Pattern synthesis method for arbitrary arrays based on LCMV criterion
Recently, pattern synthesis for arbitrary arrays has been a focus of research and many approaches have been proposed. One method [1, 2] is to apply adaptive array theory. Iteration coefficients are important, which determine stability and convergence speed, but the iteration coefficients cannot be chosen easily. Especially in , the proper value of the coefficient is dependent on the synthesis conditions, and needs modifying by an iteration process. The value is obtained by trial and error. Although the method in  is for a mainlobe control mechanism, the appropriate reference pattern Pr(y) (y is angle of arrival) in  cannot be chosen easily because it is complex-valued. Its magnitude can be easily determined according to the mainlobe shape, but its appropriate phase cannot be chosen easily. For example, we should not make Pr(y) (y in mainlobe region) equal to a real constant in order to obtain a pattern with a flat top mainlobe. Its phase is constrained to zero in all the mainlobe region if we do so, which is unnecessary because we do not mind its phase in the problem of pattern synthesis. This may cause undesirably high sidelobes and the requirement of more array elements to meet the same synthesis specifications. In this Letter, a new algorithm is presented. Its coefficient is robust to synthesis conditions and flat mainlobe patterns can be obtained easily using derivative constraints. Given mainlobe regions and sidelobe envelopes, the algorithm searches the pattern with the lowest sidelobe levels, which is different from the algorithms in  and . These fix the difference of the sidelobe level and mainlobe peak beforehand without regard to whether it can be achieved for the given array.
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