• With quadrature shift modulation QPSK (Offset QPSK) single (simultaneous) phase movements of the signal point are limited to 90 degrees. Its simultaneous movements along the I and Q channels, i.e. transition to 180 degrees is impossible, which eliminates the movement of the signal point through zero

One of the disadvantages of canonical quadrature phase modulation is that when the symbols in both quadrature modulator channels are simultaneously changed, the QPSK signal causes a 180° jump in the carrier phase. When a conventional QPSK signal is generated, at this moment the signal point moves through zero, that is, the signal point moves by 180 degrees. At the moment of such movement there occurs reduction in the amplitude of the generated RF signal to zero.

Such significant signal changes are undesirable because they increase the signal bandwidth. To amplify such a signal, which has significant dynamics, highly linear transmission paths and, in particular, power amplifiers are required. The disappearance of the RF signal at the moment the signal point crosses zero also degrades the quality of functioning of radio equipment synchronization systems.

The figure below compares the movement of the signal point on the vector diagram for the first two symbols of the sequence - from state 11 to 01 for traditional QPSK and for offset QPSK.

Comparison of signal point movements with QPSK (left) and OQPSK (right) for two symbols 11 01

A number of terms are used to denote OQPSK: offset QPSK, offset QPSK, offset QPSK modulation, four-phase PM with offset. This modulation is used, for example, in CDMA systems to organize an upward communication channel in ZigBee standard devices.

• Formation of OQPSK
  

OQPSK modulation uses the same signal coding as QPSK. The difference is that moving from one modulation state to another (from one point in the constellation to another) is performed in two steps. First, at the clock moment at the beginning of the symbol, the I component changes and after half of the symbol, the Q component changes (or vice versa).
To do this, the quadrature components of the information sequence I(t) and Q(t) are shifted in time by the duration of one information element T=Ts/2, i.e. for half the duration of the symbol, as shown in the figure.

Generating QPSK and OQPSK signals for the sequence 110100101110010011

With such a displacement of component signals, each change in the phase of the generated signal, produced in turn by quadrature signals, is determined by only one element of the original information sequence, and not simultaneously by two (dibits), as with QPSK. As a result, there are no 180° phase transitions, since each element of the original information sequence arriving at the input of the in-phase or quadrature channel modulator can cause a phase change of only 0, +90° or -90°.

Sharp phase movements of the signal point when generating an OQPSK signal occur twice as often as compared to QPSK, since the component signals do not change simultaneously, but they are blurred. In other words, the magnitude of phase transitions in OQPSK is smaller compared to QPSK, but their frequency is twice as high.

Phase transition frequency of QPSK and OQPSK signals for a repeating bit sequence 1101

In a traditional quadrature modulator circuit, the formation of a QPSK signal can be achieved by using a delay of the digital signal components by the duration of the T bit in one of the quadrature control channels.

If an appropriate filter is used when generating OQPSK, movement between different points in the signal constellation can be performed almost entirely in a circle (Figure). As a result, the amplitude of the generated signal remains almost constant.

Previously, we considered types of digital modulation, which, when transmitting one symbol, transmitted one bit of information. Now we will introduce another parameter, which we will call symbolic transfer rate. If one bit of information is encoded by one symbol, the information transmission rate always coincides with the symbol rate of the transmitter. But if we transmit 2 bits of information at once with one symbol, then the symbol rate of the transmitter is equal to . In this case, the question often arises: how to encode two impulses at once with one impulse? Below we will answer this question and consider quadrature phase shift keying (QPSK). This article will a large number of illustrative material necessary to understand the QPSK principle.

Encoding two bits of transmitted information with one symbol

QPSK modulation is based on encoding two bits of transmitted information into one symbol. In this case, the symbol rate is two times lower than the information transfer rate. In order to understand how one character encodes two bits at once, consider Figure 1.

