Link is a collection of means for transmitting signals (messages).
There are different types of channels that can be classified according to different criteria:
1. By 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. By noise immunity: channels without interference; with interference.
Communication channels are characterized by:
1. Channel capacity is defined as the product of the channel usage time Tk, the bandwidth of the frequencies transmitted by the channel Fk and the dynamic range Dk., which characterizes the channel's ability to transmit various signal levels Vk \u003d Tk Fk Dk. (1) Condition of matching the signal with the channel: Vc Vk; Tc Tk; Fc Fk; Vc Vk; Dc Dk.
2. Information transfer rate - the average amount of information transmitted per unit of time.
3.Communication channel bandwidth - the highest theoretically achievable information transfer rate, provided that the error does not exceed a given value.
4. Redundancy - ensures the reliability of the transmitted information (R \u003d 01).
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 are 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. Transfer rates up to 1 Mbps.
2. Coaxial cable... Transfer rate 10-100 Mbps
3. Fiber optic... The transmission rate is 1 Gbps.
Radio lines:
Radio channel... Transfer rate 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.
Microwave lines... Transfer rates up to 1 Gbps. Radio frequencies above 1000 MHz are used. 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.
Satellite connection. Microwave frequencies are used and the satellite serves as a regenerator.
Shannon's Theorem for Noise-Free Channelsit is always possible to create a system for efficient coding of discrete messages, in which the average number of binary code signals per message symbol will approach as close as you like to the entropy of the message source.
Let the message source have the capacity H ¢ (U) \u003d u C × H (U), and the channel has the capacity C \u003d u K × log M. Then we can encode the messages at the source output in such a way as to obtain the average number of code symbols per the message element h \u003d u K / u C \u003d (H (U) / log M) + e (2.2), where e is arbitrarily small (direct theorem). It is impossible to obtain a smaller value of h (converse theorem). The converse part of the theorem asserts that it is impossible to obtain the value h \u003d u K / u C< H(U)/ log M (2.3), может быть доказана если учесть, что неравенство (2.3) эквивалентно неравенству u C × H(U) > u K × log M, H ¢ (U)\u003e C. The last inequality cannot be satisfied because the coding in question must be a reversible transformation (i.e., without information loss). Entropy per second at channel input or encoder performance cannot exceed channel bandwidth. And the entropy of the received signals is determined from the condition of the maximum value H ’(y) \u003d log m.
Shannon's theorem for a discrete noisy channel is also called the main Shannon coding theorem. If the performance of the message source H ¢ (U) is less than the throughput of the channel C, i.e. H ¢ (U)< C, то существует такая система кодирования которая обеспечивает возможность передачи сообщений источника со сколь угодно малой вероятностью ошибки (или со сколь угодно малой ненадежностью).
If H ¢ (U)\u003e C, then the message can be encoded in such a way that the unreliability per unit time will be less than H ¢ (U) -C + e, where e ®0 (direct theorem).
There is no coding method that provides unreliability per unit of time less than H ¢ (U) -C(converse theorem).
In this formulation, this theorem was given by Shannon himself. In the literature, the second part of the direct theorem and the converse theorem are often combined in the form of an inverse theorem formulated as follows: if H ¢ (U)\u003e C, then there is no such coding method.
2. Types of signals, their sampling and restoration. Spectral density of signals. Nyquist frequency, Kotelnikov's theorem. Frequency representation of discrete signals. Orthogonal transformations of discrete signals. Interpolation and signal decimation tasks.
Signal types, sampling and recovery
By types (types) of signalsthe following stand out:
1.analog
2.discrete
3.digital
Analog signal (analog signal) is a continuous function of a continuous argument, i.e. defined for any value of the arguments. Sources of analog signals, as a rule, there are physical processes and phenomena that are continuous in the dynamics of their development in time, space or in any other independent variable, while the recorded signal is similar (―similar‖) to the process that generates it. An example of a mathematical record of a signal: y (t) \u003d 4.8 exp /2.8]. Moreover, both the function itself and its arguments can take any values \u200b\u200bwithin some intervals y J, t J. If the intervals of the values \u200b\u200bof the signal or its independent variables are not limited, then by default they are assumed to be from -Ґ to +. The set of possible signal values \u200b\u200bforms a continuum - a continuous space in which any signal point can be determined up to infinity. Examples of signals that are analog in nature are changes in the strength of the electric, magnetic, electromagnetic fields in time and space.
