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Optimal signal design and detection for fast fading channels

In this paper, we characterize optimal detection and signaling (in terms of signal-to-noise ratio) for a fast fading channel when the autocorrelation function of the channel variation is known. We find that the well known matched filter and RAKE receiver are limiting cases of our result. Also, we provide a procedure that finds a pair of signals for digital communication. With land mobile fading channels, the signals obtained with our procedure have a performance significantly better than traditional flat-top pulse in terms of probability of error rate.