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Discrete channel. Discrete Channel Models

In the study of the radio inspection, the use and models of the discrete channel are necessary. This is due to the fact that in many types of RTS, a larger information protection load under conditions of intensive interference bears the use of encoding and decoding methods. To consider the tasks of this type, it is advisable to deal with only the peculiarities of the discrete channel, excluding from considering the properties of the continuous channel. In the discrete channel, the input and output signals are pulse sequences representing the stream of code symbols. This determines this property of the discrete channel, which in addition to restrictions on the parameters of a plurality of possible signals at the input, the distribution of the conditional probabilities of the output signal at a given input signal indicates. When determining a plurality of input signals, there is information about the number of different characters. t., number pulses in the sequence p and, if necessary, duration T IN. and OI, each pulse at the inlet and outlet of the channel. In most practically important cases, these durations are the same and, consequently, the same and duration of any // - sequences at the inlet and outlet. The result of interference can be the difference between the input and output sequences. Consequently, for any // it is necessary to indicate the likelihood that when transmitting some

random sequence IN Severe appears on the output IN.

Considered // - sequences can be represented as vectors in /// "- a measuring euclide space in which under operations" addition "and" subtraction "is understood to be a bonnetic summation t. And it is similar to the integer multiplication by an integer. In the selected space, you need to enter the concept of "error vector" E, under which it is understood by the discharge difference between the input (transmitted) and output (accepted) vectors. Then the vector adopted will be the sum of the transmitted random sequence and error vector B \u003d B + E. From the form of the recording, it can be seen that the random error vector E is an analogue of interference // (/) in the model of the continuous channel. The discrete channel models differ in each other by the distribution of the probabilities of the error vector. In the general case, the distribution of probabilities E may be dependent on the sale of the vector IN. Visually explain the concept of the meaning of the error vector for the case /// \u003d 2 - binary code. The appearance of a symbol 1 in any place of the error vector informs about the presence of an error in the corresponding discharge transmitted // - sequence. Consequently, the number of non-zero characters in the error vector can be called the weight of the error vector.

The symmetric channel without memory is the simplest model of the discrete channel. In such a channel, each transmitted code character can be accepted erroneously with some probability. R and adopted correctly with probability q. = 1 - R. If an error occurred, instead of the transmitted symbol 6. Any other symbol can be transmitted with an equal probability. B

The use of the term "without memory" suggests that the likelihood of an error in any discharge "sequence does not depend on which characters are transmitted to this discharge and how they were taken.

The probability that in this channel will appear "-Mal error vector weighing ?, equal

The likelihood that took place I. Any errors located randomly throughout I sequence is determined by the law of Bernoulli:

where FROM[ = p/[(!(« - ?)] - Binomine coefficient, i.e. The number of different combinations ? Errors in "Reception.

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

The asymmetrical channel without memory differs from the symmetric variety of symbols 1 to 0 and back while maintaining the independence of their appearance from the prehistory.

In many tasks of communication theory, the structure of the modulator and demodulator is set. In these cases, the channel is the part of the communication line, which is in fig. 1.3 circled dotted line. Discrete code characters are fed to the input of such a channel, and from the output is removed by the symbol, generally speaking not matching (Fig. 2.1).

Such a channel is called discrete. When studying the transmission of messages over the discrete channel, the main task is to find coding and decoding methods that allow or another to best transfer the discrete source messages.

Note that in almost all real communication lines, the discrete channel contains a continuous channel within itself, signals are fed to the input, and the signals distorted by interference are removed from the output. The properties of this continuous channel along with the characteristics of the modulator and the demodulator uniquely define all the parameters of the discrete channel. Therefore, sometimes the discrete channel is called a discrete displays of the continuous channel. However, with a mathematical study of the discrete channel, it is usually distracted from the continuous channel and the interference acting in it and determine the discrete channel, setting the alphabet of code symbols entering his input, alphabet code symbols Removed from its output, the number of code symbols missing per unit of time, and the values \u200b\u200bof the transition probabilities, i.e. the probability that the symbol appears if the symbol is filed on the input. These probabilities depend on which symbols were transmitted and taken earlier. The alphabets of the code at the input and outlet of the channel may not coincide; In particular, it is possible that. The value is sometimes called the technical speed of the transfer.

Fig. 2.1. Communication system with discrete channel.

