Beampattern Synthesis for Linear and Planar Arrays With Antenna Selection by Convex Optimization

Synthesis of Sparse or Thinned Linear and Planar Arrays Generating Reconfigurable Multiple Real Patterns by Iterative Linear Programming

“…Note that the above array model can be considered as a more general version of the formulation in [31] which is derived for the case of rectangular-grid arrays.…”

“…The iterative reweighted 1 optimization was presented in [30], and recently this idea was used to reduce the number of elements for a single focused beam or shaped pattern, by developing the iterative second-order cone programming (SOCP) in [31][32][33] or sequential compressive sensing (CS) approach in [34]. We now apply this idea to reduce the number of elements for multiple-pattern arrays by selecting the best common elements, each with multiple optimized excitations, under multiple power pattern requirements that are all given by upper and lower bounds.…”

“…We now apply this idea to reduce the number of elements for multiple-pattern arrays by selecting the best common elements, each with multiple optimized excitations, under multiple power pattern requirements that are all given by upper and lower bounds. However, the lower bound used for a shaped power pattern is in general non-convex [31]. To overcome this problem, the excitation distribution is assumed to be conjugatesymmetrical for each pattern.…”

“…In addition, the choice of a symmetrical layout and symmetrical amplitudes can greatly simplify the beamforming network. Hence, this choice has been widely adopted by many single-pattern synthesis methods, for example, in [23] and [31]. To cast the problem of finding the common element positions for multiple patterns into the form of linear programming, we introduce an auxiliary variable to define the common upper bound of the real and imaginary parts of multiple excitations for each element.…”

“…Hence, the proposed method can be very efficiently implemented by iteratively performing the linear programming (LP) that is more computationally efficient than the iterative SOCP. This method can be applicable to the synthesis of an arbitrary array geometry with multiple pattern requirements (with the only limitation of conjugate-symmetrical excitations), and can be considered as a significant extension of the method presented in [31] where the problem of synthesizing the rectangular-grid array with a single shaped pattern has been successfully dealt.…”