MISO Broadcast Channels with Delayed Finite-Rate Feedback: Predict or Observe?

Most multiuser precoding techniques require accurate channel state information at the transmitter (CSIT) to maintain orthogonality between the users. Such techniques have proven quite fragile in time-varying channels because the CSIT is inherently imperfect due to quantization error and feedback delay. An alternative approach recently proposed by Maddah-Ali and Tse (MAT) allows for significant multiplexing gain in the multi-input single-output (MISO) broadcast channel (BC) even with CSIT that is "completely stale", i.e., uncorrelated with the current channel state. With K users, their scheme claims to lose only a log(K) factor relative to the full K degrees of freedom (DoF) attainable in the MISO BC with perfect CSIT for large K. However, their result does not consider the cost of the feedback, which is potentially very large in high mobility (short channel coherence time). In this paper, we more closely examine the MAT scheme and compare its maximum net DoF gain to single user transmission (which always achieves 1 DoF) and partial CSIT linear precoding (which achieves up to K). In particular, assuming the channel coherence time is N symbol periods and the feedback delay is N_fd, we show that when N <; (1+o(1)) K log K (short coherence time), single user transmission performs best, whereas for N>; (1+o(1)) (N_fd+ K/ log K)(1-log^-1K)^-1 (long coherence time), zero-forcing precoding outperforms the other two. The MAT scheme is optimal for intermediate coherence times, which for practical parameter choices is indeed quite a large and significant range, even accounting for the feedback cost.