Hybrid PSO – CP technique for the synthesis of non-uniform linear arrays with maximum directivity

Abstract

A technique to synthesize maximum directivity non-uniform linear layouts subjected to upper bounds on the power pattern is presented. The approach is based on a nested strategy combining an outer particle swarm-based optimization and an inner convex programming solver by taking advantage of the convexity of the synthesis with respect to the excitation coefficients when fixing the array layout. Selected numerical results are discussed to assess the effectiveness, the flexibility, and the limitations of the proposed technique.

Keywords:

• array synthesis
• non-uniform arrays
• linear arrays
• evolutionary algorithms
• convex programming
• maximum directivity

Acknowledgements

The author wishes to thank the colleagues at the ELEDIA Research Center and Prof T. Isernia for fruitful discussions on the subject.

Notes

1 The directivity maximization problem and the pattern shape control problem do not have the same solutions in general (i.e. maximizing the directivity does not automatically guarantee to achieve a desired sidelobe level (SLL)). However, for pencil-beam arrays, the two problems are almost the same because the directivity depends essentially on the pattern beamwidth.

2 Both explicit (i.e. as discussed in [22]) or implicit constraints (i.e. on the minimum spacing between the elements, as done in this work) can be used to prevent the method from reaching superdirective solutions, which otherwise could arise in synthesis processes based only on the visible range.[22]

3 Although the computation is a convex problem, the solution may not exist (e.g. if cannot be fulfilled with the user-defined ). In such a case, the procedure discards the obtained solution and exits.

4 In general and can be independently defined by the user.

5 A minimum value of has been chosen to guarantee that a sufficient number of particles are employed also when dealing with low-dimension problems.

6 Such comparisons cannot be considered as a validation against state-of-the-art approaches, but rather as an assessment of a sub-part of the overall technique.