Range Resolution Control and Fractional Fourier Domain Target Localization With Nonlinear Time-Variant Phase Diverse FDA

In addressing the degradation of range resolution and the coupling of target range and angle in the coherent frequency diverse array (FDA), which impedes the full utilization of the two-dimensional degrees of freedom for target indication, this paper proposes an array transmission mode called nonlinear time-variant phase diverse FDA (NTPD-FDA). This mode aims to controllably enhance range resolution and indicate target position without coupling and ambiguity, all without increasing system complexity. NTPD-FDA incorporates a nonlinear time-variant phase, comprising chirp diverse and constant phase diverse, into the transmitted signals of each element in coherent FDA. This technique adjusts the power spectrum of the aggregated transmitted signal to match a bandwidth-adjustable Gaussian function, achieving enhanced controllable range resolution while avoiding signal-to-noise ratio (SNR) loss and maintaining a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$-$</tex-math></inline-formula> 25dB range sidelobe level (RSL). Based on the varying chirp rates of transmitted signals in NTPD-FDA and the optimal energy concentration characteristics of the fractional Fourier transform (FRFT) for chirp signals, this paper proposes a signal processing method. This method involves extracting time-frequency points related to the target signals in the fractional Fourier domain (FRFD) and constructing steering vectors that includes range and angle, thus enabling joint estimation of target range and angle. The Cramér-Rao lower bounds (CRB) for range and angle estimation errors were derived as a performance guarantee for this signal processing method. Theoretical analysis demonstrates that NTPD-FDA is more favorable for achieving unambiguous range estimation and offers higher accuracy in range and angle estimation compared to FDA-MIMO. Numerical results validate the promised advantages of NTPD-FDA.