A communication channel is a collection of technical means for transmitting messages from one point in space to another. From the point of view of information theory, the physical structure of the channel is insignificant. The message source (IS) has an output alphabet of characters A={a i },i =1.. n - the amount of information per source symbol on average:
where p i, is the probability of the appearance of the symbol a i, at the source output, the source symbols are considered independent. The communication channel has an alphabet of symbols B = ( b j },j =1.. m, average amount of information in one channel symbol
where q j - the probability of the symbol appearing b i , in the channel.
The technical characteristics of the communication channel are:
source technical performance A - the average number of characters issued by the source per unit of time;
technical bandwidth of the communication channel B - the average number of symbols transmitted over the channel per unit of time.
Informational characteristic of a source is informational productivity. By definition, information performance is the average amount of information produced by a source per unit of time.
In a channel without interference, the information characteristics are:
1) the speed of information transfer over the channel 
2) channel bandwidth
where ( P) is the set of all possible probability distributions of alphabet symbols V channel. Taking into account the properties of entropy
C K = B. log 2 m.
In a noisy channel, in the general case, the input and output alphabets do not coincide. Let
B IN = X = (x 1, x 2, ..., x n);
B OUT = Y = (y 1, y 2, ..., y m).
If the character sent at the input channel is X To recognized in the receiver as y i and i K, then an error occurred during transmission. Channel properties are described by a matrix of transition probabilities (the probability of receiving a symbol at i , provided that sent X k):
|| P (yi | xk) ||, k = 1..n, i = 1..m.
The ratio is fair: 
Average amount of information per one input channel symbol:
p i = p (x i )
.
Average amount of information per output channel symbol:
Information carried by the channel's output about the input:
I (Y, X) = H (X) -H Y (X) = H (Y) -H X (Y).
Here Well(X) - conditional entropy of the input channel symbol when observing the output symbol (channel unreliability), N X (Y) - the conditional entropy of the output channel symbol when observing the input symbols (noise entropy).
Information transfer rate over a noisy channel:
dI (B) / dt = B I (X, Y).
Bandwidth of a noisy channel:
where ( R) - the set of all possible probability distributions of the input channel alphabet.
Let's consider an example
N 
Find the bandwidth of a binary symmetric channel (a channel with two-character input and output alphabets) and the same error probabilities (Fig. 1), if the prior probabilities of the appearance of input characters are: P (x 1
) = P 1
= P, P (x 2
) = P 2
= 1-P.
Solution. According to the channel model, the conditional probabilities
P (y 1 | x 2 ) = P (y 2 | x 1 ) = P i ,
P (y 1 | x 1 ) = P (y 2 | x 2 ) = 1-P i .
Channel bandwidth - C K = B . max (H (Y) -H (X | Y)). Let's find the entropy of the noise:
By the multiplication theorem: P(y j x i)=P(x i)P(y j | x i), hence,
P(x 1 y 1 )=P(1-P i), P(x 2 y 1 )=(1- P)P i ,P(x 1 y 2 )=PP i ,P(x 2 y 2 )=(1-P)(1-P i).
Substituting into the formula, we get:
In this way, H ( Y| X ) does not depend on the distribution of the input alphabet, therefore:
Let's define the entropy of the output:
Probabilities P(y 1 ) and P(y 2 ) we get as follows:
P(y 1 )=P(y 1 x 1 )+P(y 1 x 2 )=P(1-P i)+(1-P i)P i , P(y2)=P(y 2 x 1 )+P(y 2 x 2 )=PP i +(1-P)(1-P i).
By varying P, we make sure that the maximum value H(Y) equal to 1 is obtained for equiprobable input symbols P(y 1 ) and P(y 2 ). Hence,
Task... Find the bandwidth of a channel with three-character input and output alphabets ( x 1 ,x 2 ,x 3 and y 1 ,y 2 ,y 3 respectively). The intensity of the appearance of symbols at the channel input k = V... 10 characters / sec.
The probabilities of symbols appearing:
,
,
.
The probabilities of transmitting symbols through the communication channel:
,
,,
,
,,
,
,.
4. CODING OF INFORMATION
4.1. General information The code is called:
A rule describing the mapping from one set of characters to another set of characters or to a set of words without characters;
The set of images resulting from such a mapping.
In technical codes, letters, numbers, and other characters are almost always encoded in binary sequences called binary codewords. Many codes have words of the same length (uniform codes).
The choice of codes for encoding specific message types is determined by many factors:
Convenience of getting the original messages from the source;
The speed of transmission of messages through the communication channel;
The amount of memory required for the day of storing messages;
Convenience of data processing;
Convenience of message decoding by the receiver.
The encoded messages are transmitted via communication channels, stored in the memory, processed by the processor. The volumes of encoded data are large, and therefore, in many cases it is important to provide a data encoding rate: "., which is characterized by the minimum length of received messages, This is a data compression problem. There are two approaches to data compression:
Compression based on the analysis of the statistical properties of encoded messages.
Compression based on statistical properties of data is also referred to as lean or efficient coding theory. Thrifty coding is based on the use of codes with variable codeword length, for example, Shannon-Fano code, Huffman code /31. The idea of using variable length codes for data compression is that messages are more likely to appear to match shorter codewords and, conversely, messages are less likely to be encoded into words of longer length. The average length of the code word is determined by the s.o .:
where /, is the length of the codeword for encoding the i-th message; p t - probability of occurrence of the i-th message.
