ber simulation, Monte Carlo method, reliability

This paper introduces the basic principle and basic principle of using Monte Carlo method to simulate the BER.

1. Introduction

BER is an important index of performance evaluation of communication system, and the BER is a fixed value in a given channel and coding mode. In a few cases, the theoretical error rate can be obtained by theoretical deduction, but in most cases, the theory error rate cannot be pushed, so it is often considered that the Monte Carlo method is used to simulate the BER. (Error bit rate, BER same)

Monte Carlo method is a kind of computational method that obtains numerical solution by random sampling. The error rate, that is, the probability of transmission errors under given conditions, can be approximated to the ratio between the number of errors and the total number of codes, so it is easy to solve the numerical solution by Monte Carlo method. The basic principles are described in the next section.

2. Fundamentals

Refer to Wikipedia, the basic steps of the Monte Carlo method include

1. Define all possible inputs on a given domain
2. Randomly generate input values on a given field according to the probability distribution of the input
3. The input values are processed according to the specified calculation method
4. Calculation results

So the corresponding BER simulation of communication system, the concrete steps are

1. Randomly generate (meet the required) plaintext
2. Encrypt and modulate with a given algorithm
3. Randomly generate (meet the required) channel noise
4. The receiving signal is computed and the decision is demodulated and decoded by the given algorithm.
5. Calculate error/frame/bit

At least for the communication system BER simulation, this process is very simple and easy to understand, it can be simply considered as a real communication system of the mathematical equivalent simulation process.

3. Accuracy

A fundamental and important question is how reliable is the simulation results? Obviously, the theoretical ber is a constant under given conditions, but the results of each simulation are different. Assuming that the theoretical error rate is, the estimated value of the Monte Carlo method is, then we are generally concerned about the probability in the range of how large. Before answering this question, first analyze the probability distribution. Yes

Which is the error code word count, is the total code word count. Error-Correcting codes are not considered here, and it is considered that each code word is independent from other code words. Then for a single code word, obey the Bernoulli distribution, the probability of error occurs. , and there is

When large enough, the two-item distribution is approximate to the Gaussian distribution, so the approximate mean is the Gaussian distribution of the variance. At this point, you can answer the following questions

• When given, the reliability of the BER is obtained by simulation.
• Specify reliability requirements, calculate values
• If large enough, the value of how much to make the reliability to meet the requirements

Here we first define reliability/reliability, that is, according to the probability falls on the interval, this probability is called the confidence level, the interval is the confidence interval. A simple introduction from the Baidu Encyclopedia for

"In statistics, the confidence interval (Confidence interval) of a probabilistic sample is an interval estimate of an overall parameter of the sample. The confidence interval shows that the true value of this parameter has a certain probability of falling around the measured result. The confidence interval gives the degree of credibility of the measured value of the measured parameter, which is the "certain probability" as previously required. This probability is called the confidence level. "--Baidu Encyclopedia

This can be pushed

Which is the cumulative probability density of the normal distribution. When given, given the confidence level, you can look up the table to push the precision, given, can calculate the confidence degree. In the same vein, two other problems can be solved.

4. Reference

Monte Carlo method

Confidence interval

ber simulation, Monte Carlo method, reliability