Tutorial on Reliable Modeling and Simulation of Communication Systems

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The Advanced Digital Communication System Modeler (AdvDCSM) software System tool T1 addresses the important Need for a RELIABLE Computational Science and Engineering Systems Tool.

The AdvDCSM System Tool T1 involves the application of Expert System and Intelligent Agent concepts. This "Smart Simulator" technology in T1 is first applied to Coded and UnCoded Digital Communications Systems.

      

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Tutorial on Reliable Modeling and Simulation of Communication Systems

by Darrell A. Nolta
August 13, 2009

Today, many possible powerful and complex Digital Communication (Information-theoretic) systems could be designed and built in an attempt to satisfy a set of System Requirements for a Target (field) design. The physical study, analysis, design, and/or evaluation of such a Real World system with all of its possible channel impairments (corruption) in the laboratory or field is nearly impossible using the scientific approach.

Consider the following points:

1) this prototyping hardware effort (building & testing a laboratory mock-up) would be a very expensive and time consuming endeavor because of the total number of possible system models (apparatus) that might need to considered;

2) the creation/duplication of possible physical channel impairments such as AWGN, Fading, ISI, etc. that would occur in the field operation of a particular system model is an extremely difficult task; and

3) the knowledge and technical skills required to actually build such a hardware prototype in a laboratory is only found in a few universities, corporations or institutions in the world.

These are some of the reasons why engineers, scientists and mathematicians build computer models (software-based) of these systems and simulate (computer-based) their performance of these systems to study, analyze, design and/or evaluate Coding methods to reduce the Error Rate of Information transfer of these systems.

NOT ALL MODELING and SIMULATION SOFTWARE ARE EQUAL!

First, let us look at more details about the obvious importance of the Computational Engineering Approach (Modeling and Simulation) to the study/investigation of complex problems involving digital communication or information-theoretic systems.

C.E. Shannon ushered in the new field of Information Theory when he published the paper entitled "A Mathematical Theory of Communication" in the 1948 Bell Systems Technical Journal. This work began the breakthrough communication (& information-theoretic) system theoretical advances by R.W. Hamming, P. Elias, J.M. Wozencraft, A.J. Viterbi, G.D. Forney, J.A. Heller, J.K. Omura, J.P. Odenwalder and others.

Parallel with these digital communication system theoretical advances, there have been large technological advances in solid-state electronics, fiber optics, computing power and software tools that permitted the implementation of complex channel encoding and decoding systems such as convolutional codes and the Viterbi Decoding algorithm (VA).

Today, with these new technological developments, powerful and complex digital communications systems can be designed and built. These systems can be essentially represented by a system model as shown in a block diagram shown below in Figure 1. Figure 1. A digital communication system model.



The analytical and evaluation issues pertaining to the specification and design of a new digital communication system are numerous and interrelated. The goals of a system designer are to propose realizable system specifications to satisfy the target application requirements and arrive at a system design. These specifications will set limits on system performance and equipment complexity. Three measures of performance are information source bit error rate (BER) or bit error probability, signal-to-noise ratio (SNR) and signaling bandwidth (W).

Given these measures, the designer will focus on making a choice of the source and channel codes, their decoding algorithms, and the modulation signal set and its demodulation scheme. The design issues are complex and intertwined. For example, the BER requirements involved the identification of the information source characteristics (alphabet, probability distribution, and rate R) and the channel impairments which includes the noise characteristics. The required BER, available average received signal power (P_s), and available bandwidth will affect the choice of the channel code, its decoding scheme, the modulation signal set, and its demodulation scheme. The code and modulation scheme must match. Channel noise and carrier phase coherency are very important issues in the design of the demodulator. The demodulator and decoders design can depend on the information source statistics. If the source is equiprobable, ML demodulation and decoding rules can be used. An unequal probable information source dictates that MAP demodulation and decoding be used if the source alphabet distribution is known and an optimal BER is desired.

A critical step in this design evaluation is the determination of the power and bandwidth efficiency of the system. Power efficiency for an additive white Gaussian noise (AWGN) channel is quantified by the required E_b/N₀ where E_b = P_s/R (received energy per information bit) and N₀ (one-sided noise power spectral density) for a given BER level. A measure of the bandwidth efficiency for a waveform channel is R/W. E_b/N₀ and R/W should be evaluated to see if the system's resources of transmitted power and bandwidth are being used efficiently for the given system complexity.

A realizable design is proposed after optimal trade-offs in performance and complexity have been made. System performance must be evaluated to determine if the goals of the design have been satisfied. But accurate characterization of system performance is a complex matter given all of the relationships between the system components.

Because of the today's software tools and computing power, a proposed Digital Communication (or Information-theoretic) system can be evaluated via computer-based modeling and simulation.

The simulator's models include both the deterministic and random processes of the components of a digital communication system. Each model represents a component's inherent nature which may be deterministic; or random; or a combination of both. The source is a random process. The channel encoder and decoder are deterministic operations. The noiseless channel is a deterministic operation. The AWGN channel contains both since the modulation and demodulation are deterministic operations and the additive noise is a random process.

