Implementation Of Behavioral Models In System Level Environements ...
Proceedings of the World Congress on Engineering 2007 Vol I
WCE 2007, July 2 - 4, 2007, London, U.K.
Implementation of Behavioral Models in System
level environements and RF circuit-system
Co-simulation
A. Bennadji, E. Ngoya, R. Quéré.
Abstract— The verification of the system performances becomes
integrals in system environment. These models have proven to
of prime importance and notably with the emergence of the soc, in
be accurate for all types of signals and their extraction is
which, the spurious couplings between the functional circuits can
affordable in common circuit simulators and measurement
be critical. the needs in terms of system simulation tools become
benches.
thus very important. This paper is divided into two parts, the first
part presents a method to implement the volterra and nonlinear
In an effort to improve modeling accuracy, we have
impulse response models in matlab/simulink environment. The
developed a co-simulation interface that allows the system
second part presents a co-simulation interface between
simulator to access a circuit simulator for each time sample. In
Matlab/Simulink and Goldengate (Agilent Technologie) circuit
our example we have considered co-simulation between
simulator.
Matlab/Simulink and Goldengate (Agilent technologie) circuit
simulator.
Index Terms— System simulation environment, Volterra Model,
Nonlinear impulse response.
The paper is structured as follows, in a first section, we will
briefly present the numerical implementation of Volterra and
nonlinear impulse model in system-level environment. The
I. INTRODUCTION
section III describes the numerical implementation of these
models in Matlab/Simulink environment. The co-simulation
The applications of modern wireless communications
interface between system simulator and circuit simulator is
require the reduction of the cost and the time of the design
described in section IV. Some practical results will be presented
process in order to answer to the demand of the commercial
in section V.
marketplace. If nowadays, the top-down process is suitable, the
verification of the full system performances suffers from a lack
II. NUMMERICAL IMPLEMENTATION OF VOLTERRA MODEL AND
of system simulation tools able to predict the nonlinear effects.
NONLEANER IMPULSE RESPONSE MODEL
The accuracy of the simulations of communication systems and
nonlinear circuits is in general dependent on the availability of
Some works have been reported in last years about several
models able to describe the behavior of the different
modeling approaches based on Volterra-Wiener theory [1-5], on
components with a high level of precision. These models must
nonlinear time series [6] or on empirical structures. In
be able to predict the influence of nonlinear effects (saturation,
particular, behavioral models based on Volterra series showed
memory effects, mismatches phenomena and noise). Moreover,
their excellent capacities to reproduce the effects of short-term
they must be associated to simulation algorithms able to handle
memory (Volterra model) [7] and long-term memory (nonlinear
the information contained in these models. These two points are
impulse response model) [8]. The constitutive equations of
nowadays an important research subject in order to calculate
these two models are expressed respectively as follows (1) and
reliable link budgets.
(2) :
In this context, this paper presents a methodology for the
BW / 2
1
Ω
Y%(t) =
.
∫
%
Ω % Ω
Ω (1)
V
H ( X(t) , ).X ( ). j t
e
.d
implementation of the models based on nonlinear convolution
2π −BW /2
Tm
Y% (t) = ∫
%
−τ τ % −τ τ (2)
R
h { X (t ) , }.X (t ).d
0
Where X% (t) and Y%(t) refer to the complex envelope
Manuscript received January 12, 2007.
representation of the band pass input and output signals. BW is
Abderrazak Bennadji, Edouard Ngoya and Raymond Quéré are with the
Research Institute XLIM, Unité Mixte de Recherche Centre National de la
the signal bandwidth,
V
H ( )
L is the Volterra kernel and
Recherche Scientifique 6172, University of Limoges, 87060 Limoges, France
R
h ( )
(Phone: (33)-555-457-734; fax: (33)-555-457-666
L is the impulse response.
e-mail : abderrezak.bennadji@xlim.fr, edouard.ngoya@xlim.fr).
ISBN:978-988-98671-5-7
WCE 2007
Proceedings of the World Congress on Engineering 2007 Vol I
WCE 2007, July 2 - 4, 2007, London, U.K.
