Course work: Analysis of radio signals and calculation of characteristics of optimal matched filters. Main characteristics of signals The emergence of a spectrum of interdependent, complementary, multi-industry innovations
Amplitude modulation (AM) is the simplest and most common way in radio engineering of incorporating information into a high-frequency oscillation. With AM, the envelope of the amplitudes of the carrier oscillation changes according to a law that coincides with the law of change in the transmitted message, while the frequency and initial phase of the oscillation are maintained unchanged. Therefore, for an amplitude-modulated radio signal, the general expression (3.1) can be replaced by the following:
The nature of the envelope A(t) is determined by the type of message being transmitted.
With continuous communication (Fig. 3.1, a), the modulated oscillation takes on the form shown in Fig. 3.1, b. The envelope A(t) coincides in shape with the modulating function, i.e., with the transmitted message s(t). Figure 3.1, b is constructed under the assumption that the constant component of the function s(t) is equal to zero (in the opposite case, the amplitude of the carrier oscillation during modulation may not coincide with the amplitude of the unmodulated oscillation). Biggest change A(t) "down" cannot be greater than . The “upward” change can, in principle, be greater.
The main parameter of amplitude-modulated oscillation is the modulation coefficient.
Rice. 3.1. Modulating function (a) and amplitude-modulated oscillation (b)
The definition of this concept is especially clear for tonal modulation, when the modulating function is a harmonic oscillation:
The envelope of the modulated oscillation can be represented in the form
where is the modulation frequency; - initial phase of the envelope; - proportionality coefficient; - amplitude of envelope change (Fig. 3.2).
Rice. 3.2. Oscillation modulated in amplitude by a harmonic function
Rice. 3.3. Oscillation amplitude modulated by a pulse sequence
Attitude
called the modulation coefficient.
Thus, the instantaneous value of the modulated oscillation
With undistorted modulation, the amplitude of the oscillation varies from minimum to maximum.
In accordance with the change in amplitude, the average power of the modulated oscillation over the period of high frequency also changes. The peaks of the envelope correspond to a power 1–4 times greater than the power of the carrier oscillation. The average power over the modulation period is proportional to the mean square of the amplitude A(t):
This power exceeds the power of the carrier vibration by only a factor. Thus, with 100% modulation (M = 1), the peak power is equal to and the average power (the power of the carrier vibration is denoted by). This shows that the increase in oscillation power caused by modulation, which basically determines the conditions for isolating a message upon reception, even at the maximum modulation depth does not exceed half the power of the carrier oscillation.
When transmitting discrete messages, which are alternating pulses and pauses (Fig. 3.3, a), the modulated oscillation takes the form of a sequence of radio pulses shown in Fig. 3.3, b. This means that the phases of high-frequency filling in each of the pulses are the same as when they are “cut” from one continuous harmonic oscillation.
Only under this condition shown in Fig. 3.3b, the sequence of radio pulses can be interpreted as an oscillation modulated only in amplitude. If the phase changes from pulse to pulse, then we should talk about mixed amplitude-angular modulation.
Ministry of General and Professional Education of the Russian Federation
USTU-UPI named after S.M. Kirov
Theoretical foundations of radio engineering
ANALYSIS OF RADIO SIGNALS AND CALCULATION OF CHARACTERISTICS OF OPTIMAL MATCHED FILTERS
COURSE PROJECT
EKATERINBURG 2001
Introduction
Calculation of ACF of a given signal
Conclusion
List of symbols
Bibliography
Essay
Information has always been valued, and with the development of humanity, information is becoming more and more abundant. Information flows have turned into huge rivers.
In this regard, several problems of information transfer arose.
Information has always been valued for its reliability and completeness, so there is a struggle to transmit it without loss or distortion. With one more problem when choosing the optimal signal.
All this is transferred to radio engineering, where receiving, transmitting and processing these signals are developed. The speed and complexity of transmitted signals is constantly increasing in complexity.
To obtain and consolidate knowledge on processing the simplest signals, the training course includes a practical task.
