Although angle estimation of a source is not typically of significant interest in communication systems, because angle-of-arrival estimation is commonly addressed in treatments of multiple-antenna systems, we will consider it here in this chapter. In addition, some of the tools and intuition are helpful when considering adaptive multiple-antenna receivers. Furthermore, there are special cases of communications systems for which line-of-sight propagation is valid and for which angle-of-arrival estimation is of value. Angle estimation to the source is sometimes denoted direction finding. There is a large body of work addressing this topic [294, 223], and numerous useful approaches (for example, those in References [16, 266]), many of which will be skipped for brevity. In general, the direction to the source requires both azimuthal and elevation information, but for most examples here it is assumed that the source is in the plan of the array, so only azimuthal information encoded in the angle φ is required. A few approaches are considered here as an introduction to the area.

Within this chapter, it is assumed that any multipath scattering is minimal and that the signal is not dispersive across the array; that is, the array is small compared with the speed of light divided by the bandwidth of the signal. This assumption is sometimes denoted the narrowband signal assumption. Furthermore, to simplify the introduction, it is assumed that the direction can be characterized by a single angle φ. Here it is assumed that multiple samples of the received signal are available. The number of samples is denoted ns.