rice Fading Channels

An accurate model for performance analysis of land mobile satellite (LMS) channels is the Shadowed-Rice (SR) fading model. Recently, an approximate SR model has been proposed by the author for LMS channels. Compared with the existing models, the proposed model is analytically tractable and makes it possible to approximate very accurately the probability density function (PDF) of the SR random variable (RV) by a finite weighted sum of Rice PDFs. In this paper and based on the proposed model, the statistics of the sum of independent SR RVs is studied. While this problem is well understood for common fading models such as the Rayleigh, Rice, and Nakagami, a minor attention has been devoted to the SR case. In this paper and by using the well-known Beaulieu series approach, the PDF and the Cumulative distribution function (CDF) of the sum of independent SR RVs are derived in the form of infinite convergent series. In this regard, analytical, closed-form expressions are derived for the coefficients of the Beaulieu series. To give an application of the presented results, the performance of LMS communication system employing equal-gain combining (EGC) diversity techniques over SR fading channel is investigated and novel closed-form expression is derived for the outage probability of the system.     

Level Crossing Rate and Average Fade Duration of Dual Selection Combining With Cochannel Interference and Nakagami Fading

This letter provides closed-form expressions for the outage probability, the average level crossing rate (LCR) and the average fade duration (AFD) of a dual diversity selection combining (SC) system exposed to the combined influence of the cochannel interference (CCI) and the thermal noise (AWGN) in Nakagami fading channel. The branch selection is based on the desired signal power SC algorithm with all input signals assumed to be independent, while the powers of the desired signals in all diversity branches are mutually equal but distinct from the power of the interference signals. The analytical results reduce to known solutions in the cases of an interference-limited system in Rayleigh fading and an AWGN-limited system in Nakagami fading. The average LCR is determined by an original approach that does not require explicit knowledge of the joint PDF of the envelope and its time derivative, which also paves the way for similar analysis of other diversity systems.     

DS－SFH扩频多址系统在瑞利衰落信道中多径分集的性能研究

本文讨论了混合ＤＳ－ＳＦＨ扩频多址ＳＳＭＡ通信系统在瑞利衰落信道中多径分集接收的性能。基于多径干扰、多址干扰和信道噪声之和为一个高斯随机变量的分析，推导了在等增益组合（ＥＧＣ）和选择最大（ＳＭ）多径分集接收算法下，扩频系统的平均差错概率。理论分析和数值模拟指出：扩频多径分集接收可以明显地改善ＤＳ－ＳＦＨＳＳＭＡ系统的性能，在提高系统性能方面，等增益组合算法优于选择最大分集算法。     

Performance of differential modulation with wireless relays in Rayleigh fading channels

We propose a new amplify-and-forward scheme amenable to differential modulation for cooperative systems with wireless relays. We derive closed-form expressions of the probability density function (PDF) of the signal-to-noise ratio (SNR) and average bit-error rate (BER) for the proposed scheme and the analytical results are confirmed with numerical simulations. An asymptotic analysis reveals that the proposed cooperative scheme with one relay offers a diversity order approaching two in Rayleigh fading channels as the average SNR increases.     

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.     

Capacity evaluation for equal gain diversity schemes over Rayleigh fading channels

In this paper, closed-form expressions for the capacities per unit bandwidth for Rayleigh fading channels with equal gain combining (EGC) diversity case are derived for power and rate adaptation, constant transmit power, channel inversion with fixed rate, and truncated channel inversion adaptation policies. Channel inversion policies provide the highest capacity over the other adaptation policies with EGC diversity. The constant transmit power policy provides the lowest capacity as compared to the other policies.     

Average SNR of a generalized diversity selection combining scheme

The average signal-to-noise ratio (SNR) of a generalized selection combining scheme, in which the m diversity branches (m⩽L, where L is the total number of diversity branches available) with the largest instantaneous SNRs are selected and coherently combined, is derived. A Rayleigh fading channel is assumed, and a simple closed-form expression for the SNR is found which is upper bounded by the average SNR of maximal ratio combining, and lower bounded by average SNR of conventional selection combining     

Performance Analysis of MIMO-MRC in Double-Correlated Rayleigh Environments

We consider multiple-input multiple-output (MIMO) transmit beamforming systems with maximum ratio combining (MRC) receivers. The operating environment is Rayleigh fading with both transmit and receive spatial correlation. We present exact expressions for the probability density function (pdf) of the output signal-to-noise ratio, as well as the system outage probability. The results are based on explicit closed-form expressions which we derive for the pdf and cumulative distribution function of the maximum eigenvalue of double-correlated complex Wishart matrices. For systems with two antennas at either the transmitter or the receiver, we also derive exact closed-form expressions for the symbol-error rate. The new expressions are used to prove that MIMO-MRC achieves the maximum available spatial diversity order, and to demonstrate the effect of spatial correlation. The analysis is validated through comparison with Monte Carlo simulations     

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     

Error rates of M-ary signals with. Multichannel reception in Nakagami-m fading channels

In this letter, we present closed. form expressions for the exact average symbol-error rate (SER) of M-ary modulations with multichannel reception over Nakagami-m fading channels. The derived expressions extend already available results for the nondiversity case, to maximal-ratio combining-(MRC) and postdetection equal-gain combining (EGC) diversity systems. The average SERs are given in terms of Lauricella's multivariate hypergeometric function F/sub D//sup (n)/. This function exhibits a finite integral representation that can be used for fast and accurate numerical computation of the derived expressions.     

Analytical level crossing rates and average fade durations for diversity techniques in Nakagami fading channels

The level crossing rates (LCRs) and average fade durations (AFDs) of a fading channel find diverse applications in the evaluation and design of wireless communication systems. Analytical expressions for these quantities are available in the literature for certain diversity reception techniques, but are generally limited to the Rayleigh fading channel, with few exceptions. Moreover, the methods employed are usually specific to a certain channel/diversity pair, and thus cannot be applied to all cases of interest. Using a unified methodology, we derive analytical expressions for the LCRs and AFDs for three diversity reception techniques and a general Nakagami (1960) fading channel. We provide novel analytical expressions for selection combining (SC) and equal-gain combining (EGC), and rederive in a more general manner the case of maximal-ratio combining (MRC). It is shown that our general results reduce to some specific cases previously published. These results are used to examine the effects of the diversity technique, the number of receiving branches and severity of the fading on the concerned quantities. It is observed that as the Nakagami m-parameter and the diversity order increase, the behavior of the combined received envelope for EGC follows closely the one for MRC, and distances itself from SC.     

Closed-form expressions for the outage and ergodic Shannon capacity of MIMO MRC systems

Transmit-beamforming (TB) over multiple-input multiple-output (MIMO) fading channels steers the transmit power in the receiver's direction, so as to maximize the output signal-to-noise ratio (SNR) after maximal ratio combining (MRC) at the receiver. This letter proposes a simple algorithm that allows evaluating an exact and tractable expression for the probability density function of the SNR at the output of the TB receiver, subject to Rayleigh fading. The latter enables the derivation of closed-form expressions for the outage and ergodic capacity of MIMO MRC systems under Rayleigh fading, thereby avoiding the need for time-consuming numerical integrations or Monte Carlo simulations.