If the transition probabilities for each pair remain constant and do not depend on which characters were transmitted and taken earlier, the discrete channel is called constant or uniform. Sometimes other names are also used: a channel without memory or a channel with independent errors. If the probabilities of the transition depend on the time or from the transitions that had previously earlier, the channel is called an inhomogeneous or memory channel.

In the channel with memory, probabilistic bonds, at least in the first approximation, are distributed only on some final segment. This means that the probabilities of the transition depend on which transitions took place when transmitting previous characters, and do not depend on earlier transitions. Such a channel can be considered as having a number of discrete states defined by previous transitions, and. For each state, the conditional probabilities of transitions are determined. At the same time, only the last transmitted and accepted characters determine the state of the channel.

The average unconditional probabilities of transitions are determined by averaging the conditional probabilities in all states of the channel:

(2.1)

where is the probability of the state.

In real channels, with elementary reception, the probability of transitions are not specified, but are determined, on the one hand, interference and distortions of signals in the channel, on the other hand, the feed rate of code symbols and the first decisive scheme. Choosing the optimal decisive scheme on the basis of a particular criterion, one can change in the desired direction of the transition. Thus, in order to consider the channel as a discrete, you need to choose the first decisive scheme and, given the interference and distortion acting in the channel, calculate the probabilities of transitions. Obviously, in cases where the parameters of the real channel are constant and the interference acting in the channel represent a stationary random process, its discrete mapping is a permanent channel. If these conditions are not executed, then a discrete mapping is a memory channel.

If the channel alphabets at the entrance and output are the same and for any probability pair , then such a channel is called symmetrical. Variable channel will also be called symmetrical if the condition is performed in each state for any pair

Obviously, from (2.2), it is also necessary to exit that the transmitted character is distorted by interference and cannot be identified. Thus, part of the adopted code sequence turns out to be erased.

As will be shown further, the introduction of such a erasing symbol does not violate the possibility of proper decoding of the adopted code sequence, but, on the contrary, facilitates it with a rational choice of coding method and decisive schemes.

Fig. 2.2. The probabilities of transitions in a symmetric binary channel.

Fig. 2.3. The probabilities of transitions in a symmetric channel with erasure.

Note that the output code alphabet is determined by the choice of the first decisive circuit and therefore is considered specified only because we consider the discrete display of the channel. The choice of the first decisive scheme also largely determines the properties of the symmetry of the channel. The probabilities of transitions in a symmetric erasing channel are shown in Fig. 2.3.

Advanced discrete canal

Advanced discrete channel includes DK + encoder + channel decoder.

The channel alphabet consists of 2N messages, where N is the number of elements in code combinations.

RDK is characterized by: error coefficient according to code combinations Effective Information transfer rate

The main task of the RDK is to increase the transfer of the transfer.

Methods of improving loyalty:

Operational and prophylactic measures

- improving the stability of the generator equipment
- Power backup
- identification and replacement of failed equipment
- Improving the qualifications of the service personnel

Events to increase the noise immunity of transmission of single elements

- increasing the ratio of the signal - interference (increase in amplitude, duration)
- Application of more noblematic modulation methods
- Improving processing methods
- selection of optimal signals
- the introduction of redundancy into the transmitted sequence i.e. Noise-resistant encoding

Discrete Channel Models

The discrete channel always contains inside a continuous channel. Converting the continuous channel to the discrete produces a modem. Therefore, in principle, you can get a mathematical model of the discrete channel from the model of the continuous channel at a given modem. Figuratively speaking, a modem that transitions from the continuous channel into the error flow. The most important and fairly simple models of discrete channels are as follows. Pulse interference generator communication

Permanent symmetrical channel without memory It is defined as a discrete channel in which each transmitted code character can be accepted erroneously with a fixed probability of P and correctly with a probability of 1-p, and in case of an error, any other symbol can be accepted instead of the transmitted symbol. The term "non-memory" means that the probability of erroneous reception of the symbol does not depend on the prehistor, i.e. From what symbols were transferred to it and how they were taken. The probabilities of transitions in the binary symmetric channel can be schematically represented as a graph (Fig.3.1).

