The behavior of absolutely optimal array filters for sensor arrays in the presence of noise

A recent paper [1] described a set of array filters referred to as absolutely optimal array filters (AOAF´s) to achieve the rejection of an interference from the output of an array in order to allow observation of the signal. The array filters resulted in perfect rejection of the interference while achieving an all-pass response to the signal regardless of how close to the signal the interference occurs. However, they were developed by neglecting the presence of random noise at the sensor outputs, that is, assuming that only the interference is masking the signal. In reality, there is almost always additional noise present, even though it may be relatively small in amplitude relative to the interference. It is widely known that this noise cannot be ignored. For the important case of an array with plane wave signal and interference, it is shown that when the interference is near the signal, other random noise that is present, even if it is small in amplitude, may be amplified by the AOAF´s, so that even though the coherent interference is rejected, the total signal-to-noise ratio is reduced.