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A unified view of the large amount of progress which has been made in the analysis of systems such as radar, communications, imaging systems, etc., is presented. The basic theory of complex parameter systems and the role of phase lock in such systems is given in Section II. Performance limitations due to phase errors, stochastic delays, and clipping are discussed in Sections III and IV. Section V gives some results of ifitering for the modulus of a complex signal, and Section VI treats some problems in scatter communications. The following are some of the solutions presented. Phase lock provides a factor-two improvement in signal-to-noise ratio in coherent receivers. If r(x) denotes random deviation from constructing a straight antenna and Â¿ is the standard deviation of d2r/dx2, then there exists a Gaussian illumnation which provides a radius of gyration beamwidth of Â¿Â¿Â¿/2Â¿. Hard limiting of radar or analog communication signals prior to processing in an optimum receiver results in an rms error in signal estimation of 32 per cent in the presence of Gaussian statistics. With Gaussian statistics, the processor which minimizes E(|Jf-h|2) where f is signal and h is system output (where additive noise is present) also minimizes E [(|f|2-|h|2)2] save for a correction of mean value which is required in the latter case. In the section on scatter communications, the relation between "cloud size statistics" and coherence bandwidth is presented along with the performance gain available through the use of space diversity in the receiving system.