Figure 3.1. Transitional probabilities in binary symmetric channel

Permanent symmetrical channel without memory with erasure It differs from the previous channel by the fact that the alphabet at the channel output contains an additional (M + 1) -th symbol that is often indicated by the sign "?". This symbol appears when the demodulator cannot reliably identify the transmitted symbol. The probability of such a refusal to solve or erasing the PC symbol in this model is constant and does not depend on the transmitted symbol. Due to the introduction of erasure, it is possible to significantly reduce the likelihood of an error, sometimes it is even considered to be zero. Figure 3.2 shows the probabilities of transitions in such a model.

Figure 3.2. Transitional probabilities in binary symmetric channel with erasure

Asymmetric canal without memory It is characterized by the fact that errors in it occur independently of each other, but the probabilities of errors depend on which symbol is transmitted. Thus, in a binary asymmetric channel, the probability of a symbol of symbol 1 when transmitting a symbol 0 is not equal to the likelihood of admission 0 when transmitted 1.

The simplest model binary Channel with Memory is an markov modeldetermined by the transition probability matrix:

where P1 is the conditional probability to accept (i + 1) -th symbol is erroneously if the previous one is accepted correctly; (1-p1) -thelable probability to accept (i + 1) -th symbol correctly, if the previous character is received correctly; P2- conditional probability to adopt (i + 1) -th symbol is erroneously if the previous one is made erroneously; (1-P2) -thelable probability to accept (i + 1) -th symbol correctly, if the previous character is erroneously adopted.

Unconditional (average) probability of error P in such a channel must satisfy the equation:

p \u003d p2p + z1 (1-p)

Another approach to the construction of mathematical models of channels is associated with the method of state variables. An important feature of this method is the ability to directly simulate systems described by the status equations using an analog or digital computing device. The state equations typically are in the form of a system of differential equations of the first order, which is given to the form of a vector (matrix) differential equation of the first order. This method gives a universal approach to simulate communication channels for communication systems for a variety of messages, encoding and modulation methods, communication lines with determinimal and random parameters and additive noises.

Data transfer methods at the physical level

Chapter 2.

In accordance with the previously determination of the discrete channel, it is customary to call a set (Fig. 2.1) of the continuous channel (NK) with the signal conversion devices (UPS) on its input and output.

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

Transmission speed V. information is equal to the number of information transmitted through the channel per unit of time, where m C. -In the position of the signal positions t 0. -Mifferentity of a single signal element. For two-position signals.

The value determines the number of items transmitted via the channel per second, and is called the modulation rate (Bod). ᴀᴋᴎᴍᴀᴋᴎᴍ ᴏϭᴩᴀᴈᴏᴍ, for binary systems, the transmission rate and the modulation rate is numerically coincide.

Loyalty to data transfer is estimated by probabilities of erroneous reception of single elements p 0 and code combinations p QK.

ᴀᴋᴎᴍᴀᴋᴎᴍ ᴏϭᴩᴀᴈᴏᴍ, the main task of the discrete channel is to transmit digital data signals over the communication channel with the required velocity V and the probability of error P 0.

To clarify the process of implementing this problem, imagine the structure of the discrete channel (Fig. 2.2), indicating only those UPS blocks that determine the system characteristics of the discrete channel.

Digital data signals are received on the channel input t 0. with speed B. bit / s. In UPS, these signals are converted by frequency (modulated m and d) and pass through the PDP PF band filter and the UC amplifier, from which the output of which is transmitted to the communication channel with a defined level P with Vh and spectrum width DF C..

Communication channel (including connecting lines) is characterized by bandwidth wide DF K., residual attenuation and Ost.non-uniformity of residual attenuation Da Est. and group time passing (GVP) DT GVP. in the channels of the communication channel .

In addition, there are interference in the channel. It is customary to call any accidental impact on the signal, ĸᴏᴛᴏᴩᴏᴇ worsens the loyalty to play 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 \u003d y (u, n).

In the particular case, when the operator Y degenerates in the amount of Z \u003d U + N, the interference is called additive. Additive interference in their electrical and statistical structures are divided into:

1) fluctuation or distribution and time and time

2) harmonic or focused in frequency,

3) impulse or concentrated in time.

Fluctuation interference - ϶ᴛᴏ continuous in time random process. It is often supposed to be stationary and ergodic with a normal distribution of instantaneous values \u200b\u200band zero average. The energy spectrum of such interference within the analyzed frequency band is considered uniform. Fluctuation interference is usually set by spectral density or rms voltage value. U p er In the channel of communication channel.

