Broadband communication systems. Frequencies, antennas, broadband signal

Radio channels in different areas frequency spectrum

To clarify further presentation, we will make a technical digression here about the features of various frequency ranges and the associated principles for constructing radio networks.

Modern radio communications operate at frequencies of hundreds of megahertz, thousands of megahertz (i.e. gigahertz) and even tens of gigahertz. The radio spectrum is divided into sections allocated to the most various applications; radio communication is only one of them. The distribution of spectrum on an international scale is regulated by the relevant international committee, which includes Russia. In Russia it is regulated by the interdepartmental State Committee on Radio Frequencies (SCRF). We'll come back to this later.

Each section of the radio spectrum is cut into channels the same “width” (for example, 25 kilohertz for cellular telephony). Maximum speed data transmission in a given channel depends only on the width of the channel, and not on the portion of the spectrum in which it is located. It is clear that in the frequency range, say, from 8 gigahertz to 9 gigahertz, there will be 10 times more channels of a certain width than in the range from 800 megahertz to 900 megahertz. Thus, the higher the frequencies, the greater the overall “capacity” of the range in terms of the possibility of simultaneous transmissions: if you imagine the 800-MHz range as a thousand-core cable, then the 8-GHz range will already be a ten-thousand-core cable.

Line of sight and the cellular network principle

One might assume that the colossal capacity of the ultra-high frequency (microwave) part of the radio spectrum could solve all radio communication problems. This is almost true, but there is one purely physical feature of radio waves: the higher the frequency of the wave (i.e., the shorter its length), the smaller the obstacle it can bend. Therefore, let's say mobile cellular communication can operate at frequencies no higher than 2 gigahertz: for more high frequencies communication is already strictly limited to line of sight (almost like a light beam), so communication with mobile phone will be interrupted like the light from a lantern when you walk in front of a stockade.

At frequencies below 2 GHz, the requirement for line of sight is not so strict: a radio wave can even bend around buildings - but not the thickness of the earth, i.e. cannot "go beyond the horizon". The limited range of the transmitter by the horizon visible from the height of its antenna makes it possible to organize cellular network , i.e. such a network in which the same frequency channels can be used repeatedly in non-contiguous territorial areas (“cells”).

Note 1: When they talk about " cell phone" or "cellular network", this usually means mobile cellular telephone network . Such networks are typically deployed in accordance with recognized international standards; they occupy part of the ranges around 450 MHz, 800 MHz and 900 MHz, and the latest standard offers a frequency around 1800 MHz (i.e. 1.8 GHz). Cellular mobile telephony is a separate, specifically regulated type of telecommunications activity, and we will not touch upon it further here. The cellular principle of network construction itself is not directly related to mobility is simply a way of using the same frequencies over and over again, even within a limited area.

Note 2: The picture would be incomplete without mentioning satellite communications . All arguments about the capacity of various frequency ranges remain valid here, only the concept of “horizon” almost disappears, since even a satellite hanging above the equator at a suitable longitude (not in the opposite hemisphere) is visible from the polar regions. It is clear that even a narrowly directed antenna on a satellite produces a “spot” on the earth’s surface measuring hundreds or thousands of kilometers. Therefore, compared to terrestrial radio networks, satellites use the airwaves very uneconomically, without the ability to reuse the same frequencies, as is done in cellular networks. Satellite communications is also a separate subject for consideration, and we will not deal with it here. You just have to keep in mind that a very significant part of the frequency spectrum is occupied by existing satellite communications or reserved for future.

Antenna directivity

In radio transmission networks they are used as narrowly focused antennas, and antennas with a wider coverage sector, up to omnidirectional (circular). For connection type point-to-point two (narrowly) directional antennas are used; This is how they are built, for example, radio relay transmission lines , in which the distance between neighboring relay towers can be tens of kilometers. A highly directional antenna focuses the radio beam, increasing its energy density; Thus, a transmitter of a given power “shoots” over a greater distance.

Another type of communication will be obtained by using only omnidirectional antennas. In this case, connectivity will be achieved everyone with everyone . This topology is usually used by small institutional networks deployed over a limited area.

Finally, if in the center of the "cell" we place base station with an omnidirectional antenna and equip all subscribers served by it with directional antennas focused on it, then we obtain a topology dot-many dots . If we also connect base stations to each other in a certain hierarchy (either by radio relay lines or simply by point-to-point radio connections, or by cable channels), we will get a whole cellular network. IN in this case it will be fixed cellular network, since the mobile subscriber cannot have a directional antenna.

Comment: A mobile cellular network is built on the same principle, but using omnidirectional antennas also in mobile subscribers, which do not interfere with each other, both because they always speak on different channels (or alternating on the same channel), and because the signal from the mobile device is much weaker signal from the base station and can only be correctly received base station, but not with another mobile device.

Broadband Signal Technology (BTS)

To send a radio signal high power in the microwave range, you need an expensive transmitter with an amplifier and an expensive large-diameter antenna. In order to receive a low-power signal without interference, you also need an expensive large antenna and an expensive receiver with an amplifier.

This is the case when using a conventional "narrowband" radio signal, when transmission occurs at one specific frequency, or rather, in a narrow band of the radio spectrum surrounding this frequency ( frequency channel). The picture is further complicated by various mutual interferences between high-power narrowband signals transmitted close to each other or at similar frequencies. In particular, a narrowband signal can simply be jammed (accidentally or intentionally) by a transmitter of sufficient power tuned to the same frequency.

It was this vulnerability to interference from conventional radio signals that led to the development, first for military applications, of a completely different principle of radio transmission called technology broadband signal , or noise-like signal(both versions of the term correspond to the abbreviation ShPS ). After many years of successful defense use, this technology has found civilian applications, and it is in that capacity that it will be discussed here.

It was found that in addition to its characteristic properties (its own noise immunity and low level of generated interference), this technology turned out to be relatively cheap for mass production. Cost-effectiveness occurs due to the fact that all the complexity of broadband technology is programmed into several microelectronic components (“chips”), and the cost of microelectronics in mass production is very low. As for the remaining components of broadband devices - microwave electronics, antennas - they are cheaper and simpler than in the usual “narrowband” case, due to the extremely low power of the radio signals used.

The idea of ShPS is that it uses significantly wider frequency band than is required for normal (in a narrow frequency channel) transmission. Two fundamentally different methods for using such a wide frequency band have been developed - the Direct Sequence Spread Spectrum (DSSS) method and the Frequency Hopping Spread Spectrum (FHSS) method. Both of these methods are provided by the 802.11 (Radio-Ethernet) standard.

