Phased Array Diagram Matching

Introduction

A common problem in phased array beamforming applications is setting the weights (magnitude and phase) of each antenna to produce the desired diagram, radiation pattern of the array. If we make some simplifying assumptions, i.e. a planar antenna array, finding the weights can be expressed as a Conic LP problem, cf. Ben-Tal, Nemirovski, 2001, Lectures on Modern Convex Optimization Consider the optimization problem below, in this case we'll assume a given direction δ.

\[\begin{aligned} \underset{z_1,...,z_N \in \mathbb{C}}{minimize}\qquad & |Z_*(\delta) - \sum_{j=1}^Nz_jZ_j(\delta)| \end{aligned}\]

How to run the example

1. Ensure that you have ConicSolve installed. This can be installed as follows:

julia> ]
pkg> activate .
pkg> add ConicSolve
julia> exit()

1. Run the example from the command line

julia example.jl

Explanation

Data Acquisition

This is a simple toy problem setup. No data has been imported in this example.

Solve the problem

(i) We create a ConeQP object that represents the LP problem to solve cone_qp = get_qp(diagrams, target).

(ii) We pass the ConeQP object to the solver solver = Solver(cone_qp).

(iii) Then when we're ready we call run_solver passing the solver object run_solver(solver)`.

(iv) We can access the solution by accessing the primal solution from the solver x = get_solution(solver).

Get the solution

Further Comments