Signal modulation. Keying frequency, phase, amplitude

Modulation- the process of changing one or more parameters of a high-frequency carrier oscillation according to the law of a low-frequency information signal (message).
The transmitted information is embedded in the control signal, and the role of the information carrier is performed by a high-frequency oscillation called the carrier. Modulation, therefore, is the process of "landing" an information wave on a known carrier.
As a result modulation the spectrum of the low-frequency control signal is transferred to the region high frequencies. This allows, when organizing broadcasting, to configure the operation of all transceiver devices on different frequencies so that they don't interfere with each other.
Oscillations of various shapes (rectangular, triangular, etc.) can be used as a carrier, but the most commonly used harmonic vibrations. Depending on which of the parameters of the carrier oscillation changes, the type of modulation is distinguished (amplitude, frequency, phase, etc.). Modulation discrete signal called digital modulation or keying.
There are the following types of manipulations:
FSK
phase keying
Amplitude keying
Quadrature amplitude-shift keying
Frequency shift keying (FC) is used to transmit telegraph signals over a radio channel, which are a sequence of rectangular elementary current (positive) and currentless (negative) messages. Unlike radio signals amplitude manipulation when the transmitter emits electromagnetic oscillations only with current transmissions at FT, the radiation of the radio signal occurs continuously both with current and without current transmissions. Therefore, this method of manipulation is sometimes called work with an active pause.

Fig.1 Digital modulation (keying)
When switching from a current to a currentless message and vice versa, the amplitude of the high-frequency oscillation remains constant, and only its frequency changes by some constant value fc, which is called the frequency shift.
Currently, frequency telegraphy systems with frequency shifts of 125 (ChT-125), 250 (ChT-250), 500 (ChT-500), 1000 (ChT-1000), 1500 (ChT-1500) Hz are most widely used. In this case, the frequency deviation fm of the exciter relative to the nominal (average) oscillation frequency of the transmitter is + 62.5 Hz, respectively; + 125 Hz; + 500 Hz; +750 Hz.
The average frequency fo is called the carrier (nominally frequency. It should be noted that the term "carrier frequency" in frequency telegraphy is introduced very conditionally, since at FT the transmission never operates at the frequency fo. The expediency of introducing this term is due only to the fact that the carrier frequency is numerically equal to the average frequency of the frequency spectrum at the output of the transmitter and, therefore, is the nominal operating frequency transmitter.
The spectrum of FT signals depends not only on the speed of telegraphy (on the main frequency of telegraphy), but also on the magnitude of the frequency shift and the method of generating FT signals. There are two main ways of forming chirp signals: with a break in the phase of high-frequency oscillations and without breaking it.
In the first case, the FT signal is formed by alternately connecting two independent sources of high-frequency oscillations to the amplifying path of the transmitter. One of the sources generates oscillations with a certain frequency and is connected with currentless (negative) sendings of the primary signal. The second one generates oscillations with a frequency that differs from the first frequency (shifted relative to the frequency) by the value fc. This source is connected with current (positive) sendings of the primary signal.
Since both sources of high-frequency oscillations are independent, during switching, the oscillation phase takes on an arbitrary value, i.e. a phase break occurs.
In the second method of generating signals, one source of high-frequency oscillations is used, which, with currentless (negative) sendings of the primary signal, generates oscillations with a frequency fа, and with current (positive) oscillations with a frequency fв. Since one source is used, the change in the oscillation frequency occurs continuously, without breaking the phase of the high-frequency oscillation. This kind of signal can be viewed as special case frequency modulation of a high-frequency oscillation by a discrete signal
Using the methods of frequency telegraphy, it is possible to transmit two different telegraph messages over the radio channel. This transmission method is called double frequency telegraphy (DFT) and corresponds to emission class F.
Amplitude keying is a change in the signal, in which the amplitude of the carrier oscillation changes abruptly. AMn can be considered a special case of quadrature keying
Telegraph signals - Morse code - are most often transmitted using amplitude manipulation. In the transmitter, this method is implemented most simply compared to other types of manipulation. A receiver for receiving telegraph signals by ear, on the contrary, is somewhat more complicated: it must contain a local oscillator operating at a frequency close to the frequency of the received signal so that the difference can be distinguished at the receiver output. audio frequency. Suitable receivers are direct conversion, regenerative in the generation mode and superheterodyne with an additional "telegraph" local oscillator.
The amplitude of the high-frequency signal at the output of the radio transmitter takes only two values: on and off. Accordingly, turning on or off (“keying”) is performed by the operator using a telegraph key or using an automatic telegraph parcel generator (Morse code sensor, computer). The envelope of a radio pulse (an elementary message - dots and dashes) in practice, of course, is not rectangular (as shown schematically in the figure), but has smooth leading and trailing edges. Otherwise, the frequency spectrum of the signal may become unacceptably wide, and when receiving a signal, unpleasant clicks are felt.