Harmonic interference - ϶ᴛᴏ additive interference, the spectrum of which is concentrated in a comparatively narrow strip of frequencies, comparable or even substantially narrower than the signal frequency band. These interference is considered uniformly distributed in the bands, ᴛ.ᴇ. The probability of the appearance of this interference in some strips of frequencies is proportional to the width of this strip and depends on the average number n gp Interference exceeding the threshold level of the average signal power per unit of frequency band.

The pulse interference is an additive interference, which is a sequence of impulses excited by short-term EDC of aperiodic or oscillatory nature. The moments of the appearance of impulse interference are supposedly distributed in time. This means that the probability of impulse interference during the time interval T.proportional to the duration of this interval and the average number n IP Interference per unit time depending on the permissible level of interference. Pulse interferences are usually given by the laws of distribution with their numerical parameters, or a maximum value of the work. A 0. The duration of impulse interference on its amplitude. These include short-term breaks (crushing), set by the laws of distribution with specific numerical parameters or average breaks of interruptions. t per. and their intensity n per.

In case the operator y. must be expressed in the form of a work z \u003d ku.where k (T) - Random process, the interference is called multiplicative.

In real channels, both additive and multiplicative interference, ᴛ.ᴇ. z \u003d ku + n.

On the entry of the UPS PRM, consisting of a Ling-Easy Amplifier, the UPR, the PF PRM, demodulator of DM, devices for registration of the UR and the synchronization of the MS IN There is a mixture of an interference signal, characterized by a signal / interference ratio. q VK.. After passing a receiving filter of the PF PFM, the signal-to-noise ratio is slightly improved.

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

To reduce the probability of error due to the effect of edge distortions or fractions, the signals from the yield of DM are subjected to gating or integration, ĸᴏᴛᴏᴩᴏᴇ is carried out in the UR under the action of synchropulse generated in the USS synchronization device. Ur is characterized by correcting the ability m EF.and mustache - synchronization error e S., synchronization time t sync and synchronism maintenance time t PS..

Discrete channel - concept and types. Classification and features of the category "Discrete Channel" 2017, 2018.

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Introduction

1. Theoretical part

1.1 Discrete Channel and its parameters

1.2 Model of partial description of the discrete channel

1.3 Discrete Channel Classification

1.4 Channel Models

1.5 Modulation

1.6 Structural scheme with Ros

2. Estimated part

2.1 Determining the optimal length of the code combination at which the highest relative bandwidth is ensured.

2.2 Determining the number of verification discharges in a code combination that ensure the specified probability of an unnecessary error

2.3 Determination of the amount of transmitted information at a given tempo of TR and the failure criteria

2.4 Determination of the capacity of the drive

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

2.6 Selection of the highway

Conclusion

List of sources used

Introduction

discrete communication information message

The development of telecommunication networks has led to a more detailed study of digital data transmission systems. And the discipline of digital communication technology is devoted to this. This discipline sets the principles and methods of transmitting digital signals, scientific foundations and a modern state of digital communication technologies; gives an idea of \u200b\u200bthe possibilities and natural boundaries of the implementation of digital transmission and processing systems; Calculates patterns that determine the properties of data transfer devices and the tasks of their functioning.

The purpose of this course work is to master the course "Digital communication technology", receiving skills in solving problems in the methodology of engineering calculations of the main characteristics and training methods for the technical operation of digital systems and networks;

In the course work, it is necessary to design the data transmission path between the source and the recipient of the information using a system with a crucial feedback, continuous transmission and a receiver lock, as well as the construction of the coding and decoding cyclic code circuit using modulation and demodulation using the System View package; determination of the amount of information transmitted at a given pace and the criteria of failure; Calculation of the characteristics of the main and bypass discrete channel; Building a temporary system work chart.

The solution of these tasks discloses the fulfillment of the main purpose of the task - modeling of telecommunication systems.

1 . Theoretical part

1.1 Discrete Channel and its parameters

Discrete Channel - communication channel used to transmit discrete messages.

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

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

There are several definitions on the transmission speed.

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

where M i is the base of the code in the i-Ohm channel.