Direct Sequence Method (DSSS)

Without getting into technical details, the direct sequence method (DSSS) can be thought of as follows. The entire used “wide” frequency band is divided into a certain number of subchannels - according to the 802.11 standard, there are 11 of these channels, and we will count as such in the further description. Each transmitted bit of information is converted, according to a pre-fixed algorithm, into a sequence of 11 bits, and these 11 bits are transmitted simultaneously and in parallel, using all 11 subchannels. When received, the received bit sequence is decoded using the same algorithm as when encoding it. Another receiver-transmitter pair may use a different encoding-decoding algorithm, and there can be a lot of different algorithms.

The first obvious result of using this method is the protection of transmitted information from eavesdropping (a “foreign” DSSS receiver uses a different algorithm and will not be able to decode information not from its transmitter). But another property of the described method turned out to be more important. It lies in the fact that thanks to the 11-fold redundancy transfers can be done very low power signal (compared to the signal power level using conventional narrowband technology), without increasing the size of the antennas .

In this case, the ratio of the level of the transmitted signal to the level of noise, (i.e. random or intentional interference), so that the transmitted signal is already indistinguishable in the general noise. But thanks to its 11-fold redundancy, the receiving device will still be able to recognize it. It’s as if they wrote the same word to us 11 times, and some copies turned out to be written in illegible handwriting, others were half erased or on a burnt piece of paper - but still, in most cases, we will be able to determine what kind of word it is by comparing all 11 copies .

Another extremely useful feature of DSSS devices is that, due to their very low power level, his signal, they practically do not interfere with conventional radio devices (narrowband high power), since these latter mistake the broadband signal for noise within the permissible limits. On the other side - regular devices do not interfere with broadband signals, since their high-power signals “make noise” each only in their own narrow channel and cannot drown out the entire broadband signal. It’s as if a letter written in large size were shaded with a thin pencil with a thick felt-tip pen - if the strokes are not in a row, we will be able to read the letter.

As a result, we can say that the use of broadband technologies makes it possible to use the same section of the radio spectrum twice- conventional narrowband devices and “on top of them” - broadband.

Summarizing, we can highlight the following properties of the NPS technology, at least for the direct sequence method:

· Noise immunity.

· Does not interfere with other devices.

· Confidentiality of transmissions.

· Cost-effective for mass production.

· Possibility of reuse of the same part of the spectrum.

· Frequency Hopping Method (FHSS)

When encoding using the frequency hopping method (FHSS), the entire frequency band allocated for transmissions is divided into a number of subchannels (according to the 802.11 standard, there are 79 of these channels). Every transmitter in every at the moment uses only one of these subchannels, regularly jumping from one subchannel to another. The 802.11 standard does not fix the frequency of such jumps - it can be set differently in each country. These jumps occur synchronously at the transmitter and receiver in a pre-fixed pseudo-random sequence known to both; It is clear that without knowing the sequence of switching, it is also impossible to accept the transmission.

Another transmitter-receiver pair will use a different frequency switching sequence, set independently of the first. In one frequency band and in one line-of-sight area (in one “cell”) there can be many such sequences. It is clear that as the number of simultaneous transmissions increases, the probability of collisions also increases, when, for example, two transmitters simultaneously jumped to frequency No. 45, each in accordance with its own sequence, and jammed each other.

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Introduction

Communication systems with ShPS occupy a special place among various systems connections, which is explained by their properties. Firstly, they have high noise immunity when exposed to powerful interference. Secondly, they provide code addressing of a large number of subscribers and their code separation when operating in a common frequency band. Thirdly, they ensure the compatibility of receiving information with high reliability of measuring the parameters of an object’s movement with high accuracy and resolution. All these properties of communication systems with broadband networks have been known for a long time, but since the interference powers were relatively low, and element base did not allow the implementation of formation and processing devices in acceptable dimensions, then for a long time Communication systems with ShPS were not widely developed. By now the situation has changed dramatically. The power of interference at the receiver input can be several orders of magnitude higher than the power of the useful signal. To ensure high noise immunity in the event of such interference, it is necessary to use NPS with ultra-large bases (tens to hundreds of thousands), ensembles (systems) of signals should consist of tens to hundreds of millions of NPS with ultra-large bases. It should be noted that the basics of the theory of NPS with ultra-large bases formed only in lately. In turn, the implementation of devices for generating and processing such signals will become possible in the near future thanks to the rapid development of ultra-large integrated circuits(VLSI), specialized microprocessors (SMP), devices with surface acoustic waves (SAW), charge-coupled devices (CCD). All these reasons caused a new period of prosperity for communication systems with broadband networks, as a result of which, after some time, such second-generation systems will appear.

The comprehensive goal of this educational and methodological manual is to strengthen and increase knowledge related to the theoretical course of lectures - “ Digital methods signal processing". This manual is intended to support the theoretical course so that students can practice personal computer studied broadband signals and communication systems.

The objectives of the educational manual are:

Introduction to the main types of ShPS;

Study of ShPS processing methods;

Study of phase-shift keyed signals using examples of Barker code and M-sequences;

Study of the properties of ShPS using a special computer program

Module: “Broadband communication systems”

Understanding Broadband Signals

Definition of ShPS. Application of ShPS in communication systems.

Wideband (complex, noise-like) signals (WPS) are those signals for which the product of the active spectrum width F and duration T is much greater than unity. This product is called the signal base B. For the ShPS

B = FT>>1 (1)

Wideband signals are sometimes called complex signals in contrast to simple signals(for example, rectangular, triangular, etc.) with B=1. Since signals with a limited duration have an unlimited spectrum, then to determine the spectrum width, use various methods and techniques.

Increasing the base in ShPS is achieved by additional modulation (or manipulation) in frequency or phase during the signal duration. As a result, the spectrum of the signal F (while maintaining its duration T) is significantly expanded. Additional intra-signal amplitude modulation is rarely used.

In communication systems with broadband networks, the spectrum width of the emitted signal F is always large more width spectrum of information messages.

ShPS are used in broadband communication systems (BCS) because:

allow you to fully realize the benefits of optimal signal processing methods;

provide high noise immunity to communications;

allow you to successfully combat multipath propagation of radio waves by splitting the beams;

allow simultaneous operation of many subscribers in a common frequency band;

allow you to create communication systems with increased secrecy;

provide electromagnetic compatibility(EMC) ShPSS with narrowband radio communication and radio broadcasting systems, television broadcasting systems;

provide best use frequency spectrum in a limited area compared to narrowband communication systems.

Noise immunity of ShPSS.

It is determined by the well-known relation connecting the signal-to-noise ratio at the receiver output q2 with the signal-to-noise ratio at the receiver input c2:

where c2 = Рс/Рп (Рс, Рп - power of the ShPS and interference);

q2=2E/ Np, E - ShPS energy, Np - spectral density interference power in the broadband band. Accordingly, E = РсТ, and Nп = Рп /F;

B - ShPS base.