In this course work a rectangular coherent burst is considered, consisting of N trapezoidal (the duration of the top is equal to one third of the duration of the base) radio pulses, where:
a) carrier frequency, 1.11 MHz
b) pulse duration (base duration), 15 μs
c) repetition frequency, 11.2 kHz
d) number of pulses in a packet, 9
For a given signal type it is necessary to produce (reduce):
ACF calculation
Calculation of amplitude spectrum and energy spectrum
Calculation of impulse response, matched filter
Spectral density is a coefficient of proportionality between the length of a small frequency interval D f and the corresponding complex amplitude of the harmonic signal D A with frequency f 0.
The spectral representation of signals opens a direct path to analyzing the passage of signals through a wide class of radio circuits, devices and systems.
The energy spectrum is useful for obtaining various engineering estimates that establish the actual spectral width of a particular signal. To quantify the degree of signal difference U(t) and its time-displaced copy U(t- t) It is customary to introduce ACF.
Let's fix an arbitrary moment in time and try to choose the function so that the value reaches the maximum possible value. If such a function really exists, then the linear filter corresponding to it is called a matched filter.
Introduction
Course work on the final part of the subject "Theory of radio signals and circuits" covers sections of the course devoted to the basics of signal theory and their optimal linear filtering.
The goals of the work are:
study of the temporal and spectral characteristics of pulsed radio signals used in radar, radio navigation, radio telemetry and related fields;
acquiring skills in calculating and analyzing correlation and spectral characteristics of deterministic signals (autocorrelation functions, amplitude spectra and energy spectra).
In the course work for a given type of signal it is necessary to:
ACF calculation.
Calculation of amplitude spectrum and energy spectrum.
Impulse response of a matched filter.
This course work examines a rectangular coherent packet of trapezoidal radio pulses.
Signal parameters:
carrier frequency (radio filling frequency), 1.11 MHz
pulse duration, (base duration) 15 μs
repetition frequency, 11.2 kHz
number of pulses in a pack, 9
Autocorrelation function (ACF) of the signal U(t) serves to quantify the degree of signal difference U(t) and its time-displaced copy 
(0.1)
and at t= 0 ACF becomes equal to the signal energy. ACF has the simplest properties:
parity property:
Those. K U ( t) =K U ( - t).
at any value of the time shift t ACF module does not exceed signal energy: ½ K U ( t) ½£ K U ( 0 ), which follows from the Cauchy-Bunyakovsky inequality.
So, the ACF is represented by a symmetrical curve with a central maximum, which is always positive, and in our case the ACF also has an oscillatory character. It should be noted that the ACF is related to the energy spectrum of the signal: 
; (0.2)
where ½ G
(w) ½ square of the spectral density modulus. Therefore, it is possible to evaluate the correlation properties of signals based on the distribution of their energy over the spectrum. The wider the signal frequency band, the narrower the main lobe of the autocorrelation function and the more perfect the signal from the point of view of the possibility of accurately measuring the moment of its beginning.
It is often more convenient to first obtain the autocorrelation function and then, using the Fourier transform, find the energy spectrum of the signal. Energy spectrum - represents dependence ½ G (w) ½ of the frequency.
Filters matched to the signal have the following properties:
The signal at the output of the matched filter and the correlation function of the output noise have the form of an autocorrelation function of the useful input signal.
Among all linear filters The matched filter produces the maximum ratio of the peak signal to the rms noise at the output.
Calculation of ACF of a given signal
Fig.1. Rectangular coherent burst of trapezoidal radio pulses
In our case, the signal is rectangular pack trapezoidal (the duration of the top is equal to one third of the duration of the base) radio pulses ( see figure 1) in which the number of pulses is N=9, and the pulse duration T i =15 μs.
Fig.2. Shift a copy of the signal envelope
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For the shift value T belonging to the interval from zero to one third of the pulse duration, it is necessary to solve the integral:
Solving this integral, we obtain an expression for the main lobe of the ACF for a given shift of a copy of the signal envelope:
For T belonging to the interval from one third to two thirds of the pulse duration, we obtain the following integral:
Solving it, we get:
For T, belonging to the interval from two-thirds of the pulse duration to the pulse duration, the integral has the form:
Therefore, as a result of the solution we have:
Taking into account the symmetry (parity) property of the ACF (see introduction) and the relationship connecting the ACF of a radio signal and the ACF of its complex envelope: 
we have functions for the main lobe of the ACF of the envelope ko (T) of the radio pulse and the ACF of the radio pulse Ks (T):
in which the input functions have the form:
Thus, on Figure 3 shows the main lobe of the ACF of the radio pulse and its envelope, i.e. when, as a result of a shift in the copy of the signal, when all 9 pulses of the burst are involved, i.e. N=9.
