As answered in Relationship of Fourier Transform and Spatial Directivity Pattern the relation between directivity pattern and weights is given. But I am bit confused, I have Beamformer weights (complex valued, for each frequency bin) for a particular steering vector. The relationship mentioned in the above link needs the values to be calculated for each theta, but the beamformer weights are for a particular steering angle theta. Do I need to calculate beamformer weights for each of the theta, or I have a wrong understanding of the directivity pattern. Suggest methods for calculating directivity using beamformer weights. Thanks
You choose the weights the steer the main beam of the antenna in the particular direction you want - let's call this $\theta_s$ i.e. steering angle. Now, given that you are steering the antenna in a given direction you are also interested in the array's response to incoming signals from other directions. This is the directivity pattern and is a function of the angle $\theta$ of the source signal. For conventional beamforming (non-adaptive) the magnitude of the directivity pattern will reach a maximum when $\theta_s=\theta$.