The equations above and the FFT are estimates of the angle of arrival of different objects. Unfortunately, if there are non-linearities in the radar or antennas, or gain/phase mismatch in each individual antenna, then the FFT-matrix and equations above do not accurately estimate the angle of arrival of the object. An alternative design here is to recompute the FFT matrix experimentally by measuring the returned phase of the radar signal for targets swept over all potential angles of arrival, and using these coefficients as the ground-truth vectors. This is what is known as the steering vector algorithm for the IWRL6432AOP.

$\left(\begin{array}{cccc}{\mathit{x}}_{11}& {\mathit{x}}_{12}& \cdots & {\mathit{x}}_{1\mathit{N}}\\ {\mathit{x}}_{21}& {\mathit{x}}_{22}& \cdots & {\mathit{x}}_{2\mathit{N}}\\ ⋮& \cdots & \ddots & ⋮\\ {\mathit{x}}_{\mathit{N}-1,1}& {\mathit{x}}_{\mathit{N}-1,2}& \cdots & {\mathit{x}}_{\mathit{N}-1,\mathit{N}-1}\end{array}\right)\left(\begin{array}{c}{\mathit{\varphi }}_0\\ {\mathit{\varphi }}_1\\ \dots \\ {\mathit{\varphi }}_{\mathit{N}-1}\end{array}\right)=\left(\begin{array}{c}{\mathit{a}}_0\\ {\mathit{a}}_1\\ \dots \\ {\mathit{a}}_{\mathit{N}-1}\end{array}\right)$

Based off the collected dataset (which sweeps the FOV in regular increments), θ_est is referenced in a look up table that maps the a indices to θ indices.