Gradient-Based Optimization of PCFM Radar Waveforms

Complementary frequency modulated radar waveforms and optimised receive processing

“…The compact, discretised representation of parameterised, continuous PCFM waveforms embodied by ( 7) and ( 8) permits the use of a variety of optimisation approaches and the consideration of many different physically realisable, waveform-diverse applications. For example, in [43] (with detailed derivation in [44]) gradient-descent optimisation was performed and subsequently demonstrated experimentally to realise waveforms that can reach a lower bound on sidelobe performance for discretised FM waveforms. This general approach was also employed to optimise coded FM waveforms based on Legendre polynomials [45] (and also account for receiver range straddling), to efficiently incorporate spectral notches into FM waveforms [46], to realise an intermodulation-based formulation for non-linear harmonic radar [47], and to design different sub-classes of random FM waveforms [36,37].…”

“…which is comprised of partial derivatives with respect to each of the N phase-change parameters. Leveraging the gradient formulation in [43] (with detailed derivation in [44]), of which ( 16) is a direct extension by virtue of the summation of Z autocorrelations, realises the gradient [27] ∇…”

“…for 0 ≤ β < 1, where we have chosen to use the heavy-ball descent method [49] and the step-size is determined via a back-tracking method [50]. Further discussion of these selections can be found in [44].…”

Designing Random FM Radar Waveforms with Compact Spectrum

“…1, the spectral efficiencies are approximately 0.23, 0.43, 0.69, and 0.80, respectively. These values are also the inverse of "oversampling" factor K when performing optimization of discretized FM waveforms [12][13][14][15][16][17].…”

“…It has recently been shown [10,11] that imposing structure to RFM can provide a Gaussian spectral density in the expectation (over the set of unique waveforms), yielding a per-waveform peak sidelobe level (PSL) of ~10 log10 (B3dBT) after expectation, for 3-dB bandwidth B3dB and pulse width T. Better sidelobe performance can be achieved by optimizing each waveform to match the desired spectrum density (e.g. [12][13][14][15][16][17]).…”