Pattern synthesis with constrained excitations for transceiving arrays

A new synthesis algorithm for arbitrarily shaped patterns generated by transmitting and receiving arrays is proposed in this study. First, according to the radar range equation, the authors vividly present the definition of the joint pattern of the transceiving array. To solve the joint optimisation problem, the projectors over pattern and excitation constraints are provided based on alternating projection method. In many traditional methods, the excitations are obtained by solving the (weighted) least mean squares (WLMS) problem. Nevertheless, in this study, WLMS problem is rewritten as a constrained WLMS problem, which introduces an effective proximal splitting method to improve the convergence and stability. Besides, to make full use of transmitting module, the excitation dynamics of transmitting array is enforced to be 0 dB. To validate the good applicability of the proposed method, two arrays in different shapes are applied. Five examples with embedded patterns including phase-only synthesis, pattern with unbalanced sidelobe levels etc., are presented to highlight the various aspects of the method. In general, the new method not only can restrict the pattern shape, also can constrain the excitations of transmitting and receiving arrays, respectively.