Phase shift keyed the signal looks like this:

where g(t) determines the signal envelope; is the modulating signal. can take M discrete values.

If a M= 2, then phase keying is called binary phase keying (1 bit per 1 phase change) if M = 4 - quadrature phase shift keying(2 bits per 1 phase change), M= 8 (3 bits per phase change), etc.

So the number of bits n, transmitted by one phase jump, is the power to which two is raised when determining the number of phases required for transmission n- ordinal binary number.

phase-shift keyed signal s i(t) can be considered as linear combination two orthonormal signals y 1 and y 2.

Digital phase modulation is a versatile and widely used technique wireless transmission digital data.

In the previous article, we saw that we can use discrete changes in the amplitude or frequency of a carrier as a way to represent ones and zeros. Not surprisingly, we can also represent digital data with a phase; this method is called phase shift keying (PSK).

Binary phase shift keying

The simplest type of PSK is called binary phase shift keying (BPSK), where "binary" refers to the use of two phase shifts (one for logic one and one for logic zero).

We can intuitively recognize that the system will be more reliable if the separation between these two phases is large - of course, it will be difficult for the receiver to distinguish between a symbol with a phase shift of 90° and a symbol with a phase shift of 91°. We have a 360° phase range to work with, so maximum difference between the phases of a logical unit and a logical zero is 180 °. But we know that switching a sine wave 180° is the same as inverting it; thus we can think of BPSK as simply inverting the carrier signal in response to one logic state and leaving it at original state in response to another logical state.

To do the next step, we recall that multiplying a sinusoid by a negative unit is the same as inverting it. This results in the possibility of implementing BPSK using the following basic hardware configuration:

Basic scheme for obtaining a BPSK signal

However, this scheme can easily lead to high-slope transitions in the carrier waveform: if the transition between logic states occurs when the carrier signal is in its maximum value, the carrier signal voltage should quickly go to the minimum value.

High slope in the BPSK waveform when the logic state of the baseband signal changes

Such high slope events are undesirable because they create energy at high frequency components that can interfere with other RF signals. In addition, amplifiers have a limited ability to produce sudden changes in output voltage.

If we improve the above implementation with two additional features, then we can provide smooth transitions between characters. First, we need to make sure that the period of a digital bit is equal to one or more full cycles of the carrier signal. Second, we need to synchronize the digital transitions with the carrier signal. With these improvements, we could design the system so that a 180° phase change occurs when the carrier signal is at (or close to) the zero crossing.

QPSK

BPSK transmits one bit per character, which is what we are used to. Everything we discussed about digital modulation, assumed that the carrier signal changes depending on whether the digital voltage on low or high logical level, and the receiver recreates the digital data, interpreting each character as a 0 or 1.

Before discussing quadrature phase shift keying (QPSK), we need to introduce the following important concept: there is no reason why one symbol can only carry one bit. It is true that the world of digital electronics is built around circuits where the voltage is at one extreme or the other, so that the voltage is always one digital bit. But the radio signal is not digital; rather, we use analog signals for digital data transmission, and it is perfectly acceptable to develop a system in which analog signals are encoded and interpreted in such a way that one character represents two (or more) bits.

The advantage of QPSK is more high speed data transfer: if we keep the same symbol duration, we can double the data transfer rate from the transmitter to the receiver. The disadvantage is the complexity of the system. (You might think that QPSK is more susceptible to bit errors than BPSK because the separation between possible values it has less. This is a reasonable guess, but if you look at their math, it turns out that the error probabilities are actually very similar.)

Options

QPSK modulation is of course effective method modulation. But it can be improved.

Phase jumps

Standard QPSK modulation ensures that symbol transitions occur with high slope; since the phase jumps can be ±90°, we cannot use the approach described for the 180° phase jumps generated by BPSK modulation.

This problem can be mitigated by using one of the two QPSK options. Offset QPSK (OQPSK), which involves adding a delay to one of the two digital data streams used in the modulation process, reduces the maximum phase jump to 90°. Another option is π/4-QPSK, which reduces the maximum phase jump to 135°. Thus, OQPSK has the advantage of reducing phase discontinuities, but π/4-QPSK wins because it is compatible with differential coding (discussed below).

Another way to deal with breaks between characters is to implement additional processing signals, which creates smoother transitions between characters. This approach is included in a modulation scheme called minimum shift keying (MSK) and an enhancement to MSK known as Gaussian MSK (GMSK).

Differential coding

Another difficulty is that the demodulation of PSK signals is more difficult than FSK signals. Frequency is "absolute" in the sense that changes in frequency can always be interpreted by analyzing signal changes over time. Phase, however, is relative in the sense that it does not have a universal reference point - the transmitter generates phase changes with respect to one point in time, while the receiver can interpret phase changes with respect to another point in time.

The practical manifestation of this is that if there are differences between the phases (or frequencies) of the oscillators used for modulation and demodulation, the PSK becomes unreliable. And we have to assume that there will be phase differences (unless the receiver includes a carrier recovery circuit).

Differential QPSK (DQPSK, differential QPSK) is a variant that is compatible with non-coherent receivers (i.e., receivers that do not synchronize the demodulation generator with the modulation generator). Differential QPSK encodes data by creating a certain phase offset from the previous symbol so that the demodulation circuit analyzes the phase of the symbol using a reference point that is common to both the receiver and the transmitter.

Summary

• Binary phase shift keying (BPSK) is a simple modulation technique that can transmit one bit per symbol.
• Quadrature phase shift keying (QPSK) is more complex, but it doubles the data rate (or achieves the same data rate with half the bandwidth).
• Quadrature phase-shift keying (OQPSK), π/4-QPSK, minimum phase shift keying (MSK) are modulation schemes that mitigate the effects of high-slope carrier signal voltage changes between symbols.
• Differential QPSK (DQPSK) uses the phase difference between adjacent symbols to avoid problems due to lack of phase synchronization between transmitter and receiver.

We talked about the fact that these signals are obtained as a special case frequency modulation with a digital modulating signal in the form of a sequence of pulses corresponding to zeros and ones of the binary stream. Since the pulses of the modulating signal change sign when the information bit changes, we got frequency shift keying.
Drawing an analogy, we can consider signals with phase shift keying (PSK), if we apply as a modulating signal to a phase modulator digital signal. In this article we will talk about binary phase shift key BPSK. This type modulation has found very wide application due to the high noise immunity and simplicity of the modulator and demodulator. In the domestic literature, BPSK modulation is referred to as PSK-2.

Binary Phase Shift Keying Signals

Consider a signal in the form of a sequence of pulses digital information, as shown in figure 1.

Figure 1: Unipolar and bipolar digital signal

The upper graph shows a unipolar digital signal, in which the informational logical zero corresponds to , and the lower graph shows a bipolar digital signal, in which the informational logical zero corresponds to .
We apply a digital signal as a modulating signal to the phase modulator, as shown in Figure 2 with a phase deviation equal to rad.

Figure 2: Shaping a BPSK signal based on a phase modulator

Since it takes only values ​​equal to 0 and 1, then the in-phase and quadrature components of the complex envelope of the BPSK signal are equal to:
and the block diagram of the modulator can be simplified, as shown in Figure 3.

Figure 3: Simplified structural scheme BPSK modulator

The attentive reader will notice that this scheme is exactly the same as the previously discussed AM scheme with carrier suppression (DSB), with a modulating signal. Explanatory plots of the BPSK shaper are shown in Figure 4.

Figure 4: Explanatory plots of the BPSK modulator

Information is transmitted at a bit/s rate, the duration of one pulse of digital information is . The original modulating signal is multiplied by the carrier wave (in the figure) and we get a phase-shift keyed signal with a phase jump of rad. We observed the same phase jump when forming a DSB signal. Thus BPSK modulation is a degenerate type of phase shift keying that is the same as balanced amplitude modulation with a bipolar digital modulating signal.

Spectrum and vector diagram of a BPSK signal

Since the BPSK signal can be represented as a DSB signal, its spectrum is the spectrum of a digital bipolar modulating signal transferred to the carrier frequency. Figure 5 shows the spectrum of the BPSK signal at the information rate and carrier frequency . Figure 5 clearly shows that the spectrum of the BPSK signal has a main lobe and slowly decreasing side lobes. Figure 6 shows the main relationships between the BPSK spectrum and the parameters of the original modulating signal.

So the main lobe of the BPSK spectrum has a width equal to twice the information transfer rate and is symmetrical with respect to the carrier frequency. The level of the maximum (first) sidelobe of the spectrum is -13 dB. It can also be said that the width of the side lobes is equal to .
Consider a vector diagram of a BPSK signal. According to expression (1), the in-phase component of the complex envelope of the BPSK signal is , and the quadrature component is . In this case, it takes on the values ​​, then the vector diagram of the BPSK signal is shown in Figure 7.

Figure 7: Vector diagram of a BPSK signal

The complex envelope vector can take one of two values ​​(when transmitting an information zero) and when transmitting an information unit.

Relative (differential) binary phase shift keying (DBPSK)

When transmitting information using BPSK, it is required to use tracking systems to demodulate the signal. In this case, incoherent receiving devices are often used, which are not phase-matched with the master oscillator on the transmitting side, and, accordingly, cannot track random turn phase as a result of propagation that goes beyond the interval . For example, consider Figure 8.

Figure 8: Explanations for non-coherent BPSK reception

The original BPSK vector diagram (in the case of PSK signals, the vector diagram is often called a constellation) is shown in Figures 8a and 8d. Red indicates the value corresponding to informational zero, and blue one. As a result of propagation, the signal will acquire a random initial phase and the constellation will rotate through a certain angle. Figure 8b shows the case when the rotation of the constellation lies in the range from to rad. In this case, with non-coherent reception, the entire constellation will be rotated as shown by the arrows in Figure 8b. Then after turning the constellation will take starting position and the information will be demodulated correctly. Figure 8e shows the case when the rotation of the constellation lies in the range from to rad. In this case, when receiving, the constellation will also be rotated for a horizontal position, but as follows from Figure 8e, the information zeros and ones will be mixed up.
In order to eliminate the confusion of information symbols, relative keying is used, or as it is also called differential BPSK (DBPSK). The essence of relative manipulation is that it is not the bit of information itself that is encoded, but its change. The structure of a data transmission system using DBPSK is shown in Figure 9.

Figure 9: Structure of a data communication system using DBPSK

The original bit stream is differentially encoded, after which it is modulated with BPSK and receiving side demodulated with a non-coherent BPSK demodulator. The demodulated stream passes through the differential decoder and receives the received stream .
Consider the differential encoder shown in Figure 10.

Figure 10: Differential encoder

The summation is done modulo two, which corresponds to the logical XOR (exclusive OR). The designation means a delay of one bit of information. An example of differential coding is shown in Figure 11.

Figure 11: Example of differential bitstream encoding

The original bit stream is 011100101, we got 010111001 at the output of the differential encoder. The first bit (in the example above, the first 0 is not encoded), then the first bit is added modulo two of the previous bit at the output of the encoder and the current bit at the input. For differential decoding, it is necessary to do the reverse procedure according to the scheme shown in Figure 12 (the structure of the differential decoder is shown in Figure 9).

Figure 12: Example of differential bitstream decoding

As can be seen from the encoded bitstream 010111001, we received the original 011100101. Now consider a differential decoder if we invert all bits of the encoded stream on the receiving side, i.e. instead of 010111001 we will take 101000110. This is clearly shown in Figure 13.

Figure 13: Example of differential decoding with received stream inversion

It clearly follows from Figure 13 that when all bits of information are mixed up at the output of a differential decoder, the information is not distorted (with the exception of the first bit, shown in red), and this is the undoubted advantage of DBPSK, which can significantly simplify transmitting and receiving devices. But it is also necessary to say about the disadvantages of differential coding. The main disadvantage of DBPSK compared to BPSK is the lower noise immunity, since the reception errors propagate during the decoding stage.
Consider an example. Let the original stream be 011100101, the encoded stream be 010111001. Let the fourth bit of the encoded stream be received with an error, then the input of the decoder will be 010101001. And as a result of decoding, two whole bits will be decoded with an error (see Figure 14).

