BER performance of MQAM with L‐branch MRC diversity reception over correlated Nakagami‐m fading channels

Exact and closed form generalized expressions for bit error rate (BER) of M‐ary quadrature amplitude modulation (MQAM) with L‐branch maximal ratio combining (MRC) space diversity reception in fading channels are derived and analyzed. The fading channels are modeled as identical but correlated frequency‐nonselective slow Nakagami‐m fading channels corrupted by additive white Gaussian noise (AWGN). Analytical results obtained are in terms of few finite range integrals with an integrand composed of elementary functions. Because of their simple form, these analytical results readily allow numerical evaluation in cases of practical interest. The results are also general enough to include Nakagami‐m fading channels with and without correlation, no diversity system, Rayleigh fading channels with and without correlation, and AWGN as special cases. The numerical results for the case of 16QAM are shown graphically and also in tabular form in order to examine the effects of fading severity, order of diversity, and branch correlation on the BER performance. The two correlation models considered are constant correlation model and exponential correlation model. One may be interested to know how the BER of MQAM is related to symbol error rate (SER) of MQAM. Therefore, the BER results obtained in this paper are also compared with that obtained directly from the SER. It is expected that the analytical results presented in this paper will provide a convenient tool for design and analysis of a radio communication system with space diversity reception in uncorrelated and correlated fading environment. Copyright © 2002 John Wiley & Sons, Ltd.     

BER analysis of arbitrary QAM for MRC diversity with imperfect channel estimation in generalized ricean fading channels

Imperfect channel estimation (ICE) can severely degrade the bit error rate (BER) of digital modulations with maximum ratio combining (MRC) diversity reception. The resulting performance analysis problem in its most general setting has not been addressed before. In this paper, the effect of ICE on the BER of an arbitrary square/rectangular Gray-coded quadratic amplitude modulation (QAM) in generalized Ricean fading channels when MRC reception is employed is analyzed. A general expression for the bit error probability of an arbitrary square/rectangular QAM scheme is first derived. This general formula requires a number of conditional probabilities, which is derived in closed form for independent and nonidentically distributed (i.n.d.) Rayleigh-fading channels with MRC and ICE. An efficient numerical method is also presented to compute the conditional probabilities for i.n.d. and correlated Ricean fading. In addition, extensive Monte Carlo simulations that agree excellently with the analytical results are presented.     

Exact symbol error probability of general order rectangular QAM with MRC diversity reception over nakagami-m fading channels

Exact average symbol error probability (SEP) of the general order rectangular quadrature amplitude modulation (QAM) with maximal ratio combining (MRC) diversity over L independent and identically distributed Nakagami-m fading channels with arbitrary fading index m is derived in this letter. The average SEP expression is given in terms of the Appell and Gauss hypergeometric functions and is then used to study the impact of diversity reception on the performance of general order rectangular QAM with different values of the quadrature-to-in-phase decision distance ratio. It is shown that the derived expression includes some existing results as special cases.     

Bit error probability of the M‐QAM scheme under η‐μ fading and impulsive noise in a communication system using spatial diversity

This paper presents a new and exact expression for the bit error probability (BEP) of the square M‐ary quadrature amplitude modulation (M‐QAM) scheme, with the channel under double gated additive white Gaussian noise (G²AWGN) and η‐μ fading in a communication system using the spatial diversity technique. The expression for the BEP is written in terms of the Appell function. The BEP curves are presented under different values of the number of branches of the maximum ratio combining (MRC) receiver, order of the constellation M, and parameters that characterize mathematically the channel, corroborated by simulations performed with Monte Carlo method.     

Error rates for Nakagami-m fading multichannel reception of binaryand M-ary signals

This paper derives new closed-form formulas for the error probabilities of single and multichannel communications in Rayleigh and Nakagami-m (1960) fading. Closed-form solutions to three generic trigonometric integrals are presented as part of the main result, providing a unified method for the derivation of exact closed-form average symbol-error probability expressions for binary and M-ary signals with L independent channel diversity reception. Both selection-diversity and maximal-ratio combining (MRC) techniques are considered. The results are generally applicable for arbitrary two-dimensional signal constellations that have polygonal decision regions operating in a slow Nakagami-m fading environments with positive integer fading severity index. MRC with generically correlated fading is also considered. The new expressions are applicable in many cases of practical interest. The closed-form expressions derived for a single channel reception case can be extended to provide an approximation for the error rates of binary and M-ary signals that employ an equal-gain combining diversity receiver     

SER Analysis of QAM with Space Diversity in Rayleigh Fading Channels

This paper derives the symbol error probability for quadrature amplitude modulation(QAM) with L-fold space diversity in Rayleigh fading channels. Two combining techniques, maximal ratio combining(MRC) and selection combining(SC), are considered. The formula for MRC space diversity is obtained by averaging the symbol error probability of M-ary QAM in an additive white Gaussian noise(AWGN) channel over a chi-square distribution with 2L degrees of freedom. The obtained formula overcomes the limitations of the earlier work, which has been limited only to deriving the symbol error rate(SER) of QAM with two branch MRC space diversity. The formula for SC space diversity is obtained by averaging the symbol error probability of M-ary QAM in an AWGN channel over the distribution of the maximum signal-to-noise ratio among all of the diversity channels for SC space diversity. No analysis for QAM with SC space diversity has been reported yet. Analytical results show that the probability of error decreases with the order of diversity. We can also see that the incremental diversity gain per additional branch decreases as the number of branches becomes larger. On the other hand, the performance of 16 QAM with MRC becomes much better than that of SC as the number of branches becomes larger. By giving the order of diversity, L, and the number of signal points, M, we have been able to obtain the SER performance of QAM with general space diversity. These results can be used to determine the order of diversity to achieve the desired SER in land mobile communication system employing QAM modulation.     

