On the design of linear sparse arrays with beampattern shift invariant properties

Abstract

We investigate the design of linear sparse arrays and multiple-input multiple-output (MIMO) linear sparse arrays with beampattern shift invariant property (BSIP) and determine the necessary and sufficient conditions needed to achieve BSIP. Moreover, we show how to theoretically calculate the precise peak sidelobe level (PSL) values of their array beampatterns. We also establish the relationship between the number of antennas and the beampattern of a linear sparse array with BSIP. Furthermore, built on our theoretical analysis, we devise computationally efficient cyclic algorithms to design linear sparse arrays with BSIP and their MIMO counterparts by minimizing the PSL values of their beampatterns. In addition, we introduce a design method to avoid angle ambiguities even when the pointing direction of the linear array beampattern is the extreme case of 90∘ or -90∘. Numerical examples are provided to support our theoretical analysis and demonstrate that our proposed algorithms can be used to obtain linear sparse arrays with 3-dB main beam widths narrower while simultaneously PSL values lower than those of the existing arrays.