Figure 1: Vector diagram of BPSK and QPSK signals

Figure 1 shows vector diagrams of BPSK and QPSK signals. The BPSK signal was discussed earlier, and we said that one BPSK symbol encodes one bit of information, while on the BPSK vector diagram there are only two points on the in-phase axis, corresponding to zero and one of the transmitted information. The quadrature channel in the case of BPSK is always zero. The points on the vector diagram form a constellation of phase shift keying. In order to encode two bits of information with one symbol, it is necessary that the constellation consist of four points, as shown in the QPSK vector diagram in Figure 1. Then we obtain that and and are different from zero, all points of the constellation are located on the unit circle. Then encoding can be done as follows: split the bit stream into even and odd bits, then even bits will be encoded, and odd bits will be encoded. Two sequential bits of information are encoded simultaneously by in-phase and quadrature signals. This is clearly shown in the oscillograms shown in the figure for the information flow “1100101101100001”.

Figure 2: In-phase and quadrature components of a QPSK signal

In the top graph, the input stream is divided into pairs of bits corresponding to one point in the QPSK constellation shown in Figure 1. The second graph shows the waveform corresponding to the transmitted information. If the even bit is 1 (note that bits are numbered from zero, not one, so the first bit in the queue is numbered 0, which means it is even in order), and if the even bit is 0 (i.e. ). A quadrature channel is constructed similarly, but only using odd bits. The duration of one symbol is twice the duration of one bit of the original information. The device performing such encoding and according to the QPSK constellation is conventionally shown in Figure 3.

Figure 3: In-phase and quadrature encoder based on QPSK constellation

Depending on the pair of bits at the input, we obtain at the output constant signals within the duration of this pair of bits and , the value of which depends on the transmitted information.

Block diagram of a QPSK modulator

The block diagram of a QPSK based modulator is shown in Figure 4.

Figure 4: Block diagram of a QPSK modulator

The signal looks like:

(1)

The in-phase and quadrature components are nothing more than the real and imaginary parts of the QPSK signal, which are the input signals of the quadrature modulator. Then we can represent it through its complex envelope:

It is important to note that the arctangent must be calculated taking into account the quarter complex plane (the arctangent 2 function). The type of phase envelope for the information flow “1100101101100001” is shown in Figure 5.

Figure 5: Phase envelope of a QPSK signal

The phase envelope is a step function of time that undergoes discontinuities when the QPSK symbol changes (recall that one QPSK symbol carries two bits of information). Moreover, within one symbol, the QPSK vector diagram is always at one point in the constellation, as shown below, and when changing a symbol, it jumps to the point corresponding to the next symbol. Since QPSK has only four points in the constellation, the phase envelope can take only four values: and .

The amplitude envelope of a QPSK signal can also be derived from the complex envelope:

(4)

Note that the amplitude envelope of the QPSK signal is equal to unity everywhere, with the exception of the moments of changing transmitted symbols, i.e., at the moments of a phase jump and transition to the next point of the constellation.

An example of an oscillogram of a QPSK signal with an input bit stream of “1100101101100001” at the information transfer rate and a carrier frequency of 20 kHz is shown in Figure 6.

Figure 6: QPSK signal waveform

Please note that the phase of the carrier oscillation can take four values: and radians. In this case, the phase of the next symbol relative to the previous one may not change, or may change by or by radians. We also note that at the information transfer rate we have a symbol rate and a duration of one symbol, which is clearly visible on the oscillogram (the phase jump occurs after 0.2 ms).

Figure 7 shows the BPSK spectrum and QPSK spectrum signals at a carrier frequency of 100 kHz. It can be noted that the width of the main lobe, as well as the side lobes of a QPSK signal, is half that of a BPSK signal at the same information transfer rate. This is because the symbol rate of a QPSK signal is half the information rate, while the BPSK symbol rate is equal to the information rate. The sidelobe levels of QPSK and BPSK are equal.

