The impact of spatial correlation on the statistical properties of the capacity of nakagami-m channels with MRC and EGC

Gulzaib Rafiq,Matthias Pätzold,Valeri Kontorovich

doi:10.1186/1687-1499-2011-116

Abstract

In this article, we have studied the statistical properties of the instantaneous channel capacitya of spatially correlated Nakagami-m channels for two different diversity combining methods, namely maximal ratio combining (MRC) and equal gain combining (EGC). Specifically, using the statistical properties of the instantaneous signal-to-noise ratio, we have derived the analytical expressions for the probability density function (PDF), cumulative distribution function (CDF), level-crossing rate (LCR), and average duration of fades (ADF) of the instantaneous channel capacity. The obtained results are studied for different values of the number of diversity branches and for different values of the receiver antennas separation controlling the spatial correlation in the diversity branches. It is observed that an increase in the spatial correlation in the diversity branches of an MRC system increases the variance as well as the LCR of the instantaneous channel capacity, while the ADF of the channel capacity decreases. On the other hand, when EGC is employed, an increase in the spatial correlation decreases the mean channel capacity, while the ADF of the instantaneous channel capacity increases. The presented results are very helpful to optimize the design of the receiver of wireless communication systems that employ spatial diversity combining techniques. Moreover, provided that the feedback channel is available, the transmitter can make use of the information regarding the statistics of the instantaneous channel capacity by choosing the right modulation, coding, transmission rate, and power to achieve the capacity of the wireless channelb.

Highlights

The performance of mobile communication systems is greatly affected by the multipath fading phenomenon
It is observed that at lower levels, the level-crossing rate (LCR) is higher for channels with smaller values of the number of diversity branches L or higher severity levels of fading than for channels with larger values of L or lower severity levels of fading
The results show that the average duration of fades (ADF) of the capacity of Nakagami-m channels with maximal ratio combining (MRC) decreases with an increase in the spatial correlation in the diversity branches

Summary

Introduction

The performance of mobile communication systems is greatly affected by the multipath fading phenomenon. Holds for any arbitrary correlation model, as long as the correlation matrix R is non-negative definite It is shown in [22] that despite the diversity branches are spatially correlated, the instantaneous SNR g(t) at the combiner output of an MRC system can be expressed as a sum of weighted statistically independent gamma variates ζl2(t) , as given in (3). As given by (3), even when the diversity branches are spatially correlated and have nonidentical parameters, the process Ξ(t) is still expressed using a sum of statistically independent gamma variates, similar to the uncorrelated scenario considered in [16] to obtain (6). 3.1 Statistical properties of the capacity of spatially correlated Nakagami-m channels with MRC The PDF pg(z) of the instantaneous SNR g(t) can be found with the help of (4) and by employing the relation pg(z) = (1/gs) pΞ (z/gs).

Statistical Properties of the Capacity of Spatially

Conclusion