Discrete-continuous channels. Interference in communication channels Information transfer rate

In accordance with this earlier definition, a discrete channel is called a set (Fig. 2.1) of a continuous channel (NC) with signal conversion devices (SPS) 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 the transmission.

Transmission speed V information is equal to the amount of information transmitted over the channel per unit of time, where m c-number of signal positions, t 0- the duration of a single signal element. For on / off signals.

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

The fidelity of data transmission is estimated by the probabilities of erroneous reception of single elements p 0 and code combinations p kk.

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

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

The channel input receives digital data signals with a duration of t 0 with speed B bit / s. In the UPS prd, these signals are converted in frequency (modulated by M and G) and pass through the bandpass filter PF prd and the amplifier UC out, from the output of which they are transmitted to the communication channel with a certain level P with in and spectrum width DF c.

The communication channel (including trunks) is characterized by the bandwidth DF to, residual attenuation and ost, irregularities of residual damping Da ost and group transit time (GWT) Dt gvp in the band of the communication channel .

In addition, there is interference in the channel. Interference is defined as any accidental effect on a signal that impairs the fidelity of a transmitted message. Interference is very diverse in its origin and physical properties.

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

In the particular case when the operator y degenerates into the sum z = u + n, the noise is called additive. According to their electrical and statistical structures, additive disturbances are subdivided into:

1) fluctuating or distributed in frequency and in time,

2) harmonic or lumped in frequency,

3) impulse or time-lumped.

Fluctuation noise is a random process continuous in time. Most often, it is considered 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. Ripple noise is usually given by spectral density or voltage rms. U p eff in the band of the communication channel.

Harmonic interference is an additive interference, the spectrum of which is concentrated in a relatively narrow frequency band, comparable or even significantly narrower than the signal frequency band. This interference is assumed to be uniformly distributed over the frequency band, i.e. the probability of this interference occurring 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 of the average signal power in a unit of frequency band.

Pulse noise is an additive noise, which is a sequence of pulses excited by short-term EMF of aperiodic or oscillatory nature. The moments of the impulse noise appearance are assumed to be uniformly distributed in time. This means that the probability of occurrence of impulse noise during the time interval T proportional to the duration of this interval and the average number n sp interference per unit time, depending on the permissible interference level. 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 by its amplitude. These include short-term breaks (fragmentation), set 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 interference is called multiplicative.

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

At the input of the UPS prm, consisting of a linear amplifier US inx, a bandpass filter PF prm, a demodulator DM, devices for recording the UR and synchronizing the US with a speed V a mixture of signal with interference is received, characterized by the signal-to-interference ratio q in... After passing the receiving filter PF PRM, the signal-to-noise ratio is slightly improved.

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

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

The issues considered are investigated in laboratory work No. 3 "Characteristics of a discrete channel".

Control questions for 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 data transfer rate determined over the channel?

5-4. How is the modulation rate determined?

5-5. How is the fidelity of information transmission through the channel assessed?

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

5-7. What are the characteristics of the signals arriving at the input of the 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 signal level?

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

5-12. What is called residual channel attenuation?

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

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

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

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

5-18. What does the uneven frequency response of the channel lead to?

5-19. What is called group transit time?

5-20. What is the phase response of a channel?

5-21. How are channel harmonic distortions estimated?

5-22. What is called 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 limiting bit rate related to the channel bandwidth when transmitting modulated signals with two sidebands?

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

5-26. How does the character of the phase response of the channel affect the channel bandwidth?

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

5-28. What is called a hindrance?

5-29. What is called additive interference?

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

5-31. What is the mathematical model of fluctuation noise?

5.32. How does harmonic interference differ from fluctuation interference?

5.33. What are the parameters for harmonic interference?

5.34. How does impulse noise differ from harmonic noise?

5.35. What are the parameters of impulse noise?

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

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

5-38. What are the characteristics of the signals coming from the input of the continuous channel?

5-39. What is the numerical estimate of the distortion of the waveform at the output of the demodulator?

