We use the concept of active antenna available power to derive a generalization of the Friis transmission formula for multiport antenna systems. With beamformer weights chosen such that the array patterns are the same when transmitting and receiving, the active antenna available power at the receiving antenna divided by the input power at the transmitter is symmetric under link direction reversal in the near field as well as the far field. These results generalize the Friis transmission formula to beamformed multiport antenna systems in an arbitrary reciprocal propagation environment.

翻译：本文利用有源天线可用功率的概念，推导了适用于多端口天线系统的广义化弗里斯传输公式。通过选择波束赋形权重，使得天线阵列在发射与接收时具有相同的方向图，则接收端有源天线可用功率与发射端输入功率之比在近场和远场条件下均具有链路方向反转对称性。该结果将弗里斯传输公式推广至任意互易传播环境中采用波束赋形的多端口天线系统。