Information transfer rate is associated with channel bandwidth. It appears with the emergence and rapid development of new technologies. Information speed depends on the technical velocity, from the statistical properties of the source, on the type of COP, received signals and interference operating in the channel. The limit value is the bandwidth of the COP:

where? F - BSS strip;

By speed of transmission of discrete channels and the corresponding UPS, it is customary to:

Low-speed (up to 300 bits / s);

Medium-speed (600 - 19600 bits / s);

High-speed (more than 24000 bits / s).

Effective transmission rate is the number of signs per unit of time provided to the recipient, taking into account the non-productive time of time (SS phasing time, time allocated to excess symbols).

Relative transfer rate:

The accuracy of information transmission is used due to each channel there are extraneous emitters that distort the signal and make it difficult to determine the species of the transmitted unit element. According to the method of converting messages to the interference signal there are additive and multiplicative. Form: harmonic, impulse and fluctuation.

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

Often the probability of the transmitter is less required, therefore, take measures to increase the likelihood of errors, eliminate the errors, inclusion in the channel of some additional devices that reduce the properties of the channels, therefore, reduce errors. Improving loyalty is associated with additional material costs.

Reliability is a discrete channel, as well as any DS cannot work well.

The refusal is called an event ending in a complete or partial womb of the performance system. In relation to the data transmission system, the failure is an event that causes the delay of the received message at time tands\u003e T add. At the same time, T additional in different systems is different. The communication system property providing the normal execution of all specified functions is called reliability. Reliability is characterized by an average time of operation for failure T o, average recovery time T B, and a preparedness ratio:

The probability of trouble-free operation shows how probability the system can work without a single failure.

1.2 Model of partial description of the discrete channel

The dependence of the likelihood of the appearance of a distorted combination from its length n and the likelihood of a combination of a length n with T errors.

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

This probability is the inconspicuous value of the function n. When n \u003d 1, then p \u003d r Osh, when, p \u003d 1.

In the model of the Purthova, the likelihood is calculated:

where b is the error grouping indicator.

If B \u003d 0, the error packing is missing and the appearance 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 evaluates and the likelihood of combinations of n c t long with the specified errors.

Comparison of the results of the calculated values \u200b\u200bof probability via formulas (2) and (3) shows that the error grouping leads to an increase in the number of code combinations affected by more multiplicity errors. You can also conclude that when grouping errors, the number of distorted code combinations specified by the length n decreases. This is also clear from purely physical considerations. With the same number of errors, the packaging leads to concentrating them on individual combinations (the multiplicity of errors increases), and the number of distorted code combinations is reduced.

1.3 Classification of discrete channels

The classification of discrete channels can be carried out by various features or characteristics.

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

Continuously discrete;

Discrete-continuous;

Discrete-discrete.

Discern the concept of discrete information and discrete transmission.

From a mathematical point of view, the channel can be determined by the alphabet of single elements at the input and channel output. The dependence of this probability depends on the nature of the errors in the discrete channel. If, when transmitting an I-th unit element I \u003d J, the errors did not occur if the element received a new element differ from J, an error occurred.

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

Channels in which the probability of transition 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) \u003d const, then the channel is symmetrical, otherwise - asymmetrical.

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

1.4 Channel models

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

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:

DKS without memory;

DKS with memory;

Binary symmetric COP;

COP with binary sources.

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

Figure 1.1 - Structural CC diagram with additive noise

In this model, the transmitted signal S (T) is influenced by the effect of additional noise N (T), which may occur from extraneous electrical interference, electronic components, amplifiers, or due to the interference phenomenon. This model applied to any COP, but with the presence of the attenuation process in the total reaction, add the attenuation coefficient.

r (T) \u003d BS (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 a pulse characteristic of a linear filter.

Figure 1.2 - Linear filtered channel

The linear filtered channel with variable parameters is characterized by specific physical channels, such as an acoustic COP, ionospheric radio channels, which occur with the transmitted signal changing in time and are described by variable parameters.

Figure 1.3 - Linear filtered channel with variable parameters

Discrete models of the COP without memory is characterized by an input alphabet or a binary sequence of characters, as well as a set of input probability of the transmitted signal.

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

Binary symmetric COP is a special occasion of the discrete channel without memory, when the input and output alphabets can only be 0 and 1. Consequently, the probability has a symmetrical appearance.

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

1.5 Modulation

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

The general principle of modulation consists in changing one or more parameters of the carrier oscillation (carrier) F (T, B, B, ...) in accordance with the transmitted message. So if a harmonic oscillation F (T) \u003d UCOS (x 0 T + C) is selected as a carrier, then three types of modulation can be formed: amplitude (s), frequency (FM) and phase (FM).