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

Lecture 6. Signal propagation environment

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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 Block diagram with POC

2. Calculated part

2.1 Determination of the optimal length of the codeword, which provides the highest relative throughput

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

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

2.4 Determining storage capacity

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

2.6 Selecting the route of the trunk

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 regularities 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", to acquire skills in solving problems in the methodology of engineering calculations of the main characteristics and to teach methods of technical operation of digital systems and networks;

In the course work, it is necessary to design a data transmission path between the source and the recipient of information using a system with decisive feedback, continuous transmission and blocking of the receiver, as well as the construction of a cyclic code encoder and decoder circuit using modulation and demodulation using the "System View" package; determination of the volume of transmitted information at a given rate and criteria for refusal; calculation of the characteristics of the main and bypass discrete channel; construction of a time diagram of the system operation.

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

1 . Theoretical part

1.1 Discrete channel and its parameters

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

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

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

There are several definitions for baud 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 emergence and rapid development of new technologies. The information speed depends on the technical speed, 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 throughput of the compressor station:

where? F is the CS band;

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 (over 24000 bps).

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

Relative baud rate:

Reliability of information transmission - used in connection with the fact that in each channel there are extraneous emitters that distort the signal and complicate the process of determining the type of the transmitted unit element. According to the method of converting messages into a signal, interference can be additive and multiplicative. By shape: 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. An estimate of the transmission fidelity can be the ratio of the number of erroneous symbols to the total

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

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

Failure is an event that ends in a complete or partial womb of the 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. In this case, t add 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 T about, the mean recovery time T in, and the availability factor:

The probability of failure-free operation shows how likely the system can operate 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 the distorted combination to the total number of transmitted code combinations.

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

In Purtov's model, the probability is calculated:

where b is an indicator of grouping errors.

If b = 0, then there is no error batching 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 c t with predetermined errors.

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

1.3 Discrete channel classification

Discrete channels can be classified according to various features or characteristics.

On the transmitted carrier and the channel signal 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 the alphabet of unit 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 during transmission of the i-th unit element i = j - no errors occurred, if during reception the element received a new element different from j, 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 they are nonstationary.

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 balanced and have memory. Space communication channels are symmetrical, but they have no memory.

1.4 Channel models

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

Basic mathematical models of CS:

Channel with additive noise;

Linear filtered channel;

Linear filtered channel and variable parameters.

Mathematical models for discrete CS:

DKS without memory;

DKS with memory;

Binary symmetric CS;

CS from binary sources.

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

Figure 1.1 - Block diagram of the CS with additive noise

In this model, the transmitted signal S (t) is influenced by additional noise n (t), which can arise from extraneous electrical noise, electronic components, amplifiers, or due to the phenomenon of interference. This model was applied to any CS, but in the presence of a damping process, the damping coefficient must be added to the total reaction.

r (t) = бS (t) + n (t) (1.9)

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

Figure 1.2 - Linear filtered channel

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

Figure 1.3 - Linear filtered channel with variable parameters

Discrete models of CS 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 BCS with memory, there is interference in the transmitted data packet or the channel is affected by 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 channel without memory, when the input and output alphabets can only be 0 and 1. Therefore, the probability is symmetric.

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 generated by changing certain parameters of the physical medium in accordance with the transmitted message. This process (changing the parameters of the carrier) is usually 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 harmonic oscillation f (t) = Ucos (u 0 t + q) is chosen as a carrier, then three types of modulation can be formed: amplitude (AM), frequency (FM) and phase (FM).

Figure 1.4 - Forms of signals with a binary code for various types of discrete modulation

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

As a result, we have an AM oscillation:

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

Figure 1.6 - AM vibration spectrum

Figure 1.5 shows the graphs of 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 Щ = aX. The ratio of the amplitude of the envelope to the amplitude of the carrier (unmodulated) oscillation:

m - 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 in the form:

To determine the spectrum of AM oscillations, let us 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<

Fluctuations of the carrier frequency f 0 with an amplitude of U 0;

Oscillations of the upper side frequency f 0 + F;

Oscillations of the lower side frequency f 0 -F.

The AM vibration spectrum (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 oscillation of the side frequencies (high and low) are proportional to the modulation depth, i.e. amplitude X of the modulating signal. When m = 1, the amplitudes of the side frequency oscillations reach half of the carrier (0.5U 0).