Discrete signal (discrete signal) by its values \u200b\u200bis also a continuous function, but defined only by discrete values \u200b\u200bof the argument. In terms of its set of values, it is finite (countable) and is described by a discrete sequence of samples (samples) y (nDt), where y Ј, Dt is the interval between samples (interval or sampling step, sample time), n \u003d 0, 1, 2, ..., N. The reciprocal of the sampling step: f \u003d 1 / Dt, is called the sampling frequency. If a discrete signal is obtained by sampling an analog signal, then it is a sequence of samples, the values \u200b\u200bof which are exactly equal to the values \u200b\u200bof the original signal in coordinates nDt.
Digital signal (digital signal) is quantized in value and discrete in argument. It is described by the quantized lattice function yn \u003d Qk, where Qk is the quantization function with the number of quantization levels k, while the quantization intervals can be either uniformly distributed or nonuniform, for example, logarithmic. A digital signal is set, as a rule, in the form of a discrete series of numerical data - a numerical array of sequential values \u200b\u200bof the argument when Dt \u003d const, but in the general case, the signal can also be set in the form of a table for arbitrary values \u200b\u200bof the argument.
Sampling, restoration (interpolation) of signals.
Sampling process is the process of obtaining the values \u200b\u200bof the converted signal at certain intervals ( counts).
Sampling of signals is understood as the transformation of functions of continuous variables into functions of discrete variables, from which the original continuous functions can be restored with a given accuracy. The role of discrete samples is performed, as a rule, by quantized values \u200b\u200bof functions in a discrete coordinate scale. Quantization is understood as the transformation of a continuous value into a value with a discrete scale of values \u200b\u200bfrom a finite set of allowed values, which are called quantization levels. If the quantization levels are numbered, then the result of the conversion is a number that can be expressed in any number system. Rounding with a certain bit depth of instantaneous values \u200b\u200bof a continuous analog value with a uniform step by argument is the simplest case of sampling and quantizing signals when they are converted into digital signals.
Sampling principles. The essence of the sampling of analog signals lies in the fact that the continuity in time of the analog function s (t) is replaced by a sequence of short pulses, the amplitude values \u200b\u200bof which are determined using weighting functions, or directly by samples (counts) of the instantaneous values \u200b\u200bof the signal s (t) at times. signal s (t) on the interval T by a set of discrete values \u200b\u200bis written in the form:
(c1, c2, ..., cN) \u003d A,
where A is the discretization operator. Recording the signal recovery operation s (t):
s "(t) \u003d B [(c1, c2, ..., cN)].
The choice of operators A and B is determined by the required signal reconstruction accuracy. The simplest are linear operators. In general:
(5.1.1)
Where is the system of weighting functions.
The counts in expression (5.1.1) are associated with the integration operation, which ensures high noise immunity of sampling. However, due to the complexity of the technical implementation of "weighted" integration, the latter is used quite rarely, at high noise levels. Methods in which the signal s (t) is replaced by a set of its instantaneous values \u200b\u200bs () at times have become more widespread. The role of weighting functions in this case is performed by ridge (lattice) functions. The time interval Dt between adjacent samples is called the sampling step.Sampling is called uniform with a frequency F \u003d 1 / Dt if the value of Dt is constant over the entire range of signal conversion. With non-uniform sampling, the Dt value between samples can change according to a certain program or depending on changes in any signal parameters.
Signal recovery
Restoring continuous signalthe samples can be carried out both on the basis of orthogonal and non-orthogonal basis functions. The reproducing function s "(t) is respectively represented by an approximating polynomial: 
Where is the system of basic functions. Orthogonal basis functions ensure the convergence of the series to s (t) for n. The best are sampling methods that provide the minimum numerical series for a given signal reproduction error. For non-orthogonal basis functions, power algebraic polynomials of the form are mainly used:
If the values \u200b\u200bof the approximating polynomial coincide with the values \u200b\u200bof the samples at the moments of their reference, then such a polynomial is called interpolating. Lagrange polynomials are usually used as interpolating polynomials. To implement interpolating polynomials, a signal delay by the sampling interval is required, which in real-time systems requires certain technical solutions. Taylor polynomials are usually used as extrapolating polynomials.
