TUTORIAL 3 BEAMFORMING 9/15/2018 LECTURES 1

1-State the impact of phase weights and amplitude weights to an array radiation pattern 2-Consider an array of two uniform amplitude isotropic elements oriented on y-axis of spacing d with zero progressive phase. Prove that the nulls in azimuth plane are given by 3-A receiver equipped with a uniform amplitude three element linear array of isotropic elements oriented in y- direction required to enhance the wanted signal arriving from a transmitter located at -30o from the array boresight. Compute the required weight vector for the array to perform this function given that the elements are spaced apart by d = λ/3 4-A uniform amplitude 2x2 planar array of isotropic elements oriented in xy-plane is required to enhance the wanted signal arriving from a transmitter located at θ=10o and φ=40o. Compute the required weight matrix for the array to perform this function given that the elements are spaced apart by dx=dy= λ/2 x y 1 4 3 2 9/15/2018 LECTURES 2

5-Compute the weight vector required to steer the main beam of a uniform two isotropic element array oriented in y-direction towards the required signal at 45o from the array boresight and to minimize the interfering signal that appears at - 10o from the array boresight. Assume the element spacing d = λ/2 and the observation plane is yz plane 6-Compute the weight vector required to steer the main beam of a uniform two isotropic element array oriented in y-direction towards the required signal at -20o from the array boresight and to minimize the interfering signal that appears at 35o from the array boresight. Assume the element spacing d = λ/2 and the observation plane is yz plane (HW) 9/15/2018 LECTURES 3