Finding DC operating points of nonlinear circuits is an important and difficult task. The Newton-Raphson method adopted in the SPICE-like simulators often fails to converge to a solution. To overcome this convergence problem, homotopy methods have been studied from various viewpoints. However, the previous studies are mainly focused on the bipolar transistor circuits. Also the efficiencies of the previous homotopy methods for MOS transistor circuits are not satisfactory. Therefore, finding a more efficient homotopy method for MOS transistor circuits becomes necessary and important. This paper proposes a Newton fixed-point homotopy method for MOS transistor circuits and proposes an embedding algorithm in the implementation as well. Moreover, the global convergence theorems of the proposed Newton fixed-point homotopy method for MOS transistor circuits are also proved. Numerical examples show that the efficiencies for finding DC operating points of MOS transistor circuits by the proposed MOS Newton fixed-point homotopy method with the two embedding types can be largely enhanced (can larger than 50%) comparing with the conventional MOS homotopy methods, especially for some large-scale MOS transistor circuits which can not be easily solved by the SPICE3 and HSPICE simulators.

Recently, the compound element pseudo transient analysis, CEPTA, method is regarded as an efficient practical method to find DC operating points of nonlinear circuits when the Newton-Raphson method fails. In the previous CEPTA method, an effective SPICE3 implementation algorithm was proposed without expanding the Jacobian matrix. However the limitation of step size was not well considered. Thus, the non-convergence problem occurs and the simulation efficiency is still a big challenge for current LSI nonlinear cicuits, especially for some practical large-scale circuits. Therefore, in this paper, we propose a new SPICE3 implementation algorithm and an embedding algorithm, which is where to insert the pseudo capacitors, for the CEPTA method. The proposed implementation algorithm has no limitation for step size and can significantly improve simulation efficiency. Considering the existence of various types of circuits, we extend some possible embedding positions. Numerical examples demonstrate the improvement of simulation efficiency and convergence performance.

The traditional selection cooperation scheme selects the relay with best instantaneous receive signal-to-noise ratio to forward the message and achieves good outage performance, which may however cause poor fairness among relays. In this letter, we propose two practical selection cooperation schemes in Decode-and-Forward (DF) fashion to improve the fairness of relay selection. Numerical results suggest that both of the proposed schemes can achieve fairness close to the strict fairness scheme without outage performance deterioration. It is also validated that these schemes have lower complexities than traditional ones and therefore are practical for real networks.

Without recourse to the Shannon-Nyquist sampling theorem, a novel information sampling (IS) concept is proposed for ultra-wideband (UWB) communications. To implement IS, a random pre-coding system architecture is designed and system performance is studied. Simulation results from one of UWB channel models show that the proposed system is effective to detect UWB signals with a low-sampling-rate analog-to-digital converter (ADC) at the receiver. Moreover, it can operate in a regime of heavy inter-symbol interference (ISI).

An adaptive time-step control method is proposed for the damped pseudo-transient analysis (DPTA) method. The new method is based on the idea of switched evolution/relaxation (SER), which can automatically adapt the step size for different circuit states. Considering the number of iterations needed for the convergence of Newton-Raphson (NR) method and the states in previous steps, the proposed method can automatically optimize the time-step size. Using numerical examples, the new method is proven to improve robustness, simulation efficiency, and the convergence of DPTA for solving nonlinear DC circuit equations.

An effective time-step control method is proposed for the damped pseudo-transient analysis (DPTA). This method is based on the idea of the switched evolution/relaxation method which can automatically adapt the step size for different circuit states. Considering the number of iterations needed for the convergence of the Newton-Raphson method, the new method adapts the suitable time-step size with the status of previous steps. By numerical examples, it is proved that this method can improve the simulation efficiency and convergence for the DPTA method to solve nonlinear DC circuits.