Shaping the spectrum of a QPSK signal using Nyquist filters

Previously, we considered the issue of narrowing the signal bandwidth when using Nyquist shaping filters with a frequency response of the form of raised cosine. Shaping filters make it possible to transmit a BPSK signal at a speed of 1 bit/s per 1 Hz signal bandwidth while eliminating intersymbol interference on the receiving side. However, such filters are not feasible, so in practice, shaping filters are used that provide 0.5 bit/s per 1 Hz signal bandwidth. In the case of QPSK, the information transmission rate is twice the symbol rate, then the use of shaping filters gives us the opportunity to transmit 0.5 symbols per second per 1 Hz band, or 1 bit/s of digital information per 1 Hz band when using a filter with a frequency response of the raised cosine type. We said that the impulse response of the Nyquist shaping filter depends on the parameter and has the form:

(5)

Figure 8 shows the spectra when using Nyquist shaping filters with the parameter .

Figure 8 shows in black the spectrum of the QPSK signal without using a shaping filter. It can be seen that the use of a Nyquist filter makes it possible to completely suppress side lobes in both the BPSK spectrum and the QPSK signal spectrum. The block diagram of a QPSK modulator using a shaping filter is shown in Figure 9.

Figure 9: Block diagram of a QPSK modulator using a shaping filter

Graphs explaining the operation of the QPSK modulator are shown in Figure 10.

Figure 10: Explanatory graphs

Digital information arrives at speed and is converted into symbols and, in accordance with the QPSK constellation, the duration of one transmitted symbol is . The clock generator produces a sequence of delta pulses with a period, but related to the center of the pulse and, as shown in the fourth graph. The clock generator pulses are gated and using switches and we obtain samples and , shown in the two lower graphs, which excite the filter-shaping interpolator with an impulse response and at the output we have the in-phase and quadrature components of the complex envelope, which are fed to a universal quadrature modulator. At the output of the modulator we obtain a QPSK signal with suppression of the side lobes of the spectrum.

Please note that the in-phase and quadrature components become continuous functions of time, as a result, the QPSK complex envelope vector is no longer located at the constellation points, jumping during a symbol change, but continuously moves on the complex plane as shown in Figure 11 when using a raised cosine filter with different parameters.

, which is clearly demonstrated by the QPSK signal oscillogram shown in Figure 12. Figure 12: Waveform of a QPSK signal using a Nyquist shaping filter conclusions In this article, we introduced a new concept - symbolic information transmission rate, and looked at how it is possible to encode two bits of transmitted information with one symbol when using QPSK modulation. The constellation of the QPSK signal and the block diagram of the QPSK modulator were considered. We also analyzed the spectrum of the QPSK signal and how it was narrowed using a Nyquist (raised cosine) shaping filter. It was found that turning on the shaping filter leads to continuous movement of the complex envelope vector of the QPSK signal along the complex plane, as a result of which the signal acquires an amplitude envelope. In the next article we will continue to get acquainted with QPSK, in particular we will consider its varieties: offset QPSK and pi/4 QPSK.

where A and φ 0 are constants, ω is the carrier frequency.

Information is encoded by phase φ(t) . Since during coherent demodulation the receiver has a reconstructed carrier s C (t) = Acos(ωt +φ 0), then by comparing signal (2) with the carrier the current phase shift φ(t) is calculated. The phase change φ(t) is one-to-one related to the information signal c(t).

Binary phase modulation (BPSK – BinaryPhaseShiftKeying)

The set of information signal values ​​(0,1) is uniquely assigned to the set of phase changes (0, π). 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

Hence, s(t)=A⋅2(c(t)-1/2)cos(ωt + φ 0). Thus, to implement BPSK modulation, it is enough to multiply the carrier signal by the information signal, which has many values ​​(-1,1). At the output of the baseband modulator the signals

I(t)= A⋅2(c(t)-1/2), Q(t)=0

The time shape of the signal and its constellation are shown in Fig. 3.

Rice. 12. Temporal form and signal constellation of the BPSK signal: a – digital message; b – modulating signal; c – modulated HF oscillation; G– signal constellation

Quadrature phase modulation (QPSK – QuadraturePhaseShiftKeying)

Quadrature phase modulation is a four-level phase modulation (M=4), in which the phase of the high-frequency oscillation can take 4 different values ​​in increments of π / 2.