It can be seen that the ACF of the radio pulse has an oscillatory character, but there is always a maximum in the center. With a further shift, the number of intersecting pulses of the signal and its copy will decrease by one, and, consequently, the amplitude after each repetition period T ip = 89.286 μs.
Therefore, the final ACF will look like Figure 4 ( 16 petals, differing from the main one only in amplitudes) taking into account that , that in this figure T=T ip .:
Rice. 3. ACF of the main lobe of the radio pulse and its envelope
Rice. 4. ACF of a rectangular coherent burst of trapezoidal radio pulses
Rice. 5. Envelope of a packet of radio pulses.
Calculation of spectral density and energy spectrum
To calculate the spectral density, we will use, as in calculating the ACF, the functions of the radio signal envelope ( see Fig.2), which look like:
and the Fourier transform to obtain spectral functions, which, taking into account the limits of integration for the nth pulse, will be calculated according to the formulas:
for the radio pulse envelope and:
for a radio pulse, respectively.
The graph of this function is shown in ( Fig.5).
For clarity, the figure shows different frequency ranges
Rice. 6. Spectral density of the radio signal envelope.
As expected, the main maximum is located in the center, i.e. at frequency w =0.
The energy spectrum is equal to the square of the spectral density and therefore the spectrum graph looks like ( fig 6) those. very similar to a spectral density plot:
Rice. 7. Energy spectrum of the radio signal envelope.
The type of spectral density for a radio signal will be different, since instead of one maximum at w = 0, two maxima will be observed at w = ±wo, i.e. the spectrum of the video pulse (radio signal envelope) is transferred to the high-frequency region with a halving of the absolute value of the maxima ( see Fig.7). The type of energy spectrum of the radio signal will also be very similar to the type of spectral density of the radio signal, i.e. the spectrum will also be transferred to the high frequency region and two maxima will also be observed ( see Fig. 8).
Rice. 8. Spectral density of a packet of radio pulses.
Calculation of impulse response and recommendations for building a matched filter
As is known, along with a useful signal, noise is often present and therefore, with a weak useful signal, it is sometimes difficult to determine whether there is a useful signal or not.
To receive a time-shifted signal against the background of white Gaussian noise (white Gaussian noise “BGS” has a uniform distribution density) n (t) i.e. y(t)= + n (t), the likelihood ratio when receiving a signal of a known shape has the form:
Where No- spectral noise density.
Therefore, we come to the conclusion that optimal processing of received data is the essence of the correlation integral
The resulting function represents the essential operation that should be performed on the observed signal in order to optimally (from the standpoint of the minimum average risk criterion) make a decision about the presence or absence of a useful signal.
There is no doubt that this operation can be implemented by a linear filter.
Indeed, the signal at the output of a filter with an impulse response g(t) has the form:
As can be seen, when the condition is met g(r-x) = K ×S(r- t) these expressions are equivalent and then after replacement t = r-x we get:
Where TO- constant, and to- fixed time at which the output signal is observed.
A filter with such an impulse response g(t)( see above) is called consistent.
In order to determine the impulse response, a signal is needed S(t) shift to to to the left, i.e. we get the function S (to + t), and the function S (to - t) obtained by mirroring the signal relative to the coordinate axis, i.e. impulse response of the matched filter will be equal to the input signal, and at the same time we obtain the maximum signal-to-noise ratio at the output of the matched filter.
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Given our input signal, to build such a filter, we must first create a link for the formation of one trapezoidal pulse, the circuit of which is shown in ( Fig.9).
Rice. 10. Link for the formation of a radio pulse with a given envelope.
The signal of the radio signal envelope (in our case, a trapezoid) is supplied to the input of the radio pulse formation link with a given envelope (see Fig. 9).
