Cross-spectrum symbol synchronization

A popular method of symbol synchronization exploits one aspect of generalized harmonic analysis, normally referred to as the cross-spectrum. Utilizing nonlinear techniques, the input symbol energy is effectively concentrated onto multiples of the symbol clock frequency, facilitating application of conventional phase lock synchronization techniques. A general treatment of the cross-spectrum technique is developed and shown to be applicable across a broad class of symbol modulation formats. An important specific symbol synchronization application is then treated, focusing the general development to provide both insight and quantitative measure of the performance impact associated with variation in these key synchronization parameters: symbol modulation format, symbol transition probability, symbol energy to noise density ratio, and symbol rate to filter bandwidth ratio.