continuous channel

Channels, when a continuous signal is received at the input of which, at its output, the signal will also be continuous, are called continuous. They are always part of a discrete channel. Continuous channels are, for example, standard telephone communication channels (voice frequency channels - FC) with a bandwidth of 0.3 ... 3.4 kHz, standard broadband channels with a bandwidth of 60 ... 108 kHz, physical circuits, etc. The channel model can be represented in the form of a linear quadripole (Figure 3.4)

Figure 3.4 - Model of a linear continuous channel

In order to match the encoder and decoder of the channel with a continuous communication channel, signal conversion devices (SCD) are used, which are switched on during transmission and reception. In a particular case, this is a modulator and a demodulator. Together with the communication channel UPS form discrete channel (DC), i.e. a channel designed to transmit only discrete signals.

A discrete channel is characterized by the rate of information transfer, measured in bits per second (bps). Another characteristic of a discrete channel is the modulation rate, measured in baud. It is determined by the number of elements transferred per second.

Binary balanced channel. A binary symmetric channel (BSC) is a special case of a discrete memoryless channel whose input and output alphabets consist of binary elements (0 and I). The conditional probabilities are symmetrical.

Equation (3.6) expresses the so-called transition probabilities.

Markov models of DC. Channel states can be distinguished by the probability of error in each of the states. Changes in the error probability can, in turn, be associated with physical causes - the appearance of interruptions, impulse noise, fading, etc. The state sequence is a simple Markov chain. A simple Markov chain is a random sequence of states when the probability of a particular state in i- that point in time is completely determined by the state c i-1 V ( i- 1) th moment. The equivalent circuit of such a channel is shown in Figure 3.5.

Figure 3.5 - Equivalent circuit of a discrete symmetrical channel when described by a model based on Markov chains

Hilbert model. The simplest model based on the use of the mathematical apparatus of Markov chains is the error source model proposed by Hilbert. According to this model, the channel can be in two states - good (state 1) and bad (state 2). The first state is characterized by the absence of errors. In the second state, errors appear with a probability p osh.

In accordance with the definition given earlier, a discrete channel is a set (Fig. 2.1) of a continuous channel (NC) with signal conversion devices (SCD) switched on at its input and output.

The main characteristics that determine the quality and efficiency of data transmission are the speed and fidelity of transmission.

Transmission speed V information is equal to the amount of information transmitted over the channel per unit time , where mc-number of signal positions, t0- duration of a single signal element. For two position signals.

The value determines the number of elements transmitted over the channel per second, and is called the modulation rate (Baud). So for binary systems baud rate and modulation rate are numerically the same.

The fidelity of data transmission is estimated by the probabilities of erroneous reception of single elements p0 and code combinations p kk.

Thus, the main task of a discrete channel is to transmit digital signals data over the communication channel with the required speed V and error probability p 0 .

To clarify the process of implementing this task, let us imagine the structure of a discrete channel (Fig. 2.2), indicating on it only those blocks of the UPS that determine system characteristics discrete channel.

The channel input receives digital data signals with duration t0 with speed B bps In the UPS TX, these signals are converted in frequency (modulated by M and G) and pass through the PF TX bandpass filter and the US output amplifier, from the output of which they are transmitted to the communication channel with a certain level P with in and spectrum width D.F. c.

The communication channel (including connecting lines) is characterized by the bandwidth D.F. to, residual attenuation a ost, residual attenuation irregularities Da stop and group transit time (GWP) Dt gvp in the channel band .

In addition, there is interference in the channel. Interference is any random effect on the signal that degrades the fidelity of the reproduction of the transmitted message. Interference is very diverse in its origin and physical properties.

In general, the influence of interference n(t) on signal u(t) can be expressed by the operator z=y(u,n).

In the special case when the operator y degenerates into the sum z=u+n, the noise is called additive. Additive interference according to its electrical and statistical structures are divided into:

1) fluctuating or distributed in frequency and time,

2) harmonic or concentrated in frequency,

3) impulse or concentrated in time.

Fluctuating interference is continuous in time random process. Most often, it is assumed to be stationary and ergodic with a normal distribution of instantaneous values and zero mean. The energy spectrum of such interference within the analyzed frequency band is assumed to be uniform. Fluctuation noise is usually given spectral density or RMS voltage U p eff in the channel band.

