On power allocation for generalized cyclic-prefix based channel-equalizers

The cyclic prefix system is commonly employed for channel equalization in discrete multitone systems. The system allows one to perform bit and power allocation in the subbands of the channel. In the DMT system, the input symbol stream, typically binary, is parsed into several substreams which are then communicated over different subbands of the channel. We emphasize that the cyclic prefix can actually be used in a broader setting. For example, if we have to transmit a simple symbol stream belonging to a PAM (pulse amplitude modulation) constellation, we can use the cyclic prefix directly on this stream. More generally, the idea is applicable to the problem of compensating any linear distortion with additive noise. We derive the optimal power allocation formula for the case of a nonflat channel with possibly colored noise.