Linear receivers for multiple-antenna communication channels: an asymptotic analysis

We study the asymptotic behavior of space-time codes when a linear receiver interface is used in lieu of the maximum-likelihood interface. Specifically, we determine the behavior of pairwise error probabilities with maximum-likelihood decoding and with four types of receiver interfaces: the maximum-likelihood interface, the linear zero-forcing interface, the linear minimum-mean-square-error interface, and the matched-filter interface. An asymptotic analysis is performed by assuming that the number of receiving antennas grows to infinity while the number of transmitting antennas is finite, and that both numbers grow to infinity but their ratio remains constant. We show that with all the interfaces studied here the asymptotic performance of space-time codes is determined by the Euclidean distances between code words. Moreover, the performance of linear interfaces comes close to maximum-likelihood if the number r of receive antennas is sufficiently larger than the number t of transmit antennas. The dependence of error probabilities on Euclidean distance is valid for intermediate signal-to-noise ratios even when the number of antennas is small.