Eeective Interference and Eeective Bandwidth of Linear Multiuser Receivers in Asynchronous Systems Kiran and Tse: Eeective Interference and Eeective Bandwidth of Linear Multi-user Receivers in Asynchronous Systems

The performance of linear multiuser receivers in terms of the Signal-to-Interference Ratio (SIR) achieved by the users has been analyzed in a synchronous CDMA system under random spreading sequences. In this paper, we extend these results to a symbol-asynchronous system and characterize the SIR for linear receivers | the Matched Filter receiver, the MMSE receiver and the Decorrelator. We rst analyze receivers that demodulate a symbol with an observation window that extends over the duration of symbol of interest and then extend these results to the multiple symbol observation window. For each of the 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 eeective interference. Applying the results to a power controlled system, we derive eeective bandwidths of the users for these linear receivers and characterize the user capacity region: a set of users is supportable by a system if the sum of the eeective bandwidths is less than the processing gain of the system. We show that while the eeective bandwidth of the decorrelator 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 synchronous system, when the observation window extends innnitely on both sides of the symbol of interest. Moreover, the performance gap between the MMSE receiver and the decorrelator is signiicantly wider in the asynchronous setting as compared to the synchronous case.