Figure 14: Reception error propagation in DBPSK decoding

Thus, we considered signals with binary phase shift keying (BPSK) and showed that BPSK is a special case of PSK with an input signal in the form of a stream of bipolar pulses, which is degenerate and reduces to a DSB signal. We have considered the BPSK spectrum and its spectral characteristics: main lobe width, side lobe level. The concept of relative or differential binary phase shift keying DBPSK was also introduced, which allows eliminating symbol inversion during incoherent reception at the decoding stage, but degrades the noise immunity of DBPSK compared to BPSK due to error propagation at the decoding stage.

With digital phase shift keying, the carrier phase S(t) differs from the current phase of the unmodulated carrier wave by a finite number of values ​​in accordance with the symbols of the transmitted message FROM(t) :

There are two types of phase shift keying - binary (binary) phase shift keying (BPSK) and quadrature phase shift keying (QPSK).

4.2.1 Binary phase shift keying. There are absolute (two-level) (AFMP) and relative (differential) (RPMF) phase manipulations. With AFMP (Figure 4.7, c), the carrier phase changes with each edge of the transmitted signals. The resulting signal is as follows (for one bit period):

Binary 1

Binary 0

The signal constellation of the DPMP signal corresponding to expression (4.19) is shown in Figure (4.8).

Picture. 4.7 - Absolute and relative phase shift keying

Picture. 4.8 - Signal constellation of DPMP signal

It should be noted that DFMP is one of the most simple shapes digital keying and is widely used in telemetry when forming broadband signals. The main disadvantage of DPMT is that very sharp transitions are obtained when manipulating a square wave signal, and as a result, the signal occupies a very wide spectrum. Most DPMP modulators use certain types filters that make phase transitions less abrupt, thereby narrowing the signal spectrum. The filtering operation is almost always performed on the modulating signal prior to manipulation (Figure 4.9).

Figure 4.9 - Functional diagram formation of a DPMP radio signal

Such a filter is generally referred to as a fundamental frequency filter. However, when reducing the bandwidth occupied by the radio signal, by filtering it is necessary to take into account the problem of inter-symbol interference that arises in this case.

Here, after the modulator, a radio signal power amplifier and a narrow-band high-pass filter are added. The main purpose of the filter is to attenuate transmitter radiation at frequencies that are multiples of the fundamental carrier frequency; the danger of such emissions is due to non-linear effects in the power amplifier, which, as a rule, take place and are amplified when trying to increase the efficiency of this amplifier. Often this filter is used at the same time for the receiver - it suppresses strong third-party signals outside the frequency band of useful radio signals before frequency conversion "down".

4.2.2 Quadrature phase shift keying (QPSK). In DPMT, one channel symbol carries one transmitted bit. However, as noted above, one channel symbol can carry more information bits. For example, a pair of consecutive bits can take on four values: (0, 0)(0, 1)(1, 0)(1, 1).

If one channel symbol were used to transmit each pair, then four channel symbols would be required, say ( s 1 (t), s 2 (t), s 3 (t), s 4 (t)), so M=4. In this case, the symbol rate in the communication channel turns out to be two times lower than the rate of information bits arriving at the input of the modulator and, therefore, each channel symbol can now occupy a time interval of duration T With = 2T b. With M-ary phase shift keying, the radio signal can be written in the following form:

Here (t) can take values ​​from the set:

where is an arbitrary initial phase.

In the future, instead of four channel symbols or four radio signals, we will talk about a single radio signal, the complex amplitude of which can take on the four indicated values, presented in Figure 4.10 as signal constellation.

Each group of two bits is represented by a corresponding phase angle, all phase angles are 90° apart. It can be noted that each signal point is separated from the real or imaginary axis by =45°.

CFMP-4 signals can be generated using a device, the functional diagram of which is shown in Figure 4.11, and the timing diagrams of its operation are shown in Figure 4.12.

Figure 4.10 - Signal constellation CFMP-4 radio signal

The sequence of transmitted bits 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, ... is divided into two subsequences of odd 1, 1, 0, 1, 0, 1, ... and even 0, 1, 0, 0, 1, 0,… bits with a demuxer DD1.

Bits with the same number in these subsequences form pairs, which are conveniently considered as complex bits; the real part of the complex bit is the bit of the odd subsequence I, and the imaginary part Q– bit of an even subsequence. In this case, the bits of the odd sequence in the in-phase branch are delayed for a time Tb device DD2. Further, the duration of each sequence is reduced to a value of 2 Tb expanders DD3 and DD4.

