Capacity of time-varying channels with imperfect CSI

Mobile channels suffer from multipath fading and necessitate transmitter adaptation to achieve Shannon capacity. The capacity achieving transmitter adaptation strategy depends on how much channel side information (CSI) is available at the transmitter (CSIT) and the receiver (CSIR). When CSI is perfectly known at both sides, it is shown in [10] that for AWGN channels with flat fading, the optimal power adaptation scheme is water-filling over distribution (time). In real systems, however, perfect CSI is rarely available at either transmitter or receiver; receiver obtains an imperfect knowledge due to channel estimation error, whose accuracy further decreases by the delay and noise in the feedback link. Several researchers have recently investigated the impact of imperfect CSI on the capacity. In [5], the lower and upper bound of mutual information have been derived assuming that the channel is known only at the receiver within some mean-square error. The capacity of a finite state Markov channel (FSMC) with perfect CSIR and feedback delay is examined in [1]. In his Ph.D. thesis [3], Klein states optimal power allocations with average transmit power constraint for maximizing mutual information of FSMC under delayed feedback, feedback error, and channel estimation error. As an extension of the above [1], [3], [5], we study the capacities and optimal power adaptation schemes of typical wireless channels under three kinds of imperfections – delayed feedback, noisy feedback path, and receiver channel estimation error. We obtain FSMC models [6], [11] for Rayleigh, Rician [8], and Nakagami[9] fading channel, and evaluate their capacities with average transmit power constraint under the three kinds of imperfect CSI. We also examine the capacities of two suboptimal schemes – waterfilling and no power adaptation, and show that combining the two suboptimal schemes can produce a near-optimal performance.