Autors

Gennady Serdyuk, Boris Shelkovnikov

Abstract

Paper describes techniques and example of mixed level mixed mode simulation of complete communication link. Proposed approach uses co-simulation to compute overall link merits, allowing to simulate digital parts of link using existing commercial digital simulator(s) and RF parts using Modulation Harmonic Balance simulator. Simulation example is presented.

Keywords

Harmonic Balance, co-simulation, mixed-level simulation, RF design.

Design    of   RF    link    entails    significant   amount    of simulation   at   different   levels.   System-level   simulation allows  estimating  design  solutions  and  making  first-order estimation  of  link  merits. 

Basing  on   system-level  design, specifications  on  constituting  blocks  are  established  and those blocks are designed. This outlines to-down “waterfall” design   flow.   But, most   often,   such   design   flow   is insufficient,   as   it   does   not   take   into   account   block interaction   and   block   non-idealities,   which   may   take influence onto complete link merits (like bit or symbol error level,  unnecessary  RF  radiation,  etc.). 

To  be  sure  about system properties, system verification have to be performed, circuit element values and global merits of communication link.

In        following         sections       co-simulation        system implementation   is   described.   It   uses   discrete   complex envelopes    technique    for    system-level    simulation    and Modulation   Harmonic   Balance   (MHB)   technique   for circuit-level simulation. Simulation example of circuit-level power    amplifier    model    as    a    part    of    system-level communication link model is presented.

Complex  envelope  technique  is  a  most  widely  used  for communication    system    simulation.    According    to    it, information signal along the system is represented in a form of two orthogonal components – I and Q, which are called inphase and quadrature and considered to be continuous in time.      All   signal      transformations in            system   blocks (dissipation,    filtering,    nonlinear    distortions,    etc.)    are considered as transformations of envelope [3].

Convenient  representation  for  envelope  components  is discrete  representation  of  continuous  complex  functions. After  sampling,  reaction  of  the  block  to  input  may  be defined as:

in  more  general  nonlinear  case,  where  l –  linear  block response,    m    –   nonlinear   block   function,    i          –sample number.   If blocks  constitute directed  graph  without  loops with  incidence  matrix   A , then   resulting  system  response may be written as:

where
w _j (n) -   excitation   components   at   n-th   time sample  and
m_j () -  response  components,    j -  component index in a vector.

At   circuit   level,   RF   and   MW   circuits   in   digital communication   links   are   usually   under   excitation   of complex shape signals with much different time constants. Convenient  way  to  simulate  such  circuits  is  modulation (envelope)    harmonic   balance    (MHB)    [4,5,13].    MHB equations  are  formulated  simultaneously  in  time  domain w.r.t. to “slow” time (information component of excitation) and  in  frequency  domain  w.r.t.  “fast”  component  (carrier):

Here X _k (t) – k-th harmonic component of unknowns  X  as  function  of  time  t , I() –  vector-function  of  nonlinear responses, Q() –   vector-function   of   reactive   nonlinear responses,   L   and   M –  matrices  of  linear  components  of circuit  response:  resistive  and  reactive,   W   -  frequencies matrix,  U_k (t)  – free excitation term,  k - harmonic number.

Considering  equation  interaction,  let  us  allow  Eqs.  (1) and  (2)  to  be  coupled  only  via  their  stimuli w_j (n) and U_k (t_n ) .  So,  any y_n, _j  value  of  vector   Y_n at  (1)  can  be assigned   to U_k (t_n ) and   any X_k (t_n ) can   be   assigned to w_j (n) . Please, note that both values are complex, as both represent complex amplitudes. This simplifies consideration and shows how each part of combined task can be simulated with own specific solver.

Two  ready-made  components  were  chosen  to  build  cosimulation  system:  Matlab/Simulink [10] and Rincon  [11]. Simulink  was  chosen  for  its  extendibility  using  common programming    language    like    C/C++    and    ready-to-use communication   and   DSP   libraries.   Rincon   implements MHB   and   allows   circuits   to   be   defined   with   VHDL- AMS/FD  [8,9,11]  –  extension  of  VHDL-AMS  language, with frequency-domain modeling capabilities. In addition, it can  be  integrated  with  external  tools  via  pipe  interfaces.

Fig. 1. QPSK Link

Fig. 2. Amplifier schematic

Fig. 3. Input and output amplifier spectra.

Simulink’s capability to extend components using C or C++ programming  languages  was  used  to  code  interface  part, which  arranges  simulators  interaction.  Simulink  -  Rincon interaction  is  built  such  way,  that  Rincon  is  considered  as one   of   the   discrete   Simulink   blocks   with   fixed   signal sampling  frequency.  

Simulink   also   is   used   to   perform results visualization, as any circuit variable inside Rincon is available    in    Simulink.  Rincon,    in    turn,    get    stimuli envelopes,   simulates   circuit   and   returns   data   back   to Simulink.  Circuit  element  values,  harmonics  numbers  and additional  data  can  be  passed  into  Rincon  as  function parameters.

To    demonstrate    the    abilities    of    implemented    cosimulation   system,   model   of   communication   link   with QPSK  modulation  (Fig.  1) has been  simulated.  Link  starts with  random  number  generator,  and  then  follows  QPSK modulator  (block  from  Simulink  toolbox),  raised  cosine filter,  power  amplifier,  AWGN  channel  and  demodulator. Power amplifier, being represented at circuit level, has been co-simulated  with  the  whole  system.  Schematic  of  power amplifier is presented at Fig. 2. It is one-transistor MESFET power amplifier with reactive load. Input and output passive circuits   model   matching   circuits   and   interconnections. Schematic is shown with input source and load.

Simulink S-function (“simulink_rincon_caller”) performs all necessary initializations, starts separate process of circuit simulation  using  Modulation  Harmonic  Balance  technique and   performs   required   communication:   input   data   for circuit-level  simulation  are  got  from  Simulink  and,  after simulation,  are  returned  to  it.  That  is  performed  for  each step of Simulink simulation cycle. 16 points per transmitted digit are used in simulation.
 
Simulation results are presented at the following figures. Spectrum  at  input  and  output  of  amplifier  is  presented  at Fig.  3  to  show  regrowth  due  to  amplifier  nonlinearities. Signal  trajectories  before  and  after  amplifier  are  shown  at Fig.  4  and eye diagrams are  shown  at  Fig.  5.  Inphase  and quadrature  components  at  amplifier  input  and  output  are shown at Fig.6. Figure illustrates channel interaction due to amplifier nonlinearity.
Amplifier schematic was taken from [12].

Fig. 4. Signal trajectories after filter and after amplifier.

Fig. 5. Eye diagrams after filter and after amplifier.

Principles  of  implementation  of  multilevel  mixed-mode co-simulation  environment  for communication    link simulation  are  discussed.    Viable  methods  are  considered for  different  levels  of  representation  and  ways  of  their interaction  are presented.  New  implementation  based  onto proposed  approach  for  co-simulation  is  described,  which allows   usage   models   of  different   levels.  

Results   are illustrated   with   mixed-level  mixed-mode simulation example,  which  includes  power  amplifier  operated  under complex  modulated  signals  in  QPSK  RF  communication link. Example allows visualizing signal impairments caused by amplifier nonlinearities.

Fig. 6. Normalized inphase and quadrature components before and after amplifier, time is in ms.