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Most multiuser precoding techniques require accurate transmitter channelstate information (CSIT) to maintain orthogonality between the users. Suchtechniques have proven quite fragile in time-varying channels because the CSITis inherently imperfect due to estimation and feedback delay, as wellquantization noise. An alternative approach recently proposed by Maddah-Ali andTse (MAT) allows for significant multiplexing gain in the multi-inputsingle-output (MISO) broadcast channel (BC) even with transmit CSIT that iscompletely 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 forlarge $K$. However, their result does not consider the cost of the feedback,which is potentially very large in high mobility (short channel coherencetime). In this paper, we more closely examine the MAT scheme and compare itsDoF gain to single user transmission (which always achieves 1 DoF) and partialCSIT linear precoding (which achieves up to $K$). In particular, assuming thechannel coherence time is $N$ symbol periods and the feedback delay is $N_{\rmfd}$ we show that when $N < (1+o(1)) K \log K$ (short coherence time), singleuser transmission performs best, whereas for $N> (1+o(1)) (N_{\rm fd}+ K / \logK)(1-\log^{-1}K)^{-1}$ (long coherence time), zero-forcing precodingoutperforms the other two. The MAT scheme is optimal for intermediate coherencetimes, which for practical parameter choices is indeed quite a large andsignificant range, even accounting for the feedback cost.

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