4.2. Tasks
4.2.1. From Table 4, select the day of subsequent coding the original alphabet containing 10 characters, starting with N-ro (N - the serial number of the student in the group journal). Normalize the probabilities of symbols.
4.2.2. Normalize the one selected in p.4.2.1. original alphabet with uniform binary code, Shannon-Fano code, Huffman code. For each coding option, calculate the minimum, maximum, average value of the codeword length. Analyze the results.
4.2.3. Complete the task 4.2.2. for ternary code.
Table 4
4.3. Instructions for completing individual tasks To task 4.2.1. The probabilities are normalized according to the formula:
/ W-HO / * Pk " JC = AT
where Pi - the probabilities of the symbols appearing are given in Table 4.
To task 4.2.2. The rules for constructing binary codes are described in / 4,6 /.
To task 4.2.3. When constructing a ternary code, words written in a ternary number system are taken as code words. An optimal ternary code is constructed using the Huffman procedure (a suboptimal code is constructed using the Shannon-Fano procedure). In this case, the alphabet is divided into three groups, the first group is assigned "O", the second - "1", the third - "2".
Control
Communication, communications, electronics and digital devices
A communication channel is a system of technical means and a signal propagation medium for transmitting messages (not only data) from a source to a receiver (and vice versa). A communication channel, understood in a narrow sense (communication path), represents only the physical medium of signal propagation, for example, a physical communication line.
Question No. 3 “Communication channels. Classification of communication channels. Communication channel parameters. Condition for signal transmission over a communication channel ".
Link
Link - a system of technical means and a signal propagation medium for transmitting messages (not only data) from a source to a receiver (and vice versa). The communication channel, understood in the narrow sense ( communication path ), represents only the physical medium of signal propagation, for example, a physical communication line.
The communication channel is designed to transmit signals between remote devices. Signals carry information intended for presentation to a user (person), or for use by computer applications.
The communication channel includes the following components:
- transmitting device;
- receiving device;
- transmission medium of various physical nature (Fig. 1).
The information-carrying signal generated by the transmitter, after passing through the transmission medium, enters the input of the receiving device. Further, the information is extracted from the signal and transmitted to the consumer. The physical nature of the signal is chosen so that it can propagate through the transmission medium with minimal attenuation and distortion. The signal is necessary as a carrier of information; it itself does not carry information.
Fig. 1. Communication channel (option number 1)
Fig. 2 Communication channel (option no. 2)
Those. this (channel) is a technical device (technology + environment).
Classification
There will be exactly three types of classifications. Choose the taste and color:
Classification No. 1:
There are many types of communication channels, among which the most commonly distinguishedchannels wired communication ( aerial, cable, light-guide etc.) and radio communication channels (tropospheric, satelliteand etc.). Such channels, in turn, are usually qualified based on the characteristics of the input and output signals, as well as on the change in the characteristics of the signals, depending on such phenomena occurring in the channel as fading and attenuation of signals.
By the type of distribution medium, communication channels are divided into:
- wired;
- acoustic;
- optical;
- infrared;
- radio channels.
Communication channels are also classified into:
- continuous (continuous signals at the input and output of the channel),
- discrete or digital (discrete signals at the input and output of the channel),
- continuous-discrete (continuous signals at the channel input, and discrete signals at the output),
- discrete-continuous (discrete signals at the channel input, and continuous signals at the output).
Channels can be like linear and nonlinear, time and spatio-temporal.
Possible classification of communication channels by frequency range.
Information transmission systems are single-channel and multi-channel ... The type of system is determined by the communication channel. If a communication system is built on the same type of communication channels, then its name is determined by the typical name of the channels. Otherwise, the specification of the classification features is used.
Classification No. 2 (more detailed):
- Classification by frequency range
- Kilometer (LW) 1-10 km, 30-300 kHz;
- Hectometric (SV) 100-1000 m, 300-3000 kHz;
- Decameter (HF) 10-100 m, 3-30 MHz;
- Meter (MV) 1-10 m, 30-300 MHz;
- Decimeter (UHF) 10-100 cm, 300-3000 MHz;
- Centimeter (CMB) 1-10 cm, 3-30 GHz;
- Millimeter (MMV) 1-10 mm, 30-300 GHz;
- Decimiter (DMMV) 0.1-1 mm, 300-3000 GHz.
- By direction of communication lines
- directed ( different conductors are used):
- By direction of communication lines
- coaxial,
- twisted pairs based on copper conductors,
- fiber optic.
- non-directional (radio links);
- line of sight;
- tropospheric;
- ionospheric
- space;
- radio relay (retransmission on decimeter and shorter radio waves).
By the type of transmitted messages:
- telegraph;
- telephone;
- data transmission;
- facsimile.
- By the type of signals:
- analog;
- digital;
- impulse.
- By the type of modulation (manipulation)
- In analog communication systems:
- By the type of modulation (manipulation)
- with amplitude modulation;
- with single sideband modulation;
- with frequency modulation.
- In digital communication systems:
- with amplitude shift keying;
- with frequency shift keying;
- with phase shift keying;
- with relative phase shift keying;
- with tone shift keying (single elements manipulate the subcarrier wave (tone), after which the keying is carried out at a higher frequency).
