Transmit waveform design using Multi-Tone Sinusoidal Frequency Modulation

Abstract

This paper presents a method for generating a family of waveforms with low in-band Auto/Cross-Correlation Function (ACF/CCF) properties using the Multi-Tone Sinusoidal Frequency Modulated (MTSFM) waveform model. The MTSFM waveform's modulation function is represented using a Fourier series expansion. The Fourier coefficients are utilized as a set of discrete parameters that can be modified to optimize the waveform family's properties. The waveforms' ACF/CCF properties are optimized utilizing a multi-objective optimization problem. Each objective function is weighted to place emphasis on either low ACF or CCF sidelobes. The resulting optimized MTSFM waveforms each possess a thumbtack-like Ambiguity Function in addition to the specifically designed ACF/CCF properties. Most importantly, the resulting MTSFM waveform families possess both ideally low Peak-to-Average Power Ratios (PAPR) and high Spectral Efficiency (SE) making them well suited for transmission on practical radar transmitters.

Optimal Waveform Design Using Frequency-Modulated Pulse Trains for Active Sonar

“…All GSFM sub-pulses are the even symmetric style. The initial settings shown in Figure 2 are totally the same with those in [9,13,20]. The optimized AF shape of the GSFM pulse and the corresponding pulse train are shown in Figure 5.…”

“…To some extent, it reflects the correlations between the replicas and echoes. Moreover, as Hague suggested in [13], the ACF is of great significance to the evaluation of the range resolution. Specifically, the ACF expression can be derived if we substitute the Doppler shift φ=0 into the AF quantitative expression.…”

“…The higher sidelobe levels imply that the target detection is interfered by the reverberation more seriously. In particular, some active sonar waveforms show the AF shape that features a distinct mainlobe at the origin of the time delay–velocity pedestal and sidelobes at the rest of the pedestal evenly, which is known as the ‘thumbtack’ AF shape [13]. Furthermore, this ideal ‘thumbtack’ AF shape might be reached by optimizing specific parameters in the AF expression.…”

Waveform Design using Multi-Tone Feedback Frequency Modulation

“…The design coefficients are initialized using i.i.d Gaussian random variables scaled in magnitude to ensure that k k|z k | ≤ 1.0. Utilizing coefficients of this type produce a waveform with a thumbtack-like AF [7]. The goal of this design example is to further refine the waveform to possess reduced ACF sidelobes compared to that of the traditional thumbtack-like waveform.…”

“…Recently, the authors have proposed using Multi-Tone Sinusoidal Frequency Modulated (MTSFM) waveforms as a spectrally efficient adaptive waveform design method [7], [8]. The MTSFM's modulation function is represented as a finite Fourier series where the Fourier coefficients are utilized as a discrete set of parameters that may be adjusted to synthesize waveforms with specific user defined properties.…”