The carrier wave does not contain any information, and it does not change during modulation. Therefore, it is possible to confine ourselves to the transmission of only sidebands, which is implemented in communication systems on two sidebands (DBB) without a carrier. Moreover, since each sideband contains complete information about the primary signal, only one sideband (SSB) transmission can be dispensed with. Modulation that produces a single sideband waveform is called single sideband (SSB).

The obvious advantages of the DBP and SSB 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. In addition, with single-sideband modulation, the width of the spectrum of the modulated vibration 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 consists in a change in the phase q of the carrier, proportional to the primary signal x (t), u = U 0 cos (u 0 t + q).

The amplitude of the oscillation 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) = XsinЩt, 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. Unmodulated oscillation corresponds to the moving vector U 0. Phase modulation consists in a periodic change with a frequency of W, the rotation of the vector U relative to U 0 by the angle χ (t) = aXsinЩt. The extreme positions of the vector U are designated U "and U" ". The maximum deviation of the phase of the modulated waveform from the phase of the unmodulated waveform:

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 phase-modulated oscillation

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

u = U 0 cos (u 0 t + u 0 + Msin u t) (1.19)

Instantaneous frequency of FM oscillation

uh = U (uh 0 + MChcosucht) (1.20)

Thus, the FM oscillation at different times has different instantaneous frequencies that differ from the frequency of the carrier oscillation u0 by the value? Uc = Mshcos

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

u = u0 + ax (t) (1.21)

where a is the coefficient of proportionality.

Instantaneous phase FM wobble

The analytical expression of the FM oscillation, taking into account the constancy of the amplitude, can be written in the form:

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

Щ A = aX (1.24)

An analytical expression for this FM oscillation:

The summand (? U / U) sin? T characterizes the phase change resulting from FM. This allows us to consider the FM oscillation as an FM oscillation with a modulation index

and write it similarly:

It follows from what has been said that FM and FM oscillations have much in common. So an oscillation of the form (1.27) can be the result of both FM and FM harmonic primary signal. In addition, FM and FM are characterized by the same parameters (modulation index M and frequency deviation? F D), related to each other by the same relations: (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 of M and Δf D on the frequency F of the primary signal:

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

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

1.6 Block diagram with POC

The transmission from ROS is similar to a telephone conversation in conditions of poor audibility, when one of the interlocutors, having poorly heard any word or phrase, asks the other to repeat them again, and if audible, 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 on the transmission of the next codeword or on the repetition of the previously transmitted ones. After that, the transmitter transmits signaling signals about the adopted decision, and then the corresponding codewords. In accordance with the service signals received from the transmitter, the receiver either issues the accumulated code combination to the recipient of information, or erases it and stores the newly transmitted one.

Types of systems with POC: systems with waiting for service signals, systems with continuous transmission and blocking, systems with address transfer. Numerous algorithms for operating systems with an OS are currently known. The most common systems are: with POC with waiting for an OS signal; with addressless repetition and blocking of the receiver with addressable repetition.

Systems with waiting after transmitting a combination either wait for a feedback signal or transmit the same codeword, but the transmission of the next codeword begins only after receiving an acknowledgment for the previously transmitted combination.

Blocking systems transmit a continuous sequence of code combinations in the absence of OS signals over the previous S combinations. After detecting errors in the (S + 1) th combination, the system output is blocked for the time when S combinations are received, S previously received combinations are erased in the memory of the receiver of the PDS system, and a re-request signal is sent. The transmitter repeats the transmission of the S last transmitted codewords.

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

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

Figure 1.8 shows a block diagram of a system with ROS-standby. The systems with ROS-ozh function as follows. Coming from the source of information (IS), m is an elementary combination of the primary code through a logical OR is written into the transmitter's drive (NK 1). At the same time, control symbols are formed in the encoder (CU), which are the control sequence of the block (BSC).

Figure 1.8? Block diagram of the system with POC

The resulting n - element combination is fed to the input of the forward channel (PC). From the PC output, the combination goes to the inputs of the deciding device (RU) and decoding device (DKU). DSC on the basis of m information symbols received from the forward channel forms its control sequence of the block. The solver compares two PBCs (received from the PC and generated by the DSC) 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 DSC and the resulting m - element combination is written to the receiver's storage (NK 2).

