Types of signals used in radio communication systems. Course work: Analysis of radio signals and calculation of characteristics of optimal matched filters General information and parameters of radio signals

Radio signals are electromagnetic waves or high-frequency electrical vibrations that contain the transmitted message. To generate a signal, the parameters of high-frequency oscillations are changed (modulated) using control signals, which represent a voltage that changes according to a given law. Harmonic high-frequency oscillations are usually used as modulated ones:

where w 0 =2π f 0 – high carrier frequency;

U 0 – amplitude of high-frequency oscillations.

The simplest and most frequently used control signals include harmonic oscillation

where Ω is a low frequency, much lower than w 0; ψ – initial phase; U m – amplitude, as well as rectangular pulse signals, which are characterized by the fact that the voltage value U control ( t)=U during time intervals τ and, called pulse duration, and is equal to zero during the interval between pulses (Fig. 1.13). Magnitude T and is called the pulse repetition period; F and =1/ T and – frequency of their repetition. Pulse repetition period ratio T and to the duration τ and is called the duty cycle Q pulse process: Q=T and /τ and.

Fig.1.13. Rectangular pulse sequence

Depending on which parameter of the high-frequency oscillation is changed (modulated) using the control signal, amplitude, frequency and phase modulation are distinguished.

When amplitude modulation (AM) of high-frequency oscillations with a low-frequency sinusoidal voltage with a frequency of Ω modes produces a signal whose amplitude changes over time (Fig. 1.14):

Parameter m=U m/ U 0 is called the amplitude modulation coefficient. Its values ​​range from one to zero: 1≥m≥0. The modulation factor expressed as a percentage (i.e. m×100%), is called amplitude modulation depth.

Rice. 1.14. Amplitude modulated radio signal

During phase modulation (PM) of a high-frequency oscillation with a sinusoidal voltage, the amplitude of the signal remains constant, and its phase receives an additional increment Δy under the influence of the modulating voltage: Δy= k FM U m sinW mod t, Where k FM – proportionality coefficient. A high-frequency signal with phase modulation according to a sinusoidal law has the form

In frequency modulation (FM), the control signal changes the frequency of high-frequency oscillations. If the modulating voltage changes according to a sinusoidal law, then the instantaneous value of the modulated oscillation frequency w=w 0 + k World Cup U m sinW mod t, Where k FM – proportionality coefficient. The largest change in frequency w relative to its average value w 0, equal to Δw М = k World Cup U m is called frequency deviation. The frequency modulated signal can be written as follows:

A value equal to the ratio of frequency deviation to modulation frequency (Δw m /W mod = m FM) is called frequency modulation ratio.

Figure 1.14 shows high-frequency signals for AM, PM and FM. In all three cases the same modulating voltage is used U mode, changing according to a symmetric sawtooth law U mod ( t)= k Maud t, Where k mod >0 at time interval 0 t 1 and k Maud<0 на отрезке t 1 t 2 (Fig. 1.15, a).

With AM, the signal frequency remains constant (w 0), and the amplitude changes according to the law of modulating voltage U AM ( t) = U 0 k Maud t(Fig. 1.15, b).

A frequency-modulated signal (Fig. 1.15c) is characterized by constant amplitude and a smooth change in frequency: w( t) = w 0 + k World Cup t. In the period of time from t=0 to t 1 the oscillation frequency increases from the value w 0 to the value w 0 + k World Cup t 1 , and on the segment from t 1 to t 2, the frequency decreases again to the value w 0.

The phase-modulated signal (Fig. 1.15d) has a constant amplitude and an abrupt change in frequency. Let us explain this analytically. With FM under the influence of modulating voltage

Fig.1.15. Comparative view of modulated oscillations for AM, FM and FM:
a – modulating voltage; b – amplitude-modulated signal;
c – frequency-modulated signal; d – phase modulated signal

the signal phase receives an additional increment Δy= k FM t, therefore, the high-frequency signal with phase modulation according to the sawtooth law has the form

Thus, on the interval 0 t 1 frequency is equal to w 1 >w 0 , and on the segment t 1 t 2 it is equal to w 2

When transmitting a sequence of pulses, for example, a binary digital code (Fig. 1.16a), AM, FM and FM can also be used. This type of modulation is called manipulation or telegraphy (AT, CT and FT).

