We design an algorithmic framework using matrix exponentials for time-domain simulation of power delivery network (PDN). Our framework can reuse factorized matrices to simulate the large-scale linear PDN system with variable stepsizes. In contrast, current conventional PDN simulation solvers have to use fixed step-size approach in order to reuse factorized matrices generated by the expensive matrix decomposition. Based on the proposed exponential integration framework, we design a PDN solver R-MATEX with the flexible time-stepping capability. The key operation of matrix exponential and vector product is computed by the rational Krylov subspace method. To further improve the runtime, we also propose a distributed computing framework DR-MATEX. DR-MATEX reduces Krylov subspace generations caused by frequent breakpoints from a large number of current sources during simulation. By virtue of the superposition property of linear system and scaling invariance property of Krylov subspace, DR-MATEX can divide the whole simulation task into subtasks based on the alignments of breakpoints among those sources. The subtasks are processed in parallel at different computing nodes without any communication during the computation of transient simulation. The final result is obtained by summing up the partial results among all the computing nodes after they finish the assigned subtasks. Therefore, our computation model belongs to the category known as embarrassingly parallel model. Experimental results show R-MATEX and DR-MATEX can achieve up to around 14.4× and 98.0× runtime speedups over traditional trapezoidal integration-based solver with fixed time-step approach.

For the purpose of investigating the performance of digital radio systems, Telecom Australia established and conducted over a three year period (1982-1984), a 140 Mbit/s 16 QAM digital radio field experiment. In parallel with this experiment, analytical work was undertaken to develop an "outage prediction method" to assist with route design. This paper presents the observations and conclusions drawn from this work. Emphasis is placed on the aspects which relate to system design. We show that for digital radio outage prediction, a radio path can be characterized for multipath fading by the probability of occurrence of multipath fading and the mean echo delay, while the radio equipment can be characterized by a set of normalized parameters. The performance improvements achieved through the use of adaptive equalization and space-diversity are highlighted. Finally, we present a methodology for considering the performance of digital radio systems in the presence of interference and thermal noise, and present results for system performance with adjacent channel interference.