Design of two-dimensional rectangular array beamformers with partial adaptivity

This paper considers the problem of designing a two-dimensional (2-D) rectangular array beamformer with partial adaptivity. Using the eigenstructure of the signal data received by a 2-D rectangular array beamformer, we first show that the optimal weight matrix when using full adaptivity can be obtained from a set of singular vectors. Then the design problem of using partial adaptivity is formulated. As a result, the optimal solution for the partially adaptive weight matrix can be found by solving two basic problems, namely determining the proper dimension of the partially adaptive weight matrix and the set of the singular vectors. We develop the detection formulas for the information theoretic criteria AIC and MDL to find the proper dimension. Next, an efficient method is presented so that the optimal solution for the set of the singular vectors can be found analytically. We also investigate the required computational complexity. It is shown that 2-D partially adaptive beamforming using the proposed technique requires less computational complexity than 2-D fully adaptive beamforming using conventional techniques. Moreover, computer simulations demonstrate that the proposed 2-D partially adaptive technique provides satisfactory array performance when compared with conventional fully adaptive techniques.