Sum-Rate Analysis of General OFDM Downlink Channels with 1-bit Feedback per Sub-Carrier

The ergodic sum-rate capacity of a single-input single-output (SISO) OFDM downlink channel, with K homogenous users scales as log log K when optimal scheduling is employed under certain conditions. However, the optimal scheduling requires that the full channel state information (CSI) for all users be available to the transmitter utilizing valuable bandwidth resources. In (S. Sanayei, et. al., 2004), the authors show that almost the same capacity growth holds even if the feedback rate from the users to the transmitter is reduced to 1-bit per sub-carrier per fading block for a limited class of channels. In this work, we present an alternative simple analysis for a more general class of channels resulting in a closed form expression for the ergodic achievable sum-rate. The mechanism of setting sub-optimal thresholds for the 1-bit quantizers is elucidated by simple lower bound to the sum-rate. Setting these sub-optimal thresholds ensures the same growth rate and non-interference limited behavior (at high-SNR regime) as that of the full-CSI scheme asymptotically with K.