Time reversal, back propagation, matched field processors, correlation receivers, and the principles of radar/sonar signal design

Abstract

Time reversal and backpropagation have been demonstrated in several experiments. Similarly, while matched field processing (MFP) differs in terms of implentation—experimental vs computed replicas—both have two common properties: (i) they are based on a single, spatially coherent signal; and (ii) the conjugate transpose of the Green’s function and replica correlation are identical for self-adjoint systems. Hence, the principles for focusing and ambiguity plane properties of these processors are virtually identical to those for correlation receivers. The principles of optimal signal design for correlation receivers were the subject of much research for radar/sonar systems four decades ago and many of them seem to have been neglected in the analysis of time reversal, back propagation, and matched field processors. For example, time reversal from a point, a line array, or a random array of scatterers are duals of an impulse, a frequency modulated, and a pseudo-random noise signal, respectively. The equivalence and consequences of the time-bandwidth products for signals and array length wave number spread are demonstrated. The impact of sidelobes and multipath spread can be predicted. The generalizations of the important radar/sonar uncertainty principle, however, have yet been not demonstrated. This presentation reviews these optimal signal design principles and applies them to time reversal and MFP.