The signal-to-noise ratio at the output q2 determines the operating characteristics of the NPS reception, and the signal-to-noise ratio at the input c2 determines the energy of the signal and noise. The value of q2 can be obtained according to the system requirements (10...30 dB) even if c2<<1. Для этого достаточно выбрать ШПС с необходимой базой В, удовлетворяющей (2). Как видно из соотношения (2), прием ШПС согласованным фильтром или коррелятором сопровождается усилением сигнала (или подавлением помехи) в 2В раз. Именно поэтому величину

KShPS = q2/s2 (3)

is called the processing gain of the ShPS or simply the processing gain. From (2), (3) it follows that the processing gain KSPS = 2V. In SHPS, information reception is characterized by the signal-to-interference ratio h2= q2/2, i.e.

Relations (2), (4) are fundamental in the theory of communication systems with broadband networks. They were obtained for interference in the form of white noise with a uniform power spectral density within a frequency band whose width is equal to the width of the NPS spectrum. At the same time, these relationships are valid for a wide range of interference (narrowband, pulsed, structural), which determines their fundamental significance.

Thus, one of the main purposes of communication systems with broadband networks is to ensure reliable reception of information under the influence of powerful interference, when the signal-to-interference ratio at the receiver input c2 can be much less than one. It should be noted once again that the above relations are strictly valid for interference in the form of a Gaussian random process with a uniform spectral power density (“white” noise).

Main types of ShPS

A large number of different SPS are known, the properties of which are reflected in many books and journal articles. ShPS are divided into the following types:

frequency modulated (FM) signals;

multi-frequency (MF) signals;

phase-shift keyed (PM) signals (signals with code phase modulation - QPSK signals);

discrete frequency (DF) signals (signals with code frequency modulation - FFM signals, frequency-shift keyed (FM) signals);

discrete composite frequency (DCF) (composite signals with code frequency modulation - CFM signals).

Frequency modulated (FM) signals are continuous signals whose frequency varies according to a given law. Figure 1a shows an FM signal, the frequency of which varies according to a V-shaped law from f0-F/2 to f0+F/2, where f0 is the central carrier frequency of the signal, F is the spectrum width, in turn equal to the frequency deviation F = ?fd. The duration of the signal is T.

Figure 1b shows the time-frequency (f, t) plane, on which the shading approximately shows the distribution of the FM signal energy in frequency and time. The base of the FM signal by definition (1) is equal to:

B = FT=?fдT (5)

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Figure 1 - Frequency-modulated signal and time-frequency plane

Frequency-modulated signals are widely used in radar systems because a matched filter can be created for a specific FM signal using surface acoustic wave (SAW) devices. In communication systems, it is necessary to have many signals. At the same time, the need to quickly change signals and switch generation and processing equipment leads to the fact that the law of frequency change becomes discrete. In this case, they move from FM signals to DF signals.

Multi-frequency (MF) signals (Figure 2a) are the sum of N harmonics u(t) ... uN(t), the amplitudes and phases of which are determined in accordance with the laws of signal generation. On the time-frequency plane (Figure 2b), the distribution of the energy of one element (harmonic) of the MF signal at frequency fk is highlighted by shading. All elements (all harmonics) completely cover the selected square with sides F and T. The base of the signal B is equal to the area of the square. Width of the spectrum of the element F0?1/T. Therefore, the base of the MF signal

i.e., it coincides with the number of harmonics. MF signals are continuous and it is difficult to adapt digital techniques for their formation and processing. In addition to this disadvantage, they also have the following:

a) they have a bad crest factor (see Figure 2a);

b) to obtain a large base B, it is necessary to have a large number of frequency channels N. Therefore, MF signals are not considered further.

Phase-shift keyed (PM) signals represent a sequence of radio pulses, the phases of which change according to a given law. Usually the phase takes two values (0 or p). In this case, the radio frequency FM signal corresponds to a video FM signal (Figure 3a), consisting of positive and negative pulses. If the number of pulses is N, then the duration of one pulse is equal to Ф0 = T/N, and the width of its spectrum is approximately equal to the width of the signal spectrum F0 =1/Ф0=N/Т. On the time-frequency plane (Figure 3b)

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Figure 2 - Multi-frequency signal and time-frequency plane

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Figure 3 - Phase-keyed signal and time-frequency plane

The shading indicates the energy distribution of one element (pulse) of the FM signal. All elements overlap a selected square with sides F and T. FM signal base

B = FT =F/ф0=N, (7)

those. B is equal to the number of pulses in the signal.

The possibility of using PM signals as BPS with bases B = 104...106 is limited mainly by processing equipment. When using matched filters in the form of SAW devices, optimal reception of FM signals with maximum bases Vmax = 1000 ... 2000 is possible. FM signals processed by such filters have wide spectra (about 10 ... 20 MHz) and relatively short durations (60 ... 100 µs). Processing of FM signals using video frequency delay lines when transferring the spectrum of signals to the video frequency region makes it possible to obtain bases B = 100 at F? 1 MHz, T? 100 µs.

Matched filters based on charge-coupled devices (CCDs) are very promising. According to published data, using matched CCD filters, it is possible to process FM signals with bases of 102 ... 103 at signal durations of 10-4 ... 10-1 s. The CCD digital correlator is capable of processing signals up to base 4,104.

It should be noted that it is advisable to process PM signals with large bases using correlators (on an LSI or on a CCD). In this case, B = 4 104 seems to be the limit. But when using correlators, it is necessary first of all to resolve the issue of accelerated entry into synchronism. Since FM signals make it possible to widely use digital methods and techniques of generation and processing, and it is possible to implement such signals with relatively large bases, therefore FM signals are one of the promising types of NPS.

Discrete frequency (DF) signals represent a sequence of radio pulses (Figure 4a), the carrier frequencies of which vary according to a given law. Let the number of pulses in the DF signal be M, the pulse duration be T0=T/M, and its spectral width F0=1/T0=M/T. Above each pulse (Figure 4a) its carrier frequency is indicated. On the time-frequency plane (Figure 4b), the squares in which the energy of the DF signal pulses are distributed are shaded.

As can be seen from Figure 4b, the energy of the DF signal is distributed unevenly on the time-frequency plane. HF signal database

B = FT = МF0МТ0 = М2F0Т0 = М2 (8)

since the momentum base is F0T0 = l. From (8) follows the main advantage of MF signals: to obtain the necessary base B, the number of channels is M =, i.e., significantly less than for MF signals. It was this circumstance that led to attention to such signals and their use in communication systems. At the same time, for large bases B = 104 ... 106, it is inappropriate to use only DF signals, since the number of frequency channels is M = 102 ... 103, which seems excessively large.

