Mapping antenna precoders to equal power antenna patterns

Multiple communication standards including 3GPP LTE and IEEE 802.11, employ codebooks of antenna precoders. For these standards, feedback from the receiver is used to optimize the antenna precoder selection performed at the base station. This optimization process implicitly assumes that the antenna precoders which have equal Euclidean norm are mapped to antenna patterns with equal transmit power. However, for coupled antennas, it can be shown that that if the precoders are implemented as a vector voltage source in a Thevenin source model or as a vector current source in a Norton source model, the equal power condition is not satisfied. The effect of transmission lines between the source and the antenna array are included in the analysis, as this affects the power delivered to the array, as does the use of matching networks. To illustrate, an example is considered using two half-wavelength dipoles for which the variation in transmit power can be in excess of 3 dB even when the Euclidean norm of the precoders is held constant. Given this problem, two methods are proposed which can be used to map equal norm antenna precoders to equal power antenna patterns. The first of these two methods requires signaling of scale factors to the receiver, while the second method can be implemented in a manner that is completely transparent to the receiver.