Comparative Analysis of Spatial Spectral Estimation Algorithms: Advantages of the Maximum Entropy Method in Radio Direction Finding

Abstract

In modern radio monitoring systems, a conflict arises between the high mathematical complexity of super-resolution algorithms and the limited resources of SDR (Software Defined Radio) computational platforms. Traditional software implementations based on iterative loops result in excessive computational latency, hindering real-time performance. The issue is exacerbated during direction finding (DF) in dense urban environments, where limited antenna array aperture and highly correlated signals lead to the singularity of covariance matrices and the blurring of spatial peaks. The object of this study is the process of forming spatial power spectral estimations for wideband signals. The methodology is based on a comparative analysis of the Bartlett, Capon, and MUSIC algorithms, alongside the Maximum Entropy Method (MEM). The authors propose a shift in the computational approach: transitioning from scalar processing of individual matrix elements to a vectorized tensor kernel based on Einstein summation notation. To ensure the stability of solutions, the Tikhonov-Phillips regularization method is applied. The scientific novelty lies in the development and implementation of a tensor computing architecture for the MEM method, which achieves a ten-fold acceleration of mathematical operations and significantly reduces CPU overhead. Experimental results confirm the superiority of the MEM approach: when utilized with small-element arrays, it provides 15–20% higher angular selectivity compared to the MUSIC algorithm at noise floor levels of -20 to -40 dB. Integrating Tikhonov regularization directly into the tensor kernel mitigates the impact of matrix singularity, achieving a Mean Squared Error of 1,13⋅10⁻⁵, which ensures bearing stability even with ultra-short data snapshots. It is demonstrated that optimizing the computational algorithm through tensor utilization enables the implementation of super-resolution methods in "hard real-time" on low-cost hardware. The findings facilitate the use of mobile SDR platforms for precision radio direction finding in complex interference environments without the need for dedicated hardware accelerators.