Discrete composite frequency (DCF) signals are CD signals in which each pulse is replaced by a noise-like signal. Figure 5a shows an FM video signal, individual parts of which are transmitted at different carrier frequencies. Frequency numbers are indicated above the FM signal. Figure 5b shows the time-frequency plane, on which the distribution of the energy of the DFS signal is highlighted by shading. Figure 5b is no different in structure from Figure 4b, but for Figure 5b the area F0T0 = N0 is equal to the number of FM signal pulses in one frequency element of the DFS signal. DFS signal base

B = FT = М2F0Т0 = N0М2 (9)

Number of pulses of the total PM signal N=N0М

The DFS signal shown in Figure 5 contains FM signals as elements. Therefore, we will abbreviate this signal as a DFS-FM signal. As elements of the DFS signal, we can take DFS signals. If the base of the DF signal element is B = F0T0 = M02, then the base of the entire signal is B = M02M2

Such a signal can be abbreviated as DSCH-FM. The number of frequency channels in a DFS-FM signal is M0M. If the DF signal (see Figure 4) and the FM-FM signal have equal bases, then they have the same number of frequency channels. Therefore, the DFS-FM signal does not have any special advantages over the DF signal. But the principles of constructing an FM signal can be useful when constructing large systems of FM signals. Thus, the most promising broadband signals for communication systems are FM, MF, and DFS-FM signals.

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Figure 4 - Discrete frequency signal and time-frequency plane

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Figure 5 - Discrete composite frequency signal with phase shift keying DFS-FM and time-frequency plane.

Principles of optimal filtration. Optimal ShPS filter

Reception and processing of signals by various radio devices, as a rule, is carried out against a background of more or less intense interference. The choice of device system depends on which of the following tasks must be solved:

1. Signal detection, when you only need to answer whether the received vibration contains a useful signal or is it formed only by noise.

2. Estimation of parameters when it is necessary to determine with the greatest accuracy the value of one or more parameters of the useful signal (amplitude, frequency, time position, etc.). For the theory of radio circuits and signals, the greatest interest is in studying the possibilities of reducing the harmful effects of interference for a given signal and a given interference by correctly choosing the receiver transfer function. Therefore, in the future, the characteristics of receivers that are optimally matched to the signal and interference will be determined. Depending on which of the above problems is being solved, the criteria for the optimality of a filter for a given signal in the presence of interference with given statistical characteristics may be different. For the problem of detecting a signal in noise, the most widely used criterion is the maximum signal-to-noise ratio at the filter output.

The requirements for a filter that maximizes the signal-to-noise ratio are formulated as follows. An additive mixture of signal S(t) and noise n(t) is supplied to the input of a linear four-port network with constant parameters and transfer function (Figure 6).

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Figure 6

The signal is completely known, which means that its shape and position on the time axis are specified. Noise is a probabilistic process with given statistical characteristics. It is required to synthesize a filter that ensures that the highest possible ratio of the peak signal value to the root mean square value of the noise is obtained at the output, in other words, to determine the transfer function. In this case, there is no condition for preserving the signal shape at the filter output, since the shape does not matter for detecting it in noise.

Let us present the results of solving the problem for “standard” interference such as white noise. Let us recall that white noise is a random process with a uniform distribution of energy across the frequency spectrum, i.e. W(у) = W0 = const , and 0<щ

Here A is an arbitrary constant coefficient, a function complexly conjugate with the spectral function of the signal.

From relation (10) two conditions follow for the phase-frequency (PFC) and amplitude-frequency (AFC) characteristics of the matched filter:

1) K(s)=AS(s) (11)

those. the modulus of the transfer function, up to a constant coefficient A, coincides with the amplitude spectrum of the signal and

2) цk=-[цs(ш)+шt0] (12)

цs(ш) - phase spectrum of the signal.

The physical meaning of the obtained expressions for the frequency response (11) and phase response (12) of the optimal filter is clear from the following considerations. When relation (11) is satisfied, the energy of noise, which occupies an infinite frequency band at the filter input, is attenuated at the output much more strongly than the energy of a signal having the same spectral width as the receiver bandwidth.

The first term in the expression for the phase response -ts(φ) compensates for the phase characteristic of the input signal cis(φ); as a result of passing through the filter at time t0, all harmonics of the signal add up in phase, forming a peak in the output signal. At the same time, this leads to a change in the signal shape at the filter output. The second term ut0 means the delay of all signal components for the same time t0>Tc, where Tc is the duration of the signal. Physically, this means that in order to fully utilize the energy of the input signal, the filter response delay must be no less than the duration of the signal.

Using expression (10) reduces the problem of synthesizing a matched filter to the problem of constructing an electrical circuit using a known transmission coefficient.

Another way is to determine the impulse response of the circuit, and then design a four-terminal network with such a response.

By definition, the impulse response of a circuit g(t) is the signal at its output in response to an influence in the form of a g function, i.e. having uniform spectral density for all frequencies. In this case, the spectral density of the signal at the output and the type of signal at the output, according to the Fourier transform and taking into account relation (10),

The impulse response of the optimal filter, i.e. the response to the d pulse is thus a mirror image of the signal with which this filter is matched. The axis of symmetry passes through the point t0/2 on the abscissa axis (Figure 7).

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Figure 7

The output waveform of an optimal filter can be determined using the general relation

By definition, the signal at the output of the optimal filter is

where Bs(t-t0) is the signal autocorrelation function (ACF).

So, the signal at the output of the matched filter, up to a constant coefficient A, coincides with the autocorrelation function of the input signal. The signal-to-noise ratio at the output is the main measure of the effectiveness of the optimal filter (OF). We present only the result of calculations, according to which

where is the root mean square value of the noise at the filter output, the peak value of the output signal;

E is the signal energy at the filter input;

W0 is the power spectral density of white noise.

Expression (16), which allows us to determine the efficiency of the matched filter, shows that with white noise the signal-to-noise ratio at its output depends only on the signal energy and the energy spectrum of the noise W0. In the case of ShPS:

E = NE0 signal energy, E0 - energy of an elementary parcel, N - number of parcels in the signal, c - signal/noise ratio at the OF input.

From expressions (15.17) it follows: firstly, the OF increases the signal-to-noise ratio in terms of output power by N times, and secondly, one of the possible implementations of the optimal filter is a correlator or a program that calculates the ACF of the signal.

