On the Achievable Rate of ZF-DPC for MIMO Broadcast Channels with Finite Rate Feedback

In this paper we study a MIMO fading broadcast channel where each receiver has perfect channel state information (CSI) while the transmitter only acquires quantized CSI by finite rate feedback. We analyze the zero-forcing dirty-paper coding (ZF-DPC) scheme, which is a nonlinear precoding scheme inherently superior to linear ZF beamforming. Lower bound in closed-form expression and upper bound on the achievable ergodic rate of ZF-DPC with Gaussian inputs and uniform power allocation are derived. Based on the closed-form lower bound, sufficient conditions on the feedback channels to ensure non-zero and full downlink multiplexing gain are obtained. Specifically, in order to achieve the downlink multiplexing gain of αM (0 <α ≤ 1), it is sufficient to scale the number of feedback bits B per user as B = α(M −1)log2 P N0 where M is the number of transmit antennas and P N0 is the average downlink SNR. the results there show that the system becomes interference- limited with fixed amount of feedback while the number of feedback bits per user must increase linearly with the logarithm of the downlink SNR to maintain the full downlink multiplexing gain. In this paper, we study the achievable rate of zero-forcing dirty-paper coding (ZF-DPC) (1), a nonlinear precoding scheme inherently superior to ZF-BF due to its interference precancelation characteristic, for a MIMO broadcast channel with finite rate feedback. We adopt the vector quantization distortion measure of the angle between the codevector and the downlink channel vector, and perform random vector quantization (RVQ) (3)-(5) for analytical convenience. Our main contributions and key findings are as follows: