Reduced Complexity Antenna Array Calibration Algorithm

A phase-less algorithm of the antenna array calibration is presented in this paper. The algorithm is used to estimate and compensate the signal phase lag variation in the array channels. The estimated phase lags include the lags, caused by the channel equipment, and the lags, caused by the signal source spatial location in the case of the receiving array or, otherwise, the receiver spatial location in the case of the transmitting array. The compensation of the first-mentioned phase lags means the array calibration and the compensation of the second-mentioned phase lags means the array calibration and beam steering simultaneously, because the channel, space and phase lags are not separable. The proposed algorithm requires $\boldsymbol{4+4(M-1)}$ measurements of the array output power after the changing of the signal phase to the specific values sequentially in the pairs of the reference and each of the calibrated channels of the array. Here, $\boldsymbol{M}$ is the number of the array channels. This algorithm requires about 33% less power measurements, and therefore has less complexity comparing to the similar calibration algorithm, which requires $\boldsymbol{2+6(M-1)}$ of such measurements. The accuracy of the channel phase estimation using the proposed or known calibration algorithm does not exceed the value of one discrete of the phase quantization by means of the digitally controlled phaseshifter. The proposed algorithm can be used in arrays of arbitrary geometric configuration.