Phase Shift Keyed Signals

Phase shift keying is often used as intra-signal modulation. Phase-shift keyed (PM) signals are a sequence of radio pulses of equal amplitude, the initial phases of which vary according to a given law. In most cases, the FM signal consists of radio pulses with two initial phase values: 0 and.

Figure 8a shows an example of an FM signal consisting of 7 radio pulses. Figure 8b shows the envelope (in the general case complex) of the same signal. In the example under consideration, the envelope is a sequence of positive and negative single video pulses of a rectangular shape. This assumption about the rectangularity of the pulses forming the FM signal is valid for theoretical studies. However, when FM signals are generated and transmitted over communication channels with a limited bandwidth, the pulses are distorted, and the FM signal ceases to be as ideal as in Figure 8a. The envelope fully characterizes the FM signal. Therefore, this work examines the properties of the PM signal envelope.

A rectangular pulse u(t) with unit amplitude and duration 0, which forms the basis of FM, is written as u (t) = 1 at 0 t 0.

An envelope consisting of N unit video pulses can be represented as:

U(t) = an u

where the amplitude an takes the values +1 or -1. The total duration of the PM signal is T = N0.

The sequence of symbols (pulse amplitudes) A = (a1, a2 … an …aN) is called a code sequence. The following equivalent designations of code sequences are possible:

A =(111-1-11-1) = (1110010) =(+ + + - - + -), here N = 7.

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Figure 8 - FM signal, its complex envelope

Spectrum of FM signals

The spectral properties of PM signals are determined by the spectra of the pulse u(t) and the code sequence A. Spectrum of the rectangular video pulse S():

S() = 0 exp (- i0/2)

The spectrum of a rectangular signal consists of three factors. The first one - equal to φ0 is the pulse area 1φ0. The second factor sin(0/2)/(0/2) in the form of a reference function sin(x)/x characterizes the frequency distribution of the spectrum. The third factor is a consequence of the displacement of the pulse center relative to the origin by half the pulse duration 0/2.

The spectrum of the PM signal G(), more precisely the spectrum of the envelope, taking into account the shift theorem, has the following form:

G() = S() an exp [-i(n-1)0]

The sum on the right side is the spectrum of the code sequence A and is further denoted by H(). So,

u(t) S(), A H(), U(t) G(),

Representing the spectrum of an FM signal as a product is convenient in that you can first find the spectra S() and H() separately, and then, by multiplying them, obtain the spectrum of the FM signal. The properties of the spectrum of a rectangular pulse are well known: it has a lobe structure with zeros at points /, 2/, etc. The amplitude spectrum of the code sequence, on average, approaches the spectrum of white noise and is characterized by significant fluctuations around the average, equal to

The phase spectrum of the code sequence is also characterized by significant ruggedness.

Autocorrelation function (ACF).

The ACF of FM signals has the form typical for all types of NPS. The normalized ACF consists of a central (main) type with amplitude 1, located on the interval (-,) and side (background) maxima distributed on the interval (-,) and (,).

The amplitudes of the side types take on different values, but for signals with “good” correlation they are small, i.e. significantly less than the amplitude of the central peak. The ratio of the amplitude of the central peak (in this case 1) to the maximum amplitude of the side maxima is called the suppression coefficient K. For arbitrary NPS with base B

For FM ShPS K1. An example of the ACF of the NPS is given in Figure 9. The value of K significantly depends on the type of code sequence A. With the correct choice of the formation law A, it is possible to achieve maximum suppression, and in some cases, equality of the amplitudes of all side maxima.

Barker Signals

The Barker signal code sequence consists of 1 symbols and is characterized by a normalized ACF of the form:

where l = 0, 1, ... (N-1)/2.

The sign in the last line depends on the value of N. Figures 8-9 show the FM signal, its complex envelope and the ACF of the seven-digit Barker code.

From (18) it follows that one of the features of the Barker signal is the equality of the amplitudes of all (N-1) side maxima of the ACF, and all of them have the minimum possible level, not exceeding 1/N. Table 1 shows the known Barker code sequences and their levels of side ACF types. Code sequences with properties (18) were not found for N 13.

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Figure 9 - ACF of the seven-digit Barker code

Table 1 Barker code sequences

	Code sequence	Side lobe level



	1 1 1 -1 -1 1 -1
	1 1 1 -1 -1 -1 1 -1 -1 1
	1 1 1 1 1 -1 -1 1 1 -1 1 -1 1

Formation and processing of Barker signals. The formation of Barker signals can be carried out in several ways, just like an arbitrary PM signal. Since Barker's signals were the first PNS, and with the best ACF, we will briefly consider one of the possible ways of generating and processing Barker signals.

Figure 10 shows a Barker signal generator with N=7. The clock pulse generator (CPG) generates narrow rectangular clock pulses, the repetition period of which is equal to the duration of the Barker signal T=7f0, and f0 is the duration of a single (unit) rectangular pulse. The clock pulse generator starts a single pulse generator (SPG), which in turn generates single rectangular pulses with duration φ0 and period T. Single rectangular pulses are fed to the input of a multi-tap delay line (MLD), which has N-1=6 sections with taps at time intervals , equal to f0. The number of taps, including the beginning of the line, is 7. Since the Barker code sequence with N = 7 has the form 111-1 -11 -1, then pulses from the first, second, third and sixth taps (counting from the beginning of the line) are received at the input adder (+) directly, and pulses from the fourth, fifth and seventh taps arrive at the input of the adder through inverters (IN), which convert positive single pulses into negative ones, i.e., they change the phase by p. Therefore, inverters are also called phase shifters. At the output of the adder there is a Barker video signal (Figure 8b), which is then fed to one input of the balanced modulator (BM), the other input of which is supplied with a radio frequency oscillation at the carrier frequency, generated by a carrier frequency generator (LFO). The balanced modulator carries out phase shift keying of the radio frequency oscillation of the LFO in accordance with the Barker code sequence: a video pulse with amplitude 1 corresponds to a radio pulse with phase 0, and a video pulse with amplitude -1 corresponds to a radio pulse with phase p. Thus, at the output of the balanced modulator there is a Barker radio frequency signal (Figure 8a).

