Stochastic modeling of high-speed data links with nonlinear dynamic terminations

This paper addresses the statistical modeling and simulation of high-speed interconnects with uncertain physical properties and nonlinear dynamical terminations. The proposed approach is based on the expansion of voltage and current variables in terms of orthogonal polynomials of random variables. It extends the available literature results on the generation of an augmented deterministic SPICE equivalent of the stochastic link to the case in which the terminations are nonlinear and dynamical, like those modeling IC buffers. A single and standard SPICE simulation of the aforementioned equivalent circuit allows to efficiently compute the expansion coefficients that provide statistical information pertinent to the interconnect response. The feasibility and strength of the approach are demonstrated by means of a coupled microstrip interconnect with drivers and receiver

On Partial Response Signaling for MIMO Equalization on Multi-Gbit/s Electrical Interconnects

Because of its ability to deal with intersymbol interference (ISI) and crosstalk (XT) over mutually coupled electrical interconnects, multiple-input multiple-output (MIMO) decision feedback equalization (DFE) has proven to be a promising low-cost solution for achieving multi-Gbit/s wireline communication on- and off-chip. However, not only does the channel become very sensitive to manufacturing tolerances at very high symbol rates, the latency in the feedback loop becomes prohibitively large as well. Whereas the former issue has been addressed by adopting a stochastic MIMO approach where (part of) the equalization filters depend on the channel statistics rather than on the actual channel, we tackle in this paper the latency issue by setting to zero the first N taps of the feedback filters. Moreover, we show that precoded partial response (PR) signaling can improve the performance of the resulting scheme, although the achieved gain is smaller than in the case of single-input single-output (SISO) equalization

MIMO Equalization for Multi-Gbit/s Access Nodes Affected by Manufacturing Tolerances

While the requirements for delivering high throughputs increase exponentially with every generation of access node hardware, the device cost is of primary concern. As a result, multiple- input multiple-output (MIMO) equalization, which has been shown to facilitate multi-Gbit/s communication over low-cost parallel electrical interconnects, is emerging as an attractive high- speed interconnect solution for next-generation access nodes. Because of the high operating frequencies, however, the transfer functions of the on- and off-chip interconnects become highly susceptible to manufacturing tolerances (MTs); hence, the equalization filters must be adjusted to the specific channel realization to achieve optimal performance, which involves a high implementation and computational complexity. Considering that the MTs are usually limited, we propose a robust low-complexity transceiver consisting of a fixed MIMO linear pre-equalizer (which avoids the need for feeding back the channel state information to the transmitter), with either a fixed or adjustable MIMO decision- feedback equalizer (DFE). For a specific chip-to- chip interconnect operating at 75 Gbit/s per line and a 26 dB signal-to-noise ratio, we show that the resulting bit error rate does not exceed 10^(-12) for MTs up to 10.5% (fixed DFE) and 17.7% (adjustable DFE) of the nominal line width

A Hybrid Perturbative-Stochastic Galerkin Method for the Variability Analysis of Nonuniform Transmission Lines

In this paper, a hybridization of the classical stochastic Galerkin method (SGM) with two perturbative solution techniques is proposed to speed up the statistical analysis of nonuniform multiconductor transmission line (MTL) structures with parameters affected by uncertainty. The first method leverages a recently developed deterministic perturbation technique (PT) to deal with nonuniformity affecting the SGM-augmented MTL equations. This approach is proven to be computationally more efficient than the traditional solution based on line subdivision into uniform cascaded sections, yet its performance is still affected by the so-called 'curse of dimensionality.' To further mitigate this issue, a second method is proposed, which resorts to the solution of uncoupled MTLs having the same size as the original structure, and where the effects of both nonuniformity and stochasticity are iteratively included by means of distributed sources. The accuracy and computational efficiency of the proposed approaches are assessed based on the statistical prediction of the mixed-mode S-parameters of microstrip-line structures with different numbers of random parameters. The test cases demonstrate that the hybrid SGM-PT approach is applicable to problems with a few tens of random variables, which is an unprecedented result for state-of-the-art SGM implementations

An effective modeling framework for the analysis of interconnects subject to line-edge roughness

This letter proposes a complete and efficient simulation framework to assess the effects of line-edge roughness appearing in on-chip lines. The modeling approach consists of three steps. First, a stochastic macromodel is created for the per-unit-length RLGC parameters of the line. Secondly, random conductor edge profiles are generated using randomized splines. These are combined with the stochastic macromodel to readily provide place-dependent RLGC parameters. Finally, the resulting nonuniform transmission line is analyzed by means of a fast and accurate perturbation technique. To validate the proposed approach, a statistical analysis of the response of a coupled inverted embedded microstrip line is carried out for different roughness parameters

A Novel Implementation of the Perturbation Technique for Better Integration of NUTLs with Periodic Geometry

In this work, a novel implementation of the perturbative technique (PT) recently proposed in [1] for the solution of nonuniform transmission-lines (NUTLs) is presented. Unlike the original PT, the proposed method provides a 2n-port S- parameter representation of the NUTL under analysis, which can be afterwards used in combination with different terminal conditions and/or cascaded with other 2n-port networks. As an application example, an interdigital tabbed microstrip line terminated in SMA connectors and involving a bend discontinuity is solved by the proposed technique. The obtained predictions are validated versus those provided by a full-wave solver