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
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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 $\theta_s=\theta$.
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$\begingroup$ As you say, the output from one particular set of weights will have the peak of the beam response in the steering direction, but the output will also have components from all directions. The gain will be a maximum at $\theta_s = \theta$. BTW: +1 $\endgroup$– Peter K. ♦Commented Dec 17, 2015 at 14:26
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$\begingroup$ Thanks for the clarification, so if I use the input signal from different directions (theta) and use weights calculated from particular steering direction(angle) to find output, I will get the beam pattern ? $\endgroup$ Commented Dec 18, 2015 at 4:31
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$\begingroup$ Yes - you fix the weights and vary the angle of the source and you will get the beampattern. $\endgroup$– DavidCommented Dec 18, 2015 at 14:34