Show that in the case of a third-order DSA with a zero of multiplicity 3 in the beam pattern: a) the beamformer is given by b) the beam pattern can be approximated as c) the WNG can be approximated as...

Show that in the case of a third-order DSA with a zero of multiplicity 3 in the beam pattern:

a) the beamformer is given by

b) the beam pattern can be approximated as

c) the WNG can be approximated as

Show that for M ≥ N +1, the minimum-norm beamformer maximizes the WNG subject to 𝐃 ( f , 𝜶 ) 𝐡( f ) = 𝜷, and is given by