An algorithm for linearly constrained adaptive array processing

A constrained least mean-squares algorithm has been derived which is capable of adjusting an array of sensors in real time to respond to a signal coming from a desired direction while discriminating against noises coming from other directions. Analysis and computer simulations confirm that the algorithm is able to iteratively adapt variable weights on the taps of the sensor array to minimize noise power in the array output. A set of linear equality constraints on the weights maintains a chosen frequency characteristic for the array in the direction of interest. The array problem would be a classical constrained least-mean-squares problem except that the signal and noise statistics are assumed unknown a priori. A geometrical presentation shows that the algorithm is able to maintain the constraints and prevent the accumulation of quantization errors in a digital implementation.