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Figure 10 - Barker signal generator with N = 7

Optimal processing of Barker signals, as well as other NPS, is carried out either using matched filters or using correlators. There are several possible ways to construct matched filters and correlators, differing from each other in technical implementation, but providing the same maximum signal-to-noise ratio at the output. Figure 11 shows a diagram of a matched filter for a Barker signal with N = 7. From the output of the intermediate frequency amplifier of the receiver, the signal is fed to a matched single pulse filter (SPFI), which optimally processes (filters) a single rectangular radio pulse with a central frequency equal to the intermediate frequency of the receiver . At the output of the SFOI, the radio pulse has a triangular envelope. Triangular radio pulses with a base duration of 2 f0 are supplied to the MLZ, which has 6 sections and 7 taps (including the beginning of the line). The taps follow through f0. Since the impulse response of the matched filter is the same as the mirrored signal, the coded impulse response of the filter for the Barker signal with N=7 should be set in accordance with the sequence -11-1-1111. Therefore, radio pulses from the second, fifth, sixth and seventh taps of the MLZ enter the adder (+) directly, and radio pulses from the first, third and fourth taps - through inverters (IN), which change the phase to p. At the output of the adder there is an ACF of the Barker signal, the envelope of which is shown in Figure 9.

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Figure 11 - Matched Barker signal filter with N = 7

M - sequences

Among phase-shift keyed signals, signals whose code sequences are sequences of maximum length or M-sequences are of particular importance.

M-sequences belong to the category of binary linear recurrent sequences and represent a set of N periodically repeating binary symbols. Moreover, each current symbol dj is formed as a result of adding modulo 2 a certain number m of previous symbols, some of which are multiplied by 1, and others by 0.

For the jth character we have:

d j = a i d j - i = a 1 d j -1 . . . a m d j -m(4)

Where a1…am are numbers 0 or 1.

Technically, the M-sequence generator is built in the form of a register (series-connected flip-flops) with taps, a feedback circuit and a modulo 2 adder. An example of such a generator is shown in Figure 12. Multiplication by a1...am in (4) simply means the presence or absence withdrawal, i.e. connection of the corresponding trigger (register bit) with the adder. In an m-bit register, the maximum period is: Nm - 1. The value m is called sequence memory. If the taps are chosen arbitrarily, then a sequence of maximum length will not always be observed at the output of the generator. The rule for selecting taps, which makes it possible to obtain a sequence with a period of Nm-1, involves finding irreducible primitive polynomials of degree m with coefficients equal to 0 and 1. Non-zero coefficients in the polynomials determine the numbers of taps in the register.

So, when m=6 there are 3 primitive polynomials:

a6 a5 a4 a3 a2 a1 a0

p1 (x) = x 6 + x + 1 1 0 0 0 0 1 1

p2 (x) = x 6 + x 5 + x 2 + x + 1 1 1 0 0 1 1 1

p3 (x) = x 6 + x 5 + x 3 + x 2 + 1 1 1 0 1 1 0 1

Figure 12 shows the first option.

Figure 12 - M-sequence generator with period N = 26 - 1 = 63

Features of the M-sequence autocorrelation function. The normalized autocorrelation function (ACF) is of greatest interest. There are two cases of obtaining such a function: in periodic (PAKF) and aperiodic modes. The periodic ACF has a main peak equal to unity and a number of side emissions, the amplitudes of which are 1/N. With increasing N, the PACF approaches ideal, when the side peaks become negligibly small in comparison with the main one.

The side peaks of the ACF in the aperiodic mode are significantly larger than the side peaks of the PACF. The RMS value of the side peaks (calculated through the variance) is

Truncated M-sequences

By dividing the M-sequence (full period N) into segments of duration Nс, it is possible to obtain a large number of NPS, considering each of the segments as an independent signal. If the segments do not overlap, then their number is n = N/(Nc-1). In this way, a large number of pseudo-random sequences can be obtained. The autocorrelation properties of such sequences are much worse than those of an M-sequence of the same duration and depend on Nc. It has been established that 90% of segments have ub 3 /, and 50% have 2 /.

signal frequency filter sequence

Literature

1. Noise-like signals in information transmission systems. Ed. V.B. Pestryakov. - M., “Sov. radio”, 1973, -424c.

2. Yu.S. Lyozin. Introduction to the theory of radio engineering systems. - M.: Radio and communication, 1985, -384c.

3. L.E. Varakin. Communication systems with noise-like signals. - M.: Radio and communication, 1985, -384c.

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Initially, this technology was created for intelligence and military purposes. The main idea of the method is to distribute the information signal over a wide radio band, which ultimately makes it much more difficult to suppress or intercept the signal.

The essence of this technology is to transform the original signal in such a way that the resulting signal is expanded and distributed over the entire available range. Due to the law of conservation of energy, as the occupied frequency range expands, the energy density of the transmitted signal decreases. A direct consequence of this circumstance is a drop in maximum power, which entails “noise” of the useful signal. In fact, this is not a big deal, since there are effective methods for restoring a useful signal that is “lost” against the background noise.

A logical question arises: “Why create problems for yourself (reduce signal power) in order to solve them later (select a useful signal from the background noise)?” In fact, the reason for this illogical (only at first glance) act is very logical - the need to place as many data channels as possible within a narrow frequency range. Initially, it was envisaged to use two signal coding technologies using the spectrum allocation method. They are also called modulation methods, because as a result of their use, useful information is “superimposed” on the original high-frequency signal.

Firstbased on method FHSS (Frequency Hopping Spread Spectrum - encoding a signal with spectrum expansion using the frequency hopping method).

Rice. 10. Spectrum expansion by frequency hopping

To ensure that radio traffic could not be intercepted or suppressed by narrow-band noise, it was proposed to transmit with a constant change of carrier within a wide frequency range (see Fig. 10). As a result, the signal power was distributed over the entire range, and listening to a specific frequency produced only a small amount of noise. The sequence of carrier frequencies was pseudo-random, known only to the transmitter and receiver. An attempt to suppress a signal in a certain narrow range also did not degrade the signal too much, since only a small part of the information was suppressed.

When choosing the FHSS method, the entire 2.4 GHz band is used for data transmission (as one wide band, which is divided into 79 subchannels). The main disadvantage of this method is the low data transfer speed, which does not exceed 2 Mbit/s.

Secondof which is based on application technologies DSSS (Direct Sequence Spread Spectrum - encoding a signal with spread spectrum using a direct sequence code) together with the use of CCK modulation (Complementary Code Keying - additional code modulation), which supports data transfer rates up to 11 Mbps.

Direct Sequential Spread Spectrum also uses the entire frequency range allocated to a single wireless link. Unlike the FHSS method, the entire frequency range is occupied not due to constant switching from frequency to frequency, but due to the fact that Each bit of information is replaced by N-bits, so that the clock speed of signaling increases by a factor of N. And this, in turn, means that the signal spectrum also expands N times. It is enough to select the data rate and N value appropriately so that the signal spectrum fills the entire range.

The code that replaces the binary unit of the original information is called a spreading sequence, and each bit of such a sequence is called a chip.

Accordingly, the transmission speed of the resulting code is called the chip speed. A binary zero is encoded by the inverse of the spreading sequence. Receivers must know the spreading sequence that the transmitter uses in order to understand the information being transmitted.

