On the Fundamental Tradeoff of Spatial Diversity and Spatial Multiplexing of MISO/SIMO 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 is 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). On the other hand, when perfect CSIT is available at the transmitter, infinite diversity order can be achieved through rate adaptation. However, perfect CSIT is very difficult to obtain and in practice, we shall have imperfect CSIT (which lies between the two extremes of no CSIT versus perfect CSIT). In this paper, we analyze the role of CSIT on the fundamental performance tradeoff for a MISO/SIMO link. Defining CSIT quality order as alpha = -log sigma(2)(Delta h)/log S N R, we derived the optimal rate adaptation as well as the optimal tradeoff between the CSIT quality order, alpha, the average diversity order, (d) over bar and the average multiplexing gain, (r) over bar, as (d) over bar(alpha, (r) over bar) = (1 + alpha - (r) over bar )n, where n is the number of transmit or receive antennas. The relationship suggests that imperfect CSIT can also provide additional diversity order and interprets the CSIT quality order as the maximum achievable spatial multiplexing gain with n diversity order when alpha <= 1.