A natural requirement for the selection of the sampling rate is the introduction of minimal distortions into the dynamics of changes in signal functions. It is logical to assume that the information distortion will be the less, the higher the sampling frequency F. On the other hand, it is also obvious that the larger the F value, the more digital data the signals will be displayed, and the longer it will take to process them. Optimally, the value of the sampling frequency of the signal F should be necessary and sufficient for processing the information signal with a given accuracy, i.e. providing an admissible error in the restoration of the analog signal shape (root-mean-square as a whole over the signal interval, or according to the maximum deviations from the true shape in the characteristic information points of the signals).
Signal quantization.
Sampling of analog signals with conversion to digital form is related to the quantization of signals. The essence of quantization consists in replacing an uncountable set of possible values \u200b\u200bof a function, in the general case random, with a finite set of digital samples, and is performed by rounding the instantaneous values \u200b\u200bof the input function s (ti) at times ti to the nearest values \u200b\u200bsi (ti) \u003d niDs, where Ds is the step quantization of the scale of digital samples. Quantization with a constant step Ds is called uniform. Mathematically, the quantization operation can be expressed by the formula:
where brackets [..] denote the whole part of the value in brackets.
When quantizing signals in a large dynamic range of values, the quantization step can be non-uniform, for example, logarithmic, i.e. proportional to the logarithm of the input signal values. The set range of the quantization scale from smin to smax and the quantization step Ds determine the number of scale divisions Ns \u003d (smax-smin) / Ds and, accordingly, the digital quantization bit depth. As a result of discretization and quantization, the continuous function s (t) is replaced by the numerical sequence (s (kDt)). Rounding error ei \u003d s (kDt) -si (kDt) is within -Ds / 2 With a sufficiently small quantization step, any value within its limits can be considered equally probable, while the values \u200b\u200bof e are distributed according to a uniform law: p (e) \u003d 1 / Ds, -Ds / 2 Ј e Ј Ds / 2. Accordingly, the variance and rms value of the quantization noise: e2 \u003d Ds2 / 12, »0.3 Ds. .1) When specifying the quantization noise level using expression (5.5.1), it is easy to determine the permissible value of the quantization step. The input signal contains, as a rule, an additive mixture of the signal itself s (t) and noise q (t) with variance, respectively, sq2. If the interference is not correlated with the signal, then after quantization the total noise variance is: In practice, the quantization step is usually chosen such that there is no noticeable change in the signal-to-noise ratio, i.e. e2< To organize data transfer, you must use communication lines and channelsthat carry out communication between computers, telephones, telegraphs and other means of communication. The transmitted information resides in a physical medium, which can consist of various types of cables and wires, as well as the surrounding space. Despite the fact that both concepts are often identified, they have some differences that you need to know about to build correct information communication. Through the channels, communication is transmitted in one direction or in two, if the exchange occurs between the receiver and the transmitter. Communication lines, in turn, are formed from the connection of several channels, and there can also be only one channel in them. There are such communication lines:
Let's take a closer look at each type of line and learn about their capabilities, advantages and disadvantages. These lines can be used to carry a telegraph, telephone or computer signal. They consist of wires through which data is exchanged. This type of communication is suitable for transmitting digital and analog signals, because of its high popularity. The disadvantages of such a connection include a relatively low signal transmission rate and a low degree of immunity from interference. It is also possible a banal unauthorized connection of unscrupulous subscribers, which leads to a decrease in the quality of data transmission and financial losses of broadcasting companies. The structure of the cable can be different, but basically they all consist of groups of conductors that are processed with reliable insulation. For data exchange in computer networks, the following types of cables are used:
Lines and channels of communication can be built on the work of wireless terrestrial or satellite radio channels. Radio-relay channels are a group of repeater stations that are located in a certain order at a certain distance from each other. Stations and repeaters are used in the field of cellular communications and for the transmission of other types of signals within the same city or region. Satellite communication is provided by satellites, which are located in the earth's orbit and are repeaters. The signal from the ground transmitting station goes to the satellite, and from the satellite it is transmitted to the ground receiving station. This communication method makes it possible to provide communication for the inhabitants of the most remote parts of the planet, since satellites are most often launched not one by one, but in groups. All repeaters are located in orbit at some distance from each other, therefore together they can cover almost the entire globe. You can find out what lines and communication channels modern companies use at the specialized exhibition "Communication", which will take place at the Expocentre Fairgrounds. The exhibition will be dedicated to new products in the field of IT. The event will feature the latest technical solutions for communication. State exam (State examination) Question No. 3 “Communication channels. Classification of communication channels. Communication channel parameters. Condition of signal transmission over the communication channel ". (Plyaskin)
Link. 3 Classification. five Characteristics (parameters) of communication channels. ten Condition for the transmission of signals over communication channels. 13 Literature. fourteen 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 the user (person), or for use by computer applications. The communication channel includes the following components: 1) transmitting device; 2) receiving device; 3) 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 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 # 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 distinguished channels wired communication ( aerial, cable, light-guideand others) and radio communication channels (tropospheric, satellite and 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 (at the input and output of the channel - continuous signals), Discrete or digital (at the input and output of the channel - discrete signals), · 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, temporary and space-time. Possible classification
communication channels by frequency range
. Information transmission systems are single-channel and multichannel... 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 classification features is used. Classification No. 2 (more detailed):
1.
