A modified direct data domain approach using Centro-Hermitian matrices for beamforming.

Adaptive beam forming concept has been around for a long time and has been implemented successfully. Earlier techniques utilized complex weights which added computational complexity to the system. The techniques are mainly classified as statistical and deterministic methods. The statistical methods are computationally more complex as compared to the latter. Adaptive beamforming techniques like the direct data domain least squares (D3LS) approach has matrix inversion issues because the matrix formed during the process of calculating the weights is ill-conditioned. The D3LS approach uses the conjugate gradient method to calculate the matrix inverse which again adds to the computational complexity. Methods have been developed that utilize real weights for adaptive beam forming. But, again the problem of matrix inversion persists as the matrix formed in these cases is ill-conditioned. It has also been observed that by using real weights the beam pattern obtained exhibits a symmetric property that requires the use of a transformation matrix resulting in increased system complexity. The proposed technique in this study uses Centro-Hermitian matrix properties to convert complex matrices to real matrices by using Linear Matrix Inequalities (LMI) to eliminate the matrix inversion issues. Also, the proposed method eliminates the problem of symmetric beampattern that is common for conventional approaches.

Multiple beam forming techniques have also been investigated wherein there are multiple signals of interest and jammers. The proposed technique in this study considers three signals of interest and multiple jammers. This technique provides maximum directivity in the direction of the signal while successfully nulling jammer signals.