Very often, the value of the spreading sequence is the Barker sequence, which consists of 11 bits: 10110111000. If the transmitter uses this sequence, then the transmission of three bits 110 leads to the transmission of the following bits:

10110111000 10110111000 01001000111.

The purpose of coding using the DSSS method is the same as the FHSS method - increasing immunity to interference. Narrowband interference will distort only certain frequencies of the signal spectrum, so that the receiver is likely to be able to correctly recognize the transmitted information.

If DSSS technology is selected, several wide DSSS channels are formed in the 2.4 GHz band, and no more than three of them can be used simultaneously. This achieves a maximum data transfer rate of 11 Mbit/s, which corresponds to the later IEEE 802.11b standard.

Narrowband and wideband signals

1.Narrowband signal

A signal is called narrowband (NB) if the width of its spectrum is significantly less than the average frequency (Fig. 1.1):

Rice. 1.1

Typical representatives of UPS are modulated radio signals. UPS can also include several radio signals with their own carriers, which together occupy a fairly narrow frequency band.

As a first approximation, to analyze the passage of the UPS through radio-electronic circuits, such a signal can be represented as harmonic at an average frequency. A better approximation is provided by the representation of the UPS in the form of a quasi-harmonic oscillation, which slowly (compared to) instantaneous amplitude and frequency change. In this case, it is assumed that in a sufficiently short time (less than the changes in amplitude and frequency), the signal can be considered harmonic.

In general, the UPS can be represented as

where and -slowly changing functions of time.

For classical AM and FM oscillations, the average frequency coincides with the carrier frequency of the signal. For a clear and optimal choicethe Hilbert transform apparatus is used, according to which, for a given UPSthe conjugate function is found,defined as

at the same time

The envelope defined in this way coincides with the signalat points in time where,those. have common tangents, and at the points of tangency the functionclose to the maximums (Fig. 1.2):

Rice. 1.2

For a signal likethe Hilbert conjugate function is equal to and for .

Based on these relations for a harmonic signalenvelope and frequency are equal respectively:

as you would expect. If you choose the average frequency arbitrarily, then even for a harmonic signal you can get some rather complex envelope that does not correspond to reality.

Let us consider, as an example, a UPS consisting of the sum of harmonic components:

For such a signal

where

After transformations, we can obtain the following expression for the instantaneous frequency

For a two-frequency signal (N=2) we have

Thus, the sum of two closely spaced frequencies () signals can be written in the form of a quasi-harmonic oscillation:

Fig. 1.3 illustrates an approximate form of a signal consisting of two harmonic signals with equal amplitudes (= = ).

Rice. 1.3

Below in Fig. 1.4 and Fig. 1.5 show normalized graphs of one period of the envelope and instantaneous frequency: biharmonic signal for, 0.5 and 0.1.

Fig.1.4

As the amplitude of one of the signals decreases, the instantaneous frequency (Fig. 5) continuously changes even at low k the average frequency is close to the frequency of the larger signal. From the graphs in Fig. 3, fig. 4, fig. 5 shows that when two signals with equal amplitudes interact, the amplitude envelope changes from double the amplitude of each to zero. Moreover, at zero of the envelope phase abruptly changes to , which formally means the transition through infinity (gap) of the instantaneous frequency, and the rest of the time

As the amplitude of one of the signals decreases, the instantaneous frequency (Fig. 1.5) continuously changes even at low k the average frequency is close to the frequency of the larger signal.

Rice. 1.5

For small k the envelope can be represented in approximate form

from which it can be seen that the envelope in this case linearly depends on the amplitude of the small signal at a constant amplitude of the large one. If the small signal in turn is quasi-harmonic

those.

That

Thus, the resulting envelope contains linear information about changes in the amplitude and phase of a small signal, which makes it possible to isolate this information in the receiver without nonlinear distortions.

2 . Wideband signal

Definition of ShPS. Application of ShPS in communication systems

Wideband (complex, noise-like) signals (WBS) are those signals for which the products of the active spectrum width F for duration T much more than one. This product is called the signal base B. For ShPS

B = FT >>1 (1)

Broadbandsignals are sometimes called complex signals in contrast to simple signals(eg rectangular, triangular, etc.) with B=1. Since signals with a limited duration have an unlimited spectrum, various methods and techniques are used to determine the width of the spectrum.

Increasing the base in ShPS is achieved by additional modulation (or manipulation) in frequency or phase during the signal duration. As a result, the signal spectrum F (while maintaining its duration T ) is expanding significantly.

In communication systems with broadband networks, the spectrum width of the emitted signal is F always much greater than the width of the information spectrum messages.

ShPS are used in broadband communication systems (BCS) because:

provide high noise immunity to communications;
allow you to successfully combat multipath propagation of radio waves by splitting the beams;
allow simultaneous operation of many subscribers in a common frequency band;
allow you to create communication systems with increased secrecy;
provide better use of the frequency spectrum in a limited area compared to narrowband communication systems.
1. Noise immunity of ShPSS

It is determined by the well-known relation relating the signal-to-interference ratio at the receiver output q 2 with the signal-to-noise ratio at the receiver input ρ 2 :

q 2 = 2Вρ 2 (2)

where ρ 2 = R s / R p (R s , R p - ShPS power and interference);

B - ShPS base.

Value q 2 can be obtained according to system requirements (10...30 dB) even if ρ 2 <<1. Для этого достаточно выбрать ШПС с необходимой базой В , satisfying (2). As can be seen from relation (2), reception of NPS by a matched filter or correlator is accompanied by signal amplification (or noise suppression) by 2Vonce. That is why the value

K ShPS = q 2 /ρ 2 (3)

is called the processing gain of the ShPS or simply the processing gain. From (2), (3) it follows that the enhancement of processing K ShPS = 2V. IN ShPSS reception of information is characterizedsignal-interference ratio h 2 = q 2 /2, i.e.

h 2 = Bρ 2 (4)

T Thus, one of the main purposes of communication systems with broadband communication systems is to ensure reliable reception of information under the influence of powerful interference, when the signal-to-noise ratio at the receiver input is ρ 2 may be much less than one.It should be noted once again that the above relations are strictly valid for interference in the form of a Gaussian random process with a uniform spectral power density (“white” noise).

Main types of ShPS

There are a large number of different ShPS, which are divided into the following types:

frequency modulated (FM) signals;
multi-frequency (MF) signals;
phase-shift keyed (PM) signals (signals with code phase modulation - QPSK signals);
discrete frequency (DF) signals (signals with code frequency modulation - FFM signals, frequency-shift keyed (FM) signals);
discrete composite frequency (DCF) (composite signals with code frequency modulation - C K H M signals).

