Topicality
Telecommunications are one of the most promising areas of modern science and engineering, which is evolving continually. The requirements for telecommunication networks are increasing constantly.
Almost all modern communication systems are digital. Bit error ratio (BER) is one of the estimates of the digital communication systems functioning. BER is the characteristic of the communication system immunity. Bit error ratio is one of the most important ways to assess the quality of communication systems. Therefore the problem of its measuring is relevant.
Modern methods of measuring BER are based on a comparison of received and transmitted bit sequences. It seems that bit error rate measurement is a simple procedure. However some problems appear during the measuring process: the problem of synchronization of receiving and transmitting equipment, data loss problem during the measurement, the problem of long-duration of the measurement and others.
Different hardware and software is used to measure BER. However existing measuring bit error rate methods require some improvement.
Relationship with academic programs, plans, topics
Master’s thesis has been done during 2010-2011 according to the scientific direction of the Donetsk National Technical University Department of “Automatics and Telecommunications”.
Objective
The objective of this work is to study existing methods for measuring the bit error rate and summarize the ways that reduce the duration of measurement.
Tasks
- Researching of the existing methods for measuring the BER
- Researching and mathematical description of the fading influence on the propagation of electromagnetic waves by wireless channel
- Researching of the digital messages optimal reception algorithm
- Substantiation of the concept and mathematical description of the bit error rate recalculation method as a way of reducing the measurement duration
- Modeling and measurement evaluation fault and BER prediction.
Scientific novelty
The scientific novelty of this work lies in the fact that:
- A new method for measuring the bit error rate in the wireless data channel has been developed. It allow to reduce the duration of the measurement process.
- The fault analysis has been done.
- The practical use recommendations of the proposed method for the bit error rate measuring were proposed.
Using a bit error rate for evaluation of the performance of communication systems
The electromagnetic wave in the radio channel is affected by the whole range of factors such as fading. Radio communications are less protected from interference comparing with cable transmission systems. So the measurement errors in wireless communications is very topical [1].
Bit error ratio (BER) is a value that characterizes numerically the effect of noise on a communication system. BER can be used exclusively for digital data transmission systems because the analog system provides work with continuous signals. BER is an estimate of the noise immunity of the communication system [2].
Mathematically the bit error ratio is defined as the ratio of the number of errors to the total number of transmitted bits. It is calculated as follows:
BER = n/N,
n - number of errors;
N - number of transmitted bits.
BER can be defined as the probability that the transmitted data bits will be interpreted incorrectly. The error rate is estimated as the ratio of the number of misinterpreted bits to their total number. The quality of the bit error ratio estimates increases with the increasing of the total number of transmitted bits. In the extreme case when the number of transmitted bits tends to infinity the resulting measurement value coincides with the exact value of probability of error.
Existing methods for bit error rate measuring
Theoretical calculation of the probability of bit error is very convenient especially during the communication systems design. However there should be direct measurements for a realistic assessment of digital transmission systems. Equipment used for testing BER is called Bit Error Ratio Tester (BERT). Generally BERT consists of two main modules: data generator and error detector. Data generator creates a bit sequence that is received by the transmitter for transmission. The receiver receives the signal from the channel and reproduces the bit sequence and transmits it to the error detector. Error detector compares two bit sequences. Each difference between them is treated as an error [3].
Figure 1 - Bit error rate tester block diagram
The BER value fluctuates around a static value of the average error rate over a long period of time. The difference between the measured error rate and long-term average value depends on the number of controllable bits and the duration of the measurement.
Long duration of BER measurement is one of the main problems. When the number of bits is limited the result of BER measurement is not the probability of error but its evaluation. The level of estimate confidence is called the confidence level. It depends on the number of errors and the total number of transmitted bits N as follows [4]:
CL = 1 - eN * BER
The number of bits to be transmitted to measure the BER with a confidence level CL:
N = -ln (1-CL) / BER
Transition from the number of bits transmitted to the duration of BER measurement is obvious:
T =-ln (1-CL) / BER * f,
f - frequency of transmission of a pseudorandom sequence.
Based on these considerations we construct a table which shows the values of the normalized length of the pseudorandom sequence for different number of fixed errors and different confidence levels.
Table 1 - The normalized length (NxBER) sequence that provides a specified confidence level
|
E |
CL = 90% |
CL = 95% |
CL = 99% |
| N x BER |
| 0 |
2.3 |
3 |
4.61 |
| 1 |
3.89 |
4.74 |
6.64 |
| 2 |
5.32 |
6.3 |
8.4 |
For clarity data can be represented as the following figure.
Figure 2 - Plots of the normalized length of the sequence from a confidence level.
Reducing the bit error rate measurement duration in the channel with fading
Potential communications system immunity can be calculated by the following relation [5], [10]:
For a given noise intensity N0 potential immunity of the system depends on the equivalent signals energy
which is equal to the square of the distance between signal points in Hilbert space. For a system with frequency modulation Eэ = 2E so that the minimum probability of error is calculated as
h - signal to noise ratio at the input of the demodulator.
