Robust Beamforming via Semidefinite Rank Relaxation

The existing vector weighted robust beamforming is able to estimate the signal power of target only in situations of a small steering angle error. For a larger steering angle error case, although the matrix weighted beamforming can effectively estimate the signal power of the target as well, the system implementation is more complicated than above mentioned vector weighted. In order to solve these problems, this paper presents a new robust beamforming approach based on SemiDefinite rank Relaxation (SDR). Detailed description of the proposed method are given as follows: the optimal model has the same objective as that of the Capon algorithm; the optimization variable is the covariance matrix of weight vector with constraints posed on the ripple of mainlobe amplitude and sidelobe level, and the rank of covariance matrix is 1; the covariance matrix of the weight vector can be obtained by the SDR method, and each row or column of the matrix is translated into weight vector, then a weight vector is chosen which allows it become minimal one in the maximum distortions between the mainlobe of beampattern and 0 dB. The system implementation complexity of the proposed method is the same as the vector weighted methods, and the signal power estimation performance is similar to the matrix weighted method. The simulation results show that the desired beampattern shape and effective estimation of signal power can be obtained under the condition that the large steering angle error exists.