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The use of adaptive finite-impulse response (FIR) filters to suppress multiple access interference (MAI) in code division multiple access (CDMA) receivers has been well documented. But the linear minimum mean squared error (MMSE) detector is in fact the Kalman filter which is a first-order recursive filter for asynchronous multiuser CDMA systems. Therefore in an adaptive implementation, the filter structure should be a first-order IIR filter. Of the host of adaptive IIR filtering algorithms, we choose to study the simplest of them, the recursive least mean square (LMS) method. Although mis-convergence has been reported for this algorithm when the system order is under-estimated, in our case this does not occur since the system order is unity at all times. Exact modelling is therefore possible, and convergence to the global minimum is seen in all our simulations using an algorithm that has a complexity linear in the number of adaptive parameters.