A harmonic signal with a carrier frequency wо (in our case 1.11 MHz) is generated in the oscillatory link, so at the output of this link we have a harmonic signal with a frequency wо.
From the output of the oscillatory link, the signal is fed to the adder and to the signal delay line link at Ti (in our case, Ti = 15 μs), and from the output of the delay link, the signal is fed to the phase shifter (it is needed so that after the end of the pulse there is no radio signal at the output of the adder) .
After the phase shifter, the signal is also fed to the adder. At the output of the adder, finally, we have trapezoidal radio pulses with a radio filling frequency wо i.e. signal g(t).
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Since we need to obtain a coherent packet of 9 trapezoidal video pulses, it is necessary to apply the signal g (t) to the link for forming such a packet, a circuit that looks like in (Fig. 10):
Rice. 11. Link of formation of a coherent burst.
The signal g (t), which is a trapezoidal radio pulse (or a sequence of trapezoidal radio pulses), is supplied to the input of the coherent burst formation link.
Next, the signal goes to the adder and to the delay block, in which the input signal is delayed for the period of pulses in the packet. Tip multiplied by the pulse number minus one, i.e. ( N-1), and from the output of the delay side again to the adder .
Thus, at the output of the coherent burst formation link (i.e., at the output of the adder) we have a rectangular coherent burst of trapezoidal radio pulses, which is what needed to be implemented.
Conclusion
In the course of the work, appropriate calculations were carried out and graphs were constructed; from them, one can judge the complexity of signal processing. To simplify, mathematical calculations were carried out in MathCAD 7.0 and MathCAD 8.0 packages. this work is a necessary part of the curriculum so that students have an understanding of the features of the use of various pulsed radio signals in radar, radio navigation and radio telemetry, and can also design the optimal filter, thereby making their modest contribution to the “struggle” for information.
List of symbols
wо - radio filling frequency;
w- frequency
T, ( t) - time shifting;
Ti - duration of the radio pulse;
Tip - repetition period of radio pulses in a packet;
N - number of radio pulses in a packet;
t - time;
Bibliography
1. Baskakov S.I. "Radio engineering circuits and signals: Textbook for universities on the specialty "Radio engineering"". - 2nd ed., revised. and additional - M.: Higher. school, 1988 - 448 pp.: ill.
2. “ANALYSIS OF RADIO SIGNALS AND CALCULATION OF CHARACTERISTICS OF OPTIMAL MATCHED FILTERS: Guidelines for course work in the course “Theory of radio signals and circuits”” / Kibernichenko V.G., Doroinsky L.G., Sverdlovsk: UPI 1992.40 p.
3. "Amplification devices": Textbook: a manual for universities. - M.: Radio and Communications, 1989. - 400 pp.: ill.
4. Buckingham M. “Noises in electronic devices and systems"/Translated from English - M.: Mir, 1986
Signal - a physical process that displays a message. IN technical systems electrical signals are most often used. Signals are usually functions of time.
1. Signal classification
Signals can be classified according to various criteria:
1. Continuous ( analog) - signals that are described by continuous functions of time, i.e. take a continuous set of values on the definition interval. Discrete - are described discrete functions time i.e. take a finite set of values on the definition interval.
Deterministic - signals that are described by deterministic functions of time, i.e. whose values are determined at any point in time. Random - are described by random functions of time, i.e. whose values at any time are random variable. Random processes (RP) can be classified into stationary, non-stationary, ergodic and non-ergodic, as well as Gaussian, Markov, etc.
3. Periodic - signals whose values are repeated at intervals equal to the period
x (t) = x (t+nT), Where n= 1,2,...,¥; T- period.
4. Causal - signals that have a beginning in time.
5. Finite - signals of finite duration and equal to zero outside the detection interval.
6. Coherent - signals that coincide at all definition points.
7. Orthogonal - signals opposite to coherent.
2. Signal characteristics
1. Signal duration ( transmission time) T s- the time interval during which the signal exists.
2. Spectrum width Fc- the range of frequencies within which the main signal power is concentrated.
3. Signal base - the product of the signal spectrum width and its duration.
4. Dynamic range Dc- logarithm of the ratio of the maximum signal power - Pmax to the minimum - Pmin(minimum difference at the noise level):
D c = log (P max /P min).
