Direct Adaption Methods for Linear and Circular Antenna Arrays

Introduction. The mitigation of interferences that degrade the performance of navigation systems constitutes one of the most significant problems of contemporary satellite navigation. This problem is conventionally solved using digital adaptive space filters. Depending on a particular radio technical system, the mathematical description of digital signal processing methods may involve specific calculation structures implemented using specific calculation algorithms. For example, the use of centrosymmetric linear and circular antenna arrays in a radio navigation system allows the description of such systems in terms of Toeplitz and circulant sample covariance matrices, respectively, and the inversion of such matrices by means of special numerical methods in order to design a digital filter.

Aim. A comparative analysis of the performance of space signal processing algorithms is carried out along with an estimation of Toeplitz and circulant sample covariance matrices and numerical methods of their inversion. The previously obtained results in this field are clarified.

Materials and methods. An analysis of algorithm performance was carried out in the MATLAB environment using experimental recordings of satellite navigation signals and jammers obtained by an actual radio technical system.

Results. A new expression was derived for estimating circulant sample covariance matrices. Formulae that describe a modification of the Bareiss numerical Toeplitz matrix inversion algorithm for the case of complex Hermitian matrix were introduced. An analysis of the results of computer simulation allowed the algorithms with the highest performance to be indicated. The amount of time taken by the algorithms based on Toeplitz and circulant matrices did not exceed 2.5 10⋅ ⁻³ s and 0.04 s, respectively. The carrier-to-noise ratio in the processed signal was at least 46 dB. 

Conclusion. The formulae obtained and the algorithms analyzed can be used when implementing adaptive digital filtering of satellite navigation signals.

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