Radar Waveform Synthesis by Mean Square Optimization Techniques

The synthesis of the phase-modulated waveform whose ambiguity function is the optimum estimate of some desired ambiguity function is accomplished by expanding the phase modulation in an orthogonal series. The ambiguity function x (?, ?d)|2 and the value of an arbitrary cost function defined on the (?, ?d) plane are then expressed in terms of the coefficients of the orthogonal series. The optimum waveform can then be determined by solving the variational equations for the coefficients. Numerical examples are presented for the case where it is desired to synthesize a desired ambiguity function x(?, ?d) for some rectangular region of the (?, ?d) plane.