The relationship between the phase shift of the modulated oscillation from the set (±π / 4,±3π / 4) and the set of digital message symbols (00, 01, 10, 11) is established in each specific case by the standard for the radio channel and is displayed by a signal constellation similar to Fig. 4 . Arrows indicate possible transitions from one phase state to another.

Rice. 13. QPSK modulation constellation

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 determining the phase of an adjacent constellation point. With this encoding, although an error has occurred in determining the meaning of a symbol, this will correspond to an error in one (not two) bits of information. Thus, a reduction in the bit error probability is achieved. Specified method coding is called Gray code.

Multi-position phase modulation (M-PSK)

M-PSK is formed, like other multi-position modulations, by grouping k = log 2 M bits into symbols and introducing a one-to-one correspondence between a set of symbol values ​​and a set of modulated waveform phase shift values. The phase shift values ​​from the set differ by the same amount. For example, Fig. 4 shows the signal constellation for 8-PSK with Gray coding.

Rice. 14. 8-PSK modulation signal constellation

Amplitude-phase types of modulation (QAM)

Obviously, to encode the transmitted information, you can use not one carrier wave parameter, but two simultaneously.

The minimum level of symbol errors will be achieved if the distance between adjacent points in the signal constellation is the same, i.e. the distribution of points in the constellation will be uniform on the plane. Therefore, the signal constellation should have a lattice appearance. Modulation with this type of signal constellation is called quadrature amplitude modulation (QAM - Quadrature Amplitude Modulation).

QAM is multi-position modulation. When M=4 it corresponds to QPSK, therefore it is formally considered for QAM M ≥ 8 (since the number of bits per symbol k = log 2 M ,k∈N , then M can only take values ​​of powers of 2: 2, 4, 8, 16, etc.). For example, Fig. 5 shows a 16-QAM signal constellation with Gray coding.

Rice. 15. 16 –QAM modulation constellation

Frequency types of modulation (FSK, MSK, M-FSK, GFSK, GMSK).

In the case of frequency modulation, the parameter of the carrier vibration - the information carrier - is the carrier frequency ω(t). The modulated radio signal has the form:

s(t)= Acos(ω(t)t +φ 0)= Acos(ω c t +ω d c(t)t +φ 0)=
Acos(ω c t +φ 0) cos(ω d c(t)t) − Asin(ω c t+φ 0)sin(ω d c(t)t),

where ω c is the constant central frequency of the signal, ω d is the deviation (change) of frequency, c(t) is the information signal, φ 0 is the initial phase.

If the information signal has 2 possible values, binary frequency modulation takes place (FSK - FrequencyShiftKeying). The information signal in (4) is polar, i.e. takes values ​​(-1,1), where -1 corresponds to the value of the original (non-polar) information signal 0, and 1 to one. Thus, with binary frequency modulation, the set of values ​​of the original information signal (0,1) is associated with the set of values ​​of the frequency of the modulated radio signal (ω c −ω d,ω c +ω d). The type of FSK signal is shown in Fig. 1.11.

Rice. 16. FSK signal: a – information message; b- modulating signal; c – modulation of HF oscillation

From (4) the direct implementation of the FSK modulator follows: the signals I(t) and Q(t) have the form: I (t) = Acos(ω d c(t)t), Q(t) = Asin(ω d c(t )t) . Since the functions sin and cos take values ​​in the interval [-1..1], the signal constellation of the FSK signal is a circle with radius A.

5. OVERVIEW OF MODULATION TYPES

The transformation of a carrier harmonic oscillation (one or more of its parameters) in accordance with the law of change in the transmitted information sequence is called modulation. When transmitting digital signals in analog form, they operate with the concept of manipulation.

The modulation method plays a major role in achieving the maximum possible information transmission rate for a given probability of erroneous reception. The maximum capabilities of the transmission system can be assessed using the well-known Shannon formula, which determines the dependence of the capacity C of a continuous channel with white Gaussian noise on the used frequency band F and the ratio of signal and noise powers Pc/Psh.

where PC is the average signal power;

PSh is the average noise power in the frequency band.

