Likelihood-ratio detection of frequency-hopped signals

The optimum system for intercepting frequency-hopped signals uses a channelized receiver and a likelihood-ratio test (LRT). Previous results on the performance of the optimum system have been based on Gaussian assumptions, which are generally valid for transmissions having large time-bandwidth areas. Results, obtained by Monte Carlo simulation, for relatively small time-bandwidth transmissions are given here. The signal model is a simple one known as "pure frequency hopping." Comparisons with the LRT show that energy detection loss increases when the time-bandwidth product of the transmission is increased by increasing the number of frequencies, even when the number of pulses is also increased. The loss decreases when only the number of pulses is increased. Over the parameter range observed, binary detection loss tends to increase with the number of pulses and decrease with the number of frequencies. Results are included for a moving-window version of the LRT. A parameter of the LRT is the signal-to-noise ratio (SNR). The effect of using a design value not equal to the true SNR is shown.