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.     

Selection diversity receivers over nonidentical Weibull fading channels

The performance of selection combining (SC) receivers operating over independent, but not necessarily identically distributed, Weibull fading channels is studied. A novel closed form expression for the moments of the SC output signal-to-noise ratio (SNR) is derived, which is used to study the corresponding average output SNR and amount of fading. Second-order statistical parameters such as the average level crossing rate and average fade duration at the output of the SC are also obtained in closed form. Moreover, the average symbol error probability for several coherent and noncoherent modulations schemes as well as the Shannon capacity are extracted in terms of the tabulated Meijer's G-function. Simulations are also performed to validate the proposed formulation.     

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.     

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.     

Gaussian class multivariate Weibull distributions: theory and applications in fading channels

Ascertaining on the suitability of the Weibull distribution to model fading channels, a theoretical framework for a class of multivariate Weibull distributions, originated from Gaussian random processes, is introduced and analyzed. Novel analytical expressions for the joint probability density function (pdf), moment-generating function (mgf), and cumulative distribution function (cdf) are derived for the bivariate distribution of this class with not necessarily identical fading parameters and average powers. Two specific distributions with arbitrary number of correlated variates are considered and studied: with exponential and with constant correlation where their pdfs are introduced. Both cases assume equal average fading powers, but not necessarily identical fading parameters. For the multivariate Weibull distribution with exponential correlation, useful corresponding formulas, as for the bivariate case, are derived. The presented theoretical results are applied to analyze the performance of several diversity receivers employed with selection, equal-gain, and maximal-ratio combining (MRC) techniques operating over correlated Weibull fading channels. For these diversity receivers, several useful performance criteria such as the moments of the output signal-to-noise ratio (SNR) (including average output SNR and amount of fading) and outage probability are analytically derived. Moreover, the average symbol error probability for several coherent and noncoherent modulation schemes is studied using the mgf approach. The proposed mathematical analysis is complemented by various evaluation results, showing the effects of the fading severity as well as the fading correlation on the diversity receivers performance.     

Analysis of selection diversity on Nakagami fading channels

A theoretical framework to evaluate the performance of different pre-detection diversity techniques in various mobile radio environments is developed     

Switching rates of dual selection diversity in noisy fading channels

The effect of noise on the switching rate of a dual branch selection diversity combiner in noisy fading channels is examined. A closed-form solution is derived for independent and identically distributed (i.i.d.) and independent and nonidentically distributed (i.n.d.) fading channels. The switching rate in noisy fading channels is compared to that in noise-free conditions.     

Outage analysis of selection diversity over Rayleigh fading channels with multiple co-channel interferers

In this paper an approach to the performance analysis of signal-to-interference (SIR) based selection combining (SC) operating over the Rayleigh fading channels experiencing an arbitrary number of multiple, Rayleigh co-channel interferers is presented. We have presented a general analysis of multibranch SC where each branch experiences an arbitrary number of multiple equal power co-channel interferers. Useful closed form expressions are derived for the probability density function (PDF) and cumulative distribution function (CDF) at the output of the combiner. Also an outage analysis is performed in order to show the effects of the number of multiple interferers, diversity order and input SIR unbalance to the system performances.     

Post-detection diversity Nakagami fading channels with correlatedbranches

We derive a closed-form expression for the performance of the post-detection product detector combiner (PDC) operating on L correlated branches in Nakagami (1960) fading. We consider the 2-DPSK signaling scheme and nonselective slow fading. The average bit error rate (BER) obtained with this scheme is compared to the ideal predetection MRC, showing limited loss. Moreover, the post-detection PDC is shown to outperform the selection diversity combiner (SDC) under the considered case of Nakagami fading     

Correlated jamming on MIMO Gaussian fading channels

We consider a zero-sum mutual information game on multiple-input multiple-output (MIMO) Gaussian Rayleigh-fading channels. The players are an encoder-decoder pair as the maximizer, and a jammer as the minimizer, of the mutual information between the input and the output of the channel. There are total power constraints on both the jammer and the encoder. Also, the jammer has access to the encoder output. We find the unique saddle point of this game, and prove the somewhat surprising result that the knowledge of the channel input is useless to the jammer.     

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.     

Performance analysis of coded communication systems on Nakagami fading channels with selection combining diversity

In this paper, we develop analytical tools for the performance analysis of coded, coherent communication systems on independent and identically distributed Nakagami-m fading channels with selection combining (SC) diversity. First, we derive an exact expression for the moment generation function (MGF) of the signal-to-noise ratio (SNR) of a code symbol at the output of the selection combiner. Next, based on Gauss-Chebyshev quadrature and Gauss-Laguerre quadrature rules, we propose a simple to compute, yet accurate, numerical solution for the pairwise error probability (PEP) of coded M-phase-shift keying (PSK) signals. Using the PEP expressions, we present the union bound-based bit-error performance of trellis-coded modulation schemes and turbo codes. Finally, we derive an exact expression for the computational cutoff rate of a coded system with M-PSK signaling and SC diversity, and show that the cutoff rate expression is a simple function of the MGF of the SNR at the output of the diversity combiner.     

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 of selection diversity for DS/CDMA communications overRayleigh fading channels

An analytical model to evaluate the performance of selection diversity is presented. Results indicate that the conventional selection diversity scheme. in which the branch with the largest signal-to-noise ratio (SNR) is chosen, does not accurately reflect the performance of the more commonly implemented selection systems, in which the largest signal-plus-interference and noise (S+I) is chosen. Owing to the statistical nature of the noise, S+1 selection diversity performs better than conventional selection diversity model     

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.     

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.     

Modulation diversity for frequency-selective fading channels

In this article, modulation diversity (MD) for frequency-selective fading channels is proposed. The achievable performance with MD is analyzed and a simple design criterion for MD codes for Rayleigh-fading channels is deduced from an upper bound on the pairwise error probability (PEP) for single-symbol transmission. This design rule is similar to the well-known design rule for MD codes for flat fading and does not depend on the power-delay profile of the fading channel. Several examples for MD codes with prescribed properties are given and compared. Besides the computationally costly optimum receiver, efficient low-complexity linear equalization (LE) and decision-feedback equalization (DFE) schemes for MD codes are also introduced. Simulations for the widely accepted COST fading models show that performance gains of several decibels can be achieved by MD combined with LE or DFE at bit-error rates (BERs) of practical interest. In addition, MD also enables the suppression of cochannel interference.     

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.     

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.