1. MODEL DEVELOPMENT FOR HIGH-SPEED RECEIVERS
Bowen Li, Paul Franzon
Predict a signal accurately at the output of the receiver (RX) based on the input signal.
Use system identification to add power-supply-induced jitter into the input signal and build a receiver model.
Can get correct output without using SPICE model or measured model.
Provide a “standard” interchange format between the chip vendor and system integration.
Main Goals
Nonlinear System Identification
Nonlinear system identification models show high accuracy when predicting nonlinear signals. NNARMAX models send previous outputs, inputs, and errors into a neural networks module.
In this research, we use measured inputs and outputs to generate a NNARMAX model for each RX setting. We use Lipschitz quotients to select the lag space.
The number of previous outputs = 3
The number of previous inputs = 3
The error order = 1
The purpose of system identification modeling is to estimate a model of a system based on input-output data. It also adds noise injection.
This approach can be used in a black-box model for which the model terms are selected as part of the identification procedure.
System identification modeling can be used in both linear and nonlinear systems.
There are many model types in system identification modeling. In this research, we focus mainly on model comparison among ARX, ARMAX and State Space models for linear modeling and ARMAX based on Neural Networks (NNARMAX) models for nonlinear modeling.
System Identification Introduction
Comparison among Linear and Nonlinear System Identification models
G(z)
U(z)
Y(z)
E(z) +
H(z)
white noise
filter
disturbance
output
input
process
We compared linear System Identification models (Order=3); State Space model and nonlinear system identification models(Order=3).
Among linear System Identification models, State Space models show better accuracy. What’s more, nonlinear models have the best performance.
Case
ARX (%)
ARMAX (%)
State Space (%) 1
84.63
80.82
86.38 2
79.62
80.65
83.86 3
87.44
84.84
88.07 4
84.46
88.85
89.82 5
83.73
83.4
85.47 6
81.6
83.55 7
87.16
89.19
84.54 8
86.42
85.39
87.86 9
86.92
82.05
89.21 10
82.17
86.85
87.73 11
86.18
85.35
87.91 12
83.64
87.85
88.37 13
84.59
74.74
85.65 14
85.48
88.59 15
88.34
89.6
89.95 16
84.58
80.86 86
Case
State Space (%)
NNARMAX (%) 1
86.38
95.37 2
83.86
94.45 3
88.07
97.14 4
89.82
96.77 5
85.47
96.02 6
84.63
96.63 7
84.54
96.86 8
87.86
97.18 9
89.21
96.06 10
87.73
95.58 11
87.91
97.13 12
88.37
96.67 13
85.65
97.08 14
97.06 15
89.95 16 86
97.26
ARX:
The current output is related to previous and delayed inputs, the previous outputs and white-noise disturbance value.
ARMAX:
The current output is related to previous and delayed inputs, the previous outputs and current and previous white-noise disturbance value.
State Space:
State Space representation of a system replaces an nth order differential equation with a single first order matrix differential equation. 
Linear System Identification
Conclusion
Can generate linear and nonlinear system identification models for RX. Nonlinear system identification shows better prediction.
Trying to optimize nonlinear models to fit different measurement data.
Future work: we will add power supply jitter into the input and build a nonlinear system identification model.