Adaptive Beamforming by Compact Arrays Using Evolutionary Optimization of Schelkunoff Polynomials

In adaptive beamforming by compact arrays, the excitation amplitude and phase of each array element require dynamic optimization for controlling the radiation pattern at different angular sectors. If the objective function of adaptive beamformer is defined by some properties other than the deterministic properties of arrays such as directivity or signal-to-noise ratio, evolutionary optimization is advantageously implemented to minimize the objective function. Nevertheless, the convergence time of most of the evolutionary optimization methods exponentially increases by the number of array elements
$N$
. For large
$N$
, the above convergence issue slows down the beamforming agility. To improve the above inefficiency, we first express the array factor by a Schelkunoff polynomial of order
$N - 1$
. Second, a discrete optimization method like genetic algorithm optimally factorizes the polynomial into two polynomials of orders
$N - 1 - P$
and
$P$
, where
$N - 1 - P \ge P$
. Third, the locations of zeros of these polynomials are optimized across the visible region by a continuous optimization method like particle swarm optimization to attain the desired objective function. When these two polynomials are multiplied, the resultant polynomial of order
$N - 1$
demonstrates improved features with respect to the original polynomial of order
$N - 1$
in sensitivity, sidelobe level, and convergence. Representative examples include airborne radars.