In expressions where logarithms with any base can be used, the base of the logarithm is not indicated.
Typically, the base of the logarithm determines the unit of measurement (for example: decimal - [Bel], natural - [Neper]).
5. Signal volume is determined by the relation V c = T c F c D c .
6. Energy characteristics: instantaneous power - P(t); average power - P avg and energy - E. These characteristics are determined by the relations:
P(t) =x 2 (t); ; (1)
Where T=t max -tmin.
3. Mathematical models of random signals
Deterministic, i.e. a message known in advance does not contain information, since the recipient knows in advance what the transmitted signal will be. Therefore, the signals are statistical in nature.
A random (stochastic, probabilistic) process is a process that is described by random functions of time.
Random process X(t) can be represented by an ensemble of non-random time functions xi(t), called realizations or samples (see Fig. 1).
Fig.1. Implementations of a random process X(t)
A complete statistical characteristic of a random process is n- dimensional distribution function: F n (x 1, x 2,..., x n; t 1, t 2,..., t n), or probability density f n (x 1, x 2,..., x n; t 1, t 2,..., t n).
The use of multidimensional laws is associated with certain difficulties,
therefore, they are often limited to using one-dimensional laws f 1 (x, t), characterizing the statistical characteristics of a random process at individual points in time, called sections of a random process or two-dimensional f 2 (x 1, x 2; t 1, t 2), characterizing not only the statistical characteristics of individual sections, but also their statistical relationship.Distribution laws are comprehensive characteristics of a random process, but random processes can be quite fully characterized using the so-called numerical characteristics (initial, central and mixed moments). In this case, the following characteristics are most often used: mathematical expectation (initial moment of the first order)
; (2)mean square (second order initial moment)
; (3)dispersion (second order central moment)
; (4)correlation function, which is equal to the correlation moment of the corresponding sections of the random process
. (5)In this case, the following relation is valid:
(6)Stationary processes - processes in which numerical characteristics do not depend on time.
Ergodic processes - a process in which the results of averaging and the results of the set coincide.
Gaussian processes - processes with a normal distribution law:
(7)This law plays an extremely important role in the theory of signal transmission, since most interference is normal.
According to the central limit theorem, most random processes are Gaussian.
M Arkov process - a random process in which the probability of each subsequent value is determined only by one previous value.
4. Forms of analytical description of signals
Signals can be presented in the time, operator or frequency domain, the connection between which is determined using the Fourier and Laplace transforms (see Fig. 2).
Laplace transform:
L-1: (8)Fourier transforms:
F-1: (9)Fig.2 Signal representation areas
In this case, various forms of signal representation can be used in the form of functions, vectors, matrices, geometric, etc.
When describing random processes in the time domain, the so-called correlation theory of random processes is used, and when describing in the frequency domain, the spectral theory of random processes is used.
Taking into account the parity of functions
and and in accordance with Euler’s formulas: (10)we can write expressions for the correlation function R x (t) and energy spectrum (spectral density) of a random process S x (w), which are related to the Fourier transform or the Wiener-Khinchin formulas
; (11) . (12)5. Geometric representation of signals and their characteristics
Any n- numbers can be represented as a point (vector) in n-dimensional space, distant from the origin at a distance D,
Where . ( 13)
Signal duration T s and spectrum width F with, in accordance with Kotelnikov’s theorem is determined N samples, where N = 2F c T c.
This signal can be represented by a point in n-dimensional space or by a vector connecting this point to the origin.
The length of this vector (norm) is:
; (14)Where x i =x (nDt) - signal value at time t = n.Dt.
Let's say: X- the message being transmitted, and Y- accepted. Moreover, they can be represented by vectors (Fig. 3).
X1, Y1
0 a1 a2 x1 y1
Fig.3. Geometric representation of signals
Let us define the connections between the geometric and physical representation of signals. For the angle between vectors X And Y can be written down
cosg =cos(a 1 -a 2) =cosa 1cosa 2 +sina 1sina 2 =
Based on the principle of information exchange, there are three types of radio communications:
simplex radio communication;
duplex radio communication;
half-duplex radio communication.