Classification by frequency range Ø Kilometer (LW) 1-10 km, 30-300 kHz; Ø Hectometric (SV) 100-1000 m, 300-3000 kHz; Ø Decameter (HF) 10-100 m, 3-30 MHz; Ø Meter (MV) 1-10 m, 30-300 MHz; Ø Decimeter (UHF) 10-100 cm, 300-3000 MHz; Ø Centimeter (CMB) 1-10 cm, 3-30 GHz; Ø Millimeter (MMV) 1-10 mm, 30-300 GHz; Ø Decimitre (DMMV) 0.1-1 mm, 300-3000 GHz. 2.
By direction of communication lines
- directed (different conductors are used): Ø coaxial, Ø twisted pairs based on copper conductors, Ø fiber optic. -
non-directional (radio links); Ø line of sight; Ø tropospheric; Ø ionospheric Ø space; Ø radio relay (retransmission on decimeter and shorter radio waves). 3.
By the type of transmitted messages:
Ø telegraph; Ø telephone; Ø data transmission; Ø facsimile. 4. By the type of signals: Ø analog; Ø digital; Ø impulse. 5.
By the type of modulation (manipulation)
- In analog communication systems: Ø with amplitude modulation; Ø with single sideband modulation; Ø with frequency modulation. - In digital communication systems: Ø with amplitude shift keying; Ø with frequency shift keying; Ø with phase shift keying; Ø with relative phase shift keying; Ø with tone shift keying (single elements manipulate the subcarrier oscillation (tone), after which they are keyed at a higher frequency). 6.
By the value of the base of the radio signal Ø broadband (B \u003e\u003e 1); Ø narrowband (B "1). 7. By the number of simultaneously transmitted messages
Ø single-channel; Ø multichannel (frequency, time, code division of channels); 8. In the direction of messaging
Ø one-sided; Ø
bilateral. Ø simplex communication - two-way radio communication, in which transmission and reception of each radio station is carried out in turn; Ø duplex communication - transmission and reception are carried out simultaneously (the most efficient); Ø 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
Ø open communication; Ø closed communication (classified). 11. By the degree of automation of information exchange
Ø non-automated - radio station control and messaging is performed by the operator; Ø automated - only information is entered manually; Ø automatic - the process of messaging is performed between an automatic device and a computer without operator participation. Classification number 3 (something may 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 (transmit simultaneously 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 and 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 1.
Channel transfer function:
is presented as amplitude-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 amplitude-frequency response of a real channel allows you to determine the shape of the output signal for almost any input signal. For 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 some 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 Fig. 4 Normalized channel frequency response 2.
Bandwidth:
is a derived 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. 3.
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 by knowing 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: Signal power at the channel output, Signal strength at 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. 4.
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, the noise level, the type of coding and modulation. 5.
Channel immunity:
characterizes its ability to provide signal transmission in the presence of interference. Interference is usually divided into internal (represents thermal noise from equipment) and external (they are diverse and depend on the transmission medium). Channel immunity depends on the hardware and algorithmic solutions for processing the received signal, which are embedded in the transceiver. Immunity transmission of signals through the channel can be increased at the expense encoding and special processing signal. 6.