Figure 1.4 - Signal forms for binary code for various types of discrete modulation

The amplitude modulation consists in a proportional primary signal x (t) change the amplitude of the carrier u am \u003d u 0 + AX \u200b\u200b(T). In the simplest case of the harmonic signal x (t) \u003d xcoscht, the amplitude is equal to:

As a result, we have AM oscillation:

Figure 1.5 - x (t), u and u am

Figure 1.6 - AM Spectrum

Figure 1.5 shows the x (t), u and u am. The maximum deviation of the amplitude u am from U 0 represents the amplitude of the envelope u sh \u003d AX. The ratio of the amplitude of the envelope to the amplitude of the carrier (invertible) fluctuations:

m is called the modulation coefficient. 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) are written in the form:

To determine the spectrum of AM oscillation, we will reveal the brackets in the expression (1.13):

According to (1.14), AM oscillation is the sum of three high-frequency harmonic fluctuations 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 AM spectrum (1.14) is shown in Figure 1.6. The spectral width is double modulation frequency :? f am \u003d 2f. The amplitude of the carrier oscillation during modulation does not change; The amplitudes of the oscillation of the side frequencies (upper and lower) are proportional to the depth of the modulation, i.e. X amplitude of the modulating signal. With m \u003d 1, the amplitudes of the oscillations of the side frequencies reach half carrier (0.5U 0).

Carrying oscillation no information does not contain, and during the modulation process it does not change. Therefore, it is possible to limit the transmission of only lateral bands, which is implemented in communication systems on two sidebands (DBP) without carrier. Moreover, since each side bar contains complete information about the primary signal, you can do the transmission of only one sideband (ORP). Modulation, as a result of which oscillations of one side strip are obtained, called single-band (OM).

The obvious advantages of the DBP and ORP communication systems are the possibilities of using the transmitter power to transmit only sidebands (two or one) signal, which allows to increase the range and reliability of communication. With single-band modulation, in addition, the width of the modulated oscillation spectrum is halved, which allows you to increase the number of signals transmitted over the link in a given frequency band.

Phase modulation consists in a proportional primary signal x (t) by changing the phase C carrier U \u003d U 0 cos (x 0 T + C).

The amplitude of oscillations for phase modulation does not change, so the analytical expression of FM fluctuations

If the modulation is carried out by a harmonic signal x (t) \u003d xsinkt, then instantaneous phase

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

The phase formulated oscillation is clearly characterized by a vector diagram Figure 1.7, built on the plane rotating clockwise by an angular frequency of sh 0. Non-modulated oscillation corresponds to the movable vector U 0. Phase modulation consists in a periodic change with the rotation frequency of the vector U relative to U 0 to the angle? C (T) \u003d AxSink. The extreme positions of the vector U are designated u "and u". "Maximum deviation of the phase of modulated oscillation from the non-modulated oscillation phase:

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

Figure 1.7 - vector diagram of phase-modulated oscillation

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

u \u003d U 0 COS (x 0 T + C 0 + MSINT) (1.19)

Instant frequency FM oscillation

sh \u003d u (x 0 + mscOST) (1.20)

Thus, the FM oscillation at different times of time has different instant frequencies, differing from the frequency of the carrier oscillation of the x 0 to magnitude? Sh \u003d MSHCOST, which allows you to consider FM oscillation as modulated by frequency.

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

shch \u003d x 0 + AX \u200b\u200b(T) (1.21)

where a is the proportionality coefficient.

Instant Phase World Cup oscillation

Analytical expression of FM fluctuations, taking into account the constancy of amplitude, can be written as:

The deviation of the frequency is the maximum deviation from the carrier frequency of the SH 0, called by modulation:

Sh A \u003d AX (1.24)

Analytical expression of this World Cup oscillation:

The term (? Shk d / sh) sinct characterizes the phase change in the FM. This allows you to consider the FM oscillation, as the FM oscillation with the modulation index

and write it similar to:

From what has said it follows that FM and World Cup of oscillations have a lot in common. So the oscillation of the form (1.27) can be the result of both the FM and the FM is a harmonic primary signal. In addition, the FM and FM are characterized by the same parameters (modulation index M and the deviation of frequency? F d) related to the same ratios: (1.21) and (1.24).

