Achievable performance over fading channels with antenna diversity

There has been much interest in wireless communications and thus it is appropriate to determine the Shannon limit for such systems. There have been a number of papers that consider channel capacity and also the random coding error exponent for various scenarios, In this paper, we consider Gallager's random coding error exponent for flat fading channels with antenna (or space) diversity employed at the receiver. Receiver antenna diversity is well known to be a fundamental technique for combating fading in wireless communications. The random coding error exponent is also well known to be a key quantity in assessing the ultimate, or achievable, performance over communications channels. We derive the random coding error exponent for various fading scenarios for which diversity combining is used. The cases we consider include memoryless fading channels with complete channel state information (CSI) at the receiver as well as time-correlated fading channels with complete CSI at the receiver. We also present results for time-correlated channels with partial CSI at the receiver via some practical channel estimation technique. The results we present in this paper shed light on the achievable performance over fading channels with receiver diversity combining and provide insight regarding the amount of coding complexity required for reliable communications over such channels.