On the Achievable Diversity-Multiplexing Tradeoff in MIMO Fading Channels with Imperfect CSIT

In this paper, we analyze the fundamental tradeoff of diversity and multiplexing in multi-input multi-output (MIMO) channels with imperfect channel state information at the transmitter (CSIT). We show that with imperfect CSIT, a higher diversity gain as well as a more efficient diversity-multiplexing tradeoff (DMT) can be achieved. In the case of multi-input single-output (MISO)/single-input multi-output (SIMO) channels with K transmit/receive antennas, one can achieve a diversity gain of d(r)=K(1-r+K\alpha) at spatial multiplexing gain r, where \alpha is the CSIT quality defined in this paper. For general MIMO channels with M (M>1) transmit and N (N>1) receive antennas, we show that depending on the value of \alpha, different DMT can be derived and the value of \alpha has a great impact on the achievable diversity, especially at high multiplexing gains. Specifically, when \alpha is above a certain threshold, one can achieve a diversity gain of d(r)=MN(1+MN\alpha)-(M+N-1)r; otherwise, the achievable DMT is much lower and can be described as a collection of discontinuous line segments depending on M, N, r and \alpha. Our analysis reveals that imperfect CSIT significantly improves the achievable diversity gain while enjoying high spatial multiplexing gains.