Effective interference and effective bandwidth of linear multiuser receivers in asynchronous CDMA systems

The performance of linear multiuser receivers in terms of the signal-to-int erference ratio (SIR) achieved by the users has been analyzed in a synchron ous CDMA system under random spreading sequences. In this paper, we extend these results to a symbol-asynchronous but chip-synchronous system and char acterize the SIR for linear receivers-the matched-fitter receiver, the mini mum mean-square error (MMSE) receiver, and the decorrelator, For each of th e receivers, we characterize the limiting SIR achieved when the processing gain is large and also derive lower bounds on the SIR using the notion of e ffective interference, Applying the results to a power controlled system, w e derive effective bandwidths of the users for these linear receivers and c haracterize the user capacity region: a set of users is supportable by a sy stem if the sum of the effective bandwidths is less than the processing gai n of the system. We show that while the effective bandwidth of the decorrel ator and the MMSE receiver is higher in an asynchronous system than that in a synchronous system, it progressively decreases with the increase in the length of the observation window and is asymptotic to that of the synchrono us system, when the observation window extends infinitely on both sides of the symbol of interest. Moreover, the performance gap between the MMSE rece iver and the decorrelator is significantly wider in the asynchronous settin g as compared to the synchronous case.