Results for Infinite Integrals Involving Higher-Order Powers of the Gaussian Q-Function with Application to Average SEP Analysis of DE-QPSK

Exact results are presented for infinite integrals that consist of higher-order powers of the one dimensional Gaussian Q-function averaged over Rayleigh fading envelopes in multi-branch diversity reception with maximal ratio combining (MRC). Some known results for the average of the 1st and 2nd powers are shown as special cases. The results obtained in this paper are utilized to study the average symbol error probability (SEP) performance of differentially encoded quadri-phase shift-keying (DE-QPSK) in Rayleigh fading channels employing MRC, and new exact expressions are presented for different fading scenarios. The derived mathematical expressions are verified using Monte Carlo simulations.     

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).     

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.     

Combining PSA fading estimation techniques for TCM and diversity reception in Rician fading channels

In this paper, a novel pilot‐symbol‐aided (PSA) technique is proposed for fading estimation in the land mobile satellite fading channels. The proposed technique combines the fading estimates obtained from a bandwidth‐efficient technique and a conventional technique according to the signal‐to‐noise ratios (SNRs) of the fading estimates. To enhance the transmission quality, trellis‐coded modulation (TCM) and diversity reception are employed in the system, and the combined estimates are subsequently used to correct the channel fading effects, to weight the signals from different diversity branches, and to provide channel state information to the Viterbi decoder. Monte Carlo computer simulation has been used to study the bit‐error‐rate (BER) performance of the proposed technique on trellis‐coded 16‐ary quadrature amplitude modulation in the frequency non‐selective Rician fading channels. Results have shown that the proposed PSA technique requires a very low bandwidth redundancy to provide satisfactory BER performance at low SNRs, and thus is suitable for use with TCM and diversity reception to achieve both bandwidth and power‐efficient transmission. Copyright © 2002 John Wiley & Sons, Ltd.     

Dual MRC diversity reception of TCM-MPSK signals over Nakagamifading channels

Space diversity reception and forward error correction coding are powerful techniques for combating the multipath fading encountered in mobile radio communications. In this Letter, the authors analyse the performance of a dual maximal ratio combining (MRC) diversity system using trellis coded modulation-multiple phase shift keying (TCM-MPSK) on slow, nonselective correlated Nakagami fading channels. An alternative exact derivation is introduced for the pairwise error probability, used in calculating average bit error rate analytical upper bounds     

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     

高效频谱调制方式在蜂窝移动通信系统中的性能分析

本文研究高效频谱调制方式ＭＰＳＫ及ＭＱＡＭ在蜂窝移动通信中的应用及其性能。在综合考虑共道干扰，Ｒａｙｌｅｉｇｈ衰落以及高斯噪声等影响因素的基础上，结合分集接收技术，我们给出了ＭＰＳＫ及ＭＱＡＭ应用于蜂窝移动通信时误码率计算的通用近似公式。蒙特－卡洛仿真表明文中给出的误码率近似公式能很好地吻合实际系统的仿真结果。     

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.     

Space‐time block coded spatial modulation with labeling diversity

Space‐time block coded spatial modulation (STBC‐SM) exploits the advantages of both spatial modulation and the Alamouti space‐time block code. Meanwhile, space‐time labeling diversity has demonstrated an improved bit error rate (BER) performance in comparison to the latter. Hence, in this paper, we extend the application of labeling diversity to STBC‐SM, which is termed STBC‐SM‐LD. Under identical channel assumptions, STBC‐SM‐LD exhibits superior BER performance compared to STBC‐SM. For example, with 4 × 4, 64‐quadrature amplitude modulation (64‐QAM), STBC‐SM‐LD has a BER performance gain of approximately 2.6 dB over STBC‐SM. Moreover, an asymptotic bound is presented to quantify the average BER performance of M‐ary QAM STBC‐SM‐LD over independent and identically distributed Rayleigh frequency‐flat fading channels. Monte Carlo simulations for STBC‐SM‐LD agree well with the analytical framework. In addition to the above, low‐complexity (LC) near‐maximum‐likelihood detectors for space‐time labeling diversity and STBC‐SM‐LD are presented. Complexity analysis of the proposed LC detectors shows a substantial reduction in computational complexity compared to their ML detector counterparts. For example, the proposed detector for STBC‐SM‐LD achieves a 91.9% drop in computational complexity for a 4 × 4, 64‐QAM system. The simulations further validate the near‐maximum‐likelihood performance of the LC detectors.     

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.     

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。     

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     

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.     

Multicarrier 16QAM transmission with diversity reception

A 96 multicarrier 16QAM transmitter and a diversity receiver for 3.072 Mbit/s data transmission are described. Pilot symbol aided (PSA) coherent detection is applied. A laboratory experiment demonstrates that an irreducible bit error rate (BER) of 10^-3 can be achieved at the RMS delay spread τ_rms=6.3 μs under frequency selective Rayleigh fading when two branch maximal ratio combining (MRC) diversity is used