Bandwidth is defined as the upper limit of the actual information transmission rate V. The above expression allows us to find the maximum value of the transmission rate that can be achieved in a Gaussian channel with given values: the width of the frequency range in which the transmission takes place (DF) and the signal-to-noise ratio ( PC/RSh).

The probability of an erroneous reception of a bit in a particular transmission system is determined by the ratio PC/РШ. From Shannon's formula it follows that an increase in the specific transmission rate V/DF requires an increase in energy costs (PC) per bit. The dependence of the specific transmission speed on the signal-to-noise ratio is shown in Fig. 5.1.

Figure 5.1 – Dependence of specific transmission speed on signal-to-noise ratio

Any transmission system can be described by a point lying below the curve shown in the figure (region B). This curve is often called the boundary or Shannon limit. For any point in area B, it is possible to create a communication system whose probability of erroneous reception can be as small as required.

Modern data transmission systems require that the probability of an undetected error be no higher than 10-4...10-7.

In modern digital communications technology, the most common are frequency modulation (FSK), relative phase modulation (DPSK), quadrature phase modulation (QPSK), offset phase modulation (offset), referred to as O-QPSK or SQPSK, quadrature amplitude modulation (QAM) .

With frequency modulation, the values ​​“0” and “1” of the information sequence correspond to certain frequencies of the analog signal with a constant amplitude. Frequency modulation is very noise-resistant, but frequency modulation wastes the bandwidth of the communication channel. Therefore, this type of modulation is used in low-speed protocols that allow communication over channels with a low signal-to-noise ratio.

With relative phase modulation, depending on the value of the information element, only the phase of the signal changes while the amplitude and frequency remain unchanged. Moreover, each information bit is associated not with the absolute value of the phase, but with its change relative to the previous value.

More often, four-phase DPSK, or double DPSK, is used, based on the transmission of four signals, each of which carries information about two bits (dibit) of the original binary sequence. Typically two sets of phases are used: depending on the dibit value (00, 01, 10 or 11), the phase of the signal can change to 0°, 90°, 180°, 270° or 45°, 135°, 225°, 315° respectively. In this case, if the number of encoded bits is more than three (8 phase rotation positions), the noise immunity of DPSK is sharply reduced. For this reason, DPSK is not used for high-speed data transmission.

4-position or quadrature phase modulation modems are used in systems where the theoretical spectral efficiency of BPSK transmit devices (1 bit/(s·Hz)) is insufficient for the available bandwidth. The various demodulation techniques used in BPSK systems are also used in QPSK systems. In addition to the direct extension of binary modulation methods to the case of QPSK, 4-position modulation with a shift (offset) is also used. Some varieties of QPSK and BPSK are given in table. 5.1.

With quadrature amplitude modulation, both the phase and amplitude of the signal change, which allows you to increase the number of encoded bits and at the same time significantly improve noise immunity. Currently, modulation methods are used in which the number of information bits encoded in one baud interval can reach 8...9, and the number of signal positions in the signal space can reach 256...512.

Table 5.1 – Types of QPSK and BPSK

Binary PSK	Four-position PSK	Short description
BPSK	QPSK	Conventional coherent BPSK and QPSK
DEBPSK	DEQPSK	Conventional coherent BPSK and QPSK with relative coding and SVN
DBSK	DQPSK	QPSK with autocorrelation demodulation (no EHV)
FBPSK		BPSK or QPSK With patented Feer processor suitable for non-linear amplification systems QPSK with shift (offset) QPSK with shift and relative coding QPSK with shift and Feer's patented processors QPSK with relative coding and phase shift by p/4

The quadrature representation of signals is a convenient and fairly universal means of describing them. The quadrature representation is to express the vibration as a linear combination of two orthogonal components - sine and cosine:

S(t)=x(t)sin(wt+(j))+y(t)cos(wt+(j)), (5.2)

where x(t) and y(t) are bipolar discrete quantities.

