In this paper, the design of signature waveforms for asynchronous CDMA systems equipped with a correlation receiver is first considered. Optimal signature waveforms that minimize the average multiple access interference (MAI) at the output of a correlation receiver are found, while satisfying the constraint on available transmission bandwidth. Comparison to signature waveforms previously obtained for synchronous systems is also made to justify the superior performance of the designed signature waveforms in asynchronous systems. Furthermore, for direct-sequence CDMA (DS-CDMA) systems with random signature sequences, the use of multiple chip waveforms is also proposed as a means of suppressing MAI. Bandwidth constrained multiple chip waveforms that maximize the signal-to-interference ratio (SIR) at the output of each correlation receiver are found. Numerical results show that by using double chip waveforms instead of a single chip waveform, it is possible to reduce the MAI by 10% for a fixed transmission bandwidth (or equivalently, to save about 10% of transmission bandwidth for a given SIR requirement). The advantage of using double chip waveforms is also demonstrated in terms of the bit error rate (BER), whose calculation is based on our extension to Holtzman's approximation in.

In this paper we addresses the problem of finding feasible solutions for the Group Multicast Routing Problem (GMRP). This problem is a generalization of the multicast routing problem whereby every member of the group is allowed to multicast messages to other members from the same group. The routing problem involves the construction of a set of low cost multicast trees with bandwidth requirements for all the group members in the network. We first prove that the problem of finding feasible solutions to GMRP is NP-complete. Following that we propose a new heuristic algorithm for constructing feasible solutions for GMRP. Simulation results show that our proposed algorithm is able to achieve good performance in terms of its ability of finding feasible solutions whenever one exist.