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I am working with antenna phased arrays for direction finding. According to the manufacturer of the antenna some elements of the uniformed rectangular array (URA) have a rotational difference. This makes some elements have a positive rotation towards the azimuth direction $\theta$.

The generic form of a single antenna element of the steering vector is given as:

$$ e^{j \frac{2 \pi}{\lambda} \left(x_{k} \cos \left( \theta \right) \sin \left( \phi \right) + y_{k} \sin \left( \theta \right) \sin \left( \phi \right)\right)}$$

This assumes the elements do not have a rotational offset. How does one compensate for the the positive $\phi$ offset.

Should it be sufficient to add this offset directly?

$$ e^{j \frac{2 \pi}{\lambda} \left(x_{k} \cos \left( \theta + \theta_{off} \right) \sin \left( \phi \right) + y_{k} \sin \left( \theta + \theta_{off} \right) \sin \left( \phi \right)\right)}$$

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  • $\begingroup$ I have done some practical experiments and it seems it should be $$ e^{j ( \theta_{offset}+ \frac{2 \pi}{\lambda} \left(x_{k} \cos \left( \theta \right) \sin \left( \phi \right) + y_{k} \sin \left( \theta \right) \sin \left( \phi \right)\right))}$$ $\endgroup$
    – Yudop
    Jun 21, 2023 at 8:40

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