Application of orthogonal codes to the calibration of active phased array antennas for communication satellites

This work describes two algorithms designed for remote calibration of an N_c-element active phased-array antenna. These algorithms involve transmission of N⩾N_c time multiplexed orthogonal encoded signals. The received signals are coherently detected, accumulated in vector forms, and decoded with the inverse of the orthogonal encoding matrix. The unitary transform encoding (UTE) algorithm is most suited for digital beamforming as it requires additional encoding hardware for an analog implementation. The control circuit encoding (CCE) algorithm is ideally suited for analog beamformers as it requires no additional encoding hardware. The CCE method encodes phased-array elemental signals using a Hadamard matrix to control the switching of intrinsic phase shifter delay circuits. The UTE and CCE algorithms can reduce the average measurement integration times for the complete set of calibration parameters by ~N_c relative to the corresponding values for single-element calibration procedures. This is significant for satellite systems as calibration must be performed in a short enough time window that the process can be treated as being stationary. Proofs are given that the orthogonal codes satisfy the mathematical lower bounds for the asymptotic forms of calibration parameter estimation variances