Sd. Silverstein, APPLICATION OF ORTHOGONAL CODES TO THE CALIBRATION OF ACTIVE PHASED-ARRAY ANTENNAS FOR COMMUNICATION SATELLITES, IEEE transactions on signal processing, 45(1), 1997, pp. 206-218
This work describes two algorithms designed for remote calibration of
an N-c-element active phased-array antenna. These algorithms involve t
ransmission of N greater than or equal to N-c time multiplexed orthogo
nal encoded signals. The received signals are coherently detected, acc
umulated in vector forms, and decoded with the inverse of the orthogon
al 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 similar to N-c relative to the correspon
ding values for single-element calibration procedures. This is signifi
cant for satellite systems as calibration must be performed in a short
enough time window that the process can be treated as being stationar
y. Proofs are given that the orthogonal codes satisfy the mathematical
lower bounds for the asymptotic forms of calibration parameter estima
tion variances.