Space-time codes for high bit rate wireless communications: Asymptotic performance of space-time random codes

To quantify the diversity gain of Space-Time coding, obtained by increasing the number of transmit and receive antennas, in this paper we use the paradigm of random codes, modelling Space-Time codes as random matrices with zero mean, equal variance and independent entries having a common arbitrary distribution (discrete or continuous). This framework is especially convenient in this situation because: i) optimal codes are difficult to identify and, thus, are difficult to test; ii) the eigenvalues of this type of large matrices converge to a specific distribution, mostly known as the semicircle or circle law. This last observation allows us to derive closed form asymptotic expressions for the probability of error in Rayleigh and Rician fading that can be used to gain insight on how the fading and the number of antennas affect the system performance.