Harmonic interference is additive interference whose spectrum is concentrated in a relatively narrow frequency band, comparable to or even significantly narrower than the signal bandwidth. These interferences are assumed to be uniformly distributed in the frequency band, i.e. the probability of occurrence of this interference in a certain frequency band is proportional to the width of this band and depends on the average number n gp interference exceeding the threshold level medium power signal per unit bandwidth.

Pulse interference is an additive interference, which is a sequence of pulses excited by short-term aperiodic or oscillatory EMF. The moments of appearance of impulse noise are assumed to be uniformly distributed in time. This means that the probability of the appearance of impulse noise during the time interval T proportional to the duration of this interval and the average number n un interference per unit of time, depending on the permissible level of interference. Impulse noise is usually specified by distribution laws with their numerical parameters, or by the maximum value of the product A 0 the duration of the impulse noise on its amplitude. These include short-term breaks (crushing) specified by distribution laws with specific numerical parameters or the average duration of breaks. t lane and their intensity n lane.

If the operator y can be expressed as a product z=ku, Where k(t) is a random process, then the noise is called multiplicative.

In real channels, both additive and multiplicative interference usually occur, i.e. z=ku+n.

At the input of the UPS prm, consisting of a linear amplifier US in, a band pass filter PF pr, a demodulator DM, devices for registering the UR and synchronizing the US with a speed IN a signal-to-noise mixture arrives, characterized by the signal-to-noise ratio q in. After passing the receiving filter PF prm, the signal-to-noise ratio improves somewhat.

In DM, due to interference, the output signals are distorted in shape, the change in which is numerically expressed by the value of edge distortion d cr.

To reduce the probability of error due to the influence of edge distortion or splitting, the signals from the DM output are subjected to gating or integration, which is carried out in the SD under the action of clock pulses generated in the US synchronization device. UR is characterized by corrective ability m ef, and US is the synchronization error e c, synchronization time t sync and synchronism maintenance time t ps.

The issues discussed are being explored in laboratory work No. 3 "Characteristics of a discrete channel".

Control questions to lecture 5

5-1. What channel is called discrete?

5-2. What are the main characteristics that determine the quality and efficiency of data transmission

5-3. How is the rate at which information is transmitted over a channel determined?

5-4. How is modulation rate determined?

5-5. How is the fidelity of the transmission of information over the channel evaluated?

5-6. What characterizes the signals arriving at the input of a discrete channel?

5-7. What characterizes the signals arriving at the input of a continuous channel?

5-8. What are the main characteristics of a continuous channel?

5-9. What is called relative signal strength?

5-10. What is called the absolute level of the signal?

5-11. What is called the measuring signal level?

5-12. What is channel residual attenuation?

5-13. What is the residual attenuation of a channel containing amplifiers?

5-15. What can lead to an excess of signal power at the channel input?

5-16. What is the frequency response of a channel?

5-17. What is the effective bandwidth of a channel?

5-18. What causes the uneven frequency response of the channel?

5-19. What is called group time passing?

5-20. What is a channel FCH?

5-21. How is the non-linear distortion introduced by the channel estimated?

5-22. What is an overload level?

5-23. What does the limitation of the signal spectrum lead to when transmitting over real channels?

5-24. How is the rate limit related to the channel bandwidth in the transmission of modulated signals with two sides?

5-25. How does the nature of the frequency response of the channel affect the bandwidth of the channel?

5-26. How does the nature of the channel PFC affect the channel bandwidth?

5-27. How is the optimal transmission rate for it determined from the frequency response and phase response of the channel?

5-28. What is called interference?

5-29. What kind of interference is called additive?

5-30. What are the types of additive noise?

5-31. That is mathematical model fluctuating noise?

5.32. What is the difference between harmonic noise and fluctuation noise?

5.33. What are the characteristics of harmonic interference?

5.34. What is the difference between impulse noise and harmonic noise?

5.35. What are the characteristics of impulse noise?

5-36. What kind of interference is called multiplicative?

5-37. What type of interference is channel amplifier gain drift?

5-38. What characterizes the signals coming from the input of a continuous channel?

5-39. What serves as a numerical estimate of the waveform distortion at the demodulator output?

5-40. What are the parameters of the synchronization device?

