DESIGN OF 2-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 eigens tructure of the signal data received by a 2-D rectangular array beamfo rmer, we first show that the optimal weight matrix when using full ada ptivity can be obtained from a set of singular vectors, Then the desig n 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 dimensio n of the partially adaptive weight matrix and the set of the singular vectors, We develop the detection formulas for the information theoret ic criteria AIC and MDL to End the proper dimension. Next, an efficien t method is presented so that the optimal solution for the set of the singular vectors can be found analytically. We also investigate the re quired computational complexity. It is shown that 2-D partially adapti ve beamforming using the proposed technique requires less computationa l complexity than 2-D fully adaptive beamforming using conventional te chniques, Moreover, computer simulations demonstrate that the proposed 2-D partially adaptive technique provides satisfactory array performa nce when compared with conventional fully adaptive techniques.