Consider a system that consists of array of r arbitrary sensors that have arbitrary locations and arbitrary directions (directional characteristics) which receive signals that generated by q narrow band sources of known center frequency ω and locations θ1, θ2, θ3, θ4 ... θq. since the signals are narrow band the propagation delay across the array is much smaller than the reciprocal of the signal bandwidth and it follows that by using a complex envelop representation the array output can be expressed (by the sense of superposition) as :<br>