We use the approximated Crump function
Ф (х) = 1 - 1,3 exp (-0.44(x +0.75)2)
The error probability of binary digits at the receiver output takes the form
p = 0.5(1 - Ф(h)) = 0,507 exp(-0.44h2) exp(-0.66h)
The most common method of reducing the duration of the BER measurement is the intentional degradation of the signal to noise ratio [6]. It can be done in two ways: by introducing additional noise into the channel or decreasing the signal.
The second method is more popular today because it provides greater accuracy. Knowing how the bit error rate changes whit the signal-to-noise ratio it can be quite easily measured the actual BER. To use this method the method of modulation and error-correcting coding type used in the communication system must be known. Communication system which is discussed in this work uses a binary frequency shift keying.
Prediction the bit error rate will be done in the following way. Let SNR h12 corresponds to the probability of incorrect reception p1, and signal to noise ratio h22 to bit error ratio p2. The values of h12 and h22 are connected by the relation:
h22 / h12= N
Using the relations we can establish a connection between the values of p1 and p2:
p2 = р1*exp (-0.44(N-1)h12 - 0.66(N0.5-1) h1)
Thus by measuring the value of bit error rate p1 at low signal to noise ratio h12 we can easily calculate the probability of error at p2 level signal to noise at the input of the demodulator h22 = N*h12.
When using this method we make the assumption that the thermal Gaussian noise at the receiver input is the main source of bit errors in the communication system. In the case of wireless communication systems it is required some method of modernization. Spreading the air electromagnetic waves are exposed by such factors as fading [7].
Fading is an important factor. The amplitude of the fading is normally distributed [8]:
μ - mean
σ2 - variance.
The dispersion of this distribution also depends on external factors. But it has no effect on the value of bit error rate [9]. Dispersion of the fading can be neglected.
Signal to noise ratio is numerically equal to the ratio of bit energy Eb to noise power spectral density N0:
h2 = Eб/N0
Bit energy can be calculated as the time integral of the amplitude of the bit period. In other words:
Еб = А2Т,
A - rectangular pulse amplitude
T - duration of one pulse.
Fading is a decreasing of the amplitude of electromagnetic waves. Therefore the signal-noise ratio can be represented as:
Еб = (А - М)2Т,
M – fading depth mean.
Relation according to which we predict the value of BER.
p2 = р1*exp(-0.44(N-1)(А1-М1)2Т/N0 - 0.66(N0.5-1)(А1-М1)(Т/N0)0.5)
A1 - the signal amplitude at which the probability of error is p1,
N0 - noise spectral density,
M - average depth of fading.
M / A = K, then the ratio takes the form
p2 = р1 * exp(-0.44(N-1)(А1-К*А1)2Т/N0 - 0.66(N0.5-1)(А1-К*А1)(Т/N0)0.5),
This ratio can be reduced to:
p2 = р1*exp(-0.44(N-1)(1-К)2h12 - 0.66(N0.5-1)(1-К)h1),
p1 - bit error ratio for a signal to noise ratio h12;
p2 - bit error ratio for a signal to noise ratio h22;
N = h22/ h12.
It must be noted that the use of the above relation is valid only under the assumption that the relative depth of fading V = M / A remains constant when the signal power (М1/А1 = М2/А2).
It is planned to calculate the fault according the proposed method of conversion BER and to make recommendations about its use.
Important note: at the time of writing this abstract the master's project has not been finished yet. The final date is December 31, 2011.The full text and materials on a theme can be received from the author or the tutor of the project after this date.
References
1. Долуханов М. П. Распространение радиоволн. Учебник для вузов. М., «Связь», 1972 - с. 275
2. Бакланов И.Г. Технологии измерений в современной телекоммуникации. - М.: Эко-Трендз, 1998. - 264 с.
3. Andy Baldman. Bit Error Ratio testing: How many bits are enough?, 2003
4. Redd J. Calculating Statistical Confidence Levels for Error Probability Estimates / / Lightwave, April 2000, pp. 110-114.
5. Теория передачи сигналов: Учебник для ВУЗов / Зюко А. Г., Кловский Д. Д., Назаров М.В., Финк Л. М. - М.: Связь, 1980г.
6. Wolaver D.H. Measure Error Rates Quickly and Accurately / / Electronic Design, May 30, 1995, pp. 89-98.
7. Гавриленко В.Г., Яшнов В.А. Распространение радиоволн в Современных системах мобильной связи. Нижний Новгород, 2003.
8. Вопросы дальней связи на коротких волнах. Сб. статей под ред. В. И. Сифорова. М., «Советское радио», 1957.
9. Шур А. А. Характеристики сигналов на тропосферных радиолиния. М., «Связь», 1972.
10. B. Sklar, Digital Communications: Fundamentals and Applications, Englewood Cliffs, New Jersey: Prentice Hall, pp. 773-743, 1988.
