Convex Optimization-Based Design of Sparse Arrays for 3-D Near-Field Imaging

A convex optimization-based method of sparse array synthesis (SAS) for wideband near-field millimeter-wave (MMW) imaging is proposed by extending our previous work. We construct a monostatic SAS optimization model from the electromagnetic propagation formula. The reweighted
${l}_{{1}}$
-norm decoding algorithm is utilized to enhance the sparsity. A modified iterative element weighting merging method is also proposed to put constraints on the minimum element spacing to synthesize a practicable sparse layout. Through the proposed SAS method, the customized sparse monostatic array for near-field imaging can be generated with different schemes, such as 1-D linear arrays, 2-D planar arrays, and so on. The imaging performance of the synthesized planar sparse array is studied by examining the properties of focusing, sidelobe suppression, and grating lobe suppression both theoretically and by simulation. It is shown that the optimized array is superior to the arrays with equally spaced antennas or randomly spaced antennas, using approximately the same number of antenna elements. Experimental results further indicate the advantages of the optimized wideband sparse array through the 3-D imaging reconstruction.