Throughput analysis for MIMO systems in the high SNR regime

Outage capacity and throughput are the two key metrics through which the fundamental limits of delay-sensitive wireless MIMO links can be studied. In this paper, we show that these metrics are intimately related, and consequently, as in the case of outage capacity, the growth rate of throughput with SNR rho is t log rho for a general class of fading channels (with channel state information at the receiver (CSIR) and with or without CSI at the transmitter (CSIT)) whose channel matrix is of rank t with probability one. However, while asymptotically tight affine lower bounds of the form t log rho + 0(1) were recently derived for outage capacity for such channels, in the sense that the limit as rho rarr infin of the difference between the outage capacity and the lower bound is zero, such affine lower bounds are not possible in general for the throughput. Using the t log rho + O(1) bounds on outage capacity however, lower bounds on throughput are specified where the high SNR limit of the ratio of the throughput and its lower bound is unity. These bounds reveal that the throughput optimal outage probability approaches zero as rho rarr infin. An important exception is the scenario where both the transmitter and receiver have CSI under the long-term power constraint (LTPC), for which we obtain a lower bound of the form t log rho + O(1) which is asymptotically tight (in the stronger sense) and interestingly, this lower bound is identical to the asymptotic delay-limited capacity. The throughputs of MISO and SIMO fading channels are extensively analyzed and it is shown that asymptotically, isotropic Gaussian input is throughput optimal, correlation is detrimental whereas increase in the Rice factor is beneficial and that throughput is schur-concave in the correlation eigenvalues