The computation of the integrals in Eq. (1) and Eq (2) can’t
The coefficients of the linear filters are synthesized by the Padé
be based on the classical integration formulas like
approximation [9].
Newton-Côtes formulas. Indeed, the use of such techniques can
lead to a large consumption of CPU time and memory resources.
III. SIMULINK IMPLEMENTATION
The basic idea, to circumvent this problem, is to expand the
Simulink is a graphical extension to MATLAB for modeling,
impulse response R
h ( )
L and the Volterra kernel V
H ( )
L in
simulating, and analyzing dynamic systems. It supports linear
series of functions, like below:
and nonlinear systems, modeled in continuous time, sampled
K
time, or a hybrid of the two [10].
H
X t ,
. f
X t
(3)
V { % ( ) Ω} = ∑ α k (Ω ) k ( % ( ) )
k =0
The Volterra and nonlinear response impulse models are
K
written in C++ language and are then interfaced using the
h
X% λ ,t = ∑ β t . f
X% λ
(4)
R {
( ) }
k ( )
k (
( ) )
Simulink C MEX S-Function [11].
k =0
Where f L are well chosen basis function, we have
The figure 3 shows the flowchart which recalls the advance of
k (
)
our principle of modeling. We have developed two data
chosen in our example the simplest case of f ( )
2.k
L = X
.
k
processing modules; a module which carries out the calculation
Inserting (3) into (1) and (4) into (2), we find respectively the
of the filters’ coefficients and a module which carries out the
expression (5) and (6).
execution of the model in Simulink.
K
+BW / 2
1
The files resulting from measurement or simulation must
%
Y (t) =
∑.f { %X (t)}. ∫ α (Ω). %X (Ω) jΩ..t (5)
k
k
.e
.dτ
have a standard format (.dat). They contain all information of
2 π
. k 0
=
−BW / 2
the extracted data of the model (Volterra or nonlinear impulse
K Tm
response). Following data processing with the extraction
Y% (t) = ∑ ∫ β τ
%
−τ
%
−τ τ (6)
k ( ) . fk { X (t
)}.X (t ).d
module, the model is completely defined by a header file (.head)
k 0
= 0
containing information on the linear filters. During simulation,
The figure 1 and 2 illustrate respectively the representation of
the execution module reads these header files.
the Volterra model and the nonlinear impulse response model.
The models’ structures become basic cells called Wiener (linear
filters α L follow-up by static nonlinearity f L ) or
i (
)
i (
)
Hammerstein (static nonlinearity f L follow-up by linear
Ge
G n
e e
n r
e a
r t
a i
t o
i n
o of
o
f t
h
t e
h
e m
o
m d
o e
d l
e
l
i (
)
filters β L ).
i (
)
C+
C +
+
+l
a
l n
a g
n u
g a
u g
a e
g
α
f
X%
X
t
Si
S m
i u
m l
u a
l t
a i
t o
i n
o
n
Da
D t
a a
t
a e
x
e t
x r
t a
r c
a t
c i
t o
i n
o
0 (
(t ) )
0
α t
0 ( )
( ( )
t
0 ( )
~
He
H a
e d
a e
d r
e
r f
i
f l
i e
l
X (t
( )
Da
D t
a a
t
.d
. a
d t
a
pr
p o
r c
o e
c s
e s
s i
s n
i g
.h
. e
h a
e d
ng
a
X%
X (t )
~
Y (t
( )
+
Me
M a
e s
a u
s r
u e
r m
e e
m n
e t
n
α t
k ( )
k (
f
X%
X
t
Si
S m
i u
m l
u a
l t
a i
t o
i n
o
n
k (
(t ) )
k (
( )
Fig. 1. Volterra model.
