Sum-Rate Analysis of Downlink Channels with 1-Bit Feedback

The sum-rate capacity of a single-input single-output (SISO) downlink with Rayleigh flat fading channels and K users, grows as log log K when optimal scheduling is employed. However, the optimal scheduling requires that the full channel state information (CSI) for all users be available to the transmitter. In this work it is shown that the same rate growth holds even if the feedback rate from the users to the transmitter is reduced to 1-bit per fading block. A simple analysis for this setup is presented, resulting in a closed form expression for the achievable ergodic sum-rate. The mechanism of setting a sub-optimal threshold is elucidated by simple lower and upper bounds to the sum-rate. Among the insights afforded by the sum-rate expression and the bounds, is that application of the sub-optimal threshold demonstrates the same scaling law as the optimal full CSI scheme, asymptotically with the number of users K