Dynamic range
: logarithm of the ratio of the maximum power of the signals transmitted by the channel to the minimum. 7.
Interference immunity:
this is noise immunity, i.e. noise immunity. The main function of the information system is the storage of information and its transfer in space. The set of technical means for transmitting messages from source to consumer is called a communication system. These means are a transmitter, a communication line, and a receiver. Sometimes the concept of a communication system includes the source and the consumer of messages. The structural diagram of the simplest communication system is shown in Figure 2. Here the source of the message is the starting point. The source can generate continuous or discrete messages. The source of messages and the recipient in some communication systems can be a person, in others - various kinds of devices (automaton, computer, etc.). The transmission of messages over a distance is carried out using some material medium (paper, magnetic tape, etc.) or a physical process (sound or electromagnetic waves, current, etc.). The source of information or message is a physical object, system or phenomenon that forms the transmitted message. A message is a value or change in some physical quantity that reflects the state of an object (system or phenomenon). Typically, primary messages - speech, music, images, environmental measurements, etc., are functions of time - f
(t)
or other arguments - f
(x, y, z)
non-electrical nature (acoustic pressure, temperature, brightness distribution on a certain plane, etc.). Fig. 2. Block diagram of the communication system. Each
i
- th source message is an arbitrary sequence of alphabet elements When m
= 1
the message is one letter, that is, there is such a message elementary message
... In the general case, for m
> 1
the same letter may appear in the message Finite set of messages
X
c
the probability distribution given on it
p
(
x
) is called a discrete ensemble of messages and is denoted (
X
,
p
(
x
)}.
A device that converts a message into a signal is called a transmitter, and a device that converts a received signal into a message is called receiving device. Using a converter in the transmitting device, the message and, which can be of any physical nature (image, sound vibration, etc.), is converted into a primary electrical signal b(t). In telephony, for example, this operation is reduced to converting sound pressure into a proportionally varying electric current of the microphone. In telegraphy, coding is first performed, as a result of which the sequence of message elements (letters) is replaced by a sequence of code symbols (0, 1 or dot, dash), which is then converted into a sequence of direct current electric pulses using a telegraph apparatus. In the transmitter, the primary signal b(t) (usually low frequency) turns into a secondary (high frequency) signal u(t) suitable for transmission over the channel being used. This is done through modulation. The transformation of a message into a signal must be reversible. In this case, from the output signal, it is possible, in principle, to restore the input primary signal, that is, to obtain all the information contained in the transmitted message. Otherwise, some information will be lost during transmission, even if the signal reaches the receiving device without distortion. The physical process representing (carrying) the message being transmitted is called a signal.
A signal is a material and energy form of information presentation. In other words, a signal is a carrier of information, one or several parameters of which, changing, display a message. The information-message-signal chain is an example of the processing needed where the information comes from. On the side of the information consumer, processing is carried out in the reverse order: “signal - message - information”. Any transformation of a message into a specific signal by establishing a one-to-one correspondence between them is broadly called encoding. Coding can include processes of converting and sampling continuous messages (analog-to-digital conversion), modulation (manipulation in digital communication systems) and coding itself in the narrow sense of the word. The reverse operation is called decoding. A communication link is the medium used to carry signals from a transmitter to a receiver.
