Second-order statistics of maximal-ratio and equal-gain combining in Hoyt fading

Exact expressions for the level crossing rate and average fade duration of M-branch equal-gain and maximal-ratio combining systems in a Hoyt fading environment are presented. The expressions apply to unbalanced, nonidentical, independent diversity channels and have been validated by specializing the general results to some particular cases whose solutions are known and, more generally, by means of simulation.     

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.     

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     

Outage probability of dual-branch coherent equal-gain combining in correlated Nakagami-m fading

The exact outage probability of mobile radio receivers using dual-branch coherent equal-gain combining is analytically derived for correlated Nakagami-m fading. Expressions in the form of infinite series are obtained for the two cases of identical parameters on both diversity branches, and identical m-parameters (multiples of a half-integer) but not-necessarily identical fading powers on each branch.     

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.     

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.     

Asymptotic performance of hybrid-selection/maximal-ratio combining over fading channels

In this letter, we study the asymptotic performance of hybrid-selection/maximal-ratio combining (HS/MRC) and postdetection HS/equal-gain combining (HS/EGC) over generalized fading channels for large average signal-to-noise ratios (ASNRs). By evaluating the asymptotic moment generating function of the HS/MRC output SNR at high ASNR, we derive the diversity and coding gains for HS/MRC for a large class of modulation formats and versatile fading conditions, including different types of fading channels and nonidentical SNR statistics across diversity branches. Our analytical results reveal that the diversity gains of HS/MRC and HS/EGC are equivalent to that of MRC, and the difference in the coding gains for different modulation formats is manifested in terms of a modulation factor defined in this letter. Some new analytical results about effects of the number of combined branches for HS/MRC and noncoherent combining loss of HS/EGC are also provided.     

Channel capacity and second-order statistics in Weibull fading

The second-order statistics and the channel capacity of the Weibull fading channel are studied. Exact closed-form expressions are derived for the average level crossing rate, the average fade duration, as well as the average Shannon's channel capacity of the Weibull fading process. Numerical results are presented to illustrate the proposed mathematical analysis and to examine the effects of the fading severity on the concerned quantities.     

SER of threshold-based hybrid selection/maximal-ratio combining in correlated Nakagami fading

The average symbol-error rate of threshold-based hybrid selection/maximal-ratio combining (T-HS/MRC) with correlated Nakagami-m fading channels is obtained for positive integer values of fading parameter m for a special correlation structure. An accurate approximate analysis of T-HS/MRC in arbitrarily correlated Nakagami-m fading channels is presented by using a Green matrix approximation. The derivation allows different M-ary linear modulation schemes. We illustrate our methodology using M-ary phase-shift keying as an example.     

SER of threshold-based hybrid selection/maximal-ratio combining in equicorrelated Nakagami fading

The average symbol error rate (SER) of threshold-based hybrid selection/maximal-ratio combining (T-HS/MRC) in equicorrelated Nakagami-m fading is obtained for positive integer values of fading parameter, m. The derivation allows different M-ary linear modulation schemes. We illustrate our methodology using M-ary phase-shift keying as an example.     

双分集最大比合并相关瑞利衰落的误码性能

给出MPSK与CFSK在双分集最大比合并相关瑞利衰落信号下的误比特率的解析结果,无需冗长的模拟,易于研究分集合并与信道相关性对系统性能的影响,其数值结果与先前的研究结果一致.     

BER performance of DQPSK in Nakagami fading with selection diversity and maximal-ratio combining

A new expression for the average bit-error rate (BER) of differential quadrature phase-shift keying in slow frequency-nonselective Nakagami fading is derived for a space-diversity receiver having a cascade arrangement of L groups of M-branch selection combiners and an L-branch maximal-ratio combiner (MRC). This allows the use of a large number of antennas, for performance improvement, and a small number of M inputs to the combiners, for low complexity. The average BER performance of the cascade receiver is investigated for different fading severity conditions characterized by the Nakagami m factor, and compared with the conventional MRC receiver. As the fading gets less severe (m increases), performance improvement over the conventional MRC scheme is only noticeable for the larger range of average signal-to-noise ratio.     

SER of triple hybrid selection/maximal-ratio combining in exponentially correlated Nakagami fading

The average symbol error rate (SER) of triple hybrid selection/maximal-ratio combining in exponentially correlated Nakagami-m fading is obtained when the fading parameter m is a positive integer.     