- By the value of the base of the radio signal
- broadband (B >> 1);
- narrowband (B "1).
7. By the number of simultaneously transmitted messages
- single-channel;
- multichannel (frequency, time, code division of channels);
8.
In the direction of messaging
- one-sided;
- bilateral.
9. By order of message exchange - simplex communication- two-way radio communication, in which the transmission and reception of each radio station is carried out in turn;
- duplex communication- transmission and reception are carried out simultaneously (the most efficient);
- half-duplex communication- refers to the simplex, which provides for an automatic transition from transmission to reception and the possibility of re-asking the correspondent.
10. By methods of protection of transmitted information
- open communication;
- private communication (classified).
11. By the degree of automation of information exchange
- non-automated - radio station control and messaging is performed by the operator;
- automated - only information is entered manually;
- automatic - the process of message exchange is performed between an automatic device and a computer without the participation of an operator.
Classification number 3 (something can be repeated):
1. By appointment
Telephone
Telegraph
Television
- broadcasting
2. By transfer direction
- simplex (transmission in one direction only)
- half duplex (alternate transmission in both directions)
- duplex (simultaneous transmission in both directions)
3. By the nature of the communication line
Mechanical
Hydraulic
Acoustic
- electrical (wired)
- radio (wireless)
Optical
4. By the nature of the signals at the input and output of the communication channel
- analog (continuous)
- discrete in time
- discrete by signal level
- digital (discrete both in time and in level)
5. By the number of channels per communication line
Single channel
Multichannel
And another drawing here:
Fig. 3. Classification of communication lines.
Characteristics (parameters) of communication channels
- Channel transfer function: is presented in the formamplitude-frequency characteristic (AFC) and shows how the amplitude of the sinusoid at the output of the communication channel decays in comparison with the amplitude at its input for all possible frequencies of the transmitted signal. The normalized frequency response of the channel is shown in Fig. 4. Knowing the frequency response of a real channel allows you to determine the shape of the output signal for almost any input signal. To do this, it is necessary to find the spectrum of the input signal, transform the amplitude of its constituent harmonics in accordance with the amplitude-frequency characteristic, and then find the shape of the output signal by adding the transformed harmonics. For experimental verification of the amplitude-frequency characteristic, it is necessary to test the channel with reference (equal in amplitude) sinusoids over the entire frequency range from zero to a certain maximum value that can occur in the input signals. Moreover, it is necessary to change the frequency of the input sinusoids with a small step, which means that the number of experiments should be large.
- - the ratio of the spectrum of the output signal to the input
- bandwidth
Fig. 4 Normalized frequency response of the channel
- Bandwidth: is a derivative of the characteristic from the frequency response. It is a continuous range of frequencies for which the ratio of the amplitude of the output signal to the input signal exceeds a certain predetermined limit, that is, the bandwidth determines the range of signal frequencies at which this signal is transmitted through the communication channel without significant distortion. Typically, the bandwidth is measured at 0.7 times the maximum frequency response. The bandwidth has the greatest impact on the maximum possible data transfer rate over the communication channel.
- Attenuation: is defined as the relative decrease in the amplitude or power of a signal when a signal of a certain frequency is transmitted over a channel. Often, during channel operation, the fundamental frequency of the transmitted signal is known in advance, that is, the frequency whose harmonic has the highest amplitude and power. Therefore, it is enough to know the attenuation at this frequency in order to approximately estimate the distortion of the signals transmitted over the channel. More accurate estimates are possible if one knows the attenuation at several frequencies corresponding to several fundamental harmonics of the transmitted signal.
Attenuation is usually measured in decibels (dB) and is calculated using the following formula:, where
- signal power at the channel output,
- signal power at the channel input.
The attenuation is always calculated for a specific frequency and is related to the channel length. In practice, the concept of "linear attenuation" is always used, i.e. signal attenuation per unit of channel length, for example, attenuation 0.1 dB / meter.
- Transmission speed: characterizes the number of bits transmitted over the channel per unit of time. It is measured in bits per second - bit / s , as well as derived units:Kbps, Mbps, Gbps... The transmission rate depends on the channel bandwidth, noise level, type of coding and modulation.
- Channel immunity: characterizes its ability to provide signal transmission in the presence of interference. It is customary to divide the interference into internal (representsthermal noise of the apparatus) and external (they are diverse anddepend on the transmission medium). Channel immunity depends on hardware and algorithmic solutions for processing the received signal, which are embedded in the transceiver.Immunitytransmission of signals through the channelcan be increased at the expense of encoding and special processing signal.
- Dynamic range: the logarithm of the ratio of the maximum power of the signals transmitted by the channel to the minimum.
- Interference immunity:this is noise immunity, i.e.e. noise immunity.
Condition for signal transmission over communication channels.
The channel is essentially a filter. For the signal to pass through it without distortion, the volume of this channel must be greater than or equal to the signal (see figure).
