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Beam-forming of broadband QFM signals using generalized time–frequency transform

ABSTRACT Detection and localisation of contacts using sensor array play a significant role in the area of array signal processing. In this paper, a new beam-forming analysis for broad-banded quadratic frequency modulated (QFM) signals using generalised time–frequency transform (GTFT) is presented by extending the conventional fractional Fourier transform (FrFT). As FrFT is constrained to the analysis of linear chirps, detection using GTFT is found to be the appropriate selection for higher-order chirps with the suitable choice of the kernel. The parameters of the QFM signal is extracted using the polynomial chirplet transform time–frequency distribution method. Subsequently, the direction of arrival (DoA) estimation algorithms viz. conventional beam-former (CBF), minimum variance distortionless response (MVDR), multiple signal classification (MUSIC) and minimum norm (MN) are re-cast using the quadratic steering vector derived for QFM chirps and hence renamed as GTFT-CBF, GTFT-MVDR, GTFT-MUSIC and GTFT-MN, respectively. The efficacy of the algorithm is validated through various signals including practical sonar array data. It is seen from the theoretical analysis as well as simulations that GTFT-MUSIC excels other DoA (bearing) estimation techniques. The GTFT analysis on back propagated signals using sonar array aided in effective underwater channel modelling.