Propagation of false alarms through a binary integrator with range walk

This paper presents formulae for calculating the way in which false alarm rates propagate through binary scan to scan integrators in a radar processor. It considers the non-trivial case where a genuine target can ‘walk’ through a number of cells during the integration time. This ‘walk’ is usually much more significant in range than in bearing, so only the one-dimensional case need be considered. Even when such ‘walk’ is considered, an integrator requiring detections in M scans has the power to reduce the false alarm rate to a rate proportional to the Mth power of the input false alarm rate. An expression is also derived for the average life time of a false alarm. As well as the case of the scan to scan integrators which is analysed here, the underlying mathematics are also applicable to the burst-to-burst correlators used in pulse-Doppler radars..