A constrained reference signal based beamformer based on symmetrically distributed antenna arrays

A class of reference signal based (RSB) beamforming algorithms is proposed based on a symmetrically distributed array (SDA) by constraining its weight vector to a specific conjugate symmetric form, which is derived from the beamformer with a minimum mean square error (MSE). The effect of the additional constraint is equivalent to adding a second step in the derived adaptive algorithms. Moreover, since no direction of arrival (DOA) information of the desired signal is available, it leads to a two-stage structure for incorporating the imposed constraint. Compared to the traditional algorithms, the proposed ones, including an LMS (least mean square) based algorithm and an RLS (recursive least square) based algorithm, can achieve a faster convergence speed and a lower steady state mean square error (MSE), given the same stepsize.