On the Outage Probability of a Multiple-Input Single-Output Communication Link

We investigate the outage probability of a 2 times 1 multiple-input single-output (MISO) communication link subjected to quasi-static flat Rayleigh fading, under total and individual (per antenna) average power constraints and under a maximum correlation constraint. For a system with normalized fading and noise powers and a total power constraint P, it is shown that up to a rate of approximately log (1 + 1.2564 ldr P) it is best to divide the power equally between the two antennas, while for higher rates it is preferable to use all of the power in a single antenna. When individual power constraints are imposed on each antenna, and in addition, the correlation between the transmitted signals from each antenna can not be made larger than rho_max, it is shown that for rates smaller than log(1 + P) the optimal correlation is zero, while for rates higher than log(1 + gammaP), where gamma is a constant in [1,3/2], the best correlation is rho_max. For the remaining rates, the optimal correlation is either 0 or rho_max- Finally, we consider the outage performance of a two-user multiple access channel with a common message. The effect of the rate of the common message on the optimal correlation and on the optimum outage performance is examined.