Mathematically, the condition can be written as follows:, where
; (1)
In the above formulas
- the channel bandwidth, or the frequency band that the channel can pass with the normalized signal attenuation;
- dynamic range, equal to the ratio of the maximum allowable signal level in the channel to the level of interference, normalized for this types of channels;
- the time during which the channel is used for data transmission;
- the width of the signal frequency spectrum, i.e., the interval on the frequency spectrum scale occupied by the signal;
- dynamic range equal to the ratio of the average signal power to the average interference power in the channel;
- the duration of the signal, or the time of its existence.
Another form of writing a condition (expanded):
P. S .: The parameter "Channel volume" in some sources is also indicated as one of the parameters of the communication channel, but not everywhere. The mathematical formula is given above in (1).
Literature
1. http://edu.dvgups.ru/METDOC/ENF/BGD/BGD_CHS/METOD/ANDREEV/WEBUMK/frame/1.htm;
2. http://supervideoman.narod.ru/index.htm.
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In fig. 1 the following designations are adopted: X, Y, Z, W- signals, messages ; f- hindrance; LS- communication line; AI, PI- source and receiver of information; P- converters (coding, modulation, decoding, demodulation).
There are different types of channels that can be classified according to different criteria:
1.By the type of communication lines: wired; cable; fiber optic;
power lines; radio channels, etc.
2... By the nature of the signals: continuous; discrete; discrete-continuous (signals at the input of the system are discrete, and at the output are continuous, and vice versa).
3... For noise immunity: channels without interference; with interference.
Communication channels are characterized by:
1. Channel capacity defined as the product of the channel usage time T to, bandwidth of the frequencies passed by the channel F to and dynamic range D to... , which characterizes the channel's ability to transmit different signal levels
V to = T to F to D to. (1)
Condition for matching the signal with the channel:
V c £ V k ; T c £ T k ; F c £ F k ; V c £ V k ; D c £ D k.
2.Information transfer rate - the average amount of information transmitted per unit of time.
3.
4. Redundancy - ensures the reliability of the transmitted information ( R= 0¸1).
One of the tasks of information theory is to determine the dependence of the information transfer rate and communication channel capacity on the channel parameters and characteristics of signals and interference.
The communication channel can be figuratively compared to roads. Narrow roads - low traffic, but cheap. Wide roads - good traffic but expensive. The bandwidth is determined by the "bottleneck".
The data transfer rate largely depends on the transmission medium in the communication channels, which are various types of communication lines.
Wired:
1. Wired- twisted pair (which partially suppresses electromagnetic radiation from other sources). Transfer rates up to 1 Mbps. Used in telephone networks and for data transmission.
2. Coaxial cable. Transfer rate 10-100 Mbps - used in local networks, cable TV, etc.
3... Fiber optic. The transmission rate is 1 Gbps.
In environments 1–3, the attenuation in dB is linear with distance, i.e. power drops exponentially. Therefore, after a certain distance, it is necessary to install regenerators (amplifiers).
Radio lines:
1.Radio channel. The transmission speed is 100-400 Kbps. Uses radio frequencies up to 1000 MHz. Up to 30 MHz, due to reflection from the ionosphere, electromagnetic waves can propagate beyond the line of sight. But this range is very noisy (for example, amateur radio). From 30 to 1000 MHz - the ionosphere is transparent and line of sight is required. Antennas are installed at a height (regenerators are sometimes installed). Used in radio and television.
2.Microwave lines. Transfer rates up to 1 Gbps. Use radio frequencies above 1000 MHz. This requires line-of-sight and highly directional parabolic antennas. The distance between the regenerators is 10–200 km. Used for telephony, television and data transmission.
3. Satellite connection... Microwave frequencies are used, and the satellite serves as a regenerator (and for many stations). The characteristics are the same as for microwave lines.
2. Bandwidth of a discrete communication channel
A discrete channel is a collection of means for transmitting discrete signals.
Communication channel bandwidth - the highest theoretically achievable information transfer rate, provided that the error does not exceed a given value. Information transfer rate - the average amount of information transmitted per unit of time. Let us define expressions for calculating the information transfer rate and the bandwidth of the discrete communication channel.
When each symbol is transmitted, on average, the amount of information passes through the communication channel, determined by the formula
I (Y, X) = I (X, Y) = H (X) - H (X / Y) = H (Y) - H (Y / X) , (2)
where: I (Y, X) - mutual information, i.e. the amount of information contained in Y relatively X ;H (X)- entropy of the message source; H (X / Y)- conditional entropy, which determines the loss of information per symbol associated with the presence of noise and distortion.
When sending a message X T duration T, composed of n elementary symbols, the average amount of transmitted information, taking into account the symmetry of the mutual amount of information, is equal to:
I (Y T , X T) = H (X T) - H (X T / Y T) = H (Y T) - H (Y T / X T) = n. (4)
The information transfer rate depends on the statistical properties of the source, the encoding method and the properties of the channel.
Discrete communication channel bandwidth
. (5)
The maximum possible value, i.e. the maximum of the functional is sought on the entire set of probability distribution functions p (x) .
The throughput depends on the technical characteristics of the channel (speed of the equipment, type of modulation, level of interference and distortion, etc.). The units of measurement of the channel capacity are:,,,.
2.1 Discrete communication channel without interference
If there is no interference in the communication channel, then the input and output signals of the channel are linked by an unambiguous, functional relationship.
In this case, the conditional entropy is equal to zero, and the unconditional entropies of the source and receiver are equal, i.e. the average amount of information in the received symbol relative to the transmitted one is
I (X, Y) = H (X) = H (Y); H (X / Y) = 0.
