Signal excess in K-distributed reverberation

Active sonar systems have recently been developed using larger arrays and broad-band sources to counter the detrimental effects of reverberation in shallow-water operational areas. Increasing array size and transmit waveform bandwidth improve the signal-to-noise ratio-and-reverberation power ratio (SNR) after matched filtering and beamforming by reducing the size of the range-bearing resolution cell and, thus, decreasing reverberation power levels. This can also have the adverse effect of increasing the tails of the probability density function (pdf) of the reverberation envelope, resulting in an increase in the probability of a false alarm. Using a recently developed model relating the number of scatterers in a resolution cell to a K-distributed reverberation envelope, the effect of increasing bandwidth (i.e., reducing the resolution cell size) on detection performance is examined for additive nonfluctuating and fluctuating target models. The probability of detection for the two target models is seen to be well approximated by that for a shifted gamma variate with matching moments. The approximations are then used to obtain the SNR required to meet a probability of detection and false-alarm performance specification (i.e., the detection threshold). The required SNR is then used to determine that, as long as the target and scatterers are not over-resolved, decreasing the size of the resolution cell always results in an improvement in performance. Thus, the increase in SNR obtained by increasing bandwidth outweighs the accompanying increase in false alarms resulting from heavier reverberation distribution tails for K-distributed reverberation. The amount of improvement is then quantified by the signal excess, which is seen to be as low as one decibel per doubling of bandwidth when the reverberation is severely non-Rayleigh, as opposed to the expected 3-dB gain when the reverberation is Rayleigh distributed.