Lecture 6

When studying radio systems, it is also necessary to use discrete channel models. This is due to the fact that in many types of RTS heavy load for the protection of information in conditions of intense interference is the use of coding and decoding methods. To consider problems of this type, it is advisable to deal only with the features of a discrete channel, excluding from consideration the properties of a continuous channel. In a discrete channel, the input and output signals are sequences of pulses representing a stream of code symbols. This determines such a property of a discrete channel that, in addition to restrictions on the parameters of the set of possible signals at the input, the distribution of conditional probabilities of the output signal for a given input signal is indicated. When defining a set input signals there is information about the number various characters T, the number of pulses in the sequence P and, if necessary, the duration T in and Goi, each pulse at the input and output of the channel. In most practically important cases, these durations are the same and, consequently, the durations of any //-sequences at the input and output are the same. The result of interference can be a difference between the input and output sequences. Therefore, for any // it is necessary to indicate the probability that when passing some

random sequence IN the output will be the score IN.

The considered //-sequences can be represented as vectors in ///"-dimensional Euclidean space, in which the operations "addition" and "subtraction" are understood as bitwise summation modulo T and similarly, it defines multiplication by an integer. In the chosen space, it is necessary to introduce the concept of "error vector" E, which is understood as the bitwise difference between the input (transmitted) and output (received) vectors. Then the received vector will be the sum of the transmitted random sequence and the error vector B = B + E. It can be seen from the notation form that the random error vector E is analogous to the noise //(/) in the continuous channel model. Discrete channel models differ in the probability distribution of the error vector. In general, the probability distribution E can be dependent on the implementation of the vector IN. Let us visually explain the concept of the meaning of the error vector for the case /// = 2 - a binary code. The appearance of the character 1 anywhere in the error vector informs about the presence of an error in the corresponding bit of the transmitted //-sequence. Therefore, the number of non-null characters in the error vector can be called the weight of the error vector.

The symmetric memoryless channel is the simplest discrete channel model. In such a channel, each transmitted code symbol can be received erroneously with some probability R and accepted correctly with probability q = 1 - R. If there was an error, instead of the transmitted character 6. any other character can be transmitted with equal probability b.

The use of the term "memoryless" means that the probability of an error in any bit of the "-sequence does not depend on what characters were transmitted before this bit and how they were received.

The probability that a n-dimensional error vector of weight will appear in this channel ?, is equal to

The likelihood that it took place I of any errors located arbitrarily throughout the n-sequence is determined by Bernoulli's law:

Where WITH[ = P/[(!(« - ?)] - binomial coefficient, i.e. number of different combinations ? errors in the "-sequence.

The model of a symmetrical channel without memory (binomial channel) is an analogue of a channel with additive white noise at a constant signal amplitude - its approximation.

An asymmetric memoryless channel differs from a symmetric one in the different probabilities of the transition of symbols 1 to 0 and vice versa, while maintaining the independence of their appearance from the prehistory.

Send your good work in the knowledge base is simple. Use the form below

Students, graduate students, young scientists who use the knowledge base in their studies and work will be very grateful to you.

Posted on http://www.allbest.ru/

Introduction

1. Theoretical part

1.1 Discrete channel and its parameters

1.2 Model of partial description of a discrete channel

1.3 Classification of discrete channels

1.4 Channel models

1.5 Modulation

1.6 Structural scheme with ROS

2. Settlement part

2.1 Determining the optimal length of the code combination, which provides the greatest relative throughput

2.2 Determination of the number of check digits in the code combination, providing a given probability of an undetected error

2.3 Determination of the amount of transmitted information at a given rate T tr and failure criteria t otk

2.4 Determine storage capacity

2.5 Calculation of the characteristics of the main and bypass channels of PD

2.6 Selecting the route of the highway

Conclusion

List of sources used

Introduction

discrete communication information message

The development of telecommunication networks has led to the need for a more detailed study of digital data transmission systems. And the discipline "Digital Communication Technologies" is dedicated to this. This discipline sets out the principles and methods of digital signal transmission, scientific foundations and the current state of digital communication technologies; gives an idea of the possibilities and natural boundaries of the implementation of digital transmission and processing systems; understands the patterns that determine the properties of data transmission devices and the tasks of their functioning.

The purpose of this course work is to master the course "Digital Communication Technologies", gaining skills in solving problems in the methodology of engineering calculations of the main characteristics and teaching methods of technical operation of digital systems and networks;

IN term paper it is necessary to design a data transmission path between the source and the recipient of information using a system with a decisive feedback, continuous transmission and blocking of the receiver, as well as the construction of an encoder and decoder circuit cyclic code using modulation and demodulation using the "System View" package; determination of the amount of transmitted information at a given rate and failure criteria; calculation of the characteristics of the main and bypass discrete channels; construction of a time diagram of the system operation.

