Statistical Signal Processing in Engineering

19Array Processing

In wavefield processing, array processing refers to the inference and processing methods for a set of sensors (these can be antennas for radar and wireless communication systems, acoustic microphones, hydrophones for sonar systems, geophones for elastic waves, etc.) when the set of signals are gathered synchronously and processed all together by accounting for the propagation model. The sensors of the array spatially sample the impinging wavefield over a discrete set of points. The arrangement of the sensors (array geometry, Figure 19.1) depends on the application and the parameters to be estimated, or the processing to be employed. There are linear, planar, or even spatial arrays depending on whether sensors are arranged along a line in space, or plane, or volume. A uniform array refers to uniform spatial sampling and it is by far the most common situation, but irregular or pseudo‐irregular arrays are equally possible.

Figure 19.1 Array geometry.

A general treatment of array processing would be broad and far too ambitious as it depends on the nature of the wavefield and the scope of the wavefield propagation. However, one common scenario is to consider the wavefield generated by some (countable set of) sources in space modeled as a superposition of L independent wavefields, one for each source, with time‐varying signatures s₁(t), …, s_L(t). The wavefield ...