Asymptotic performance of ML sequence estimator using an array of antennas for coded synchronous multiuser DS-CDMA systems

The optimal joint maximum-likelihood sequence estimator using an array of antennas is derived for synchronous direct sequence-code division multiple access (DS-CDMA) systems. Each user employs a rate 1/n convolutional code for channel coding for the additive white Gaussian noise (AWGN) channel. The array receiver structure is composed of beamformers in the users´ directions followed by a bank of matched filters. The decoder is implemented using a Viterbi algorithm whose states depend on the number of users and the constraint length of the convolutional code. The asymptotic array multiuser coding gain (AAMCG) is defined to encompass the asymptotic multiuser coding gain and the spatial information on users´ locations in the system. We derive the upper and lower bounds of the AAMCG. As an example, the upper and lower bounds of AAMCG are obtained for the two user case where each user employes the maximum free distance convolutional code with rate 1/2. The near-far resistance property is also investigated considering the number of antenna elements and user separations in the space.