If X T- the number of characters for the time T, then the information transfer rate for a discrete communication channel without interference is
(6)where V = 1/ - the average bit rate of one symbol.
Bandwidth for a discrete communication channel without interference
(7)
Because the maximum entropy corresponds for equiprobable symbols, then the bandwidth for uniform distribution and statistical independence of the transmitted symbols is:
. (8)
Shannon's first channel theorem: If the flow of information generated by the source is close enough to the bandwidth of the communication channel, i.e.
, where is an arbitrarily small quantity,
then you can always find such a coding method that will ensure the transmission of all messages from the source, and the information transfer rate will be very close to the channel capacity.
The theorem does not answer the question of how to carry out the coding.
Example 1. The source generates 3 messages with probabilities:
p 1 = 0,1; p 2 = 0.2 and p 3 = 0,7.
Messages are independent and are transmitted in a uniform binary code ( m = 2 ) with a symbol duration of 1 ms. Determine the speed of information transmission over the communication channel without interference.
Solution: The entropy of the source is
[bit / s].
To transmit 3 messages with a uniform code, two bits are required, while the duration of the code combination is 2t.
Average signal rate
V =1/2 t = 500 .
Information transfer rate
C = vH = 500 × 1.16 = 580 [bps].
2.2 Discrete communication channel with interference
We will consider discrete communication channels without memory.
Channel without memory A channel is called in which each transmitted signal symbol is affected by interference, regardless of which signals were transmitted earlier. That is, interference does not create additional correlations between symbols. The name "without memory" means that during the next transmission, the channel does not seem to remember the results of previous transmissions.
Using Internet resources, find answers to questions:
Exercise 1
1. What is the process of transferring information?
Transfer of information- the physical process by which the movement of information is carried out in space. We wrote down the information on disk and transferred it to another room. This process is characterized by the following components:
2. General scheme of information transfer
3. List the communication channels known to you
By the type of distribution medium, communication channels are divided into:
4. What is telecommunications and computer telecommunications?Telecommunications(Greek tele - into the distance, far away and Latin communicatio - communication) is the transmission and reception of any information (sound, image, data, text) over a distance through various electromagnetic systems (cable and fiber-optic channels, radio channels and other wired and wireless channels communication).
Telecommunication network is a system of technical means through which telecommunications are carried out.
Telecommunication networks include:
1. Computer networks (for data transmission)
2. Telephone networks (voice transmission)
3. Radio networks (transmission of voice information - broadcast services)
4. Television networks (voice and image transmission - broadcast services)
Computer telecommunications - telecommunications, the terminal devices of which are computers.
The transfer of information from a computer to a computer is called synchronous communication, and through an intermediate computer, which allows messages to be accumulated and transmitted to personal computers as requested by the user, is called asynchronous.
Computer telecommunications are starting to take root in education. In higher education, they are used to coordinate scientific research, operational exchange of information between project participants, distance learning, and consultations. In the school education system - to increase the efficiency of students' independent activities related to various types of creative work, including educational activities, based on the widespread use of research methods, free access to databases, exchange of information with partners both domestically and abroad.
5. What is the bandwidth of the information transmission channel?Bandwidth- metric characteristic showing the ratio of the limiting number of passing units (information, objects, volume) per unit of time through a channel, system, node.
In computer science, the definition of bandwidth is usually applied to a communication channel and is determined by the maximum amount of transmitted / received information per unit of time.
Bandwidth is one of the most important factors from the point of view of users. It is estimated by the amount of data that the network can transfer at the limit per unit of time from one device connected to it to another.
The speed of information transfer depends to a large extent on the speed of its creation (source performance), methods of encoding and decoding. The highest possible information transfer rate in a given channel is called its bandwidth. The channel bandwidth, by definition, is the information transfer rate when using the "best" (optimal) source, encoder and decoder for a given channel, therefore it characterizes only the channel.
Transmission channels, their classification and basic characteristics
Basic concepts and definitions: transmission channel, its dynamic range, effectively transmitted frequency band, time during which the channel is provided for transmission of the primary signal, channel capacity. Main parameters and characteristics of the channel. Principles of normalization of residual attenuation deviation, frequency response, the concept of "template". Phase-frequency response. Amplitude characteristic and its various forms. Typical channels and their main characteristics.
The key concepts of the technology of telecommunication systems and networks are the transmission channel and the telecommunication channel.
Transmission channel is a set of technical means and a propagation medium that ensures the transmission of telecommunication signals in a certain frequency band or at a certain transmission rate between terminal or intermediate points of telecommunication networks.
According to the methods of transmission of signals, telecommunications are distinguished analog and digital channels.
1) Analog channels, in turn, are subdivided into continuous and discrete depending on the change in the information parameter of the signal.
2) Digital channels are divided into channels using pulse code modulation (ICM ) , channels using differential PCM and channels based on delta modulation ... Channels in which analogue methods of signal transmission are used in some areas and digital signal transmission methods in others are called mixed transmission channels.
