| Waveform design that allows for a wide variety of frequency-modulation (FM) has proven benefits. However, dictionary based optimization is limited and gradient search methods are often intractable. A new method is proposed using differential evolution to design waveforms with instantaneous frequencies (IFs) with cubic FM functions whose coefficients are constrained to the surface of the three dimensional unit sphere. Cubic IF functions subsume well-known IF functions such as linear, quadratic monomial, and cubic monomial IF functions. In addition, all nonlinear IF functions sufficiently approximated by a third order Taylor series over the unit time sequence can be represented in this space. Analog methods for generating polynomial IF waveforms are well established allowing for practical implementation in real world systems. By sufficiently constraining the search space to these waveforms of interest, alternative optimization methods such as differential evolution can be used to optimize tracking performance in a variety of radar environments. While simplified tracking models and finite waveform dictionaries have information theoretic results, continuous waveform design in high SNR, narrowband, cluttered environments is explored. |
