Optimization of “over-coded” radar waveforms

Abstract

Polyphase-Coded FM (PCFM) radar waveforms generated using the power and spectrally efficient continuous phase modulation (CPM) framework can be further enhanced through the use of finer time control by subdividing each phase transition into sub-transitions and by allowing a greater phase excursion per transition interval, herein referred to as overphasing. These two strategies are denoted collectively as "overcoding". It is shown that various combinations of sub-transitions and over-phasing can greatly improve waveform design capabilities by expanding the available degrees-of-freedom. It is also demonstrated that the commensurate increase in computational complexity for optimization under the overcoding paradigm can largely be offset through GPGPU processing.

Complementary frequency modulated radar waveforms and optimised receive processing

“…The most obvious of these is that here the degrees of freedom from Z different waveforms are being made use of in a collective manner, as opposed to the optimisation of a single waveform in [43, 44]. The relevant consequence of that difference is that the single‐waveform optimisation in [43, 44] subsequently requires use of “over‐coding” (see [51]), which provides an expansion of available degrees of freedom, to achieve sidelobe performance commensurate with that observed here. However, expansion of spectral content can arise as an undesired by‐product of over‐coding, thus necessitating further spectral containment measures.…”

Waveform-diverse stretch processing

“…which, by linearity can be expressed as For the range swath of interest ∆R = R far − R near with R near and R far the near and far range boundaries respectively, the necessary duration of the reference signal is 37) where ∆τ = 2∆R/c is the delay swath of interest. To capture these ranges, the reference signal…”

“…The use of nonlinear FM (NLFM) waveforms is proposed (e.g. [9,10,12,13,34,35,36,37,18]) in place of the typical LFM waveform, which, borrowing from the same idea as the aforementioned distortion compensating methods, involves a compensation to the traditional Fourier transform that is applied after sampling. Since the Fourier transform is essentially a matched filter bank for the collection of scaled sinusoids (whose delay shifts correspond to frequency shifts) produced by mixing the LFM receive waveform with the LFM reference, as is done in standard stretch processing, then it should be possible to generate similar filters matched to a different scenario of transmit waveform.…”

Physical emission of spatially‐modulated radar

“…Furthermore, as defined by the structure of the CPM implementation in (1)–(3), the maximum phase changes over the transition interval T p are ±π for the LFM waveform. These limits on the phase change were defined in [21] to aid in spectral containment but there is no physical or mathematical reason why they cannot be exceeded (see [29] for further discussion of this ‘over‐coding’ effect).…”