Fig.1.16. Comparative view of manipulated oscillations in AT, CT and FT

With amplitude telegraphy, a sequence of high-frequency radio pulses is formed, the amplitude of which is constant during the duration of the modulating pulses τ and, and is equal to zero the rest of the time (Fig. 1.16, b).

With frequency telegraphy, a high-frequency signal is formed with a constant amplitude and a frequency that takes on two possible values ​​(Fig. 1.16c).

With phase telegraphy, a high-frequency signal is formed with a constant amplitude and frequency, the phase of which changes by 180° according to the law of the modulating signal (Fig. 1.16, d).

Pulse signals are current dependent. Their use in the electric power industry is mainly determined by systems of telemetric monitoring, control, and repair protection. Pulse signals are not used for energy transmission. This is due to their wide energy (frequency) spectrum. They can be either periodic, that is, repeated after a certain time interval, or non-periodic. The main purpose of such signals is informational.

Basic characteristics of pulse signals.

1) The instantaneous value of the pulse signal (U(t)), similar to the sinusoidal one, can be determined using instruments that represent the signal shape.

2) The amplitude value of U n characterizes the highest value of the instantaneous voltage in the interval of period T. The period of study of the pulse signal is determined by points at the level of 0.5 amplitude.

3) The rise time of the leading edge t f + is the time interval between the points corresponding to 0.1U m and 0.9U m. The leading edge characterizes the degree of signal increase, i.e. how quickly the impulse from level 0 reaches U m. Ideally, t f + should be equal to zero, but in practice this interval is never equal to zero, t f » 10 nS.

4) Decay time (rear edge) t f - is determined similarly from the level of 0.1 to 0.9 at the amplitude, but at the decay of the pulse. The time of the trailing edge, like the leading one, is also finite. They strive to reduce it, since the decline affects the pulse duration t u.

5) Pulse duration t u – time interval determined at the level of 0.5 amplitude from the leading to the trailing edge. The ratio of the pulse repetition period to the pulse duration, called the duty cycle, is important for the signal. The higher the duty cycle, the greater the number of times the pulse “fits” into the repetition period T/m = q.

A special case of a pulse signal is a square wave, which has a duty cycle of q = 2. The duty cycle indirectly indicates the energy characteristic of the signal: the larger it is, the less energy the signal carries over a period. Since the signal is characterized by different voltage levels, it is also used: effective voltage value, analogue form; average rectified voltage value.

For rectangular signals these values ​​are equal. The energy characteristic - signal power - is often considered. Power per period P is defined for a square wave as:

Where P u is the pulse power, q is the duty cycle

The pulse power can reach large values, while the average power remains low. Devices are tested using short pulses with large amplitude.

6) Copy link Y =

Spectrum of pulse signals

w 0 2w 0 3w 0 4w 0 5w 0 6w 0 t

According to the Fourier series expansion of periodic signals, a pulse signal is also represented as consisting of the sum of many components. First of all, this is the fundamental harmonic – the frequency of signal research and its multiple components. But along with them, this expansion includes many other harmonics that are not multiples of the main one. These are harmonics smaller than the fundamental one and combinations of these harmonics with the fundamental ones. This representation shows that the pulse signal has a wide bandwidth. Everything is on one line.

Low frequencies provide the roof in pulse form. The smaller these components are, the smaller the decline in the top of the pulse. At the same time, the duty cycle of the rise and fall of the pulse depends on the high-frequency components in the signal decomposition. The higher the frequency, the steeper the pulse edges. To transmit a signal, you need a device that has the same transmission coefficients over the entire range of the pulse spectrum. But such a device is technically difficult to implement. Therefore, they always solve the problem: choose a narrower spectrum and a better pulse parameter.

The main optimization criterion: duty cycle of pulse signal transmission. But today in real systems it reaches 100 Mbaud = 10 8 units of information per second.