Such discrete modulation (manipulation) is carried out over two channels on carriers shifted by 90° relative to each other, i.e. located in quadrature (hence the name of the representation and signal generation method).

Let us explain the operation of the quadrature circuit (Fig. 5.2) using the example of generating QPSK signals.

Figure 5.2 – Quadrature modulator circuit

The original sequence of binary symbols of duration T is divided, using a shift register, into odd Y pulses, which are supplied to the quadrature channel (coswt), and even X pulses, supplied to the in-phase channel (sinwt). Both sequences of pulses arrive at the inputs of the corresponding manipulating pulse shapers, at the outputs of which sequences of bipolar pulses x(t) and y(t) are formed.

Manipulating pulses have an amplitude and duration of 2T. Pulses x(t) and y(t) arrive at the inputs of channel multipliers, at the outputs of which two-phase phase-modulated oscillations are formed. After summing, they form a QPSK signal.

The above expression for describing the signal is characterized by the mutual independence of multi-level manipulating pulses x(t), y(t) in the channels, i.e. A level of one in one channel may correspond to a level of one or zero in another channel. As a result, the output signal of the quadrature circuit changes not only in phase, but also in amplitude. Since amplitude manipulation is carried out in each channel, this type of modulation is called amplitude quadrature modulation.

Using a geometric interpretation, each QAM signal can be represented as a vector in signal space.

By marking only the ends of the vectors, for QAM signals we obtain an image in the form of a signal point, the coordinates of which are determined by the values ​​x(t) and y(t). The set of signal points forms the so-called signal constellation.

In Fig. 5.3 shows the block diagram of the modulator, and Fig. 5.4 – signal constellation for the case when x(t) and y(t) take values ​​±1, ±3 (QAM-4).

Figure 5.4 – QAM-4 signal diagram

The values ​​±1, ±3 determine the modulation levels and are relative in nature. The constellation contains 16 signal points, each of which corresponds to four transmitted information bits.

A combination of levels ±1, ±3, ±5 can form a constellation of 36 signal points. However, of these, ITU-T protocols use only 16 points evenly distributed in the signal space.

There are several ways to practically implement QAM-4, the most common of which is the so-called superposition modulation (SPM) method. The scheme that implements this method uses two identical QPSKs (Fig. 5.5).

Using the same technique for obtaining QAM, you can obtain a diagram for the practical implementation of QAM-32 (Fig. 5.6).

Figure 5.5 – QAM-16 modulator circuit

Figure 5.6 – QAM-32 modulator circuit

Obtaining QAM-64, QAM-128 and QAM-256 occurs in the same way. Schemes for obtaining these modulations are not given due to their cumbersome nature.

It is known from communication theory that with an equal number of points in the signal constellation, the noise immunity of QAM and QPSK systems is different. With a large number of signal points, the QAM spectrum is identical to the spectrum of QPSK signals. However, QAM signals have better performance than QPSK systems. The main reason for this is that the distance between signal points in a QPSK system is smaller than the distance between signal points in a QAM system.

In Fig. Figure 5.7 shows the signal constellations of the QAM-16 and QPSK-16 systems with the same signal strength. The distance d between adjacent points of a signal constellation in a QAM system with L modulation levels is determined by the expression:

(5.3)

Likewise for QPSK:

(5.4)

where M is the number of phases.

From the above expressions it follows that with an increase in the value of M and the same power level, QAM systems are preferable to QPSK systems. For example, with M=16 (L = 4) dQAM = 0.47 and dQPSK = 0.396, and with M=32 (L = 6) dQAM = 0.28, dQPSK = 0.174.

Thus, we can say that QAM is much more efficient compared to QPSK, which allows the use of more multi-level modulation with the same signal-to-noise ratio. Therefore, we can conclude that the QAM characteristics will be closest to the Shannon boundary (Fig. 5.8) where: 1 – Shannon boundary, 2 – QAM, 3 – M-position ARC, 4 – M-position PSK.

Figure 5.8 - Dependence of the spectral efficiency of various modulations on C/N

In general, linear gain M-position QAM systems such as 16-QAM, 64-QAM, 256-QAM have spectral efficiency higher than linear gain QPSK, which has a theoretical efficiency limit of 2 bits/(s∙Hz) .