Along with the marked similarity of frequency and phase modulation between them, there is a significant difference associated with the different characteristic of the dependence of the values \u200b\u200bM and? F d from the frequency F of the primary signal:

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

At World Cup, the frequency deviation does not depend on the frequency F, and the modulation index is inversely proportional to F.

1.6 Structural scheme with grew

The transfer with Ros is similar to a telephone conversation in conditions of bad audibility, when one of the interlocutors, I feel bad for some word or phrase, asks for another to repeat them again, and with good audibility or confirms the fact of obtaining information, or in any case, does not ask for a repetition .

The information received over the channel information is analyzed by the transmitter, and according to the analysis of the analysis, the transmitter decides on the transfer of the following code combination or the repetition of previously transmitted. After that, the transmitter transmits service signals about the accepted solution, and then the corresponding code combinations. In accordance with the receiver received from the transmitter, the receiver or gives the accumulated code combination to the recipient of the information, or erases it and remembers the newly transmitted.

Types of system with grew: systems with expectation of service signals, continuous transmission systems and blocking systems, systems with address transfer. Currently, numerous system operation algorithms from OS are known. Systems are the most common: with grew with the expectation of the OS signal; With the bezadresic repetition and the receiver lock with the address repetition.

Systems with waiting after transmission of the combination or expect a signal from feedback, or transmit the same code combination, but the transmission of the next code combination is started only after receiving confirmation over the previously transmitted combination.

Systems with blocking transmitting a continuous sequence of code combinations in the absence of OS signals according to preceding S combinations. After detecting errors in (S + 1) -th combination, the system output is blocked during the reception time of the combinations, in the storage device of the PDS system, s had previously received combinations are erased, and the aspects of the aspects. The transmitter repeats the transmission of the last transmitted code combinations.

Systems with address repetition distinguishes that the code combinations with errors are marked with conventional numbers, according to which the transmitter re-transmit only these combinations.

Algorithm for protection against imposition and loss of information. Systems with OS may discard or use the information contained in rejected code combinations in order to make a more correct solution. The system of the first type received the name of systems without memory, and the second - memory system.

Figure 1.8 shows the structural scheme of the system with Ros-ож. Systems are functioning with Ros-ож, as follows. Coming from the source of information (AI), M is an element combination of the primary code through a logical or written to the drive of the transmitter (NK 1). At the same time, control characters are formed in the coding device (kU), which are a control sequence of the block (PBC).

Figure 1.8? Structural scheme of the system with Ros

The resulting N is an element combination is fed to the input of the direct channel (PC). From the PC output, the combination enters the inputs of the decisive device (RU) and the decoding device (DCU). DCU on the basis of M information symbols taken from the direct channel generates its control sequence of the unit. The decisive device compares the two PBCs (received from the PC and the developed DCA) and receives one of the two solutions: either the information part of the combination (M-element primary code) is issued to the recipient of the PI information, or is erased. At the same time, the information part is selected in the DCU and the record of the obtained M - element combination into the receiver drive (NK 2).

Figure 1.9 - Structural scheme of the system algorithm with Ros NP

In the absence of errors or unnecessary errors, a decision is made to issue PI information and the receiver control device (UU 2) displays a signal that opens the element and 2, which ensures the issuance of a M - element combination from NK 2 to PI. A feedback signal forming device (UFS) is generated a confirmation signal of a combination reception, which is transmitted to the transmitter over the reverse channel (OK). If the signal coming out of OK is decoded with a feedback signal decoding (UDS) as a confirmation signal, then the corresponding pulse is applied to the transmitter control device (UU 1) input, according to which UU 1 provides a request from the following combination. The logic scheme and 1 in this case is closed, and the combination recorded in NK 1 is erased when new.

In case of detection of errors, it decides to erase the combination recorded in the NK 2, and the UU 2 is generated by control pulses, locking the logical circuit and 2 and form a surrosion signal in UFS. When decryption by the UDS scheme of the signal incoming to its input as a signal of aspects, the UU 1 block generates control pulses, with the help of which through the circuits and 1, or and ku in the PC, the combination stored in NK 1 is re-transmitted.

