| In this dissertation, we characterize the optimal detection and signaling in terms of signal-to-noise for a fast or frequency-selective fading channel when the autocorrelation function of the channel is known. Our result characterizes the optimization problem as an eigenvalue/eigenfunction problem with integral operators. For detection, the well-known matched-filter and RAKE receiver are limiting cases of our results. Besides, we provide a closed-form expression of the probability-density function and the cumulative function of a quadratic form for zero-mean-complex-Gaussian vectors, which is used to evaluate the probability of error rate of quadratic receivers. Additionally, we provide a procedure that finds pairs of signal or filter for digital communication. With the land-mobile-fading channel, the signal/filter pairs obtained with our procedure have a performance significantly better than that of the traditional flat-top pulse and raised-cosine pulse in a pulse-position modulation pair in terms of the probability of error rate. |
