Wigner/cycle spectrum analysis of spread spectrum and diversity transmissions

A high-resolution t-ω estimator, termed the Wigner distribution (WD), is shown to form a sound basis for representing nonstationary acoustic returns. Signal returns are modeled as the output of a time-variant random filter where the WD of the nonstationary signal return defines a random process whose expectation reduces to the instantaneous power spectral density defined for dispersive communication channels. From the WD, a set of relations describing time-variant channel effects on spread-spectrum and diversity transmissions are developed. These relations are shown to be useful in comparing spreading techniques under differing channel conditions and for estimating channel-imposed bounds on the spreading parameters required for effective transmission. A mapping from the Wigner distribution to the cycle spectrum is shown to produce cyclic correlations characteristic of the modulation rate. The WD-based formulation is applied to an example of spread-spectrum transmission through a reverberation-limited channel