Comparison of Receiver Operating Characteristics of Four Different Processors for the Detection of Random Signal Transmissions

摘要

When a segment of a random sequence is used as the transmitted signal waveform and is made available to a receiver attempting to detect tne presence of a weak target echo, an extra degree of freedom is injected into the optimum processing scheme. Optimum and nearoptimum processing of the received data then involves neither the energy detector nor the standard crosscorrelator; rather, a normalized crosscorrelator is found to perform virtually at the level of the optimum processor. The characteristic functions of the decision variables of all four processors (namely, the energy detector, crossconelator, normalized crosscorrelator, and optimum processor) are derived in closed form in terms of M, the signal time bandwidth product, and R, the input signal to noise ratio per sample. These analytic results are numerically transformed to yield the corresponding receiver operating characteristics for a wide range of values of false alarm and detection probabilities.