Based on the type of equipment used in the radio communication channel, the following types of radio communications are distinguished:
telephone;
telegraph;
data transmission;
facsimile;
television;
radio broadcasting.
Based on the type of radio communication channels used, the following types of radio communication are distinguished:
surface wave;
tropospheric;
ionospheric;
meteoric;
space;
radio relay.
Types of documented radio communications:
telegraph communication;
data transfer;
fax communication.
Telegraph communication - for transmitting messages in the form of alphanumeric text.
Data transfer for the exchange of formalized information between a person and a computer or between computers.
Facsimile communication for the transmission of still images by electrical signals.
1 – Telex – for the exchange of written correspondence between organizations and institutions using typewriters with electronic memory;
2 – Tele (video) text – for receiving information from the computer to monitors;
3 – Tele (bureau) fax – fax machines are used for receiving (either from users or from enterprises).
The following types of radio communication signals are widely used in radio networks:
A1 - AT with manipulation of continuous oscillations;
A2 - manipulation of tone-modulated oscillations
ADS - A1 (B1) - OM with 50% carrier
AZA - A1 (B1) - OM with 10% carrier
AZU1 - A1 (Bl) - OM without carrier
3. Features of the propagation of radio waves of various ranges.
Propagation of radio waves in the myriameter, kilometer and hectometer ranges.
To assess the nature of the propagation of radio waves of a particular range, it is necessary to know the electrical properties of the material media in which the radio wave propagates, i.e. know and ε A of the earth and atmosphere.
The total current law in differential form states that
those. A change in magnetic induction flux over time causes the appearance of conduction current and displacement current.
Let us write this equation taking into account the properties of the material environment:
λ < 4 м - диэлектрик
4 m< λ < 400 м – полупроводник
λ > 400 m – conductor
Sea water:
λ < 3 м - диэлектрик
3 cm< λ < 3 м – полупроводник
λ > 3 m – conductor
For myriameter wave (SVD):
λ = 10 ÷ 100 km f = 3 ÷ 30 kHz
and kilometer (DV):
λ = 10 ÷ 1 km f = 30 ÷ 300 kHz
ranges, the earth's surface in its electrical parameters approaches an ideal conductor, and the ionosphere has the highest conductivity and the lowest dielectric constant, i.e. close to the conductor.
RV ranges VLF and LW practically do not penetrate the earth and the ionosphere, being reflected from their surface and can propagate along natural radio paths over considerable distances without significant loss of energy by surface and spatial waves.
Because Since the wavelength of the VHF range is commensurate with the distance to the lower boundary of the ionosphere, the concept of a simple and surface wave loses its meaning.
The RV propagation process is considered as occurring in a spherical waveguide:
Inner side - ground
External side (at night - layer E, during the day - layer D)
The waveguide process is characterized by insignificant energy losses.
Optimal RV – 25 ÷ 30 km
Critical RV (strong attenuation) - 100 km or more.
Inherent phenomena: - fading, radio echo.
Fading (fading) as a result of the interference of RVs that have traveled different paths and have different phases at the receiving point.
If the surface and spatial waves are in antiphase at the reception point, then this is fading.
If the spatial waves are in antiphase at the receiving point, then this is far fading.
A radio echo is a repetition of a signal as a result of sequential reception of waves reflected from the ionosphere a different number of times (near radio echo) or arriving at the receiving point without and after circling the globe (far radio echo).
The earth's surface has stable properties, and the places where the ionospheric ionization conditions are measured have little effect on the propagation of the RV VLF range, then the amount of radio signal energy changes little over the course of a day, a year, and in extreme conditions.
In the km wave range, both surface and spatial waves are well expressed (both day and night), especially at waves λ> 3 km.
Surface waves when emitted have an elevation angle of no more than 3-4 degrees, and spatial waves are emitted at large angles to the earth's surface.
The critical angle of incidence of the RV km range is very small (during the day on layer D, and at night on layer E). Rays with elevation angles close to 90° are reflected from the ionosphere.