The complex bits obtained in this way are converted into a complex sequence of rectangular electrical pulses with a duration of 2 Tb with values ​​+1 or -1 of their real and imaginary parts, which are used to modulate the carrier wave exp(
). The result is a CFMP-4 radio signal.

Picture. 4.11 - Functional diagram of the device for the formation of CFMP-4

radio signal

Figure 4.12 - Timing diagrams during the formation of CFMP-4

radio signal

The diagram of phase transitions for QFMP-4 is shown in Figure 4.13.

Figure 4.13 - Diagram of phase transitions for CFMP-4 radio signal

In this diagram, the signal point with coordinates (+1, +1) is located on a line forming an angle of +45° with the coordinate axes, and corresponds to the transmission of symbols +1 and +1 in the quadrature channels of the modulator. If a next pair characters will be ( - 1, +1), which corresponds to the angle +135°, then from the point (+1, +1) to the point ( - 1,+1), you can draw an arrow characterizing the transition of the phase of the radio signal from the value +45 to +135°. The usefulness of this diagram can be illustrated by the following example. It follows from Figure 4.13 that four phase trajectories pass through the origin. For example, a transition from a signal constellation point (+1, +1) to a point (-1, -1) means a change in the instantaneous phase of the high-frequency carrier wave by 180°. Since a narrow-band high-pass filter is usually installed at the output of the modulator (see Figure 4.9), such a change in the phase of the signal is accompanied by a significant change in the values ​​of the signal envelope at the output of this filter and, consequently, in the entire transmission line. The variability of the values ​​of the envelope of the radio signal for many reasons is undesirable in digital transmission systems. CFMP with an offset is free from this shortcoming.

4.2.3 Quadrature phase shift keying. This method of signal formation is almost completely similar to the quadrature method of forming a QPSK-4 signal, however, with the only difference that the subsequence in the quadrature branch is shifted in time (delayed) by time T b or, equivalently, half the duration of the channel symbol. To implement this method, it is necessary to remove the time delay element T b DD2 in the in-phase branch. With such a change, the quadrature subsequence of the channel symbols will be delayed for a time T with a relatively in-phase subsequence (Figure 4.14).

Figure 4.14 - Timing diagrams during the formation of CFMP-4

offset radio signal

As a result, on the phase transition diagram (Figure 4.15) for this method manipulations there are no trajectories passing through the origin. This means that the instantaneous phase of the radio signal does not have jumps of +180° and, therefore, the envelope of this signal does not have deep dips, as was the case with the quadrature QPSK-4 (Figure 4.11).

Figure 4.15 - Diagram of phase transitions of the QPSK-4 radio signal

offset

4.2.4 KFMP-8 signals. The stream of information bits arriving at the input of the modulator can be divided into groups of 3, 4 bits, etc., then forming QPSK-8, QPSK-16 signals, etc. Figure 4.16 shows the signal constellation for the CFMP-8 radio signal.

Figure 4.16 - Signal constellation for CFMP-8 radio signal

For this modulation method, it is necessary to have eight channel symbols, the initial phases of which differ from the instantaneous phase of the unmodulated carrier wave by an angle that is a multiple of 45°. If the amplitudes of all channel symbols are the same, then the signal points are located on the circle. The possible values ​​of the real and imaginary parts of the complex amplitudes of these symbols are proportional to the coefficients I and Q taking values ​​from the set

. (4.23)

Not quite simple is the question of establishing correspondences between the points of the signal constellation and triplets of information bits. This process is usually called signal coding. AT Table 4.1 gives an example of such a match, which is possible, but not the best, because to establish the best match, you must first determine how to demodulate such a signal in the presence of interference, and then calculate the error probability when receiving either one channel symbol or one information bit. The best method of signal coding can be called the one in which the probability of error is the smallest.

Table 4.1 - Correspondence between signal constellation points and triplets _ of information bits

Figure 4.17 shows a functional diagram of the device for generating a CFMP-8 radio signal.

The work of the shaper is as follows: demultiplexer DD1 distributes an input stream of information bits of duration Tb into three subsequences, delay elements DD2 and DD3 align these subsequences in time, expanders DD4- DD6 increase the duration of each symbol to the value of the channel symbol duration T c = 3 T b. Signal coding in this case is reduced to the calculation of the values ​​of the in-phase and quadrature components of the complex envelope of the QPSK-8 radio signal. This operation is performed by the signal encoder, which includes the transcoder DD7 , having two digital outputs with 3 - bit words, which in digital-to-analog converters (DACs) DD1 andDD2 are converted to analog values ​​with the required values ​​(4.23).

