A novel iterative multiuser detector for complex modulation schemes

In the past decade, the search for feasible multiuser detectors for direct sequence code{ division multiple{access (DS{CDMA) systems has attracted high interest. Especially iterative multiuser detection schemes have gained attention due to their tractable complexity and good performance for moderate system loads = K=N (K denotes the number of users and N the spreading factor). So, various iterative receivers for uncoded as well as coded transmission have been proposed (see [1, 2, 3] and references therein). In general, it is presumed that the residual interference in the inphase and the quadrature component of the lter output are mutually uncorrelated and have equal variance. Applying as interference suppression lter for example a matched lter or a minimum mean{squared error (MMSE) lter [4], it can be easily shown that this is true for long random spreading sequences, nite load, and bounded receive power from each user. However, investigating the interference at the input of these lters and assuming real channel symbols and complex spreading sequences, it turns out that the pseudocovariance matrix (for a de nition see [5]) of the interference is nonzero, i.e., the multiuser interference represents a rotationally variant complex noise. This kind of noise is also referred to as improper noise [5] and, in this case, this property is simply a consequence of the real modulation scheme. The fact that the multiuser interference is for binary modulation rotationally variant was rst used in [6] to present the optimum linear MMSE lter for DS{CDMA and in [7] the corresponding decorrelating lter was proposed. In both situations considerable gains can be obtained compared to the corresponding conventional linear receivers and we can report that this holds for the respective iterative algorithms, too. However, as real modulation schemes are generally less bandwidth eÆcient than their complex counterparts, we are particularly interested in the latter ones. Here, we face a completely di erent situation. If only rotationally invariant additive channel noise is present, for complex signal modulation with equal power in the inphase and quadrature component the pseudocovariance matrix of the received signal vanishes identically. Thus, before the rst iteration the rotational invariance is given and the standard receiver need not to be modi ed. Nevertheless, after the feedback of soft decisions it turns out that the interference becomes rotationally variant. In order to bene t from this, we propose the application of a modi ed MMSE lter which accounts for the rotational variance of the residual interference in the signal. In this way, signi cant gains in terms of power eÆciency and convergence speed are reached.