Digital Beamforming of Subarrays of Unequal Size

Hybrid beamforming involves digital beamforming of the data streams from digital receivers attached to analog subarrays. This paper examines the special signal weighting required to perform hybrid beamforming when the analog subarrays have unequal sizes. The need arises because signals from the antenna elements in each analog subarray are summed in power with RF power combiners while the digital beamformer sums voltages, thus adding quantities with different units. We show that the signal from the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</tex> th analog subarray with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Mᵣ</tex> elements must be weighted by a correction factor of sqrt( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Mᵣ</tex> ) prior to summation in the digital beamforming processor if the proper array output is to be obtained. Array SNR and dynamic range are then computed using these correction factors. Patterns for a quasi-circular phased array with and without taper are provided as examples.