The performance and optimization of switched diversity systems are considered. First, the one-dimensional distribution and probability density functions of the envelope of the received signal are obtained for three different switching strategies. This information is used to obtain the average probability of bit error for the case of non-coherent detection of binary FSK signals with Rayleigh fading envelopes and additive white Gaussian noise. The optimization of two of these switching strategies is then considered, and it is shown that by proper selection of switching thresholds, the average probability of bit error during detection can be minimized. It is also shown that these optimized switching strategies yield a significant improvement in performance over non-diversity systems and can approach the performance of more complex receivers such as maximal ratio combining. Computer simulations of switched diversity systems using a practical field model are used to verify the analysis.

Channels (i.e., operators) are studied that produce time warping, or delay modulation, in signals passing through them, and many interesting properties of these channels are developed. It is shown that a first-in first-out (FIFO) assumption for such channels is compelling on physical grounds and vastly simplifies ensuing analysis. Two descriptions of the channel, the "send-delay" and "receive-delay" functions, are compared, and it is shown that one is precisely the shape needed to equalize or unwarp signals warped by the other. A series expansion for time-warped signals is developed, and the unitary nature of the warp operators is exploited to generate rich sets of orthonormal signals. The random time-warp channel is then analyzed, and certain statistics such as the autocorrelation function of the output signals are developed, along with conditions on their stationarity. Finally, optimum linear filters for extracting a signal from a noisy and time-warped version are derived and compared with some previous results.

An interesting and long-standing problem in probability theory is surveyed, and its applications to analyzing the effects of intersymbol interference in digital transmission systems are discussed. Old and new results are presented which enable one to obtain analytical forms for the probability density function of the intersymbol interference in special eases. The probability of error is then computed and compared with some popular upper bounds.