CSI feedback scaling rate vs multiplexing gain tradeoff for DPC-based transmission in the Gaussian MIMO broadcast channel

The operation of the multiple input multiple output (MIMO) Gaussian broadcast channel (BC) with K transmit antennas and K over r users with r receive antennas each is analyzed when channel state information (CSI) is obtained at the transmitter from the i^th user via finite-rate feedback link of capacity B_i bits. It is proved that if B_i is scaled at the rate of α_ir(K - r) log₂ P, where P is the transmit power and α ∈ [0, 1], then using dirty paper coding (DPC), the multiplexing gain of α_ir can be achieved for user i. This result on the feedback scaling rate rests on an elegant achievability scheme, the construction of which brings to light several new insights on the manner in which DPC achieves the complete multiplexing gain in the perfect-CSIT case.