Interference in communication channels. Discrete channel Gaussian channel with indefinite signal phase

In many problems in communication theory, the structure of the modulator and demodulator is given. In these cases, the channel is that part of the communication line that is shown in Fig. 1.3 is circled with a dotted line. Discrete code symbols are supplied to the input of such a channel, and are removed from the output with the symbol, which generally do not coincide with (Fig. 2.1).

Such a channel is called discrete. When studying the transmission of messages over a discrete channel, the main task is to find encoding and decoding methods that, in one sense or another, make it possible to best transmit messages from a discrete source.

Note that in almost all real communication lines, a discrete channel contains within itself a continuous channel, to the input of which signals are supplied, and signals distorted by interference are removed from the output. The properties of this continuous channel, along with the characteristics of the modulator and demodulator, uniquely determine all the parameters of the discrete channel. Therefore, sometimes a discrete channel is called a discrete display of a continuous channel. However, in the mathematical study of a discrete channel, one usually abstracts from the continuous channel and the interference operating in it and determines the discrete channel by specifying the alphabet of code symbols arriving at its input, an alphabet of code symbols taken from its output, the number of code symbols passed per unit time, and the values ​​of the transition probabilities, i.e., the probabilities that the symbol will appear at the output if the symbol is given at the input. These probabilities depend on which symbols were previously transmitted and received. The code alphabets at the input and output of the channel may not be the same; in particular, it is possible that . The value is sometimes called the technical transmission speed.

Rice. 2.1. Communication system with a discrete channel.

If the transition probabilities for each pair remain constant and do not depend on which symbols were transmitted and received earlier, then the discrete channel is called constant or homogeneous. Sometimes other names are also used: a channel without memory or a channel with independent errors. If the transition probabilities depend on time or on previously occurring transitions, then the channel is called heterogeneous or a channel with memory.

In a channel with memory, probabilistic connections, at least to a first approximation, extend only to a certain finite segment. This means that the transition probabilities depend on what transitions took place during the transmission of previous symbols, and do not depend on earlier transitions. Such a channel can be considered as having a number of discrete states determined by previous transitions, and . For each state, conditional transition probabilities are determined. At the same time, only the last transmitted and received symbols determine the state of the channel.

The average unconditional transition probabilities are determined by averaging the conditional probabilities over all channel states:

(2.1)

where is the probability of the state.

In real channels with element-by-element reception, the transition probabilities are not given, but are determined, on the one hand, by interference and distortion of signals in the channel, on the other hand, by the feed rate of code symbols and the first decision circuit. By choosing the optimal decision scheme based on one or another criterion, the transition probability can be changed in the desired direction. Thus, in order to consider the channel as discrete, it is necessary to select the first decision circuit and, taking into account the interference and distortion operating in the channel, calculate the transition probabilities. It is obvious that in those cases when the parameters of a real channel are constant and the interference acting in the channel represents a stationary random process, its discrete representation is a constant channel. If these conditions are not met, then the discrete display, as a rule, turns out to be a channel with memory.

If in a channel the alphabets at the input and output are the same and for any probability pair , then such a channel is called symmetrical. We will also call a variable channel symmetrical if in each state for any pair the condition is satisfied

Obviously, from (2.2) it also follows at the output that the transmitted symbol is distorted by interference and cannot be recognized. Thus, part of the received code sequence is erased.

As will be shown later, the introduction of such an erasing symbol does not interfere with the possibility of correct decoding of the received code sequence, but, on the contrary, facilitates it with a rational choice of the encoding method and decision circuits.

Rice. 2.2. Probabilities of transitions in a symmetric binary channel.

Rice. 2.3. Probabilities of transitions in a symmetric channel with erasure.

Note that the output code alphabet is determined by the choice of the first decision circuit and is therefore considered given only because we are considering a discrete channel mapping. The choice of the first decision scheme also largely determines the symmetry properties of the channel. The transition probabilities in a symmetric erasing channel are shown in Fig. 2.3.

Information is a collection of information about an event, phenomenon, or object. In order for information to be stored and transmitted, it is presented in the form of messages.

Message– is a set of signs (symbols) containing this or that information. To transmit messages, communication systems can use physical media (for example, paper, magnetic disk or tape storage devices) or physical processes (varying electric current, electromagnetic waves, a beam of light).

The physical process that displays the transmitted message is called signal. The signal is always a function of time.

If the signal is a function S(t), taking for any fixed value t, only certain, preset values S k, such a signal and the message it displays are called discrete. If a signal takes any value in a certain time interval, it is called continuous or analog.

Many possible values ​​of a discrete message (or signal) DS represents alphabet messages. The message alphabet is indicated by a capital letter, e.g. A, and all its possible values ​​are indicated in curly brackets - symbols.

SDS – source of discrete messages SDS – recipient of discrete messages

SPDS – discrete message transmission system

Let us denote the alphabet of the message on transmission (alphabet of the input message, input alphabet) - A, the alphabet of the message on reception (alphabet of the output message, output alphabet) - B.

In general, these alphabets can have an infinite number of meanings. But in practice they are finite and coincide. This means that when receiving a symbol b k it is considered that the symbol was transmitted a k.

There are two types of discrete signals:

· Discrete random processes of continuous time(START), in which a change in signal values ​​(symbols) can occur at any time over an arbitrary interval.

· Discrete time discrete random processes(DSDV), in which a change of symbols can only occur at fixed times t 0, t 1, t 2 …t i …, where t i =t 0 +i* 0. The quantity   is called unit interval.

The second type of discrete signals is called discrete random sequences of DSP.

