3.1 Introduction

The receivers described in Chapter 2 are "direct" in the sense that they are constructed directly from the data observations. Such approaches are adequate but often suboptimum for a perfectly parameterized problem. For example, in constructing the DRAKE receiver, only the SOI is completely parameterized while no assumption is made on the functional form of the MAI. As a result, the number of coefficients that need to be determined from the data is L _c ( L + L _c) for each user, which is quite large considering that the actual number of unknowns per user is only L _c the number of channel coefficients.

In contrast with the partially parametric approach discussed in Chapter 2, a full parametric approach in CDMA signal reception first estimates all unknowns and then constructs multiuser detectors based on the reconstructed effective signature waveforms. When used properly, the two-step (indirect) approach can make better use of the available data and yield higher detection performance, provided that the system model is accurate. The trade-off, in most cases, is the higher complexity incurred in multiuser parameter estimation. Since for the CDMA system described in (2.3) the model mismatch mainly comes from multipath with delays beyond L _c chips, and since signal energyattenuates rapidly with the delay (distance), the model error can be controlled to be arbitrarily small by increasing the maximum channel length L _c. In most cases, the model form is a reasonable description of reality. For...