General formula for transmit power rise in CDMA systems with fast power control

Transmit power rise (TPR) in code-division multiple-access (CDMA) systems can be defined as the ratio of the average transmit power to the average receive power, where the average total channel power attenuation is assumed to be one. The TPR has been practically used in the Universal Mobile Telecommunications System radio network planning for modeling of the joint impact of the fast power control, the propagation channel power attenuations, and the antenna diversity. In this letter, we present a general analytical formula for the calculation of TPR in CDMA systems with fast power control, for an arbitrary multipath power profile, arbitrary numbers of transmit and receive antennas, and arbitrary maximum transmit power.