Depending on the bandwidth in which telecommunication signals are transmitted, and the compliance of channel parameters with established standards, analog typical voice frequency channels, typical primary, secondary, tertiary and quaternary broadband channels. Typical channels for transmitting sound broadcasting signals, image signals and soundtrack of television;
Depending on the transmission rate and the compliance of the channel parameters with the established standards, they are distinguished: main digital channel, primary, secondary, tertiary, quaternary and quaternary digital channels ;
By the type of environment for the propagation of telecommunication signals, they are distinguished: wired channels organized by cable and, less often, overhead communication lines and radio communication channels organized by radio relay and satellite communication lines.
Telecommunication channel is called a set of technical means and a distribution environment that provides transmission of primary signals telecommunication from the message-to-primary signal converter to the primary signal-to-message converter.
In addition to the above classification, telecommunication channels are subdivided
By the type of transmitted primary signals (or messages), they are distinguished telephone channels, sound broadcasting channels, television channels, television
graph channels and data transmission channels ;
According to the methods of organizing two-way communication, they distinguish two-wire single-sideband, two-wire two-way and four-wire single-sideband channel;
On a territorial basis, telecommunication channels are subdivided to international, intercity, trunk, zone and local .
The considered classification of transmission and telecommunication channels (hereinafter simply channels) corresponds to the established practice of their organization and the development of requirements for their main parameters and characteristics, which are usually associated with the corresponding parameters and characteristics of primary signals.
The channel can be characterized by three parameters:
1) effectively transmitted bandwidth DF To, which the channel is able to pass while meeting the requirements for the quality of signal transmission;
2) time T To during which the channel is provided for the transmission of signals or messages;
3) dynamic range D To, which is understood as a relation of the form
where P kmax- the maximum undistorted power that can be transmitted over the channel; P cmin- the minimum signal power at which the necessary immunity from interference is provided.
It is obvious that signal transmission with parameters DF c ,T With, and D c by channel with parameters DF To ,T To and D To possible on condition
Product of three channel parameters V To = D To × F To × T To called him capacity... A signal can be transmitted over a channel if its capacity is not less than the signal volume (see lecture 2). If the system of inequalities (3.2) does not hold, then it is possible deformation one of the signal parameters that allow matching its volume with the channel capacity. Consequently, the condition for the possibility of signal transmission over the channel can be represented in a more general form
V To ³ V With . (3.3)
The channel is characterized by security
,
(3.4)
where P P Is the power of interference in the channel.
The channel bandwidth is described by the following expression
,
(3.5)
where P Wed Is the average power of the signal transmitted over the channel.
The transmission channel is like a four-port network
The transmission channel, as a set of technical means and a medium for the propagation of an electrical signal, is a cascade connection of various four-poles. v filtering, converting signals, amplifying and correcting them. Therefore, the channel can be represented an equivalent four-pole, the parameters and characteristics of which determine the quality of signal transmission, Fig. 3.1.
Rice. 3.1. The transmission channel is like a four-port network
In Fig.3.1, the following designations are adopted: 1-1 and 2-2 - input and output terminals, respectively; I in (jw) and I out (jw) - complex input and output currents; U in (jw) and U out (jw) - complex input and output voltages; Z in (jw) and Z out (jw) - complex input and output resistances (as a rule, values are purely active and equal, i.e. Z in = R in = Z out = R out);K(jw) =U out (jw) /U in (jw) =TO(w )× e jb (w) - complex voltage transfer coefficient, TO(w) Is the modulus of the transmission coefficient and b(w) - phase shift between input and output signals; if the ratio of the output current to the input current is taken, then we speak of the current transfer ratio; u in (t), u out (t) - instantaneous voltage values of the input and output signals and R in and R out - input and output levels of voltage or signal power.
Transmission channels work between real loads Z n1 (jw) and Z n2 (jw) connected to terminals 1-1 and 2-2, respectively.
The properties of channels and their compliance with the requirements for the quality of message transmission are determined by a number of parameters and characteristics.
The first and one of the main parameters of the channels is residual attenuation A r, which is understood as operating attenuation of the channel, measured or calculated under conditions of connection to the terminals 1-1and 2-2 (fig. 3.1) active resistances corresponding to the nominal valuesR in andR out respectively. The input and output resistances of individual devices of the transmission channel are in good agreement with each other. Under this condition, the operating attenuation of the channel can be considered equal to the sum characteristic(own) damping separate devices without considering reflections. Then the residual attenuation of the channel can be determined by the formula;
,
(3.1)
where R in and R out- levels at the input and output of the channel (see Fig. 3.1); A r- attenuation i- th and S j - gain j- th four-port networks that make up the transmission channel.
It means that residual attenuation(OZ) channel representsis the algebraic sum of damping and gain and is convenient for calculations A r when the attenuation of the gain sections and the gain of the amplifiers are known. OZ is measured at a specific for each channel measuring frequency.
During operation, the channel OZ does not remain constant, but deviates from the nominal value under the influence of various destabilizingfactors. These changes in OZ are called instability, which is estimated by the maximum and root-mean-square values of OZ deviations from the nominal value or the value of their variance.
The residual attenuation of a channel is related to its bandwidth. The channel frequency band, within which the residual attenuation differs from the nominal one by no more than a certain value DA r, is called effectively transmitted bandwidth (EPHP). Permissible deviations of OZ are normalized within the ESPC DA r from the nominal value. The most common method of standardization is the use of “templates” of permissible deviations of OZ. An approximate view of such a template is shown in Fig. 3.2.
