Unimodular multiple‐input‐multiple‐output radar wave‐form design with desired correlation properties

Abstract

Unimodular waveforms with good correlation properties are desired for multiple-inputmultiple-output radar to achieve an increased transmitting/receiving virtual aperture. In this study, a new optimisation framework is introduced to design waveforms with good correlations. It is shown that many existing waveform design problems can be incorporated into this framework. Since the considered problem is in general highly non-linear and non-convex, an iterative optimisation method based on majorisation-minimisation is developed. By carefully devising the surrogate function, the only requirement is to deal with a series of simple problems, which have closed-form solutions. The proposed algorithm can be implemented via fast Fourier transform and hence is computationally efficient. In addition, the proposed algorithm is extended to deal with spectral constraints. Numerical results demonstrate the efficiency of the proposed algorithm compared with the state-of-the-art techniques.

The fast continuous wavelet transformation (fCWT) for real-time, high-quality, noise-resistant time–frequency analysis

“…Figure 3 shows fCWT's capability of analyzing signals up to 200 kHz in real time, whereas the fastest implementation of CWT fails at f s = 30 kHz. Consequently, fCWT enables real-time analysis of high-frequency signal dynamics, as exist in audio (for example, loudspeaker characterization 22 , full band speech coding 23 and paralinguistic analysis 24 ), biosignals (for example, brain-computer interfaces 12 and peripheral signals such as ECG, electromyography, electrodermal activity and respiration 11,13 ), image and video (for example, distance transforms 25,26 ), sonar and radar 27,28 , network analysis (for example, renewable Fig. 3 | Benchmarking with fCWT and six state-of-the-art time-frequency methods.…”

“…With custom wavelets, fCWT performance can be improved even further 51 . As such, fCWT enables the real-time analysis of high-frequency nonstationary signals, such as in audio [22][23][24]52 , biosignals (for example, brain-computer interfaces 12 and ECG 11,13 ), image and video 25,26 , sonar and radar 27,28 , renewable energy management 16,17 , cybersecurity 14,15 and machine fault diagnosis 29,30,53 (Fig. 1).…”