Pre-Equalization in the Downlink of a Multicarrier Wireless Network Under Utility and Sum-Rate Optimization

This paper studies the problem of downlink pre-equalization in a multicarrier wireless network under utility and sum-rate maximization. The network utility depends on two main factors: 1) an efficiency mapping which is a function of the signal-to-interference-noise ratio (SINR), and 2) the power of the pre-equalization variables. Meanwhile, the sum-rate index is constructed by the summation of a logarithmic function of the SINRs of the active users. The network utility and sum-rate maximization problems are formulated here by assuming that the data estimation at the mobile units (MUs) is carried out by a simple matched filter. The optimal solutions are derived in this work for the pre-equalization factors by following a strategy that is distributed with respect to the channel state information (CSI) and data rates, but centralized with respect to the spreading sequences of all active users. The construction of these optimal solutions requires in each case a two step procedure. First, the optimal SINR is computed for the maximum utility and sum-rate solutions based on the efficiency mapping and on the bound of the transmission power, respectively. Then, exploiting the induced diversity by the multiple subcarriers, the pre-equalization algorithms cancel the multiple-access interference (MAI) and channel distortions, minimize the transmission power and achieve the optimal SINR after signal detection. A comprehensive numerical evaluation is presented at the end of the paper to validate the analytical derivations. Applications of the proposed pre-equalization schemes could be associated among others to cellular communication systems, and wireless networks of actuators.