Linear Equation Method

How it works:

Generate matrix of phase settings according to the size of the array using the 3 provided (a2, a3, a5) well conditioned arrays such that its dimensions are NxN.

Loop N times, set the phase shifters to the settings in the nth column of the settings matrix.

Pass the test signal through the array

collect with a single pre-calibrated antenna.

Store each of the N number of measurements in a matrix.

For the number (S) of samples taken,

Take in the index (s, :) of the matrix such that all N measurements for sample s are retrieved and store in a vector

Take the equation Ax = b and solve for x. “A” is the phase settings matrix, b is the single sample output vector. X is the vector of absolute phase corrections for all elements at sample S

Compare the phase correction settings to return the average relative excitation for each element at sample s. Store this in index (s, :) of a new matrix

Take the mean of each element’s phase corrections across the entire sequence to retrieve the final corrected settings

Set the phase settings to the inverse of each of the final settings