Optimal polarised pattern synthesis of wideband arrays via convex optimisation

The digital wideband arrays with data converters and digital signal processing capability permit greater flexibility in the pattern synthesis than conventional time-delay steered wideband arrays, which provides an opportunity to solve the polarised pattern synthesis of wideband arrays by using numerical optimisation algorithms. A finite-impulse response (FIR) filter is placed at each element to directly optimise the synthesised polarisation and wideband power patterns. Both the optimisations of the sum and difference patterns are formulated as convex programming problems to obtain efficient solutions. The proposed synthesis method, which has no special requirement on the array geometry and element pattern, is flexible and applicable to arbitrary arrays. By optimising the complex coefficients of FIR filters, any state of polarisation can be synthesised in a given angle-frequency space with frequency-invariant main beams and arbitrary sidelobe upper bounds. Various design examples are presented to testify the potentiality of the proposed method.