Joint Transceiver Power Allocation with Minimax MSE Criterion for Uplink MC-CDMA Transmissions

We investigate the problem of joint transmitter and receiver power allocation with the minimax mean square error (MSE) criterion for uplink transmissions in a multi-carrier code division multiple access (MC-CMDA) system. The objective of power allocation is to minimize the maximum MSE among all users each of which has limited transmit power. We first show that the problem is a non-linear optimization problem. Using the Lagrange multiplier method, we derive the Karush-Kuhn-Tucker (KKT) conditions which are both necessary and sufficient for a power allocation to be optimal. Numerical results indicate that, compared to the minimum total mean square error (MMSE) criterion, the minimax MSE criterion yields a higher total MSE but provides a fairer treatment across the users. The advantages of the minimax MSE criterion are more evident when we consider the bit error rate (BER) estimates. Numerical results show that the minimax MSE criterion yields a lower maximum BER and lower average BER. We also observe that, with the minimax MSE criterion, some users do not transmit at full power. For comparison, with the minimum total MSE criterion, all users transmit at full power.