Pulse signals tend to convey positive polarities, since the polarity is determined by the supply voltage, although pulses of negative polarity are used to transmit information. When measuring the voltage value of pulse signals, pay attention to the device: peak voltmeter (amplitude), average values, rms values. Average and rms voltage values ​​depend on the pulse duration. Peak value - no. Transmission of pulsed signals over wire lines leads to noticeable signal distortion: the signal spectrum narrows in the HF part, so the rise and fall of the pulse increases.

By nature, any electrical signals are divided into 2 groups: deterministic, random.

The former at any time can be described by a specific value (instantaneous value U(t)). Deterministic signals make up the majority.

Random signals. The nature of their appearance is unpredictable in advance, so they cannot be calculated or designated at a specific point. Such signals can only be studied, an experiment can be conducted to determine the probabilistic characteristics of the signals. In the energy sector, such signals include: interference from electromagnetic fields that distort the main signal. Additional signals appear when there are complete or partial discharges between transmission lines. Random signals are analyzed and measured using probabilistic characteristics. From the point of view of measurement errors, random signals and their influence are classified as additional random errors. Moreover, if their value is an order of magnitude smaller than the main random ones, they can be excluded from the analysis.

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

Abstract

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.

This course work examines a rectangular coherent burst 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 the analysis of 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 peak signal to rms noise output ratio.

Calculation of ACF of a given signal

Fig.1. Rectangular coherent burst of trapezoidal radio pulses

In our case, the signal is a rectangular packet of 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

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 nature, 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 a 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. The 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.

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).

Rice. 11. Link of formation of a coherent pack.

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 drawn from which 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 shift;

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. “Noise in electronic devices and systems” / Trans. from English - M.: Mir, 1986

1 Classification of types of modulation, main characteristics of radio signals.

To carry out radio communication, it is necessary to somehow change one of the parameters of the radio frequency wave, called the carrier wave, in accordance with the transmitted low-frequency signal. This is achieved using radio frequency modulation.

It is known that harmonic oscillation

characterized by three independent parameters: amplitude, frequency and phase.

Accordingly, there are three main types of modulation:

Amplitude,

Frequency,

Phase.

Amplitude modulation (AM) is a type of influence on a carrier vibration, as a result of which its amplitude changes according to the law of the transmitted (modulating) signal.

We assume that the modulating signal has the form of a harmonic oscillation with frequency W

much lower than the carrier frequency w.

As a result of modulation, the voltage amplitude of the carrier oscillation should change in proportion to the voltage of the modulating signal uW (Fig. 1):

UAM = U + kUWcosWt = U + DUcosWt, (1)

where U is the voltage amplitude of the carrier radio frequency oscillation;

DU=kUW - amplitude increment.

The equation of amplitude-modulated oscillations, in this case, takes the form

UAM = UAM coswt = (U + DUcosWt) coswt = U (1+cosWt) coswt. (2)

According to the same law, the iAM current will change during modulation.

The quantity characterizing the ratio of the change in the amplitude of oscillations DU to their amplitude in the absence of modulation U is called the modulation coefficient (depth)

It follows from this that the maximum amplitude of oscillations is Umax = U + DU = U (1+m) and the minimum amplitude Umin = U (1-m).

As is easy to see from equation (2), in the simplest case, modulated oscillations are the sum of three oscillations

UAM = U(1+ mcosWt)coswt = Ucoswt U/2+ cos(w - W)t U/2+ cos(w + W)t . (4)

The first term is the oscillations of the transmitter in the absence of modulation (silent mode). The second is oscillations of side frequencies.

If modulation is carried out with a complex low-frequency signal with a spectrum from Fmin to Fmax, then the spectrum of the received AM signal has the form shown in Fig. The frequency band Δfc occupied by the AM signal does not depend on m and is equal to

Δfс = 2Fmax. (5)

The occurrence of side frequency oscillations during modulation leads to the need to expand the bandwidth of the transmitter circuits (and, accordingly, the receiver). She must be

where Q is the quality factor of the circuits,

Df - absolute detuning,

Dfк - circuit passband.

In Fig. spectral components corresponding to lower modulating frequencies (Fmin) have smaller ordinates.

