Power control for a spread spectrum system with multi-user receivers

The power control problem has received a lot of attention in CDMA systems employing single-user receivers because of the `near-far´ effect under certain conditions. Multi-user receivers suffer less from this problem, but adaptive power control is still necessary for the following reasons: (i) to compensate for the motion of the mobile, (ii) the actual amount of power needed to achieve the required performance is also a function of the code correlations, (iii) it is necessary to conserve the battery power and (iv) if we assume that multi-user detection is employed only for users with known codes with the other interfering users being treated as noise, the amount of interference caused by these users is in terms of their powers, just as with single-user receivers. This case could occur, for example, if multi-user detection were used in the uplink for the users in the given cell with the interference from adjacent cells treated as stationary noise. In this paper, we consider multi-user receivers based on the minimum mean squared error (MMSE) approach for a synchronous CDMA system where external cell interference is treated as stationary noise. We consider the convergence of the algorithm and show sufficient conditions for convergence to a unique optimal power vector that minimizes the total transmitted power