Rice. 3.2. An approximate template of permissible deviations of the residual attenuation of the transmission channel
In fig. 3.2 the following notation is adopted f 0 - the frequency at which the nominal value of OZ is determined; f n , f v - lower and upper boundary frequencies of the ESPC; 1,2 - limits of permissible deviations of OZ; 3 is a view of the measured OZ frequency response. OZ deviations from the nominal are determined by the formula
,
(3.2)
where f - current frequency and f 0 – the frequency of determining the nominal value of OZ.
Closely related to the concept of EHPR frequency response -Frequency response(or simply frequency response ) of the channel, which is understood as dependence of residual attenuation on frequency A r =j h (f)at a constant level at the channel input, i.e. R in = const. This characteristic evaluates the amplitude-frequency (just frequency) distortions introduced by the channel due to the dependence of its OZ on frequency. The permissible distortions are determined by the OZ deviation pattern within the ESPC. An approximate view of the frequency response of the channel is shown in Fig. 3.3.
For the transmission of a number of telecommunication signals, it is important phase-frequency response - PFC(simply phase characteristic ) channel, which is understood as the dependence of the phase shift between the output and input signals on the frequency, i.e. b = j f (f). The general view of the phase response of the channel is shown in Fig. 3.4
(line 1).
Fig. 3. 3. Frequency response of the channel. Fig. 3. 4. Phase characteristic of the channel.
In the middle part of the ESPH, the specified characteristic is close to linear, and at its boundaries there is a noticeable nonlinearity due to the filters that are part of the transmission channel. Due to the fact that direct measurement of the phase shift introduced by the channel is difficult, the frequency response is considered to assess the phase distortion group transit time - GWP(or slowing down - GVZ)
t (w ) = db(w) / dw, (3.3)
where b (w) - phase-frequency characteristic. An approximate view of the frequency response of the SHG is shown in Figure 3.4 (line 2).
The frequency characteristics of the residual attenuation, phase shift, or group transit time determine linear distortion introduced by transmission channels when telecommunication signals pass through them.
The dependence of power, voltage, current or their levels at the output of the channel on the power, voltage, current or their levels at the input of the channel is called amplitude characteristic –OH... The AX channel is also understood as the dependence of the residual attenuation of the channel on the signal level at its input, i.e. A r =j a (R in), measured at a certain conditioned constant frequency of the measuring signal at the channel input, i.e. f rev= const.
The amplitude characteristic of the channel can be represented by various dependencies shown in Fig. 3.5: U out =j n (U in) (Figure 3.5 a, lines 1 and 2), A r = j A (R in) (Fig.3.5 b, line 1), R in =j R (R out) (Figure 3.5 b, lines 2 and 3), where the following designations are adopted: U in , U out- signal voltage at the input and output of the channel, respectively; R in , R out - levels (voltage, power) of signals at the input and output of the channel, respectively; A r- residual attenuation of the transmission channel.
From an examination of the graphs shown in Figure 3.5, it can be seen that AX has three sections:
1) nonlinear section at low voltage values or signal levels at the channel input. In this case, the nonlinearity of the AH is explained by the commensurability of the voltage or signal level with the noise of the channel itself;
2) a linear section at the values of the voltage or the input signal level, which is characterized by a direct proportional relationship between the voltage (level) of the signal at the channel input and the voltage (level) of the signal at the channel output;
Fig. 3. 5. Amplitude characteristics of the transmission channel
3) a section with significant nonlinearity at values of the input voltage (level) of the signal above the maximum U Max (R Max), which is characterized by the appearance nonlinear distortion. If the angle of inclination of the straight line corresponding to the linear section AX is equal to 45 0, then the voltage (level) of the signal at the output of the channel is equal to the voltage (level) at its input. If the tilt angle is less than 45 0, then attenuation takes place in the channel, and if the tilt angle is greater than 45 0, then amplification takes place in the channel. If A r > 0, then the channel introduces attenuation (attenuation), if A r <0, то канал передачи вноситresidual gain.
The insignificant nonlinearity of АХ at low values of the input voltage or signal level does not affect the transmission quality and can be neglected. AX nonlinearity at significant values of voltage or input signal level, going beyond the linear section of AX, are manifested in the occurrence of harmonics or combinational output signal frequencies. According to AH, one can only approximately estimate the amount of nonlinear distortion. More precisely, the amount of nonlinear distortion in the channels is estimated coefficient of nonlinear distortion or attenuation of nonlinearity.
or 
,
(3.4)
where U 1g - the effective value of the voltage of the first (fundamental harmonic of the measuring signal; U 2g ,U 3d etc. - RMS voltage values of the second, third, etc. signal harmonics arising from the nonlinearity of the AX transmission channel. In addition, in the technology of multichannel telecommunication systems, transmission is widely used the concept damping of nonlinearity by harmonics
A ng = 20lg ( U 1g / U n G) =R 1g - R n G ,n = 2, 3 …, (3.5)
where R 1g - absolute level first harmonic measuring signal, R n G - absolute level n-Ohharmonics due to the nonlinearity of the AX channel.
