Adaptive beamforming in the spectral domain

The adaptive array process is cast into a constrained optimization problem in the spectral domain. Basically, the process allows the array to maintain constant gain in a desired look-direction while simultaneously rejecting undersired interference. The solution to the problem leads to two versions of a "spectral-domain constrained least-mean-squares" (SD-CLMS) iterative algorithm. Convergence considerations lead to optimization of the algorithm in the noiseless case. Smoothing techniques are recommended for the noisy case. A numerical example is included.