Analytical Spectrum Representation for Physical Waveform Optimization Requiring Extreme Fidelity

Optimization of physically realizable radar waveforms necessitates operating on a discretized representation that possesses sufficient fidelity, which can usually be achieved via adequate oversampling with respect to 3-dB bandwidth. However, it has been experimentally observed that the design of practical waveforms containing spectral notches requires an even higher degree of fidelity to achieve the low notch depths that may be needed for useful interference avoidance. Because such extreme fidelity translates into very high dimensionality, here an alternative approach is explored that involves the analytical Fourier transform of polyphase-coded FM (PCFM) waveforms, the continuous-time model for which is readily amenable to optimization and physical emission by real radar systems. The cost function and iterative solution that arises from this formulation, which is denoted as Analytical Spectrum Notching (ASpeN), facilitates the design of waveforms that are implementable in arbitrary waveform generation (AWG) hardware without the need for further “notch depth compensation” after up-sampling. This property is confirmed through experimental evaluation using RF test equipment in a loopback configuration.