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

In the absence of errors or undetected errors, a decision is made to issue PI information and the receiver control unit (CU 2) issues a signal that opens the AND 2 element, which provides an m - element combination from NC 2 to PI. The feedback signal conditioning device (FSC) generates a combination confirmation signal, which is transmitted to the transmitter via the reverse channel (OC). If the signal coming from the OK is decoded by the feedback signal decoding device (MAC) as a confirmation signal, then the corresponding pulse is sent to the input of the transmitter control device (CU 1), according to which CU 1 makes a request from the AI of the next combination. Logic circuit AND 1 in this case is closed, and the combination written in NC 1 is erased when a new one arrives.

If errors are detected, the RU makes a decision to erase the combination recorded in the NK 2, while the UU 2 generates control pulses that lock the logic circuit AND 2 and form a re-request signal in the UU. When the MAC circuit decrypts the signal arriving at its input as a re-request signal, the CU 1 unit generates control pulses, with the help of which, through the AND 1, OR and CU circuits to the PC, the combination stored in the NC 1 is re-transmitted.

2 . Calculated part

2.1 Determination of the optimal length of the codeword, which provides the highest relative throughput

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

B = 1200 Baud - modulation rate;

V = 80,000 km / s is 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 an initial error;

L = 3500 km - distance between source and receiver;

t open = 180 sec - failure criterion;

T lane = 220 sec - a given pace;

d 0 = 4 - minimum code distance;

b = 0.6 - error grouping factor;

AM, FM, FM - modulation type.

Let us calculate the throughput R corresponding to a given value of n using the formula (2.1):

where n is the length of the codeword;

Table 2.1

From table 2.1 we find the highest value of the throughput R = 0.997, which corresponds to the length of the codeword n = 4095.

2.2 Determination of the number of check bits in a 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 related through the dependence k = n-r. Hence k = 4089 characters.

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

The amount of information transmitted 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 Determining storage capacity

The storage capacity is determined by the formula (2.4):

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

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

2.5 Calculation of the characteristics of the main and bypass channels of the 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 distribution of the probability of occurrence of errors of multiplicity t and more over the length n is determined by the formula (2.6):

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

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

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

The redundancy of the code is determined by the 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 the system with POC is determined by the formula (2.11):

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

t standby - waiting time when transmitting information in the channel with POC.

where t ak and t ac is the time difference in the asynchronous mode of operation 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 trunk

On the geographic 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 one will be Kostanay, therefore, our highway will be called “Pavlodar - Kostanay”.

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

Pavlodar (starting point);

Ust-Kamenogorsk;

Shymkent;

Kostanay.

Figure 2.1 - Highway with transfer points

Conclusion

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

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

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

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

At the end of the work, a data transmission line was selected, along the entire length of which data transfer points 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. - (Mass radio library; Issue 1132).

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

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

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

5 Sklyar B. Digital communication. Theoretical foundations and practical applications: 2nd ed. / Per. from English M .: Publishing house "Williams", 2008. 1104 p.

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Continuous channel

Channels, when a continuous signal arrives at the input at its output, the signal will also be continuous, are called continuous... They are always part of the discrete channel. Continuous channels are, for example, standard telephone communication channels (voice frequency channels - PM) 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 four-port network (Figure 3.4)

Figure 3.4 - Model of a linear continuous channel

Discrete channel

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

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

Binary balanced channel . Binary balanced channel(binary symmetric channel - BSC) is a special case of a discrete memoryless channel, the input and output alphabets of which consist of binary elements (0 and I). Conditional probabilities are symmetrical.

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

Markov DC models. 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 reasons - the appearance of interruptions, impulse noise, fading, etc. The sequence of states is a simple Markov chain. A simple Markov chain is a random sequence of states when the probability of a particular state in i- this moment 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 symmetric channel when described by a model based on Markov chains

Hilbert's model. The simplest model based on the use of the mathematical apparatus of Markov chains is the model of the source of errors 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 the probability p osh (2).

Interference in communication channels

In a real channel, the signal is distorted during transmission, and the message is reproduced with some error. These errors are caused by channel distortion and signal interference. Distortion should be clearly distinguished from random noise. The interference is not known in advance and therefore cannot be completely eliminated.

