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 rhomax, 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 rhomax. For the remaining rates, the optimal correlation is either 0 or rhomax- 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.

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