2 . Calculated part

2.1 Determining the optimal length of the code combination at which the highest relative bandwidth is ensured.

In accordance with the option, write the source data to perform this course work:

B \u003d 1200 Bod - modulation speed;

V \u003d 80000 km / s - the speed of distribution of information on the communication channel;

P Osh \u003d 0.5 · 10 -3 - the probability of error in the discrete channel;

P but \u003d 3 · 10 -6 - the likelihood of initial error;

L \u003d 3500 km - the distance between the source and the recipient;

t ot \u003d 180 seconds - failure criterion;

T per \u003d 220 seconds - specified pace;

d 0 \u003d 4 - the minimum code distance;

b \u003d 0,6 - error grouping coefficient;

AM, FM, FM - modulation type.

Calculate the bandwidth R corresponding to the specified value n formula (2.1):

where n is the length of the code combination;

Table 2.1

From Table 2.1, we find the largest value of the bandwidth R \u003d 0.997, which corresponds to the code combination length n \u003d 4095.

2.2 Determining the number of verification discharges in a code combination that ensure the specified probability of an unnecessary error

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

R value is in formula (2.2)

The parameters of the cyclic code n, k, r are connected via the dependence k \u003d n-r. Consequently k \u003d 4089 characters.

2.3 Determining the amount of information transmitted at a given pace T per and criteria of refusalt. oPC

The amount of information transmitted is in formula (2.3):

W \u003d 0.997 1200 (220 - 180) \u003d 47856 bits.

Use the value obtained by module, RWP \u003d 95712bits.

2.4 Determination of the tank of the drive

The storage capacity is determined by formula (2.4):

where T p \u003d L / V is the time distribution time on the communication channel, C;

t k \u003d n / b - the duration of the code combination from n discharges, p.

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

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

The distribution of the probability of errors of multiplicity T and more on the length n is determined by formula (2.6):

where T is \u003d D 0 -1 - the time of the bypass channel of data transfer or multiplicity of one error at the length n.

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

The probability of detection code error is determined by formula (2.8):

Code redundancy is determined by formula (2.9):

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

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

where F 0 is the reverse maximum channel operation rate or time reverse modulation rate (2.12);

t OH - waiting time when transferring information to the channel with Ros.

where T AK and T AC is the time difference in asynchronous operation for code error in the channel and for the main signal, respectively (2.14);

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

2.6 Selection of the highway

In the geographical map of the Republic of Kazakhstan, choose two points, which will be 3500 km away from each other. Due to the fact that the territory of Kazakhstan does not allow you to choose such items, carry a highway from the south to the east, from the east to the north, from the north to the east, and after from the east to the south (Figure 2.1). The initial point will be Pavlodar, and the final -Kostani, therefore, our highway will be called "Pavlodar - Kostanay".

This highway will break into areas with a length of 500-1000 km, as well as install the campuses, which will be tied by major cities of Kazakhstan:

Pavlodar (initial item);

Ust-Kamenogorsk;

Shymkent;

Kostanay.

Figure 2.1 - Highway with copper points

Conclusion

This course work produced basic calculations for designing cable lines of communication.

The theoretical part of the work was studied by the PRUTOVA model, which is used as a model of a partial description of the discrete channel, a structural scheme of the system Ros NLBB is constructed and the principle of operation of this system is described, and the relative phase modulation is considered.

In accordance with the specified option, the parameters of the cyclic code n, k, r were found. The optimal length of the code combination n is determined, which provides the highest relative bandwidth R, as well as the number of test discharges in the code combination of R, ensuring the specified probability of no error detection.

The main data transmission channel calculated the main characteristics (distribution of the probability of at least one error at length n, the distribution of the probability of errors of multiplicity T and more on the length n, the code rate, the redundancy of the code, the probability of detection of error code and other).

At the end of the work, the route highway route was selected, along the entire length of which the data sources were selected.

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

List of sources used

1 Biryukov S. A. Digital devices on MOS integrated microcircuits / Biryukov S. A. - M.: Radio and Communication, 2007 - 129 p.: Il. - (Mass Radobibilities; Vol. 1132).

2 Gelman M.M. Analog-Digital Converters for Information and Measuring Systems / Gelman M. M. - M.: Publishing House Standards, 2009. - 317c.

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

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

5 Square B. Digital communication. Theoretical Fundamentals and Practical Application: 2nd ed. / Lane from English M.: Publishing House "Williams", 2008. 1104 p.

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