In the case of continuous time, a discrete random process can have an infinite number of implementations on the time interval , and in the case of a signal in the form of a DSP, the number of possible implementations is limited by the set

Where k is an index indicating the number of the alphabet character, i is an index indicating a moment in time. With an alphabet volume equal to K and sequence length n symbols the number of possible implementations is equal to K n.

In general, source of discrete messages or signals (IDS) is any object that generates a discrete random process at its output.

Discrete channel (DC)– call any section of the transmission system at the input and output of which interconnected discrete random processes take place.

Let's consider the block diagram of transformations in the discrete message transmission system.

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

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

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

There are several definitions for transmission speed.

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

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

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

where?F - KS band;

Based on the transmission speed of discrete channels and the corresponding UPS, they are usually divided into:

• - low-speed (up to 300 bits/sec);
• - medium-speed (600 - 19600 bps);
• - high-speed (more than 24,000 bps).

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

Relative transfer rate:

Reliability of information transmission - is used due to the fact that in each channel there are extraneous emitters that distort the signal and complicate the process of determining the type of transmitted single element. According to the method of converting messages into a signal, interference can be additive or multiplicative. In form: harmonic, pulse and fluctuation.

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

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

Reliability - a discrete channel, like any DS, cannot work without failure.

A failure is an event that ends in the full or partial womb of the performance system. In relation to a data transmission system, a failure is an event that causes a delay in the received message for a time t set >t add. In this case, tadd is different in different systems. The property of a communication system that ensures the normal performance of all specified functions is called reliability. Reliability is characterized by the mean time between failures T o, the mean recovery time T b, and the availability factor:

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

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

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

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

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

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

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

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

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

The communication channel (including trunks) is characterized by its bandwidth DF to, residual attenuation and ost, uneven residual attenuation Yes ost and group transit time (GTT) Dt gvp in the communication channel band .

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

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

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

1) fluctuation or distributed in frequency and time,

2) harmonic or concentrated in frequency,

3) pulsed or concentrated in time.

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

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

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

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

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

At the input of the UPS prm, consisting of a linear amplifier US in, a bandpass filter PF prm, a demodulator DM, devices for recording UR and synchronizing the US with speed IN a mixture of signal and noise is received, characterized by the signal/noise ratio q in. After passing through the PF prm receiving filter, the signal-to-noise ratio improves somewhat.

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

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

The issues considered are examined in laboratory work No. 3 “Characteristics of a discrete channel”.

Test questions for lecture 5

5-1. Which channel is called discrete?

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

5-3. How is the speed of information transmission over a channel determined?

5-4. How is the modulation rate determined?

5-5. How is the accuracy of information transmission over a channel assessed?

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

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

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

5-9. What is relative signal level?

5-10. What is the absolute signal level?

5-11. What is the measurement signal level?

5-12. What is the residual channel attenuation?

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

5-15. What can result from exceeding the signal power at the channel input?

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

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

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

5-19. What is group travel time?

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

5-21. How are nonlinear distortions introduced by the channel assessed?

5-22. What is the overload level?

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

5-24. How is the maximum transmission rate related to the channel bandwidth when transmitting modulated signals with two sidebars?

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

5-26. How does the nature of the channel's phase response affect the channel's bandwidth?

5-27. How can the optimal transmission speed for it be found based on the frequency response and phase response of a channel?

5-28. What is a hindrance?

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

5-30. What types of additive noise are divided into?

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

5.32. How does harmonic interference differ from fluctuation interference?

5.33. What parameters characterize harmonic interference?

5.34. How does impulse noise differ from harmonic noise?

5.35. What are the parameters of impulse noise?

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

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

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

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

5-40. What parameters characterize the synchronization device?

Lecture 6. Signal propagation medium

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

Data from the information source, after converting the parallel code to serial, is usually presented in the form of a non-pause signal without returning to zero (BVN), which corresponds to a signal from bipolar AM (Fig. 2.1). To transmit rectangular pulses without distortion, a frequency band from zero to infinity is required. Real channels have a finite frequency band to which the transmitted signals must be matched by modulation.

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

The transmitted message from the AI ​​information source in a parallel code arrives at the CC channel encoder, which converts the parallel code into a serial binary BVN code. In this case, the channel encoder introduces redundant characters into the message (for example, a parity bit) and generates start and stop bits for each frame of transmitted data. Thus, the output signal from the encoder is the modulating signal for the modulator.

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

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

AI is a source of information; IP - source of interference; CC - channel encoder; PF2 - receiver bandpass filter; M - modulator; UO - amplifier-limiter; PF1 - band pass filter; DM - demodulator; DK - channel decoder; LS - communication line; P - recipient of information II - source of information; IP - source of interference; CC - channel encoder; PF2 - receiver bandpass filter; M - modulator; UO - amplifier-limiter; PF1 - band pass filter; DM - demodulator; DK - channel decoder; LS - communication line; P - recipient of information

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

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

.

Rice. 14.3 - FM signal spectrum

The transmitter's bandpass filter PF1 limits the spectrum of the signal transmitted to the communication channel in accordance with the lower and upper limits of the channel band. Signal spectrum width at the modulator output depends on the binary modulation speed and frequency deviation. Approximately . The higher the modulation index, the wider, other things being equal, the spectrum of the FM signal.

The PF2 receiver's bandpass filter selects the frequency band of the telephone channel, which allows you to get rid of interference that is outside the PF2 passband. The signal is then amplified by a limiting amplifier. The amplifier compensates for the loss of signal energy in the line due to attenuation. In addition, the amplifier performs an additional function - the function of limiting the signal by level. In this case, it is possible to ensure a constant signal level at the input of the frequency demodulator D when the level at the receiver input changes within a fairly wide range. In the demodulator, alternating current pulses are converted into direct current pulses. The channel decoder converts symbols into messages. In this case, depending on the encoding method used, errors are detected or corrected.