Broadband detection in K-distributed reverberation

In active sonar, broadband waveforms can improve the signal-to-reverberation power ratio (SRR) by decreasing the size of the resolution cell. Unfortunately, this can adversely affect detection performance by spreading the target across several cells and adversely affect false alarm performance by making the reverberation more severely non-Rayleigh. The performance of a detector that integrates the matched filter intensity is examined as a function of bandwidth. It is observed that performance depends only on the total target energy (E_t), not how it is distributed throughout the processing window. Thus, for this detector, the shape of the target echo is less important than E_t. Given a constant E_t, it was observed that the probability of detection (P_d) increased with bandwidth, but was bounded above by a number less than one. The performance is coarsely quantified by the deflection, which was seen to increase with either bandwidth or E_t and decrease with the size of the target, the density of reverberation scatterers (e.g., number per meter down-range) and their average power. The deflection is most sensitive to bandwidth when the density of scatterers is high (i.e., the reverberation is nearly Rayleigh). Thus, increasing bandwidth provides the most added value when the reverberation is nearly Rayleigh distributed. As an example, P_d for a fixed probability of false alarm (P_fa) is examined for a cylindrical target shape and compared to that of a detector that takes the maximum value over the processing window. The detection performance comparison showed that the maximum value detector outperforms the summation detector when the target echo is essentially a single highlight, but can perform significantly worse when the target echo energy is spread.