The solution of these problems reveals the fulfillment of the main goal of the task - modeling of telecommunication systems.

1 . Theoretical part

1.1 Discrete channel and its parameters

Discrete channel - a communication channel used to transmit discrete messages.

Composition and parameters electrical circuits at the input and output of DC are determined by the relevant standards. Characteristics can be economical, technological and technical. The main ones are specifications. They can be external and internal.

External - informational, technical and economic, technical and operational.

There are several definitions for transfer rate.

Technical speed characterizes the speed of the equipment included in the transmitting part.

where m i is the code base in the i-th channel.

Information transfer rate - related to the bandwidth of the channel. It appears with the advent and rapid development of new technologies. The information rate depends on the technical rate, on the statistical properties of the source, on the type of CS, received signals and interference acting in the channel. The limiting value is the capacity of the COP:

where? F - band COP;

According to the transmission rate of discrete channels and the corresponding UPS, it is customary to subdivide into:

Low-speed (up to 300 bps);

Medium speed (600 - 19600 bps);

High-speed (more than 24000 bps).

Effective transmission rate - the number of characters per unit of time provided to the recipient, taking into account overhead time (SS phasing time, time allocated for redundant symbols).

Relative transfer rate:

Reliability of information transmission - is used due to the fact that in each channel there are extraneous emitters that distort the signal and make it difficult to determine the type of transmitted single element. According to the method of converting messages into a signal, interference can be additive and multiplicative. By form: harmonic, impulse and fluctuation.

Interference leads to errors in the reception of single elements, they are random. Under these conditions, the probability is characterized by the error-free transmission. The transmission fidelity can be estimated by the ratio of the number of erroneous symbols to the total

Often the transmitter's probability turns out to be less than required, therefore, measures are taken to increase the probability of errors, eliminate received errors, include some additional devices in the channel that reduce the properties of the channels, therefore, reduce errors. Improving fidelity is associated with additional material costs.

Reliability - a discrete channel, like any DC, cannot work flawlessly.

A failure is an event that ends in the full or partial womb of a health system. With regard to the data transmission system, a failure is an event that causes a delay in the received message for a time t set>t add. At the same time, t additional in different systems is different. The property of a communication system that ensures the normal performance of all specified functions is called reliability. Reliability is characterized by the mean time between failures Tо, the average recovery time Tv, and the availability factor:

Probability uptime shows the probability with which the system can work without a single failure.

1.2 Model of partial description of a discrete channel

Dependence of the probability of occurrence of a distorted combination on its length n and the probability of occurrence of a combination of length n with t errors.

The dependence of the probability of occurrence of a distorted combination on its length n is characterized as the ratio of the number of distorted combinations to the total number of transmitted code combinations.

This probability is a non-decreasing value of the function n. When n=1, then P=P OSH, when, P=1.

In the Purtov model, the probability is calculated:

where b is the error grouping index.

If b = 0, then there is no error bundling and the occurrence of errors should be considered independent.

If 0.5< б < 0.7, то это пакетирование ошибок наблюдается на кабельных линиях связи, т.к. кратковременные прерывания приводят к появлению групп с большой плотностью ошибок.

If 0.3< б < 0.5, то это пакетирование ошибок наблюдается в радиорелейных линиях связи, где наряду с интервалами большой плотности ошибок наблюдаются интервалы с редкими ошибками.

If 0.3< б < 0.4, то наблюдается в радиотелеграфных каналах.

The distribution of errors in combinations of different lengths also estimates the probability of combinations of length n with t predetermined errors.

Comparison of the results of the calculated probabilities according to formulas (2) and (3) shows that the grouping of errors leads to an increase in the number of code combinations affected by errors of higher multiplicity. It can also be concluded that when grouping errors, the number of distorted code combinations of a given length n decreases. This is also understandable from purely physical considerations. With the same number of errors, packetization leads to their concentration on individual combinations (the error multiplicity increases), and the number of distorted code combinations decreases.

1.3 Classification of discrete channels

Classification of discrete channels can be carried out according to various features or characteristics.

According to the transmitted carrier and signal to the channel, there are (continuous signal - continuous carrier):

Continuous-discrete;

Discrete-continuous;

Discrete-discrete.

