On the Statistical Analysis of the Channel Capacity of Double Rayleigh Channels with Equal Gain Combining in V2V Communication Systems

In this article, we present a detailed study on the statistical properties of the channel capacity of vehicle-to-vehicle (V2V) fading channels with equal gain combining (EGC). Assuming perfect channel state information (CSI) at the receiver, we have modeled the received signal envelope at the output of the equal gain (EG) combiner as a sum of double Rayleigh processes. These double Rayleigh processes are assumed to be independent but not necessarily identical processes. It is illustrated that the probability density function (PDF) of this sum process can efficiently be approximated using the gamma distribution. Furthermore, exploiting the properties of the gamma distribution, other statistical properties of the sum process are also evaluated. Thus, given the analytical approximations for the statistical properties of the received signal envelope at the output of the EG combiner, the theoretical results associated the statistics of the channel capacity just involves transformation of random variables. Here, simple and closed-form analytical approximations for the PDF, the cumulative distribution function (CDF), the level-crossing rate (LCR), and the average duration of fades (ADF) of the channel capacity are derived. The correctness of the theoretical results is validated by simulations. The presented results can be utilized to optimize the performance of spatial diversity receivers employed in the forthcoming V2V multiple-input multiple-output (MIMO) wireless communication systems.