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 multioutput (SIMO) channels with K transmit/receive antennas, one can achieve a diversity gain of d(r) = K(1 − r + Kα) at spatial multiplexing gain r, where α 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 α, different DMT can be derived and the value of α has a great impact on the achievable diversity, especially at high multiplexing gains. Specifically, when α is above a certain threshold, one can achieve a diversity gain of d(r) = MN(1 + MNα) − (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 α. Our analysis reveals that imperfect CSIT significantly improves the achievable diversity gain while enjoying high spatial multiplexing gains. Index Terms Diversity-multiplexing tradeoff, MIMO, channel state information, channel estimation. The authors are with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, 639798 (e-mail: [email protected], [email protected]). 2