Fast computation of macro basis functions interactions in non uniform arrays

The proposed method is an alternative to multipoles to compute interactions between MBFs when dealing with non uniform arrays. The multipole approach for non regular arrays requires a number of operations of the order of N²middotM, where N is the number of antennas in the array and M is the number of considered directions (of the order of one or two hundreds). Furthermore, this approach can be only applied to MBFs located on elements not to close to each other. On the other hand, with baselines we will need a number of elementary calculations of the order of PmiddotB² + N²middotS. The first term refers to the operations due to the baselines computation, where P (~N) is the number of points in the baseline domain and B is the number of basis functions per antenna. Then second term stands for the pattern based computation of interactions, where S is a very small factor corresponding to the far-field estimation and interpolation in the near-field table; this term is negligible compared to the first one. Therefore, for intermediate size and large non regular arrays a speed-up of the order of N can be achieved with the computation method using baseline interaction.