Distinguish between the concept of discrete information and discrete transmission.

From a mathematical point of view, a channel can be defined by an alphabet of single elements at the input and output of the channel. The dependence of this probability depends on the nature of the errors in the discrete channel. If there were no errors during the transmission of the i-th single element i=j - if the element received a new element different from j during the reception, then an error occurred.

Channels in which P(a j /a i) does not depend on time for any i and j are called stationary, otherwise - non-stationary.

Channels in which the transition probability does not depend on the value of the previously received element, then this is a channel without memory.

If i is not equal to j, P(a j /a i)=const, then the channel is symmetrical, otherwise it is asymmetric.

Most channels are symmetrical and have memory. Space communication channels are symmetrical, but do not have memory.

1.4 Channel Models

When analyzing CS systems, 3 main models are used for analog and discrete systems and 4 models for discrete systems only.

The main mathematical models of the CS:

Channel with additive noise;

Linear filtered channel;

Linear filtered channel and variable parameters.

Mathematical models for discrete CS:

DCS without memory;

DCS with memory;

Binary symmetric CS;

COP from binary sources.

CS with additive noise is the simplest mathematical model implemented according to the following scheme.

Figure 1.1 - Structural diagram of the COP with additive noise

In this model, the transmitted signal S(t) is affected by additional noise n(t), which may arise from extraneous electrical noise, electronic components, amplifiers or due to the phenomenon of interference. This model applied to any COP, but if there is a damping process, the damping factor must be added to the overall reaction.

r(t)=6S(t)+n(t) (1.9)

The linear filtered channel is applicable to physical channels containing linear filters to limit the frequency band and eliminate the interference phenomenon. c(t) is impulse response linear filter.

Figure 1.2 - Linear filtered channel

A linear filtered channel with variable parameters is characteristic of specific physical channels, such as acoustic CS, ionospheric radio channels, which occur with a time-varying transmitted signal and are described by variable parameters.

Figure 1.3 - Linear filtered channel with variable parameters

Discrete CS models without memory are characterized by an input alphabet or a binary sequence of symbols, as well as a set of input probability of the transmitted signal.

In a DCS with memory, there is interference in the transmitted data packet or the channel is subject to fading, then the conditional probability is expressed as the total joint probability of all elements of the sequence.

Binary symmetric CS is a special case of a discrete memoryless channel, when the input and output alphabets can only be 0 and 1. Therefore, the probabilities are symmetrical.

The DCS of binary sources generates an arbitrary sequence of symbols, while the final discrete source is determined not only by this sequence and the probability of their occurrence, but also by the introduction of such functions as self-information and mathematical expectation.

1.5 Modulation

Signals are formed by changing certain parameters of the physical carrier in accordance with the transmitted message. This process (changing the parameters of the carrier) is called modulation.

The general principle of modulation is to change one or more parameters of the carrier wave (carrier) f(t, b, c, ...) in accordance with the transmitted message. So if the carrier is chosen harmonic oscillation f(t)=Ucos(w 0 t+c), then three types of modulation can be formed: amplitude (AM), frequency (FM) and phase (PM).

Figure 1.4 - Waveforms for binary code for various kinds discrete modulation

Amplitude modulation is proportional to the primary signal x(t) change in the amplitude of the carrier U AM =U 0 +ax(t). In the simplest case of a harmonic signal x(t)=XcosЩt, the amplitude is equal to:

As a result, we have the AM oscillation:

Figure 1.5 - Graphs of fluctuations x(t), u and u AM

Figure 1.6 - AM oscillation spectrum

Figure 1.5 shows the fluctuations x(t), u and u AM . The maximum deviation of the amplitude U AM from U 0 represents the amplitude of the envelope U W =aX. The ratio of the amplitude of the envelope to the amplitude of the carrier (unmodulated) oscillation:

m - is called the modulation factor. Usually m<1. Коэффициент модуляции, выраженный в процентах, т.е. (m=100%) называют глубиной модуляции. Коэффициент модуляции пропорционален амплитуде модулирующего сигнала.

Using expressions (1.12), expression (1.11) is written as:

To determine the spectrum of AM vibrations, let's open the brackets in expression (1.13):

According to (1.14), the AM oscillation is the sum of three high-frequency harmonic oscillations of close frequencies (since<<щ 0 или F<

Oscillations of the carrier frequency f 0 with amplitude U 0 ;

Oscillations of the upper side frequency f 0 +F;

Oscillations of the lower side frequency f 0 -F.