One of the characteristic features of QAM is low values ​​of out-of-band power (Fig. 5.9).

Figure 5.9 – Energy spectrum of QAM-64

The use of multi-position QAM in its pure form is associated with the problem of insufficient noise immunity. Therefore, in all modern high-speed protocols, QAM is used in conjunction with trellis coding (TCM). The TCM signal constellation contains more signal points (signal positions) than required for modulation without trellis coding. For example, 16-bit QAM converts to a trellis-coded 32-QAM constellation. Additional constellation points provide signal redundancy and can be used for error detection and correction. Convolutional coding combined with TCM introduces dependency between successive signal points. The result was a new modulation technique called Trellis modulation. A combination of a specific QAM noise-resistant code selected in a certain way is called a signal-code structure (SCC). SCMs make it possible to increase the noise immunity of information transmission along with reducing the requirements for the signal-to-noise ratio in the channel by 3 - 6 dB. During the demodulation process, the received signal is decoded using the Viterbi algorithm. It is this algorithm, through the use of introduced redundancy and knowledge of the history of the reception process, that allows, using the maximum likelihood criterion, to select the most reliable reference point from the signal space.

The use of QAM-256 allows you to transmit 8 signal states, that is, 8 bits, in 1 baud. This allows you to significantly increase the data transfer speed. So, with a transmission range width of Df = 45 kHz (as in our case), 1 baud, that is, 8 bits, can be transmitted in a time interval of 1/Df. Then the maximum transmission speed over this frequency range will be

Since in this system transmission is carried out over two frequency ranges with same width, then the maximum transmission speed of this system will be 720 kbit/s.

Since the transmitted bit stream contains not only information bits, but also service bits, the information speed will depend on the structure of the transmitted frames. The frames used in this data transmission system are formed on the basis of the Ethernet and V.42 protocols and have a maximum length of K=1518 bits, of which KS=64 are service bits. Then the information transmission speed will depend on the ratio of information bits and service bits

This speed exceeds the speed specified in the technical specifications. Therefore, we can conclude that the chosen modulation method satisfies the requirements set in the technical specifications.

Since in this system transmission is carried out over two frequency ranges simultaneously, it requires the organization of two modulators operating in parallel. But it should be taken into account that it is possible for the system to switch from the main frequency ranges to the backup ones. Therefore, generation and control of all four carrier frequencies is required. A frequency synthesizer designed to generate carrier frequencies consists of a reference signal generator, dividers and high-quality filters. A quartz square pulse generator acts as a reference signal generator (Fig. 5.10).

Figure 5.10 - Generator with quartz stabilization

In order to assess the state of information security; - managing access of meeting participants to the premises; - organizing monitoring of the entrance to the allocated room and the surrounding environment during the meeting. 2. The main means of ensuring the protection of acoustic information during a meeting are: - installation of various noise generators, monitoring of the room...

Using printing computer technology? 10. Describe the criminal acts provided for in Chapter 28 of the Criminal Code of the Russian Federation “Crimes in the field computer information" SECTION 2. COMBATING CRIMES IN THE FIELD OF COMPUTER INFORMATION CHAPTER 5. CONTROL OVER CRIME IN THE FIELD OF HIGH TECHNOLOGY 5.1 Control over computer crime in Russia Control measures over...

LickSec > Radio communication

Four-position phase shift keying (QPSK)

It is known from communication theory that binary phase modulation BPSK has the highest noise immunity. However, in some cases, by reducing the noise immunity of the communication channel, it is possible to increase its throughput. Moreover, when using noise-resistant coding, you can more accurately plan the area covered by the system mobile communications.

Four-position phase modulation uses four carrier phase values. In this case, the phase y(t) of the signal described by expression (25) should take four values: 0°, 90°, 180° and 270°. However, other phase values ​​are more commonly used: 45°, 135°, 225° and 315°. This type of representation of quadrature phase modulation is shown in Figure 1.

