On the achievable rate of ZF-DPC for MIMO broadcast channels with finite rate feedback

Abstract—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 PN0 where M is the number of transmit antennas and P N0 is the average downlink SNR. Index Terms—Broadcast channel, finite rate feedback, multi-plexing gain, multiuser MIMO, zero-forcing dirty-paper coding (ZF-DPC). I