The spectrum of AM oscillations (1.14) is shown in Figure 1.6. The spectrum width is equal to the doubled modulation frequency: ?f AM =2F. The amplitude of the carrier wave does not change during modulation; the amplitudes of the oscillations of the side frequencies (upper and lower) are proportional to the modulation depth, i.e. amplitude X of the modulating signal. When m=1, the oscillation amplitudes of the side frequencies reach half the carrier (0.5U 0).

The carrier wave does not contain any information, and it does not change during the modulation process. Therefore, we can limit ourselves to the transmission of only sidebands, which is realized in communication systems on two sidebands (DBS) without a carrier. Moreover, since each sideband contains complete information about the primary signal, transmission of only one sideband (SSB) can be dispensed with. Modulation that results in single sideband oscillations is called single sideband (SW).

Obvious advantages of DBP and OBP communication systems are the possibility of using the transmitter power to transmit only the side bands (two or one) of the signal, which makes it possible to increase the range and reliability of communication. With single-sideband modulation, in addition, the width of the spectrum of the modulated oscillation is halved, which makes it possible to correspondingly increase the number of signals transmitted over the communication line in a given frequency band.

Phase modulation is proportional to the primary signal x(t) change in the phase q of the carrier u=U 0 cos(w 0 t+c).

The oscillation amplitude during phase modulation does not change, therefore, the analytical expression for the FM oscillation

If the modulation is carried out by a harmonic signal x(t)=XsinШt, then the instantaneous phase

The first two terms (1.17) determine the phase of the unmodulated oscillation, the third - the change in the phase of the oscillation as a result of modulation.

The phase-modulated oscillation is clearly characterized by the vector diagram in Figure 1.7, built on a plane rotating clockwise with an angular frequency u 0 . An unmodulated oscillation corresponds to a moving vector U 0 . Phase modulation consists in a periodic change with a frequency W in the rotation of the vector U relative to U 0 by an angle? c (t) \u003d aXsin Wt. The extreme positions of the vector U are indicated by U" and U"". The maximum deviation of the phase of the modulated oscillation from the phase of the unmodulated oscillation:

where M is the modulation index. The modulation index M is proportional to the amplitude X of the modulating signal.

Figure 1.7 - Vector diagram of a phase-modulated oscillation

Using (1.18), we rewrite the FM oscillation (1.16) as

u \u003d U 0 cos (u 0 t + c 0 + Msin t) (1.19)

Instantaneous frequency of PM oscillation

u \u003d U (u 0 + MU cos t) (1.20)

Thus, the FM oscillation at different instants of time has different instantaneous frequencies that differ from the frequency of the carrier oscillation w 0 by the value?

Frequency modulation consists in a proportional change to the primary signal x(t) of the instantaneous frequency of the carrier:

w=w 0 +ax(t) (1.21)

where a is the proportionality factor.

Instantaneous phase of FM oscillation

The analytical expression of the FM oscillations, taking into account the constancy of the amplitude, can be written as:

Frequency deviation - its maximum deviation from the carrier frequency w 0, caused by modulation:

W A = aX (1.24)

The analytical expression for this FM oscillation is:

The term (?sh D /sh)sinsht characterizes the phase change resulting from the FM. This allows us to consider the FM oscillation as a PM oscillation with a modulation index

and write it like this:

From what has been said, it follows that FM and FM oscillations have much in common. So an oscillation of the form (1.27) can be the result of both a FM and a FM harmonic primary signal. In addition, FM and FM are characterized by the same parameters (modulation index M and frequency deviation? f D), interconnected by the same relationships: (1.21) and (1.24).

Along with the noted similarity of frequency and phase modulation, there is also a significant difference between them, associated with the different nature of the dependence of the values M and?f D on the frequency F of the primary signal:

With PM, the modulation index does not depend on the frequency F, and the frequency deviation is proportional to F;

With FM, the frequency deviation does not depend on the frequency F, and the modulation index is inversely proportional to F.

1.6 Structural diagram with ROS

Transmission with ROS is similar to a telephone conversation in conditions of poor hearing, when one of the interlocutors, having poorly heard a word or phrase, asks the other to repeat them again, and with good audibility, either confirms the fact of receiving information, or in any case, does not ask for repetition .