.h
. e
h a
e d
a
He
H a
e d
a e
d r
e
r f
i
f l
i e
l
f
X%
X t
0 (
( ) )
0 (
( )
β t
0 ( )
0 (
~
Re
R
e
Re
R
e
X (t )
Si
S m
i u
m l
u i
l n
i k
n
Im
I
m
Im
I
m
Bl
Bo
l c
o k
c
X%
X (t )
~
Y (t )
+
β t
Fig. 3. Principle of modeling.
k ( t )
k (
f
X%
X t
k (
( ) )
k (
( )
Fig. 2. Nonlinear impulse response model
ISBN:978-988-98671-5-7
WCE 2007
Proceedings of the World Congress on Engineering 2007 Vol I
WCE 2007, July 2 - 4, 2007, London, U.K.
Fig. 4. Communication Chain (Satellite Link)
In co-simulation, the system simulator instantiates an or
Figure 6 shows the ACPR comparison between the AM/AM
several Envelope Transient [12] circuit engines to compute the
AM/PM, Volterra and response impulse models with the results
output signals of the critical parts of the system. The interface
obtained from a co-simulation. The agreement between the
between the two simulators is based on a parent/child
response impulse model and the co-simulation is fairly good, the
interaction (figure 5). Simulink acts as the parent simulator,
AM/AM AM/PM and the Volterra models give predictions that
which calls GoldenGate (Agilent technologie) at the beginning
are 4 to 7 dB off. This figure shows also that the Volterra model
of the simulation as its child. The co-simulated amplifier block
dedicated to take into account short term memory effects is not
is instantiated into Simulink model thanks to a bloc based on a C
able to predict accurately the ACPR, because, in this case the
MEX S-Function, during the simulation, the two simulation
QAM signal is stimulating mainly long term memory effects.
kernels are synchronized and share data on their I/O. On the
Simulink side, a special S-Function block acts as the coupling
System
m Simulator (S
( imu
m link)
element and it is configured for shared memory communication
between Simulink and GoldenGat (Agilent technologie),
Ampl
p ifi
f er
e
Circ
r uit Simulator r
running on a single computerNumber equations consecutively
(G
( o
G ldenGa
G te)
with equation numbers in parentheses flush with the right
margin, as in (1). First use the equation editor to create the
Bi
B d
i e rc
r tio
i nel
l Co
C mmu
m nic
i at io
i n
equation.
Ampl
p ifi
f er
e
We have run a Simulink simulation using alternatively the
models presented above and the co-simulation interface for a
satellite communication chain. This chain represents a satellite
link composed by a Satellite Downlink Transmitter, Downlink
Path, and Ground Station Downlink Receiver (figure 4). The
OL
signal transmitted over the channel is 16-QAM waveform flows
with speed of 5 Mbits/s, the carrier frequency of the link equal to
8 GHz. The Volterra kernel and the impulse response of the
Fig. 5. Co-simulation principle
LNA (operating at 1.96 GHz) located after the reception
antenna were extracted from GoldenGateTM simulations.
ISBN:978-988-98671-5-7
WCE 2007
Proceedings of the World Congress on Engineering 2007 Vol I
WCE 2007, July 2 - 4, 2007, London, U.K.
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AM
A
M /
A
/ M
A
M A
M
A /
M P
/ M
P
M m
o
m d
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d l
e
Vo
V l
o t
l e
t r
e r
r a
r
a m
o
m d
o e
d l
e
l
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Co-simulation
AM/AM AM/PM model
Complete chain
1 h.12 min
14 sec
simulation time
Volterra model
Nonlinear impulse model
2 min. 18 sec
2 min. 23 sec
Table. 1. Simulation performances.
We have shown that nonlinear convolution integral based
model can be efficiently implemented in system simulators,
guarantying both simulation speed and higher accuracy.
Combining a DSP behavioral Simulink simulator in a
cosimulation environment with a time domain nonlinear circuit
simulator in the complex envelope domain increases simulation
flexibility and improves accuracy
ACKNOWLEDGMENT
The authors are grateful to Dr. A. Soury of Agilent
Technologies for editing and fruitful suggestions to the
manuscript.
ISBN:978-988-98671-5-7
WCE 2007
