Optimal maximal ratio combining with correlated diversity branches

It is proved that a maximal ratio combiner operating on correlated branches and weighting the branch signals as though they were independent is optimal. It is also proved that performance measures of maximal ratio combining operating with correlated Rayleigh or Ricean fading input branches are identical to performance measures of an equivalent diversity system operating with independent and, in general, unbalanced inputs     

Variable-rate multiuser diversity in correlated MIMO channel via virtual channel representation

This paper studies the multiuser diversity with constellation selection based on a virtual representation of realistic Multiple Input Multiple Output （MIMO） correlated channels. To realize multiuser diversity in slow fading channels, random beamforming is adopted. Random beamforming matrix exploiting virtual channel representation is constructed, which can match the channel matrix of the desired user better. Sirnultaneously, adaptive coded modulation is applied to each sub-channel of the selected user to improve the system performance further.     

On the average output SNR in selection combining with three correlated branches over Nakagami-m fading channels

An exact and rapidly converging infinite series for the average output signal-to-noise ratio in a triple selection diversity system, over correlated Nakagami-m fading channels, is presented. Numerical results are presented to illustrate the proposed approach and to point out the effect of the fading correlation to the performance of the combiner, as well as the improvement achieved by the triple selection combining compared to the dual diversity case.     

Probability of error analysis of predetection generalized selection combining receivers with correlated unbalanced Nakagami branches

In this paper we determine the probability of error of a predetection generalized selection combining (GSC) receiver with correlated and unbalanced diversity branches in a Nakagami‐m multipath fading channel. We start by finding the joint probability density function (PDF) of the decision variables. This involves the derivation of the joint PDF of the L largest random variables (L maxima) of an input population of N > L correlated nonidentically distributed random variables, based on the statistics of the input population. The results obtained are then used in the derivation of the error probabilities of noncoherent FSK (NCFSK) and DPSK receivers. Copyright © 2006 John Wiley & Sons, Ltd.     

Switching rates of two-branch selection diversity in correlated Doppler fading

The switching rate of a correlated dual branch selection diversity combiner in Rayleigh and Rician fading is derived in noise-free conditions. Balanced and unbalanced branches are considered. Numerical results are presented for a space-diversity system with horizontally spaced omnidirectional antennas at a mobile station.     

Performance analysis of dual selection diversity in correlated Weibull fading channels

Ascertaining the importance of the dual selection combining (SC) receivers and the suitability of the Weibull model to describe mobile fading channels, we study the performance of a dual SC receiver over correlated Weibull fading channels with arbitrary parameters. Exact closed-form expressions are derived for the probability density function, the cumulative distribution function, and the moments of the output signal-to-noise ratio (SNR). Important performance criteria, such as average output SNR, amount of fading, outage probability, and average bit-error probability for several modulation schemes are studied. Furthermore, for these performance criteria, novel closed-form analytical expressions are derived. The proposed analysis is complemented by various performance evaluation results, including the effects of the input SNR's unbalancing, fading severity, and fading correlation on the overall system's performance. Computer simulation results have verified the validity and accuracy of the proposed analysis.     

选择式合并方法在Nakagami信道上的性能分析

本文根据最大输出电平准则，对选择式合并在Nakagami信道上的性能作了比以往理论分析更符合实际的评价，导出了误码率的闭式解，并与最大信噪比准则时作了比较。结果表明，采用最大输出电平准则时系统的性能稍有恶化，但实现的复杂度却大为降低。     

Performance analysis of SIR-based dual selection diversity over correlated Nakagami-m fading channels

Signal-to-interference-ratio (SIR)-based selection diversity is an efficient technique to mitigate fading and cochannel interference in wireless communications systems. An approach to the performance analysis of dual SIR-based selection diversity over correlated Nakagami-m fading channels with arbitrary parameters is presented. Useful formulae for the outage probability, the average output SIR, and the average error probability for coherent, noncoherent, and multilevel modulation schemes are derived. The main contribution of the paper is that, for the first time, the proposed analysis is carried out assuming correlated Nakagami-m fading with arbitrary parameters for both the desired signals and the cochannel interferers, which is the real scenario in practical dual selection diversity systems with insufficient antenna spacing. It is shown that the presented general results reduce to the specific ones for the independent fading case, previously published. Numerical and simulation results are also presented to show the effects of various parameters, such as the fading severity, input SIR unbalance, and level of correlation, to the system's performance.     

