Optimal pre-equalisation for wireless multi-carrier code division multiple access systems under quality of service requirements

This work addresses an optimal pre-equalisation scheme to provide power and phase compensation in multi-carrier code division multiple access wireless systems under quality of service (QoS) restrictions. Two assignation schemes are studied: independent and uniform pre-equalised transmission (IPT and UPT) per subcarrier. First, the QoS was quantified in terms of the signal-to-interference noise ratio (SINR) after using a linear detector in the receiver. The SINR expressions for IPT and UPT were explicitly derived, to highlight their dependence on the pre-equalisation factors. These relations are exploited to derive analytical procedures to obtain the required pre-equalisation factors that satisfy an objective SINR per active user. The author´s proposal for IPT achieves the lowest power while requiring a simple detector independent of the channel state information (CSI). For IPT, two minimum norm solutions are derived by translating the SINR restrictions into linear equations: one based on spectral factorisation, and a second one based on a simultaneous zero-forcing effect plus an energy scaling. On the other hand, for UPT, multi-user detectors like zero-forcing (ZF) and minimum-mean-square error (MMSE) have to be employed at the receiver to achieve a solution to the QoS requirements. In the numerical evaluations, IPT attained roughly a 2.5-3% reduction in the overall transmission power compared to UPT with ZF and MMSE by varying the objective SINR and noise variance. Although this reduction is further expanded as the number of active users increases, achieving a reduction in transmission power larger than 50% for a fully-loaded system.