TABLE OF CONTENTS The 1-D phased array algorithm employed in many applications uses the parallel-rays approximation. This assumption greatly simplifies the beamforming calculation. However, this simplifying assumption is only valid if the target is far away from the phased array. If the scanning field is not sufficiently far away, the parallel ray approximation error becomes significant, and eventually the method breaks down. The need hence exists for a generic phased-array formulation that does not rely on the parallel rays approximation, and hence can be used both in the near field and far field. Such a generic formulation will be presented in this section. In addition, the formulation will be kept sufficiently general such as not to be limited to the simple case of 1-D linear arrays. In fact, we will adopt a generic formulation in which the phased array elements could have arbitrary spatial locations.
In our derivation, we will first review the array signal processing assumptions. Then, we will develop a generic delay-and-sum formulation and then discuss its applicability in the near field and far field. After developing this generic approach, we will verify that it reduces to the simpler 1-D parallel-ray solution when a linear PWAS phased array and a target in the far field are assumed.
Array processing is a specialized branch of signal processing that focuses on signals conveyed by propagating waves transmitted and received simultaneously by several sensors or transducers. An array processing system spatially samples the propagating field.
