A Constraint-Elimination Technique for Linearly Constrained Array Processing

A new technique is presented for the problem of linearly constrained multi-channel-array processing. The purpose of the array processing is to reject undesired noise, in the minimum-mean-squared-error sense, while responding to any signal coming from a particular direction with a preset, constrained frequency response. In the constraint-elimination technique proposed in this paper, the original constrained-array-processing problem is transformed to the simple unconstrained-Wiener-filtering problem. Transformation of the problem is achieved by introducing a "compensating" channel to the multichannel processor. Input to the compensating channel is the channel-averaged input. The constraint is then eliminated by expressing the filter weights of the compensating channel in terms of those of the original processor. An adaptive algorithm is derived by applying the stochastic approximation to the simplified Wiener-filtering problem. Simulation experiments verify that the constrained-array-processing problem is properly transformed to the unconstrained one by the proposed technique. Additional experiments show that the adaptive algorithm generally reduces output power while maintaining the constrained frequency response to the desired signal.