Spectrally compact SFSK radar waveforms

Abstract

Phase coded waveforms offer great variability in radar signal design. Unfortunately, rectangular subpulses (required to keep the signal envelope constant and thus friendly to amplify) lead to discontinuous phase changes. This implies rather slow spectral decay −6 dB/octave potentially not attractive in future applications. Familiar biphase-to-quadriphase transform modifies a biphase code into a quadriphase code which (when modulated by half-cycle sine subpulse) yields constant envelope waveform (similar to Minimum Shift Keying (MSK) modulation) with spectral decay −12 dB/octave and Peak Sidelobe Level (PSL) of Auto Correlation Function (ACF) equal to the original code. In this paper, we show that the quadriphase coded waveform is equivalent to the known Laurent Decomposition (LD) of MSK with differentially encoded code symbols. This relation can be extended to any binary minimum-shift full-response continuous phase modulation such as Sinusoidal Frequency Shift Keying (SFSK) with 1RC (Raised-Cosine) subpulse. Proposed differential LD-SFSK scheme offers attractive −24 dB/octave spectrum roll-off keeping the same PSL of ACF as the original biphase code.