The same figure shows the bit values ​​conveyed by each carrier phase state. Each state transmits two bits of useful information at once. In this case, the contents of the bits are selected in such a way that the transition to an adjacent state of the carrier phase due to a reception error leads to no more than a single bit error.

Typically, a quadrature modulator is used to generate a QPSK modulation signal. To implement a quadrature modulator, you will need two multipliers and an adder. The multiplier inputs can be supplied with input bit streams directly in NRZ code. The block diagram of such a modulator is shown in Figure 2.

Since with this type of modulation two bits of the input bit stream are transmitted at once during one symbol interval, the symbol rate of this type of modulation is 2 bits per symbol. This means that when implementing a modulator, the input stream should be divided into two components - the in-phase component I and the quadrature component Q. Subsequent blocks should be synchronized at symbol rate.

With this implementation, the spectrum of the signal at the output of the modulator is unlimited and its approximate form is shown in Figure 3.

Figure 3. Spectrum of a QPSK signal modulated by an NRZ signal.

Naturally, this signal can be limited in spectrum using a bandpass filter included at the output of the modulator, but this is never done. The Nyquist filter is much more efficient. The block diagram of a QPSK signal quadrature modulator, built using a Nyquist filter, is shown in Figure 4.

Figure 4. Block diagram of a QPSK modulator using a Nyquist filter

The Nyquist filter can only be implemented using digital technology, so in the circuit shown in Figure 17, a digital-to-analog converter (DAC) is provided in front of the quadrature modulator. A peculiarity of the operation of the Nyquist filter is that in the intervals between reference points there should be no signal at its input, therefore at its input there is a pulse shaper that outputs a signal to its output only at the time of reference points. The rest of the time there is a zero signal at its output.

An example of the shape of the transmitted digital signal at the output of the Nyquist filter is shown in Figure 5.

Figure 5. Example Q signal timing diagram for four-position QPSK phase modulation

Since a Nyquist filter is used in the transmitting device to narrow the spectrum of the radio signal, there is no intersymbol distortion in the signal only at signal points. This can be clearly seen from the Q signal eye diagram shown in Figure 6.

In addition to narrowing the signal spectrum, the use of a Nyquist filter leads to a change in the amplitude of the generated signal. In the intervals between reference points of the signal, the amplitude can either increase in relation to the nominal value or decrease to almost zero.

In order to track changes in both the amplitude of the QPSK signal and its phase, it is better to use a vector diagram. The phasor diagram of the same signal shown in Figures 5 and 6 is shown in Figure 7.

Figure 7 vector diagram of QPSK signal with a = 0.6

The change in the amplitude of the QPSK signal is also visible on the oscillogram of the QPSK signal at the modulator output. The most characteristic section of the signal timing diagram shown in Figures 6 and 7 is shown in Figure 8. In this figure, both dips in the amplitude of the modulated signal carrier and an increase in its value relative to the nominal level are clearly visible.

Figure 8. Timing diagram of a QPSK signal with a = 0.6

The signals in Figures 5 ... 8 are shown for the case of using a Nyquist filter with a rounding factor a = 0.6. When using a Nyquist filter with a lower value of this coefficient, the influence of the side lobes of the impulse response of the Nyquist filter will have a stronger effect and the four signal paths clearly visible in Figures 6 and 7 will merge into one continuous zone. In addition, surges in signal amplitude will increase relative to the nominal value.

Figure 9 – spectrogram of a QPSK signal with a = 0.6

The presence of amplitude modulation of the signal leads to the fact that in communication systems using this type of modulation, it is necessary to use a highly linear power amplifier. Unfortunately, such power amplifiers have low efficiency.

Frequency modulation with a minimum frequency spacing MSK allows you to reduce the bandwidth occupied by a digital radio signal on the air. However, even this type of modulation does not satisfy all the requirements for modern mobile radio systems. Typically, the MSK signal in the radio transmitter is filtered with a conventional filter. That is why another type of modulation has appeared with an even narrower spectrum of radio frequencies on the air.