Angle Estimation via WFRFT Spatial-Domain Basis Decomposition: Breaking the Rayleigh Resolution Limit with Structured Waveform Diversity

Abstract

We propose a MIMO radar angle estimation framework that uses the four-component weighted-type fractional Fourier transform (4-WFRFT) as a spatial-domain waveform diversity mechanism. Unlike conventional fractional Fourier (FrFT) MIMO radar where FrFT serves as a receiver-side time-frequency processing tool, our approach decomposes a data sequence into four WFRFT basis functions,original signal, its Fourier transform, time-reversal, and inverse Fourier transform, and transmits them simultaneously from a four-element uniform linear array. The spatial superposition of these basis functions at each far-field angle creates a unique angle-dependent waveform structure, enabling angle estimation through time-domain matched filtering with known waveforms. We demonstrate that this spatial-domain mixing achieves angular resolution surpassing the Rayleigh diffraction limit by a factor of 1.4$\times$ to 12.8$\times$, with the advantage most pronounced at low SNR where conventional beamforming fails completely. The Cramér-Rao bound is derived with a full 3-parameter Fisher information matrix, and the Fisher information is decomposed into geometry and waveform contributions, revealing that the WFRFT waveform structure contributes approximately 3$\times$ more information than array geometry alone. Extension to $M$-element arrays with $M$-component WFRFT demonstrates resolution gain scaling with array size. Simulations with linear chirp base sequences achieve 0\,dB PAPR and validate sub-Rayleigh resolution with a four-element array.