# How to compensate for rotational offset for Steering vector of a phased antenna array

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?

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

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