If perfect channel state information were available to the receiver, it is known that the total capacity increases monotonically with the number of users. If the channel state information is available to both the receiver and to all transmitters, the throughput maximizing strategy implies for N=1 that only the single user who enjoys the best channel condition transmits. In the absence of channel state information one is forced to a radically different conclusion. In particular we show that if the propagation coefficients take on new independent values for every symbol (e.g., T=1) then the total capacity for any M>1 users is equal to the capacity for M=1 user, in which case TDMA is an optimal scheme for handling multiple users. This result follows directly from a recent treatment of the single-user multiple antenna block-fading channel.

Again, motivated by the single-user results, one is lead to the following conjecture for the multiple user case: for any T>1 the maximum total capacity can be achieved by no more than M=T users. The conjecture is supported by establishing the asymptotic result that, for a fixed N and a constant M/T for large T, the total capacity is maximized when M/T approaches 0, which yields a total capacity per symbol of N log(1+rho), where rho is the expected SNR at the receiver. We further support the conjecture by examining the asymptotic behavior with large rho for fixed M,T and N <= T.

Status: Submitted to IEEE Trans. Info. Theory, December 2000.

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