Optimum Signals for Radar

The research reported herein deals with the general problem of the selection of radar waveforms. The investigation is specifically concerned with the synthesis of radar signals which are optimum in the sense that they are characterized by ambiguity surfaces minimized over certain predetermined regions of the ambiguity plane. The weighted ambiguity surface is utilized as the weighted error criterion. This error criterion is mathematically tractable and pertinent to radar system performance but is not unduly restrictive as some orientation parameters are left unspecified for subsequent cost or penalty function analysis. The signal optimization is approached by variational techniques augmented by equality and inequality constraints, for example, limiting the amount of bandwidth or frequency modulation to be less than some system requirement. Several examples are presented demonstrating the optimization techniques and providing a minimum error for the stated problem. It is shown that for any given type of amplitude modulation of the radar signal, the variance or dispersion of the ambiguity surface is not decreased for any type of phase modulation added. The optimum signal for an elliptical weighting function is derived for several cases. The minimum error is shown to depend upon the constraints and the unspecified orientation parameters and, for one case, on the second moment of the signal.