This is explained by the following circumstance. For most types of signals (for example, speech) entering the transmitter input, the amplitudes of the high-frequency components of the spectrum are small compared to the components of low and medium frequencies. As for the noise at the detector input in the receiver, its spectral density is constant within the passband

receiver As a result, the modulation coefficient and the signal-to-noise ratio at the input of the receiver detector for high frequencies of the modulating signal are small. To increase the signal-to-noise ratio, the high-frequency components of the modulating signal during transmission are emphasized by amplifying the high-frequency components by a greater number of times compared to the low- and mid-frequency components, and when receiving before or after the detector, they are attenuated by the same amount. Attenuation of high-frequency components before the detector almost always occurs in the high-frequency resonant circuits of the receiver. It should be noted that artificially emphasizing the upper modulating frequencies is acceptable as long as it does not lead to overmodulation (m > 1).

Lecture No. 5

T Issue No. 2: Transmission of DISCRETE messages

Lecture topic: DIGITAL RADIO SIGNALS AND THEIR

Features Introduction

For data transmission systems, the requirement for the reliability of the transmitted information is most important. This requires logical control of the processes of transmitting and receiving information. This becomes possible when using digital signals to transmit information in a formalized form. Such signals make it possible to unify the element base and use correction codes that provide a significant increase in noise immunity.

2.1. Understanding Discrete Message Transmission

Currently, so-called digital communication channels are usually used to transmit discrete messages (data).

The carriers of messages in digital communication channels are digital signals or radio signals if radio communication lines are used. The information parameters in such signals are amplitude, frequency and phase. Among the related parameters, the phase of harmonic oscillation occupies a special place. If the phase of the harmonic oscillation at the receiving side is precisely known and this is used during reception, then such a communication channel is considered coherent. IN incoherent communication channel, the phase of the harmonic oscillation on the receiving side is unknown and it is considered that it is distributed according to a uniform law in the range from 0 to 2  .

The process of converting discrete messages into digital signals when transmitting and digital signals into discrete messages when receiving is explained in Fig. 2.1.

Fig.2.1. The process of converting discrete messages during their transmission

Here it is taken into account that the basic operations of converting a discrete message into a digital radio signal and back correspond to the generalized block diagram of the discrete message transmission system discussed in the last lecture (shown in Fig. 3). Let's consider the main types of digital radio signals.

2.2. Characteristics of digital radio signals

2.2.1. Amplitude-shift keying (AMK) radio signals

Amplitude manipulation (AMn). Analytical expression of the AMn signal for any moment in time t has the form:

s AMn (t, )= A 0  (t) cos(  t ) , (2.1)

Where A 0 ,   And  - amplitude, cyclic carrier frequency and initial phase of the AMn radio signal,  (t) – primary digital signal (discrete information parameter).

Another form of notation is often used:

s 1 (t) = 0 at  = 0,

s 2 (t) = A 0 cos(  t ) at  = 1, 0  t T(2.2)

which is used when analyzing AMN signals over a period of time equal to one clock interval T. Because s(t) = 0 at  = 0, then the AMn signal is often called a signal with a passive pause. The implementation of the AMS radio signal is shown in Fig. 2.2.

Fig.2.2. Implementation of AMS radio signal

The spectral density of the AMS signal has both continuous and discrete components at the carrier frequency   . The continuous component represents the spectral density of the transmitted digital signal  (t), transferred to the carrier frequency region. It should be noted that the discrete component of the spectral density occurs only when the initial phase of the signal is constant  . In practice, as a rule, this condition is not met, since as a result of various destabilizing factors, the initial phase of the signal randomly changes in time, i.e. is a random process  (t) and is uniformly distributed in the interval [-  ;  ]. The presence of such phase fluctuations leads to “blurring” of the discrete component. This feature is also typical for other types of manipulation. Figure 2.3 shows the spectral density of the AMn radio signal.

Fig.2.3. Spectral density of the AMn radio signal with a random, uniform

distributed in the interval [-  ;  ] initial phase 

The average power of the AMn radio signal is equal to
. This power is equally distributed between the continuous and discrete components of the spectral density. Consequently, in an AMS radio signal, the continuous component due to the transmission of useful information accounts for only half of the power emitted by the transmitter.

To generate an AMS radio signal, a device is usually used that provides a change in the amplitude level of the radio signal according to the law of the transmitted primary digital signal  (t) (for example, an amplitude modulator).