On the fundamental tradeoff of spatial diversity and spatial multiplexing of MIMO links with imperfect CSIT

Multiple antennas can be used for increasing the packet reliability (spatial diversity) or the spectral efficiency (spatial multiplexing) in wireless communication systems operating under a slow fading environment. Zheng and Tse showed that both types of gains can be simultaneously obtained for a given multiple antenna channel, but there exist a fundamental tradeoff between spatial diversity and spatial multiplexing. They considered the case of no Channel State Information at the Transmitter (CSIT) but perfect Channel State Information at the Receiver (CSIR). In this paper, we provide an alternative derivation of the fundamental tradeoff with no CSIT and extend the framework to analyze the role of CSIT on the fundamental performance tradeoff for a MIMO link. Defining CSIT quality order as α = -log σ _Δ²/log p, where σ_Δ² is the CSIT error variance, we showed that the diversity order d(α, r̄) is a piecewise linear function interpolating the points (k, (m - k)(n - k) + α max(m, n)), for k = 0, 1,..., min(m, n) where m is the number of transmit antennas and n is the number of receive antennas. The relationship suggests that if the imperfect CSIT is asymptotically "good", (a ≠ 0) then an additional diversity order of α max(m, n) can be realized compared to the no CSIT case. This additional diversity gain is independent of the average spatial multiplexing gain. © 2006 IEEE