The outage capacity of linear space-time codes

An inner space-time code, i.e., one that is complemented by an outer error-control code, calls for vastly different design strategies than a space-time code that stands alone. This letter investigates the design of a linear inner space-time code for a t-input r-output Rayleigh fading channel by examining its outage capacity, which assumes an idealized outer code. We show that a linear space-time code with rate R < min(t, r) can achieve at most a fraction R/ min(t, r) of the underlying channel's outage capacity at high signal-to-noise ratio (SNR). Conversely, we find that a space-time code with low raw diversity order (as calculated using the rank rule) does not necessarily suffer a capacity penalty. Under very general conditions, a rate of R = min(t, r) is sufficient to ensure that the outage capacity of the space-time code approaches that of the underlying channel at high SNR. Simulation results are presented to support the claims.