In electrical communication systems, this is a cable or waveguide, in radio communication systems, an area of \u200b\u200bspace in which electromagnetic waves propagate from a transmitter to a receiver. Signal transmission may be distorted and interfering with n(t). Receiver processes the received waveform z(t)=u(t)+n(t), which is the sum of the incoming distorted signal u(t) and interference n(t), and restores the message from it A communication channel is a set of means that ensure the transmission of a signal from some point A of the system to point B (fig. 3). Points AND and IN can be chosen arbitrarily, as long as the signal passes between them. The part of the communication system located up to the point AND, is the signal source for this channel. Figure: 3. Communication channel. The channel, as a source of interference, has some influence on the transmitted signal. The tasks of the receiver are to extract the transmitted message from the noisy signal and send it to the consumer. Communication channels are classified according to various criteria, including mathematical description (continuous and discrete channels, continuous and discrete time). If the signals arriving at the input of the channel and received from its output are discrete in states, then the channel is called discrete. If these signals are continuous, then the channel is called continuous. There are also discrete-continuous and continuous-discrete channels, at the input of which discrete signals are received, and continuous signals are taken from the output, or vice versa. It can be seen from the above that the channel can be discrete or continuous, regardless of the nature of the messages being transmitted. Moreover, in the same communication system, both discrete and continuous channels can be distinguished. It all depends on how the points are selected AND and IN channel input and output. In this tutorial, we will consider discrete communication channel
. If the harmful effect of interference in the channel can be neglected, then the analysis uses a model in the form of an idealized channel, called channel without interference... In an ideal channel, each input message has a unique output ratio and vice versa. When accuracy requirements are high and disregard for ambiguity between messages x and y
unacceptable, a more complex model is used - a noisy channel. The simplest class of channel models is formed by discrete channels without memory; they are defined as follows. The input is a sequence of letters (elements) from a finite alphabet, let
Figure: 4. Binary balanced channel. A much wider class of channels - channels with memory, form channels in which the input signals are sequences of letters from finite alphabets, but in which each letter at the output can statistically depend not only on the corresponding letter of the input sequence. 1. Communication channel 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. The communication channel is designed to transmit signals between remote devices. Signals carry information intended for presentation to the user (person), or for use by computer applications. 2 The communication channel includes the following components: 1) transmitting device; 2) receiving device; 3) transmission medium of different physical nature The information-carrying signal generated by the transmitter, after passing through the transmission medium, enters the input of the receiving device. Further 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. communication channel remote recipient Those. this (channel) is a technical device (technology + environment). 3. Characteristics (parameters) of communication channels 1. Transfer function of the channel: it is represented in the form of amplitude-frequency characteristic (AFC) and shows how the amplitude of the sinusoid at the output of the communication channel is attenuated in comparison with the amplitude at its input for all possible frequencies of the transmitted signal. Knowing the amplitude-frequency response of a real channel allows you to determine the shape of the output signal for almost any input signal. For 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 converted 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 some maximum value that can occur in the input signals. Moreover, it is necessary to change the frequency of the input sinusoids in small steps, which means that the number of experiments should be large. 2. Bandwidth: is the derivative of 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. 3. Attenuation: 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 attenuation at this frequency to roughly estimate the distortion of signals transmitted over the channel. More accurate estimates are possible by knowing 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 Рвх - signal power at the channel output, Рвх - 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. 4. Baud rate: 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, the noise level, the type of coding and modulation. 5. Channel immunity: characterizes its ability to provide signal transmission in the presence of interference. Interference is usually divided into internal (it is the thermal noise of the equipment) and external (they are diverse and depend on the transmission medium). Noise immunity of the channel depends on the hardware and algorithmic solutions for processing the received signal, which are embedded in the transceiver. The immunity of signal transmission through the channel can be increased by coding and special signal processing. 6. Dynamic range: the logarithm of the ratio of the maximum power of the signals transmitted by the channel to the minimum. 7. Interference immunity: this is interference immunity, i.e. noise immunity.How do communication channels differ from communication lines?
Wire (overhead) communication lines
Cable communication lines
Wireless communication channels
Examples of communication lines and channels at the exhibition
9. By order of message exchange
- bandwidth
where
(
,
,
...,
) length
m
where the superscript of the elements is the sequence number, and the subscript only means the place of the letter in the message, but not its kind.
repeatedly. A common property of an elementary message is its indivisibility into smaller messages.
, which reflects the transmitted message with some error
a... In other words, the receiver should, based on the fluctuation analysis z(t) determine which of the possible messages was transmitted. Therefore, the receiving device is one of the most critical and complex elements of the communication system.
,
output - a sequence of letters of the same or a different alphabet, say 
... Finally, each letter of the output sequence depends statistically only on the letter at the corresponding position in the input sequence, and is determined by a given conditional probability 
defined for all letters 
input alphabet and all letters 
at the exit. An example is a binary symmetric channel (Fig. 4), which is a discrete memoryless channel with binary sequences at the input and output, in which each symbol of the sequence at the input with a certain probability 1-q is reproduced at the output of the channel correctly and with probability q changes noise to the opposite symbol. In the general case, in a discrete memoryless channel, the transition probabilities exhaust all known information about how the input signal interacts with the noise to form the output signal.
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