Inclusion of signal and noise coupling in sparse wideband array synthesis

It is well known that non-regular sparse arrays can strongly reduce the number of active channels while avoiding the appearance of grating lobes [1]. Such configurations avoid “intersecting” effective areas and space tapering can to a certain extent, replace amplitude tapering, with a positive impact on sensitivity. The combination of space tapering and amplitude tapering has been analysed in [2], where the amplitudes compensate for the local variation of the array density. In [3], this has been extended by describing the space tapering through a change of coordinates. In this case, the amplitude tapering is applied before space tapering, i.e., on the initial array, which has a constant average density. This allows one to limit the amplitude variations imposed on the elements, which is favourable in terms of signal-to-noise ratio, while the main lobes and first few sidelobes have a very smooth behaviour. In the present paper, this work is extended to include mutual coupling between the elements. The work relies on a fast in-house solver, making use of Macro Basis Functions (MBFs) and on a modelbased technique for computing the interactions between MBFs without computing the method-of-moments impedance matrix. Regarding the signal analysis, the amplitudes are modulated by the product between the local area allotted to the element, multiplied by the embedded element pattern. In this work, noise-coupling is also accounted for. Numerical examples will be shown for arrays made of log-periodic antennas, foreseen for the Square Kilometre Array (SKA) telescope. The impact of the proposed combination of amplitude and space tapering on the array sensitivity will be illustrated.