Analytical modelling of transmit power control error process for S-UMTS

Transmit power control is indispensable in direct sequence code division multiple access (DS/CDMA) based systems such as the Satellite Universal Mobile Telecommunication System (S-UMTS). The performance of fixed step-size closed loop power control is significantly affected by command delay due to processing and propagation. This calls for insights into the dynamics of transmit power control taking into account the effects of delays. In this paper, therefore, we have developed an analytical model for the dynamic behaviour of the error process as a stochastic difference equation. We have modelled the effects of delays in the presence of random external disturbances as a random walk process. Using the stochastic difference equation, we have developed an expression for the steady-state pdf of the power control error process as a lognormal distribution. However, we demonstrate that in cases where the quantisation errors of the power control command are significant, the error process departs from the lognormal distribution approximation. This shows that the generally assumed lognormal distribution for power control error process may not always be valid.