Performance analysis of triple selection diversity over exponentially correlated Nakagami-m fading channels

An approach to the performance analysis of a triple selection-diversity system over exponentially correlated Nakagami-m fading channels is presented. Closed-form expressions of converged sums for both outage and average error probabilities are derived. Numerical results are presented to point out the effect of the fading correlation, the fading severity, as well as the improvement achieved by the triple selection combining compared with the corresponding dual diversity case.     

Error probability and channel capacity analysis of wireless system over inverse gamma shadowed fading channel with selection diversity

In this paper, we present an analytical framework to analyse the error probability and the channel capacity of the inverse gamma (I‐Gamma) shadowed fading channel. First, the work discusses the utility of the I‐Gamma over log‐normal (LN) and gamma fading models where the closeness of I‐Gamma with other existing shadowing models is carried out. Utilising the probability density function (PDF) of the I‐Gamma shadowed fading channel, various metrics of the communication system, namely, the average symbol error probability (SEP), the channel capacity under optimal rate adaptation (ORA), channel inversion with fixed rate (CIFR), and truncated CIFR (TIFR) are derived. Further, the work is extended to derive a novel selection combining (SC) PDF, and the analytical results for the SEP and the channel capacity of SC diversity are presented. Furthermore, we also provide simpler asymptotic expressions for the average SEP. In addition, the simplified high and low signal‐to‐noise‐ratio (SNR) solutions to channel capacity are also provided. The derived mathematical formulations have been endorsed by comparing with Monte Carlo simulations.     

Effects of correlated shadowing signals on channel reuse in mobileradio systems

The authors present a study to evaluate the cochannel interference probability for the desired and interference signals which are correlated due to shadowing. The effects of correlation on the normalized reuse distance are investigated. A generalized expression for the cochannel interference probability is derived by combining uncorrelated (fast) Rayleigh fading and correlated (slow) log-normal signals. The cochannel interference probability for sectorized cell layouts is compared with the lower bound of cochannel interference probability for omnidirectional antenna systems. It is found that omnidirectional cell layouts cause the highest level of cochannel interference probability. An omnidirectional system requires a higher cluster size than a directional system to maintain acceptable cochannel interference     

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.     

Ultra‐wideband multiple‐access relay channel with correlated noises and its diversity analysis

In this study, we investigate a new and practical model, ultra‐wideband Slepian–Wolf multiple‐access relay channel (UWB‐SW‐MARC) with correlated noises at the relay and receiver, which includes two important models, that is, UWB‐SW multiple‐access channel with correlated noises and UWB relay channel with correlated noises, as its special cases. We derive a general rate region for UWB‐SW‐MARC and obtain an outer bound for this model and, thereby, prove two certain capacity theorems for two important and different classes of MARC. Also, we analyze outage probability and diversity gain as the practically important concepts in wireless communications and prove that adding a relay to the multiple‐access channel improves the diversity gain. Finally, we evaluate some results numerically and illustrate that the noise correlation coefficient plays an important role in determining the relay position, and show that the channel performance depends on the noise variances. Copyright © 2014 John Wiley & Sons, Ltd.     

On the bounds of frequency-selective channel capacity with doubly correlated geometrical MIMO channel model

The multi-input multi-output (MIMO) technology plays an important role in link transmissions. This article considers the general case for the ergodic capacity in doubly correlated frequency-selective MIMO channel. In the study, the geometrical MIMO channel model is presented. Based on the formula of MIMO ergodic capacity, the capacity limits are studied with arbitrary finite number of antennas in the frequency-selective MIMO channel. It first derives the exact expressions for the upper bound and lower bound in doubly correlated MIMO channel. The results for the single-ended correlation and independent identically distributed (i.i.d.) MIMO channel are also obtained as special cases. Then the simple expressions of the capacity bounds are attained at high SNR. Finally, results are provided by Monte Carlo simulations to verify the tightness of the derived bounds.     

Ergodic channel capacity of the spatial correlated rayleigh MIMO channel

The theoretical capacity of the spatial correlated Rayleigh multiple input multiple output (MIMO) channel is an important issue in MIMO technology. In this article, an ergodic channel capacity formula of the spatial correlated rayleigh MIMO channel is provided, which is deduced when two antennas exist at either the transmitter or the receiver. The multi-dimensional least-squares fit algorithm is employed to narrow the difference between the theoretical formula capacity and the practical capacity. Simulation results show that the theoretical capacity approaches the practical one closely.     