Key Concept: to accurately model these random phenomena, the simulator generates a set of sequences of Independent and Identically Distributed (i.i.d.) random variables as pseudo-random numbers that exhibit the property of i.i.d. randomness. A random sequence of uniformly distributed numbers with a range between 0 and 1 is produced by a random number generator with a very very large period. A Gaussian random number generator converts uniformly distributed random numbers into i.i.d. Gaussian distributed random numbers with zero mean and unit variance.

The fidelity of a random process (es) simulation is dependent on this generation of "perfect" random numbers (perfect: no failure of a statistical test by these random numbers).

Individual probabilistic and deterministic subsystems can be efficiently constructed and integrated together to form a simulation system. Simulated system and subsystem performance can be easily observed and can be compared to design specifications and design issues can be addressed and sorted out with relatively ease.

Note that exact performance analysis will not be available for these complex systems under study or problems under investigation.

Second, let us discuss one of the most important but very unappreciated issues pertaining to the Results of a computer-based Simulation, its Reliability.

Reliability of a Simulated Result is defined as the degree of Confidence in the Validity of that Result.

This Validity is dependent on the Fidelity of a computer model description and its implementation that is derived from a mathematical description that is abstracted from a physical description of a given System Under Study.

First, this Modeling fidelity is dependent on the correctness of the mappings of the physical system and its underlying processes to its three abstractions (representations):

1) physical description;
2) mathematical (&/or heuristical) description; and
3) computational model description.

Second, this Simulation fidelity is dependent on the correctness of the mapping (Machine executed behavior) of the Computer-based User-Specified/Desired System and its components as implemented in a computer program to its Simulated Result.

Thus, a competent student or Engineer/Scientist (User) applying the Computational Engineering approach must answer the following question when reviewing his/her computer-generated results:

Is the Simulated Result (s) Reliable?: Does the computer program result correspond to the simulated behavior of the User-Specified/Desired System as defined by its System Definition/Requirements?

Today, a widespread big problem is the commonly held belief that computer-generated results are valid (one of the fallacies of the computer and software industry). The complex system examples of global warming (human caused warming) and hurricane event (s) (& wind damage) and their associated computer forecasts/predictions via modeling and simulation highlight the importance of this problem.

One must realize that it is possible for a computer simulation to run hours, days or weeks. The duration of this simulation run time is dependent on the complexity of the target system model abstraction and its performance requirements.

The complexity factor determines the computational load (e.g. number of floating-point operations) on the computing engine per a single operational system cycle or trial. This complexity factor for a complicated system model may be time-varying that depends on the nature of the particular subsystem being exercised during a particular trial. And, the operation of the system at a given trial may be conditioned on a previous trial or trials (e.g., a nth order Markov process model).

The performance requirements will dictate the number of trials that must be performed by the computing engine. If the system's key function is probabilistic, this system function will be modeled as a random process. A key assumption for this probabilistic system is that the corresponding random process is a stationary process and an ergodic process, i.e., its probabilities are not time-varying and its time (sample) average converges to the ensemble average as the number of trials approach infinity. For a deterministic system, this convergence is not dependent on probability theory but is dependent on the characteristics of the mathematical models of the system's key functions.

So if the wrong system was constructed and simulated, its simulated results are worthless and the expended engineering effort and time has been wasted. And, of course, given the complexity factor, the student or engineer/scientist will most likely not even realize the worthlessness of the results.

Today, a student or engineer/scientist can use MATLAB®, an ERECTOR SET-like program to construct or develop an application and run it to produce a simulated result. This User may spend a large amount of time and effort in the construction of a complicated application. These actions do not make the results valid or worth anything. And, this User has no assurance of the Reliability of the Simulated Result.

But the AdvDCSM System tool T1 addresses the important Need for a RELIABLE Computational Science and Engineering Systems Tool.

MATLAB® has none of these Reliability Solutions.

Important Note: In the cases where MATLAB® and T1 can be used to produce a set of Simulated Performance Results for a given Coded/UnCoded Digital Communication System, the T1's results can provide an Independent Check on the possible Validity of the results of MATLAB®.

Check out T1 vs. MATLAB® for additional comparison.

The Advanced Digital Communication System Modeler (AdvDCSM) Technology section of this website discusses these Needs. This technology involves the application of Expert System and Intelligent Agent concepts. This "Smart Simulator" technology in T1 is first applied to Coded and UnCoded Digital Communications Systems.

T1 is NOW AVAILABLE as a TRIAL VERSION that will allow you to use T1, a Digital Communication (Information-Theoretic) System Modeling and Simulation software tool, for a Limited Period without Charge and to learn about the valuable utility of T1 in the study, evaluation, and possibly design of certain Complex Digital Communication Systems first hand before purchase.

      

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