Sparse Arrays: Fundamentals

This chapter is an introduction to sparse arrays. It begins by reviewing the basics of Array Signal Processing. Sparse arrays are then introduced and their advantages explained. A typical application of sensor arrays is in determination of the angles of arrival of different sources from various directions in space. One of the main advantages of sparse arrays is that, under some conditions, they can identify more number of sources than the number of sensors in the array. This unique property is explained using the notion of a difference coarray, and is valid under the assumption that the impinging sources are uncorrelated. A well‐designed sparse array has a difference coarray with many more consecutive elements than the number of sensors and this is one of the key properties which makes sparse arrays special. The chapter not only discusses recent sparse arrays such as nested and coprime arrays, but also reviews classical sparse arrays such as minimum redundancy arrays and Golomb rulers. The use of certain classes of sparse arrays in beamforming applications is also elaborated.