Figure 4.17 - Functional diagram of the formation device

KFMP-8 radio signal

4.2. 5 π/4 - quadrature relative phase shift keying. At KFMP-4 and CFMP-4 with an offset, the maximum change in the instantaneous phase of the radio signal is 180° and 90°, respectively. Currently widely used π/4-quadrature relative phase shift keying, at which the maximum phase jump is 135°, and all possible values ​​of the instantaneous phase of the radio signal are multiples of π/4. None of the phase transition trajectories for this modulation method passes through the origin. As a result, the radio signal envelope has smaller dips compared to quadrature phase shift keying. The functional diagram of the device for generating such a radio signal is shown in Figure 4.18.

Figure 4.18 - Functional diagram of the formation device

radio signal with π/4-quadrature relative

phase keying

The sequence of information bits ( n i,i= 1,2,…) is divided into two subsequences: odd ( n 2 i-1 ,i= 1,2,…) and even ( n 2 i,i= 1, 2,...) bits, from which bits are chosen in pairs. Each new pair of such bits defines phase increment carrier vibration by the value
according to table 4.2

Table 4.2 – Carrier phase increment from bit values

If we introduce the designation for the deviation of the phase of the radio signal from the phase of the unmodulated carrier wave in the previous interval, then the new values ​​of the deviation of the phase of this signal and the complex amplitude in the current interval are determined by the equalities:

As a result, the values ​​of the real and imaginary parts of the complex envelope of this signal in the current time interval with a duration of 2 T b turn out to be equal:

(4.24)

(4.25)

It follows from equalities (4.24), (4.25) that the possible values ​​of the phase on the interval with the number i depend on the value of the phase of the radio signal on the interval with the number ( i- one). According to Table 4.2, the new values ​​are multiples of π/2.

Figure 4.19, a shows a constellation of possible signal points for the interval with the number i, if
; a similar constellation for the case when, is shown in Figure 4.19, b. The general constellation of signal points for this modulation method is shown in Figure 4.19, c and is obtained by superimposing Figure 4.19, a, b on top of each other. In Figure 4.19, c, the directions of the transitions are not indicated by arrows, since for each transition, directions in both directions are possible.

Figure 4.19 - Signal constellations of a radio signal with π / 4-quadrature

relative manipulation

It is also important to emphasize that with this modulation method, each new pair of information bits determines not the complete phase of the carrier wave, but only the increment of this phase for the interval with the number i with respect to the total phase of the complex envelope on the interval with the number ( i- one). Such modulation methods are called relative.

4.2. 6 Signal spectrum with FMP. Denoting the modulating signal through С(t), we write the modulated signal in the following form:

Such a signal changes during modulation its initial phase from -  /2 before +  /2 and vice versa when changing the modulating signal C(t) from 0 before 1 and back.

the value

, (4.27)

characterizing the maximum deviation of the phase from the average value is called the index of phase manipulation. After trigonometric transformations, expression (4.26) can be written in the following form:

To find the spectrum of the FMP signal, it suffices to find the spectra of the function cos( C(t)) and sin( C(t)). This method is suitable for any occasion. AT this case, i.e. for rectangular modulating pulses, you can use a simpler visual method for calculation.

Figure 4.7, b-d shows that the signal with keying on 180  can be viewed as the sum of an AMP signal with twice the amplitude of the unmodulated waveform, the phase of which is opposite to the carrier phase of the AMP signal. This regularity can be generalized to the case of any value of the phase jump ( <> 180  ) . Therefore, the FMP at the angle  can be thought of as the sum of the AMP signal and the unmodulated carrier. From this we can conclude that the spectrum of the signal, manipulated in phase, coincides in shape with the spectrum of the AMP signal (with the exception of the carrier).

If we use any of the two methods discussed above, the expressions for the FMP spectrum have the form

It can be seen from expression (4.29) that the amplitudes of all spectral components depend on the magnitude of the phase jump  and duty cycle of the pulse sequence.

For FMP on  = 180  get more simple expressions:

. (4.30)

Examples of spectra calculated using expressions (4.29) and (4.30) are shown in Figure 4.20.

