Detection of a distributed target

The influence of increasing range resolution on the detectability of targets with dimensions greater than the resolution cell is studied. An N-cell target model is assumed, which contains k reflecting cells, each reflecting independently according to the same Rayleigh amplitude distribution. It will be referred to as the (N,k) target. Detection based on one transmitted pulse is performed against a background of white normal noise. Detection in stationary clutter is also considered. The optimum detector is obtained but, in view of its complexity, the performance of a simpler detector, the square-law envelope detector with linear integrator (SLEDLI), is analyzed, and a formula for the probability of detection is obtained. Graphs are presented which show the probability of detection as a function of signal-to-noise ratio (SNR) for various values of N k, and false alarm probability. For N/k not too large it is shown that the SLEDLI is near optimum