Calculation of Far-Field Radiation Pattern Using Nonuniformly Spaced Antennas by a Least Square Method

The far field pattern from a nonuniformly spaced antenna array is computed using a least squares method. The method originally developed for spectral estimation for a nonuniformly spaced finite data set is applied for the analysis of the far field pattern from unevenly spaced antennas, as the far field pattern is due to the spectrum of the location of the antenna elements. The advantage of using a nonuniformly sampled data is that it is not necessary to satisfy the Nyquist sampling criterion as long as the average value of the sampling rate is less than the Nyquist rate. For a Fourier-based technique which also computes a least squares solution for the spectrum using a periodic data set, the finite data set then has to be periodically repeated resulting in bias in the solution. The methodology presented in the paper does not assume a periodic extension of the data set and can discern between the positive and negative frequencies of the spectrum unlike in the well-known Lomb periodogram. Finally, by exploiting a Hilbert transform relationship between the coefficients of the parameters in the least squares formulation an approximate fast way to compute the spectrum from unevenly spaced finite-sized non-periodic samples of the data can be realized. The example presented in this paper deals with a one-dimensional array even though this methodology is general in nature and can easily be extended to the two-dimensional case.