On the sum rate of channel subspace feedback for multi-antenna broadcast channels

When a base-station with multiple antennas is transmitting to a single user with one antenna, feeding back the normalized channel vector (channel subsapce feedback) to the transmitter can achieve the same capacity as if the exact channel state information is available at the transmitter. For the multiuser scenario, however, perfect channel knowledge is usually required at the transmitter to obtain the sum rate advantage provided by the multiple transmit antennas. In this paper, we consider the sum rate of a multi-antenna broadcast channel when each user only feeds back the normalized channel vector. We show that in such situation the zero-forcing dirty paper (ZFDP) encoding scheme designed using channel subspace feedback achieves the throughput of full channel knowledge ZFDP encoding without optimal power allocation. It is shown to be asymptotically optimal for high signal-to-noise ratios. The closed-form expression of the ergodic sum rate for an independent Rayleigh fading channel is derived. The throughput performance of the regularized channel inversion technique under channel subspace feedback is also analyzed. We show that channel subspace feedback in the multi-antenna broadcast channel enables the system to achieve most of the sum rate advantage provided by the multiple antennas.