Limited-Rate Channel State Feedback for Multicarrier Block Fading Channels

The capacity of a fading channel can be substantially increased by feeding back channel state information from the receiver to the transmitter. If the feedback rate is limited, what state information to feed back and how to encode it are important questions. This paper studies power loading in a multicarrier system using no more than one bit of feedback per subchannel. The subchannels can be correlated and full channel state information is assumed at the receiver. First, a simple model with N parallel two-state (good/bad) memoryless subchannels is considered, where the channel state feedback is used to select a fixed number of subchannels to activate. The optimal feedback scheme is the solution to a vector quantization problem, and the associated performance for large N is characterized using a rate distortion function. As N increases, the loss in forward rate from the asymptotic (rate-distortion) value is shown to decrease as (logN)/N and √{(logN)/N} with optimal variable- and fixed-length feedback codes, respectively. These results are subsequently extended to parallel Rayleigh block fading subchannels, where the feedback designates a set of subchannels to be activated with equal power. Rate-distortion feedback codes are proposed for designating subsets of (good) subchannels with signal-to-noise ratios (SNRs) that exceed a threshold. The associated performance is compared with that of a simpler lossless source coding scheme, which designates groups of good subchannels, where both the group size and threshold are optimized. The rate-distortion codes can provide a significant increase in forward rate at low SNRs.