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 preceding 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 alphaM (0 < alpha les 1), it is sufficient to scale the number of feedback bits B per user as B = alpha (M- 1) log₂ P/N₀ where M is the number of transmit antennas and P/N₀ is the average downlink SNR.