Frequency modulated (FM)signals are continuous signals, the frequency of which varies according to a given law. In Fig. 2.1a, an FM signal is depicted, the frequency of which varies according to V -shaped law from f 0 - F /2 to f 0 + F /2, where f 0 - central carrier frequency of the signal, F - spectrum width, in turn, equal to frequency deviation F = ∆ f d. The duration of the signal is T.

On rice. 2.1b shows the time-frequency ( f , t ) - plane, on which approximately shows the distribution of FM signal energy by frequency and time by shading.

The base of the FM signal by definition (1) is equal to:

B = FT = ∆ f d T (5)

Multi-frequency (MF)signals (Fig. 2.2a) are the sum N harmonics u (t) ... u N (t), the amplitudes and phases of which are determined in accordance with the laws of signal formation. Onfrequency-time plane (Fig. 2.2b), the distribution of the energy of one element (harmonic) of the MF signal at the frequency is highlighted by shading fk . All elements (all harmonics) completely cover the selected square with sides F and T. Signal Base B equal to the area of the square. Element spectrum width F 0 ≈1/T. Therefore, the base of the MF signal

B = F / F 0 = N (6)

Rice. 2.1 - Frequency modulated

a) they have a bad crest factor (see Fig. 2.2a);

b) to obtain a large base IN it is necessary to have a large number of frequency channels N. Therefore, MF signals are not considered further.

Phase-shift keyed (PM)the signals represent a sequence of radio pulses, the phases of which vary according to a given law. Typically, the phase takes two values (0 or π). In this case, the radio frequency FM signal corresponds to a video FM signal (Fig. 2.3a), consisting of positive and negative pulses. If the number of pulses N, then the duration of one pulse is equal to τ 0 = T/N, and the width of its spectrum is approximately equal to the width of the signal spectrum F 0 = 1/τ 0 = N /T. On the time-frequency plane (Figure 3b)The shading indicates the energy distribution of one element (pulse) of the FM signal. All elements overlap the selected square with sides F and T. FM signal base

B = FT = F /τ 0 = N , (7)

those. B equal to the number of pulses in the signal.

Possibility of using FM signals as BPS with bases B = 10 4 ...10 6 limited mainly by processing equipment. When using matched filters in the form of SAW devices, optimal reception of FM signals with maximum bases Vmax = 1000 ... 2000 is possible. FM signals processed by such filters have wide spectra (about 10 ... 20 MHz) and relatively short durations (60 ... 100 µs). Processing of FM signals using video frequency delay lines when transferring the spectrum of signals to the video frequency region makes it possible to obtain bases B= 100 at F ≈1 MHz, T ≈ 100 µs.

Matched filters based on charge-coupled devices (CCDs) are very promising. According to published data, using matched CCD filters, it is possible to process PM signals with bases of 10 2 ... 10 3 with signal durations of 10-4 ... 10 -1 With. A digital correlator on a CCD is capable of processing signals up to a base of 4∙10 4 .

Fig 2.2 - Multi-frequencysignal and time-frequency plane

Fig 2.3 - Phase keyedsignal and time-frequency plane

It should be noted that it is advisable to process PM signals with large bases using correlators (on an LSI or on a CCD). In this case, B = 4∙10 4 seems to be extreme. But when using correlators, it is necessary first of all to resolve the issue of accelerated entry into synchronism.Since FM signals make it possible to widely use digital methods and techniques of generation and processing, and it is possible to implement such signals with relatively large bases, then y FM signals are one of the promising types of broadband.

Discrete frequency (DF)the signals represent a sequence of radio pulses (Figure 4a), the carrier frequencies of which vary according to a given law. Let the number of pulses in the DF signal be M, the pulse duration is T 0 =T/M, its spectrum width F 0 =1/T 0 =M/T. Above each pulse (Figure 4a) its carrier frequency is indicated. On the time-frequency plane (Figure 4b), the squares in which the energy of the DF signal pulses are distributed are shaded.

As can be seen from Figure 4b, the energy of the DF signal is distributed unevenly on the time-frequency plane.HF signal database

B = FT =M F 0 MT 0 =M 2 F 0 T 0 = M 2 (8)

since the momentum base F 0 T 0 = l . From (8) follows the main advantage of DF signals: to obtain the necessary base B number of channels M = , i.e., significantly less than for MF signals. It was this circumstance that led to attention to such signals and their use in communication systems. At the same time, for large bases B = 10 4 ... 10 6 It is not practical to use only DF signals, since the number of frequency channels is M = 10 2 ... 10 3 , which seems excessively large.

Discrete Composite Frequency (DCF)The signals are HF signals in which each pulse is replaced by a noise-like signal. In Fig. Figure 2.5a shows an FM video frequency signal, individual parts of which are transmitted at different carrier frequencies. Frequency numbers are indicated above the FM signal. Figure 2.5b shows the time-frequency plane, on which the distribution of the energy of the DFS signal is highlighted by shading. Fig. 2.5b is no different in structure from Fig. 2.4b, but for Fig. 2.5b area F 0 T 0 = N 0 -equal to the number of FM signal pulses in one frequency element of the DFS signal. DFS signal base

B = FT = M 2 F 0 T 0 = N 0 M 2 (9)

Number of pulses of the total PM signal N = N 0 M

Rice. 2.4 - Discrete frequencysignal and time-frequency plane

Shown in Fig. 2.5 The DFS signal contains FM signals as elements. Therefore, we will abbreviate this signal as a DFS-FM signal. As elements of the DFS signal, we can take DFS signals. If the base of the DF signal element B = F 0 T 0 = M 0 2 then the base of the entire signal B = M 0 2 M 2

Fig 2.5 - Discrete composite frequencyDFS-FM phase-shift keying signal and time-frequency plane.

Such a signal can be abbreviated as DSCH-FM. The number of frequency channels in the DFS-FM signal is M 0 M. If the DF signal (see Figure 2.4) and the FM-FM signal have equal bases, then they have the same number of frequency channels. Therefore, the DFS-FM signal does not have any special advantages over the DF signal. But the principles of constructing an FM signal can be useful when constructing large systems of FM signals. Thus, the most promising broadband signals for communication systems are FM, MF, and DFS-FM signals.

U(t)

f 0 +F/2

f 0 -F/2

U 1 (t)

f 0 +F/2

f 0 -F/2

U N (t)

U(t)

f 0 +F/2

f 0 -F/2

∙ ∙ ∙

∙ ∙ ∙ N

τ 0

U(t)

f 0 +F/2

f 0 = f 3

f 0 -F/2

U(t)

f 0 +F/2

f 0 = f 3

f 0 -F/2