Scalable Alternating Projection and Proximal Splitting for Array Pattern Synthesis

Abstract

Array synthesis with embedded element patterns is a problem of great practical importance. In this paper, an array pattern synthesis method using scalable alternating projection and proximal splitting is proposed which considers the scaling invariance property of design specifications and constraints for the amplitudes of pattern and excitation. Under the framework of alternating projection, the scalable pattern and excitation constraint sets are first defined. Then the scalable pattern projection and iterative procedure for optimum pattern scaling factor are studied in detail. For the scalable excitation projection, it is designed as the solution to a constrained weighted least mean squares optimization, which can be solved by an effective forward-backward splitting iterative process. Finally, the selection of the weighted matrix and computational complexity are discussed briefly. Several typical linear and planar synthesis examples with or without the embedded element patterns are provided to demonstrate the effectiveness and power of the proposed method.

Synthesis of linear and planar arrays with sidelobes of individually arbitrary levels

“…Transformation Equation (14), gives us a planar sum pattern from a linear sum pattern. Also, transformations Equations (15) and (16) are applied to a linear difference pattern so as give us two types of difference planar patterns in ψ x and ψ y directions, respectively. Figures 18-20, illustrate these three transformations, in which the ring contours are obvious.…”

“…8 In another procedure, sidelobe levels are controlled by iterative adjustment of virtual interference on the basis of adaptive array theory. [9][10][11] Also, many kinds of optimization methods such as genetic algorithm, 12,13 convex algorithms, 14 alternating projection, 15 and numerical pattern synthesis, 16 have been presented to control sidelobe levels.…”

Phase-Only Antenna Array Reconfigurability with Gaussian-Shaped Nulls for 5G Applications

“…Many phase-only null synthesis techniques for antenna arrays proposed in the recent years [6][7][8][9][10][11][12][13][14][15][16][17][18] may be nowadays reconsidered for addressing the expected 5G requirements. In particular, a deterministic method for linear arrays is presented in [6], where the phase-only approach and the possibility to generate multiple close nulls are outlined.…”

“…The same options are enabled in [14], which alternatively applies a metaheuristic backtracking search optimization approach based on an iterative process controlled by a single parameter. The method of alternate projections is adopted in [15], to develop an iterative algorithm for null synthesis problems in arrays of arbitrary geometry, which includes the possibility of imposing the phase-only constraint. In [16], a phase-only beamformer based on the adaptive bat algorithm is designed to impose nulls in a certain number of undesired directions when a uniformly spaced linear array of half-wave dipoles is employed.…”

3D Multi-Beam and Null Synthesis by Phase-Only Control for 5G Antenna Arrays

“…This requirement derives from the dimension of the 5G cells, whose radii are expected to be not larger than a few hundred meters [16], which makes situations where a source and a destination lie overground or underground relative to one another likely. Interesting solutions addressing this aspect have been developed by considering the synthesis of both the amplitudes and the phases of the array excitations [17][18][19]. Unfortunately, this choice does not match a second relevant constraint that characterizes the beamforming network of a 5G device: its simplicity.…”