Minimum time-RMS bandwidth product for synchronous CDMA with multiple classes of users

We explore a symbol-synchronous CDMA system in which each user is guaranteed a certain quality of service (QoS). The QoS requirements need not be the same for all users so that multiple classes of users can be supported. In the context of root-mean-square (RMS) bandwidth, we show how to optimally design the users´ signature waveforms so that the required time-bandwidth product is minimized while meeting the QoS constraints. This is accomplished for two receiver architectures, namely the linear and decision-feedback receivers. For both scenarios, we reformulate the problem so that efficient interior-point methods may be applied. The optimality of the resulting design is practically verified by checking the Kuhn-Tucker conditions. Our approach is also found to yield an efficient technique for solving the problem of signal design for capacity-maximization that was posed and solved in [1].