Digital channels are characterized by transmission speed, and the quality of signal transmission is evaluated error rate , which is understood as the ratio of the number of digital signal chips received with errors to the total number of signal chips transmitted during the measurement time
TO osh = N osh / N =N osh / VT, (3.6)
where N osh- the number of erroneously accepted elements; N - the total number of items transferred; V- baud rate; T- measurement (observation) time.
Telecommunication systems should be built in such a way that the channels would have a certain versatility and would be suitable for the transmission of various types of messages. These properties are possessed by typical channels , parameters and characteristics of which are normalized. Typical channels can be simple, those. not passing through the transit equipment, and constituent, i.e. passing through the transit equipment.
Typical transmission channels
Tone frequency channel . A typical analog transmission channel with a frequency band of 300 ... 3400 Hz and with normalized parameters and characteristics is called the channel of the tone frequency - KTCH.
The normalized (nominal value) of the relative (measuring) level at the input of the CTF is R in = - 13dBm 0, at the output of KTCH R out = + 4dBm 0. The frequency of the measuring signal is taken to be f rev = 1020Hz(previously 800 Hz). Thus, the nominal residual attenuation of the CTF is A r = - 17dB, i.e. CTCH introduces a gain equal to 17 dB.
Effectively transmitted bandwidth KTCH (composite and maximum length) is the band, at the extreme frequencies of which (0.3 and 3.4 kHz) the residual attenuation Ar is 8.7 dB higher than the residual attenuation at a frequency of 1020 Hz (previously 800 Hz).
Frequency response of residual attenuation deviations DA r from the nominal value (- 17 dB) must remain within template shown in Fig. 3.6.
Rice. 3.6. Template of permissible deviations of the residual attenuation of the CTF
To meet the requirements for the frequency response of the residual attenuation, its irregularity for a simple channel with a length of 2500 km must fit into the redistributions indicated in Table. 3.1.
Table 3.1
|
f, kHz | |||||
|
DA r , dB |
Phase-frequency distortions have little effect on the quality of speech signal transmission, but since the QFT is used for transmission of other primary signals, large phase-frequency distortions or uneven frequency response of the group transit time (GTP) are unacceptable. Therefore, the deviations of the GWP from its value at a frequency of 1900 are normalized. Hz for a simple channel with a length of 2500 km, Table 3.2.
Table 3.2
|
f,kHz | ||||||||||||
|
Dt,ms |
Naturally, for composite channels, the GWG deviations will be as many times as there are simple channels that organize the composite.
The amplitude characteristic of the CTF is normalized as follows: the residual attenuation of a simple channel must be constant with an accuracy of 0.3 dB when the level of the measuring signal changes from -17.5 to +3.5 dB at a point with a zero measuring level at any frequency within the ESPC range. Total harmonic distortion for a simple channel should not exceed 1.5% (1% at 3rd harmonic) at a nominal transmission level at a frequency of 1020 Hz.
The standardization also concerns the degree of coordination of the input and output resistances of the CTF with the resistances of external circuits - loads: the internal resistance of the source of transmitted signals and the load resistance. The input and output resistance of the CTF must be purely active and equal R in =R out = 600Ohm... Channel input and output must be symmetrical, coefficient reflectionsd or decay mismatch(reflections)A d equal, respectively, should not exceed 10% or 20 dB.
(3.7)
should not exceed 10% or 20 dB... Here Z n is the nominal, and Z p is the real value of the resistance.
An important indicator of the transmission quality over CTCH is the interference power, which is measured by a special device called psophometer (“Psophos” - in Greek means noise). The psophometer is a voltmeter with a square-law rectification characteristic. The choice of this characteristic is explained by the fact that the ear adds up the noise from individual sources in terms of power, and the power is proportional to the square of the voltage or current. Psophometers differ from ordinary quadratic voltmeters by the frequency dependence of their sensitivity. This dependence takes into account the different sensitivity of the ear at individual frequencies included in the spectrum of interference and noise, and is formed by the weighting psophometricfilter.
When voltage is applied to the input of the psophometer with a frequency of 800 Hz with a zero measuring level, its reading will be equal to 775 mV... To obtain the same value at different frequencies, the levels should be mostly higher. Interference voltage measured by psophometer U psof, is related to the effective voltage U eff ratio U psof = k P × U eff, here k P = 0.75 is called psophometric coefficient.
The voltage of interference or noise, measured with a psophometer, is called psophometric stress... Power determined by psophometric voltage at some resistance R is called psophometric power, which is equal P psof = k P × U 2 eff / R = 0,56U 2 eff R.
The average power level of interference with a uniform spectrum appears during psophometric measurements in the frequency band 0.3 ... 3.4 kHz by 2.5 dB(or 1.78 times) less than when measuring the effective (effective) values. Magnitude 2.5 dB called logarithmic psophometric coefficient.
The psophometric power of interference at a point with a zero measuring level of the CTF of the maximum length, consisting of the maximum number of simple channels, should not exceed 50,000 pwp 0 (picowatt psophometric at the point of zero relative level). The corresponding value of the effective ( unweighted) the admissible interference power is 87000 pW. Psophometric interference power of a simple channel with a length of 2500 km should not exceed 10000 pwp 0.
The permissible values of the average and peak power of telephone signals at the input of the CTF are also normalized: at the point of zero relative level, the average power value is 32 μW, and the peak is 2220 μW.
