 
Summary: Direction of Arrival Estimation
1 Introduction
We have seen that there is a onetoone relationship between the direction of a signal and the
associated received steering vector. It should therefore be possible to invert the relationship and
estimate the direction of a signal from the received signals. An antenna array therefore should
be able to provide for direction of arrival estimation. We have also seen that there is a Fourier
relationship between the beam pattern and the excitation at the array. This allows the direction
of arrival (DOA) estimation problem to be treated as equivalent to spectral estimation.
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Figure 1: The DOA estimation problem.
The problem set up is shown in Fig. 1. Several (M) signals impinge on a linear, equispaced,
array with N elements, each with direction i. The goal of DOA estimation is to use the data
received at the array to estimate i, i = 1, . . . M. It is generally assumed that M < N, though
there exist approaches (such as maximum likelihood estimation) that do not place this constraint.
In practice, the estimation is made difficult by the fact that there are usually an unknown
number of signals impinging on the array simultaneously, each from unknown directions and with
unknown amplitudes. Also, the received signals are always corrupted by noise. Nevertheless, there
are several methods to estimate the number of signals and their directions. Figure 2 shows some