Capacity of correlative nakagami-m fading channels under adaptive transmission and maximal-ratio combining diversity technique

The study of channel capacity evaluation in conjunction with maximal ratio diversity-combining (MRC) is presented in this paper. Analysis of the capacity in correlative Nakagami-m fading channels is observed. Using the proposed fading model, the power and rate adaptation, constant transmit power, channel inversion with fixed rate and truncated channel inversion adaptation policies are analyzed. Our results show that the power and rate adaptation policy, being only slightly higher than capacity of constant transmit power policy, provides the highest capacity over the other adaptation policies. The results also show that truncated channel inversion adaptation policy is better alternative compared to complete channel inversion policy for all values of fading severity, diversity order and correlation coefficient.     

Performance of generalized selection combining over Weibull fading channels

The literature is relatively sparse in performance analysis of diversity combining schemes over Weibull fading channels, despite the fact that the Weibull distribution is often found to be suitably fit for empirical fading channel measurements. In this paper, we capitalize on some interesting results due to Lieblein on the order statistics of Weibull random variables to derive exact closed‐form expressions for the combined average signal‐to‐noise ratio (SNR) as well as amount of fading (AF) at a generalized selection combining (GSC) output over Weibull fading channels. We also use some simple AF‐based mappings between the fading parameters of the Weibull distribution and those of the Nakagami, Rice, and Hoyt distributions to obtain the approximate but accurate average SNR and AF of GSC over these types of channels. The mathematical equations are validated and illustrated by some numerical examples for scenarios of practical interest. Copyright © 2006 John Wiley & Sons, Ltd.     

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.     

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     

Transmit selection diversity with maximal-ratio combining for multicarrier DS-CDMA wireless networks over Nakagami-m fading channels

We propose the scheme to integrate transmit selection diversity/maximal-ratio combining (TSD/MRC) with multicarrier (MC) direct-sequence code-division multiple access (DS-CDMA) for various wireless networks. Applying this TSD/MRC-based scheme, the transmitter jointly selects the optimal subcarrier-and-antenna pair to significantly decrease the peak-to-average power ratio (PAPR), which is one of the main problems inherently associated with MC DS-CDMA communications. Over the frequency-selective Nakagami-m fading channels, we develop the unified analytical framework to analyze the symbol-error rate (SER) of the scheme implemented in different types of wireless networks, while dealing with the perfect and imperfect channel state information (CSI) feedbacks, respectively. The imperfect feedbacks we focus on include delayed feedbacks and erroneous feedbacks. Taking the imperfectness of the feedback into account, the resultant SER is compared with that of both conventional selection diversity (SD)/MRC-based and space-time block coding (STBC)/MRC-based schemes. Our analyses show that in a wide variation of the feedback imperfectness, our proposed TSD/MRC-based scheme has significant advantages over the other two schemes for both downlink cellular networks and ad hoc wireless networks. However, our analytical findings indicate that TSD/MRC-based scheme cannot always outperform SD/MRC-based and STBC/MRC-based schemes even when the perfect CSI feedbacks are available.     

SNR of generalized diversity selection combining with nonidenticalRayleigh fading statistics

A closed-form expression for the average signal-to-noise-ratio (SNR) of generalized diversity selection combining, using the m largest (in instantaneous SNR) diversity signals, for arbitrary m, assuming that the Rayleigh fading statistics on each diversity branch are identically, independently distributed (i.i.d.), already exists in the literature. In this paper, a similar closed-form expression, but for nonidentically distributed statistics, is derived, This expression specializes to known results, such as the average SNRs of maximal-ratio combining with either i.i.d. or non-i.i.d. diversity statistics and that of conventional selection combining (CSC) with i.i.d. diversity statistics. In addition, it provides, for the first time, a simple closed-form solution to the combined SNR of CSC with non-i.i.d. diversity statistics. Further, the closed-form solution for the SNR of selecting the m, largest diversity signals has negligible computational complexity     

Analysis of hybrid selection/maximal-ratio combining in Rayleighfading

We use a novel virtual branch technique to succinctly derive the mean and variance of the combiner output signal-to-noise ratio for hybrid selection/maximal-ratio combining in a multipath-fading environment