A Space-Time Correlation Model for MRC Receivers in Rayleigh Fading Channels

Abstract

This paper presents a statistical model for maximum ratio combining (MRC) receivers in Rayleigh fading channels enabled with a temporal combining process. This means that the receiver effectively combines spatial and temporal branch components. Therefore, the signals that will be processed by the MRC receiver are collected not only across different antennas (space), but also at different instants of time. This suggests the use of a retransmission, repetition or space-time coding algorithm that forces the receiver to store signals in memory at different instants of time. Eventually, these stored signals are combined after a predefined or dynamically optimized number of time-slots or retransmissions. The model includes temporal correlation features in addition to the space correlation between the signals of the different components or branches of the MRC receiver. The derivation uses a frequency domain approach (using the characteristic function of the random variables) to obtain closed-form expressions of the statistics of the post-processing signal-to-noise ratio (SNR) under the assumption of equivalent correlation in time and equivalent correlation in space. The described methodology paves the way for the reformulation of other statistical functions as a frequency-domain polynomial root analysis problem. This is opposed to the infinite series approach that is used in the conventional methodology using directly the probability density function (PDF). The results suggest that temporal diversity is a good complement to receivers with limited spatial diversity capabilities. It is also shown that this additional operation could be maximized when the temporal diversity is adaptive (i.e., activated by thresholds of SNR), thus leading to a better resource utilization.