Performance of Iterative Coded CDMA Receivers with APP Feedback: A Use of a Weighted Delay Filter

The prohibitive computational complexity of optimal coded multiuser detection necessitates using suboptimal detectors in practical implementations. The filter is very computationally simple and is also demonstrated to provide faster convergence and superior bit error rate (BER) performance. Further investigation of the weighted delay filter concept produces a second filter—derived via the joint likelihood function. It is analytically demonstrated that extrinsic feedback systems will not benefit from weighted delay filtering. A system model is provided that introduces the notion of feedback ‘residue’, which is shown to be the key difference between a-posterior probability (APP) and extrinsic systems when determining the parallel interference cancellation (PIC) output statistics. It is analytically shown that the weighted delay filter derived via a maximum signal-to-noise ratio (SNR) approach is identical to a weighted delay filter derived via the joint likelihood function. It is analytically shown that when extrinsic feedback is used in a coded-code division multiple access (C-CDMA) system, no benefit will be realised by weighted delay filtering, as soft outputs from previous cycles are a merely scaled, noisy version of the most recent data. The notion of a ‘feedback residue’ for systems with APP feedback is introduced, and it is empirically shown that this residue term is a key consideration when determining the PIC output statistics. Using the ‘residual feedback’ model, it is shown that when APP feedback is utilised, data from previous cycles is not simply “a scaled, noisy version” of the current data. For this reason, benefits may be realised by APP feedback use. The simulation results shows that the residue may be trivial at small loads, the residue builds to the substantial value of nearly 0.4 at a reasonably modest load of K/N=15/10, and continues to grow as the load increases.