Under hindrance any impact that is superimposed on a useful signal and makes it difficult to receive is understood. Interference is diverse in its origin: thunderstorms, interference with electric vehicles, electric motors, engine ignition systems, etc.

In almost any frequency range, there is an internal noise of the equipment caused by the chaotic movement of charge carriers in amplifying devices, the so-called thermal noise.

Interference classification. Harmonic interference- represent a narrow-band modulated signal. The reasons for such interference are a decrease in the crosstalk between cable circuits, the influence of radio stations. Pulse interference are time-focused noise. They represent a random sequence of pulses with random time intervals, and the transients caused by them do not overlap in time.

The most common type of channel is a telephone channel with a bandwidth of kHz and a frequency range of = 0.3 kHz to = 3.4 kHz.

The data from the information source, after converting the parallel code into serial, is usually presented in the form of a non-return to zero non-return-to-zero signal (BVN), which corresponds to a signal with a bipolar AM (Fig. 2.1). To transmit rectangular pulses without distortion, a frequency bandwidth from zero to infinity is required. Real channels have a finite frequency band with which it is necessary to match the transmitted signals by modulation.

The block diagram of a discrete FM channel is shown in Fig. 2.2.

The transmitted message from the AI information source in a parallel code is sent to the KK channel encoder, which converts the parallel code into a serial binary BVN code. In this case, the channel encoder inserts redundant symbols into the message (for example, a parity bit) and generates start and stop bits for each frame of transmitted data. Thus, the output from the encoder is the baseband signal for the modulator.

Depending on the state of the modulating signal ("0" or "1"), the frequency modulator generates frequency messages with frequency and. When a signal of positive polarity arrives at the modulator, the modulator generates a frequency called the upper characteristic frequency.

Rice. 14.2 - Block diagram of a frequency modulation information transmission system:

AI is a source of information; IP - a source of interference; KK - channel encoder; PF2 - bandpass filter of the receiver; M - modulator; UO - amplifier-limiter; PF1 - bandpass transmission filter; DM - demodulator; DC - channel decoder; ЛС - communication line; P - recipient of information; AI - source of information; IP - a source of interference; KK - channel encoder; PF2 - bandpass filter of the receiver; M - modulator; UO - amplifier-limiter; PF1 - bandpass transmission filter; DM - demodulator; DC - channel decoder; ЛС - communication line; P - recipient of information

The frequency is the average frequency - the deviation (deviation) of the frequency. When a negative message arrives at the input of the modulator, a frequency appears at its output called the lower characteristic frequency. The signal at the output of the modulator can be considered as a superposition of two AM signals, one of which has a carrier and the other. Accordingly, the spectrum of the FM signal can be represented as a superposition of the spectra of two AM signals (Fig. 2.3).

The width of the spectrum of the FM signal is wider than that of the AM signal by an amount determined by the distance between the carriers and. Meaning characterizes the change in frequency when transmitting one or zero relative to its average value and is called frequency deviation. Frequency deviation to modulation rate ratio V called the frequency modulation index:

Rice. 14.3 - Spectrum of the FM signal

The bandpass filter of the transmitter PF1 limits the spectrum of the signal transmitted to the communication channel in accordance with the lower and upper boundaries of the channel bandwidth. Signal spectrum width at the modulator output depends on the bit modulation rate and frequency deviation. Approximately ... The larger the modulation index, the wider, all other things being equal, the spectrum of the FM signal.

The bandpass filter of the receiver PF2 selects the frequency band of the telephone channel, which allows you to get rid of the interference that is outside the bandwidth of the PF2. Further, the signal is amplified by the UO limiter amplifier. The amplifier compensates for the loss of signal energy in the line due to attenuation. In addition, the amplifier performs an additional function - the function of limiting the signal by level. In this case, it is possible to ensure the constancy of the signal level at the input of the frequency demodulator D when the level at the receiver input changes over a fairly wide range. In the demodulator, AC pulses are converted to DC bursts. The channel decoder converts symbols to messages. At the same time, depending on the coding method used, errors are detected or corrected.

Discrete-continuous channels. Interference in communication channels Information transfer rate

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