Real-Valued Arithmetic Linearly-Constrained Beamforming in Symmetric Adaptive Arrays

This paper presents computational procedures of two adaptive filtering algorithms for antenna arrays with odd symmetry. The algorithms are designed for the antenna arrays of radio systems, which receive information signals below the thermal noise. The linearly constrained versions of the algorithms without desired signal are often used in this scenario. The constraints are imposed onto the adaptive filtering algorithms to protect the distortion of main lobe of the antenna array radiation pattern. In the case of the antenna array with odd symmetry, it is possible to modify Toeplitz correlation matrix of the received signals to the persymmetric one and to obtain the adaptive filtering algorithms, which have the most of calculations in real-valued arithmetic. This allows to decrease the computational complexity of the algorithms and to improve the steady-state performance of the adaptive antenna array. The considered algorithms are the Linearly Constrained Recursive Least Squares and the Least Mean Square ones. The simulation example demonstrates the performance of a circular adaptive antenna array, which uses these algorithms for the weight calculation and spatial filtering of the incoming signals.