Figure 4.20 - Spectra of PMF signals

As can be seen from the spectra, the required frequency band is twice as wide as for video pulses, i.e.

ω=2/ or F=2/, (4.31)

and with FMP on  = 180 and Q = There is no carrier 2 in the spectrum.

As we have seen, when transmitting discrete messages, not only the on-off FMP is used. The methods of quadrature four-position and eight-position PMF are being used more and more widely. The values ​​of the signal phase jump in these cases can take 4 and 8 values, respectively. For such cases, the results obtained above are also applicable. The spectrum of the sidebands, while retaining the same shape, will change its amplitude as the magnitude of the jump changes.

For more complex cases, when phase jumps of different sizes alternate, the above formulas are unfair. The spectrum can change significantly.

The phase-shift keyed signal has the form:

where and are constant parameters and is the carrier frequency.

Information is transmitted through a phase. Since there is a carrier in the receiver during coherent demodulation, by comparing the signal (3.21) with the carrier, the current phase shift is calculated. The phase change is one-to-one with the information signal.

Binary phase shift keying(BPSK - Binary Phase Shift Keying)

The set of values ​​of the information signal is put in one-to-one correspondence with the set of phase changes. When the value of the information signal changes, the phase of the radio signal changes by 180º. Thus, the BPSK signal can be written as

Consequently, . Thus, to implement BPSK, it is enough to multiply the carrier signal by information signal, which has many values. At the output of the modulator, the signals

, .

Rice. 3.38. Time shape and signal constellation of the BPSK signal:

a – digital message; b – modulating signal; (c) modulated HF oscillation; d - signal constellation

The time waveform and its constellation are shown in Figure 3.38.

A subspecies of the BPSK family is differential (relative) BPSK (DBPSK). The need for relative modulation is due to the fact that most carrier frequency recovery schemes result in phase ambiguity in the recovered carrier. As a result of restoration, a constant phase shift, a multiple of 180º, can be formed. Comparison of the received signal with the restored carrier will lead in this case to inversion (changing the values ​​of all bits to the opposite ones). This can be avoided if we encode not the absolute phase shift, but its change relative to the value in the previous bit interval. For example, if in the current bit interval the bit value has changed compared to the previous one, then the value of the phase of the modulated signal changes by 180º, if it remains the same, then the phase also does not change.

The power spectral density of the BPSK signal is the same as the density of the OOK signal, except for the absence of a carrier frequency signal in the spectrum:

, (3,22)

Quadrature phase shift keying(QPSK - Quadrature Phase Shift Keying)

Quadrature phase shift keying is a four-level phase shift keying (=4), in which the phase of the high-frequency oscillation can take 4 different meanings with a step that is a multiple of π / 2.

The relationship between the phase shift of the modulated oscillation from the set and a set of symbols (dibits) of a digital message is set in each specific case by the standard for the radio channel and is displayed by the signal constellation in Fig. 3.39. The arrows show possible transitions from one phase state to another.

It can be seen from the figure that the correspondence between the values ​​of the symbols and the phase of the signal is established in such a way that at neighboring points of the signal constellation the values ​​of the corresponding symbols differ in only one bit. When transmitting in noisy conditions, the most likely error will be to determine the phase of an adjacent constellation point. With the specified encoding, despite the fact that an error occurred in determining the value of the symbol, this will correspond to an error in one (not two) bits of information. Thus, a reduction in the bit error rate is achieved. This encoding method is called Gray code.

Each value of the phase of the modulated signal corresponds to 2 bits of information, and therefore the change in the modulating signal with QPSK modulation occurs 2 times less than with BPSK modulation at the same information transfer rate. It is known that the power spectral density of a multilevel signal coincides with the power spectral density of a binary signal when the symbol interval is replaced by a symbol interval. . For four-level modulation =4 and, therefore, .

The power spectral density of a QPSK signal with a modulating signal with rectangular pulses based on (3.22) is determined by the expression:

.

It can be seen from this formula that the distance between the first zeros of the power spectral density of the QPSK signal is equal to , which is 2 times less than for the BPSK signal. In other words, the spectral efficiency of QPSK quadrature modulation is 2 times higher than that of BPSK binary modulation.

The QPSK signal can be written as

where .

QPSK signal can be represented as in-phase and quadrature components

where - in-phase component of the -th symbol,