Iterative receivers, which perform MMSE detection and decoding iteratively, can provide significant performance improvement compared with noniterative method. However, due to the high computational cost and numerical instability, conventional MMSE detection using a priori information can not be implemented in hardware. In this letter, we propose a newly-built iterative receiver which is division-free and numerically stable, and then we analyze the results of a fixed-point simulation and present the hardware implementation architecture.

Numerical Stability of the Finite Element/Finite Difference Time Domain Hybrid algorithm is dependent on the hybridization mechanism adopted. A framework is developed to analyze the numerical stability of the hybrid time marching algorithm. First, the global iteration matrix representing the hybrid algorithm following different hybridization schemes is constructed. An analysis of the eigenvalues of this iteration matrix reveals the stability performance of the algorithm. Thus conclusions on the performance with respect to numerical stability of the different schemes can be arrived at. Further, numerical experiments are carried out to verify the conclusions based on the stability analysis.

The numerical property of the recursive least squares (RLS) algorithm has been extensively, studied. However, very few investigations are reported concerning the numerical behavior of the predictor-based least squares (PLS) algorithms which provide the same least squares solutions as the RLS algorithm. In Ref. [9], we gave a comparative study on the numerical performances of the RLS and the backward PLS (BPLS) algorithms. It was shown that the numerical property of the BPLS algorithm is much superior to that of the RLS algorithm under a finite-precision arithmetic because several main instability sources encountered in the RLS algorithm do not appear in the BPLS algorithm. This paper theoretically shows the stability of the BPLS algorithm by error propagation analysis. Since the time-variant nature of the BPLS algorithm, we prove the stability of the BPLS algorithm by using the method as shown in Ref. [6]. The expectation of the transition matrix in the BPLS algorithm is analyzed and its eigenvalues are shown to have values within the unit circle. Therefore we can say that the BPLS algorithm is numerically stable.

This paper describes the waveform relaxation (WR) algorithm with the under relaxation method based on the virtual state formulation (VSF) technique and the effect of multirate behavior in this algorithm. First, we present the virtual state relaxation method using VSF technique. Next, we introduce the VSF method into WR algorithm in order to exploit the multirate behavior. Furthermore, we construct the relaxation-based circuit simulator DESIRE2 and apply this simulator to the transient analysis of MOS circuits. Finally, we show that the present technique enables to use efficiently the multirate integration method in VSR and reduce the total simulation time without losing the waveform accuracy.