The information received via the OS channel is analyzed by the transmitter, and based on the results of the analysis, the transmitter makes a decision to transmit the next code combination or to repeat the previously transmitted ones. After that, the transmitter transmits service signals about the decision made, and then the corresponding code combinations. In accordance with the service signals received from the transmitter, the receiver either issues the accumulated code combination to the recipient of the information, or erases it and stores the newly transmitted one.

Types of systems with ROS: systems with waiting for service signals, systems with continuous transmission and blocking, systems with address transfer. Currently, numerous algorithms for operating systems with OS are known. The most common systems are: with ROS with the expectation of an OS signal; with unaddressed repetition and blocking of the receiver with address repetition.

Post-pattern waiting systems either wait for a feedback signal or transmit the same code pattern, but start transmitting the next code pattern only after receiving an acknowledgment for the previously transmitted pattern.

Blocking systems transmit a continuous sequence of code combinations in the absence of OS signals for previous S combinations. After errors are detected in the (S + 1)th combination, the system output is blocked for the time of receiving S combinations, S previously received combinations are erased in the memory device of the PDS system receiver, and a callback signal is sent. The transmitter repeats the transmission of the S most recently transmitted patterns.

Systems with address repetition are distinguished by the fact that code combinations with errors are marked with conditional numbers, according to which the transmitter retransmits only these combinations.

Algorithm for protection against overlap and loss of information. OS systems can discard or use the information contained in the rejected code combinations in order to make a more correct decision. Systems of the first type are called systems without memory, and systems of the second type are called systems with memory.

Figure 1.8 shows a block diagram of a system with ROS-exp. The system with ROS-ozh operates as follows. Coming from the information source (II), m - elemental combination of the primary code through a logical OR is recorded in the transmitter drive (NK 1). At the same time, control symbols are formed in the encoder (CU), which represent the block control sequence (BPS).

Figure 1.8 ? Structural diagram of a system with ROS

The resulting n - element combination is fed to the input of the direct channel (PC). From the output of the PC, the combination enters the inputs of the decision device (RU) and the decoding device (DCU). The DCU, based on m information symbols received from the direct channel, forms its block control sequence. The decision device compares two CPBs (received from the PC and generated by the DCU) and makes one of two decisions: either the information part of the combination (m-element primary code) is issued to the recipient of the PI information, or it is erased. At the same time, the information part is selected in the DCU and the received m-element combination is recorded in the receiver drive (NC 2).

Figure 1.9 - Structural diagram of the algorithm of the system with ROS NP

In the absence of errors or undetected errors, a decision is made to issue information to the PI and the receiver control device (CU 2) issues a signal that opens the AND 2 element, which ensures the issuance of an m-element combination from NK 2 to the PI. The feedback signal generator (UFS) generates a combination reception confirmation signal, which is transmitted to the transmitter via the reverse channel (OK). If the signal coming from OK is decoded by the feedback signal decoding device (VDS) as a confirmation signal, then the appropriate pulse is applied to the input of the transmitter control device (CU 1), according to which the CU 1 makes a request from the AI of the next combination. The logic circuit AND 1 in this case is closed, and the combination recorded in the NC 1 is erased when a new one arrives.

In case of detection of errors, the RU decides to erase the combination recorded in the NC 2, while the CU 2 generates control pulses that lock the AND 2 logic circuit and form a callback signal in the UFS. When the UDS circuit decrypts the signal arriving at its input as a callback signal, the control unit 1 generates control pulses, with the help of which the combination stored in the NK 1 is retransmitted through the AND 1 , OR and KU circuits in the PC.

2 . Settlement part

2.1 Determining the optimal codeword length that provides the highest relative throughput

In accordance with the option, we write the initial data for the implementation of this course work:

B = 1200 Baud - modulation rate;

V = 80,000 km/s - the speed of information propagation through the communication channel;

P osh = 0.5·10 -3 - error probability in a discrete channel;

P but = 3·10 -6 - the probability of the initial error;

L = 3500 km - distance between source and receiver;

t otk = 180 sec - failure criterion;

T lane \u003d 220 seconds - a given pace;

d 0 = 4 - minimum code distance;

b = 0.6 - error grouping coefficient;

AM, FM, FM - modulation type.

Let's calculate the throughput R corresponding to the given value n, according to the formula (2.1):

where n is the length of the code combination;

Table 2.1

From Table 2.1 we find the largest throughput value R=0.997, which corresponds to the length of the code combination n = 4095.

