Mixedmode
Simulation of RF
Communication Link
Gennady Serdyuk*, Boris Shelkovnikov **
Abstract – Paper describes techniques and example of mixed level mixed mode simulation of complete communication link. Proposed approach uses cosimulation 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, cosimulation, mixedlevel simulation, RF design.
I. Introduction
Design of RF link entails significant amount of simulation at different levels. Systemlevel simulation allows estimating design solutions and making firstorder estimation of link merits. Basing on systemlevel design, specifications on constituting blocks are established and those blocks are designed. This outlines todown “waterfall” design flow. But, most often, such design flow is insufficient, as it does not take into account block interaction and block nonidealities, 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, which very often brings to new design iterations.
That laborious iterative approach may be alleviated, providing more information t each level of development, so that designers of each block can estimate behavior of their units in realistic system environment.
Multilevel multidomain simulation can make sufficient influence onto overall RF system design process, simplifying it and speeding it up. It allows mix on one simulation environment digital and analog subsystems, which usually constitute modern communication systems. Also, such approach helps in simulation of particular analog blocks in system environment, helping out to create proper excitations and estimate reactions. Another one important feature of such approach is ability to match circuit elements in circuitlevel simulation to fit system merits.
Many authors paid their attention to this topic [1,2,14]. Similar objectives also can be met using macromodeling, but those approach does not allow to establish links between circuit element values and global merits of communication link.
In following sections cosimulation system implementation is described. It uses discrete complex envelopes technique for systemlevel simulation and Modulation Harmonic Balance (MHB) technique for circuitlevel simulation. Simulation example of circuitlevel power amplifier model as a part of systemlevel communication link model is presented.
II. Simulation Techniques
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:
_{} (1)
for linear blocks or as:
_{} (2)
in more general nonlinear case, where _{ }– linear block response, _{ } – nonlinear block function, _{ } –sample number. If blocks constitute directed graph without loops with incidence matrix _{ }, then resulting system response may be written as:
_{} (3)
where _{ }  excitation components at nth time sample and _{ } response components, _{ } 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):
_{} (4)
Here _{ }– kth harmonic component of unknowns _{ } as function of time _{ }, _{ }– vectorfunction of nonlinear responses, _{ }– vectorfunction of reactive nonlinear responses, _{ } and _{ }– matrices of linear components of circuit response: resistive and reactive, _{ }  frequencies matrix, _{ } – free excitation term, _{ } harmonic number. It is an extension of Harmonic Balance technique [6,7,9].
MHB Eq. (4) can be sampled in discrete moments of time of Eq. (3). That will allow substituting terms of Eq. (4) in Eq. (3) composing equations into one system.
Considering equation interaction, let us allow Eqs. (1) and (2) to be coupled only via their stimuli _{ }and _{ }. So, any _{ }value of vector _{ } at (1) can be assigned to _{ } and any _{ } can be assigned to_{}. 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.


III.
Cosimulation System Implementation




Two
readymade 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
readytouse communication and DSP libraries. Rincon implements MHB
and allows circuits to be defined with VHDLAMS/FD [8,9,11] –
extension of VHDLAMS language, with frequencydomain modeling
capabilities. In addition, it can be integrated with external tools
via pipe interfaces. 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.
IV. QPSK Link Simulation
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 cosimulated with the whole system. Schematic of power amplifier is presented at Fig. 2. It is onetransistor 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
Sfunction (“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 circuitlevel 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].
V. Conclusion
Principles of implementation of multilevel mixedmode cosimulation 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 cosimulation is described, which allows usage models of different levels. Results are illustrated with mixedlevel mixedmode 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.



References
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