Surface waves in the km range, due to their good diffraction ability, can provide communications over distances of up to 1000 km or more. However, these waves attenuate greatly with distance. (At 1000 km, the surface wave is less intense than the spatial wave).
Over very long distances, communication is carried out only by spatial km wave. In the region of equal intensity of surface and spatial waves, near-fading is observed. The conditions for the propagation of km waves are practically independent of the season, the level of solar activity, and weakly depend on the time of day (at night the signal level is higher).
Reception in the km range is rarely degraded due to strong atmospheric interference (thunderstorm).
When moving from CM (LW) km to the hectometer range, the conductivity of the earth and the ionosphere decreases. ε of the earth and approaches ε of the atmosphere.
Losses in the ground are increasing. The waves penetrate deeper into the ionosphere. At a distance of several hundred km, spatial waves begin to dominate, because surface ones are absorbed by the earth and attenuate.
At a distance of approximately 50-200 km, surface and sky waves are equal in intensity and short-range fading may occur.
Freezing is frequent and deep.
As λ decreases, the depth of fading increases with decreasing duration of blocking.
Fading is especially strong at λ greater than 100 m.
The average duration of fading ranges from several seconds (1 sec) to several tens of seconds.
Radio communication conditions in the hectometer range (HF) depend on the season and time of day, because layer D disappears, and layer E is higher, and in layer D there is a large absorption.
The communication range at night is greater than during the day.
In winter, reception conditions improve due to a decrease in the electron density of the ionosphere and are weakened in atmospheric fields. In cities, reception is highly dependent on industrial interference.
SpreadingRV- decameter range (HF).
When moving from SW to HF, losses in the ground increase greatly (the ground is an imperfect dielectric), while in the atmosphere (ionosphere) they decrease.
Surface waves on natural HF radio paths are of low importance (weak diffraction, strong absorption).
2.1.1.Deterministic and random signals
Deterministic signal is a signal whose instantaneous value at any time can be predicted with a probability equal to one.
An example of a deterministic signal (Fig. 10) can be: sequences of pulses (the shape, amplitude and time position of which are known), continuous signals with given amplitude-phase relationships.
Methods for specifying a MM signal: analytical expression (formula), oscillogram, spectral representation.
An example of a MM of a deterministic signal.
s(t)=S m ·Sin(w 0 t+j 0)
Random signal– a signal, the instantaneous value of which at any time is unknown in advance, but can be predicted with a certain probability, less than one.
Example random signal(Fig. 11) there may be tension corresponding to human speech, music; sequence of radio pulses at the input of the radar receiver; interference, noise.
2.1.2. Signals used in radio electronics
Continuous in magnitude (level) and continuous in time (continuous or analog) signals– take any values s(t) and exist at any moment in a given time interval (Fig. 12).
Continuous in magnitude and discrete in time signals are specified at discrete time values (on a countable set of points), the magnitude of the signal s(t) at these points takes on any value in a certain interval along the ordinate axis.
The term “discrete” characterizes the method of specifying a signal on the time axis (Fig. 13).
Magnitude-quantized and time-continuous signals are specified on the entire time axis, but the value s(t) can only take discrete (quantized) values (Fig. 14).
Magnitude-quantized and time-discrete (digital) signals– the values of signal levels are transmitted in digital form (Fig. 15).
2.1.3. Pulse signals
Pulse- an oscillation that exists only within a finite period of time. In Fig. 16 and 17 show a video pulse and a radio pulse.
For a trapezoidal video pulse, enter the following parameters:
A – amplitude;
t and – video pulse duration;
t f – front duration;
t cf – cut duration.
S р (t)=S in (t)Sin(w 0 t+j 0)
S in (t) – video pulse – envelope for a radio pulse.
Sin(w 0 t+j 0) – filling the radio pulse.
2.1.4. Special signals
Switching function (single function(Fig. 18) or Heaviside function) describes the process of transition of some physical object from a “zero” to a “unit” state, and this transition occurs instantly.
Delta function (Dirac function) is a pulse whose duration tends to zero, while the height of the pulse increases indefinitely. It is customary to say that the function is concentrated at this point.
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