2.2 Determination of the number of check digits in the code combination, providing a given probability of an undetected error

Finding the parameters of the cyclic code n, k, r.

The value of r is found by the formula (2.2)

The parameters of the cyclic code n, k, r are connected through the dependence k=n-r. Hence k=4089 characters.

2.3 Determining the amount of transmitted information at a given rate T laneand rejection criteriat open

The amount of transmitted information is found by the formula (2.3):

W = 0.997 1200(220 - 180) = 47856 bits.

We use the obtained value, modulo, РWР = 95712bit.

2.4 Determine storage capacity

The storage capacity is determined by formula (2.4):

where t p =L/V - signal propagation time over the communication channel, s;

t k =n/B - duration of the code combination of n bits, s.

2.5 Calculation of the characteristics of the main and bypass channels of PD

The distribution of the probability of occurrence of at least one error over the length n is determined by the formula (2.5):

The probability distribution of errors of multiplicity t and more over length n is determined by formula (2.6):

where t about =d 0 -1 - the time of the bypass data transmission channel or the multiplicity of one error on the length n.

The probability of occurrence of the initial error is determined by the formula (2.7):

The probability of detecting an error code is determined by the formula (2.8):

Code redundancy is determined by formula (2.9):

The rate of the encoded symbol in the input data transmission channel is determined by the formula (2.10):

The average relative data transfer rate in a system with ROS is determined by the formula (2.11):

where f 0 - time reciprocal to the maximum speed of the channel or time reciprocal to the modulation rate (2.12);

t exp - waiting time when transmitting information in a channel with ROS.

where t ak and t ac are the time difference in the asynchronous operation mode for the code error in the channel and for the main signal, respectively (2.14);

The probability of correct reception is determined by the formula (2.15):

2.6 Selecting the route of the highway

On the geographical map of the Republic of Kazakhstan, we select two points that are 3500 km apart from each other. Due to the fact that the territory of Kazakhstan does not allow choosing such points, we will lay the highway from south to east, from east to north, from north to east, and then from east to south (Figure 2.1). The starting point will be Pavlodar, and the final point - Kostanay, therefore, our highway will be called "Pavlodar - Kostanay".

We will divide this highway into sections with a length of 500-1000 km, and also establish crossing points, which we will tie to large cities of Kazakhstan:

Pavlodar (starting point);

Ust-Kamenogorsk;

Shymkent;

Kostanay.

Figure 2.1 - Highway with checkpoints

Conclusion

In this course work made the basic calculations for the design of cable communication lines.

In the theoretical part of the work, the L.P. Purtov model, which is used as a model for a partial description of a discrete channel, was studied, a structural diagram of the npbl ROS system was built and the operating principle of this system was described, and relative phase modulation was also considered.

In accordance with the given variant, the parameters of the cyclic code n, k, r are found. The optimal codeword length n is determined, which ensures the highest relative throughput R, as well as the number of check bits in the codeword r, which provide a given probability of not detecting an error.

For the main data transmission channel, the main characteristics are calculated (the probability distribution of at least one error over a length n, the probability distribution of errors of multiplicity t or more over a length n, code rate, code redundancy, error detection probability, etc.).

At the end of the work, the route of the data transmission line was selected, along the entire length of which points of data transfer were selected.

As a result, the main task of the course work was completed - modeling of telecommunication systems.

List of sources used

1 Biryukov S. A. Digital devices on MOS integrated circuits / Biryukov S. A. - M .: Radio and communication, 2007 - 129 p.: ill. - (Mass Radio Library; Issue 1132).

2 Gelman M. M. Analog-to-digital converters for information-measuring systems / Gelman M. M. - M.: Publishing house of standards, 2009. - 317p.

3 Oppenheim A., Schafer R. Digital signal processing. Ed. 2nd, rev. - M.: "Technosfera", 2007. - 856 p. ISBN 978-5-94836-135-2

4 Sergienko A. B. Digital signal processing. Peter Publishing. - 2008

5 Sklyar B. Digital communications. Theoretical foundations and practical application: 2nd ed. / Per. from English. M.: Williams Publishing House, 2008. 1104 p.

Hosted on Allbest.ru

...

discrete channel. Electronic means of collecting, processing and displaying information

Send your good work in the knowledge base is simple. Use the form below

Introduction

Similar Documents