Limited feedback for multicarrier block fading channels: A rate distortion approach

This paper studies power loading in a multicarrier system with channel state feedback of no more than one bit per sub-channel. Full channel state information is assumed known at the receiver. A simple model with parallel two-state (good/bad) memoryless sub-channels is considered first, where feedback is used to select a given fraction of sub-channels to activate. The optimal feedback scheme is the solution to a vector quantization problem, the performance of which is characterized by a rate distortion function in the limit of infinite number of sub-channels. Bounds for performance loss with finite number of sub-channels are also developed. We then consider a second model of a bank of block Rayleigh fading sub-channels with total power constraint, where the feedback describes which sub-channels to activate with equal power. A scheme based on rate distortion code is proposed to describe which sub-channels exceed a threshold in signal-to-noise ratio and should be activated. With optimized threshold and moderate amount of feedback, the resulting capacity is known to be of the same order in the number of sub-channels as that achieved by water-filling with full channel state information at the transmitter. This scheme performs more favorably than alternative schemes based on channel state reduction (such as by grouping them) and subsequent entropy coding.