An efficient approximation to the correlated Nakagami-m sums and its application in equal gain diversity receivers

There are several cases in wireless communications theory where the statistics of the sum of independent or correlated Nakagami-m random variables (RVs) is necessary to be known. However, a closed-form solution to the distribution of this sum does not exist when the number of constituent RVs exceeds two, even for the special case of Rayleigh fading. In this paper, we present an efficient closed-form approximation for the distribution of the sum of arbitrary correlated Nakagami-m envelopes with identical and integer fading parameters. The distribution becomes exact for maximal correlation, while the tightness of the proposed approximation is validated statistically by using the Chi-square and the Kolmogorov-Smirnov goodness-of-fit tests. As an application, the approximation is used to study the performance of equal-gain combining (EGC) systems operating over arbitrary correlated Nakagami-m fading channels, by utilizing the available analytical results for the error-rate performance of an equivalent maximal-ratio combining (MRC) system

BER of MRC for M-QAM with imperfect channel estimation over correlated Nakagami-m fading

In this contribution, we provide an exact BER analysis for M-QAM transmission over arbitrarily correlated Nakagami-m fading channels with maximal-ratio combining (MRC) and imperfect channel estimation at the receiver. Assuming an arbitrary joint fading distribution and a generic pilot-based channel estimation method, we derive an exact BER expression that involves an expectation over (at most) 4 variables, irrespective of the number of receive antennas. The resulting BER expression includes well-known PDFs and the PDF of only the norm of the channel vector. In order to obtain the latter PDF for arbitrarily correlated Nakagami-m fading, several approaches from the literature are discussed. For identically distributed and arbitrarily correlated Nakagami-m channels with integer m, we present several BER performance results, which are obtained from numerical evaluation and confirmed by straightforward computer simulations. The numerical evaluation of the exact BER expression turns out to be much less time-consuming than the computer simulations

A Unified Exact BER Performance Analysis of Asynchronous DS-CDMA Systems Using BPSK Modulation over Fading Channels

Abstract—An asynchronous binary DS-CDMA system using random spreading sequences is considered when communicating over various fading channels. New closed-form expressions are derived for the conditional Characteristic Function (CF) of the multiple access interference. A unified analysis is provided for calculating the exact average Bit Error Rate (BER) expressed in the form of a single numerical integration based on the CF approach. The numerical results obtained from our exact BER analysis are verified by our simulation results and are also compared to those obtained by the Standard Gaussian Approximation (SGA), confirming the accuracy of the SGA for most practical conditions, except for high Signal-to-Noise Ratios (SNR) and for a low number of interferers. Index Terms—BER analysis, CDMA, fading, Rayleigh, Ricean, Hoyt, Nakagami-m, random spreading sequence