Spectral efficiency of dual diversity selection combining schemes under correlated Nakagami-0.5 fading with unequal average received SNR

The spectral efficiency results for different adaptive transmission schemes over correlated diversity branches with unequal average signal to noise ratio (SNR) obtained so far in literature are not applicable for Nakagami-0.5 fading channels. In this paper, we investigate the effect of fade correlation and level of imbalance in the branch average received SNR on the spectral efficiency of Nakagami-0.5 fading channels in conjunction with dual-branch selection combining (SC). This paper derived the expressions for the spectral efficiency over correlated Nakagami-0.5 fading channels with unequal average received SNR. This spectral efficiency is evaluated under different adaptive transmission schemes using dual-branch SC diversity scheme. The corresponding expressions for Nakagami-0.5 fading are considered to be the expressions under worst fading conditions. Finally, numerical results are provided to illustrate the spectral efficiency degradation due to channel correlation and unequal average received SNR between the different combined branches under different adaptive transmission schemes. It has been observed that optimal simultaneous power and rate adaptation (OPRA) scheme provides improved spectral efficiency as compared to truncated channel inversion with fixed rate (TIFR) and optimal rate adaptation with constant transmit power (ORA) schemes under worst case fading scenario. It is very interesting to observe that TIFR scheme is always a better choice over ORA scheme under correlated Nakagami-0.5 fading channels with unequal average received SNR.     

Error rate analysis of threshold-based hybrid selection/maximal-ratio diversity over correlated nakagami-m fading channels

An exact performance analysis of triple-branch threshold-based hybrid selection/maximal-ratio combining (T-HS/MRC) receivers over correlated Nakagami-m fading channels is presented. Our analysis is valid for integer-order fading parameters and an arbitrary covariance matrix. Following the moment-generating function-based approach, the error rate performance of T-HS/MRC receivers for various modulation formats is analytically obtained. Various performance evaluation results are also presented and compared to equivalent simulation ones.     

Multiple-antenna capacity in correlated Rayleigh fading with channel covariance information

We analyze a mobile multiple input multiple output wireless link with M transmit and N receive antennas operating in a spatially correlated Rayleigh flat fading environment. Only the correlations between the channel coefficients are assumed to be known at the transmitter and the receiver. The channel coefficients are correlated in space and uncorrelated in time from one coherence interval to another. These coefficients remain constant for a coherence interval of T symbol periods after which they change to another independent realization according to the spatial correlation model. For this system we characterize the structure of the input signal that achieves capacity. The capacity achieving transmit signal is expressed as the product of an isotropically distributed unitary matrix, an independent nonnegative diagonal matrix and a unitary matrix whose columns are the eigenvectors of the transmit fade covariance matrix. For the case where the number of transmit antennas M is larger than the channel coherence interval T, we show that the channel capacity is independent of the smallest M-T eigenvalues of the transmit fade covariance matrix. In contrast to the previously reported results for the spatially white fading model where adding more transmit antennas beyond the coherence interval length (M>T) does not increase capacity, we find that additional transmit antennas always increase capacity as long as their channel fading coefficients are spatially correlated with the other antennas. We show that for fast hopping or fast fading systems (T=1) with only channel covariance information available to the transmitter and receiver, transmit fade correlations are beneficial. Mathematically, we prove this by showing that capacity is a Schur-convex function of the vector of eigenvalues of the transmit fade correlation matrix. We also show that the maximum possible capacity gain due to transmitter fade correlations is 10logM dB.     

Analysis of diversity schemes employing antenna selection in the presence of channel estimation errors and feedback delay

The main objective of this paper is to provide an extensive and complete examination on the effect of practical impairments such as channel estimation errors (CEEs) and feedback delay (FD) on the performance of diversity schemes over Nakagami‐m fading channels. Under erroneous channel estimation and outdated feedback cases, statistical expressions and several performance metrics related to the post‐processing signal‐to‐noise ratio (SNR) are derived for four different diversity schemes: transmit antenna selection (TAS)/orthogonal space–time block coding, TAS/maximal‐ratio transmission (MRT), MRT/receive antenna selection (RAS), and joint transmit and RAS. Exact analytical expressions for outage probability and average error rates of M‐ary modulations are derived in order to provide insightful perspectives on the capacity and error performance of diversity schemes that experience both CEE and FD. The asymptotic diversity order of the investigated diversity schemes are derived via a high‐SNR approximation approach. In order to assess the real‐world performance of the investigated diversity schemes and to observe their robustness or sensitivities in practical imperfections, various configurations are considered together with several performance comparisons. Also, Monte Carlo simulations are performed in order to validate the theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.