Four-position phase shift keying (QPSK). Digital phase modulation: BPSK, QPSK, DQPSK How many information symbols does each qpsk signal contain?

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

The quadrature representation of signals is a convenient and fairly universal means of describing them. The quadrature representation is to express the oscillation 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 ​​of 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 the same width, 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

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Today, communications specialists will no longer be surprised by the mysterious phrase Spread Spectrum. Broadband (and that is what is hidden behind these words) data transmission systems differ from each other in the method and speed of data transmission, type of modulation, transmission range, service capabilities, etc. This article attempts to classify broadband systems based on the modulation used in them.

Basic provisions

Broadband data transmission systems (BDSTS) are subject to the unified IEEE 802.11 standard in terms of protocols, and in the radio frequency part - to the uniform rules of the FCC (US Federal Communications Commission). However, they differ from each other in the method and speed of data transmission, type of modulation, transmission range, service capabilities, and so on.

All these characteristics are important when choosing a broadband accessory (by a potential buyer) and an element base (by a developer, manufacturer of communication systems). In this review, an attempt is made to classify broadband networks based on the least covered characteristic in the technical literature, namely their modulation.

Using various types of additional modulations used in conjunction with phase (BPSK) and quadrature phase modulation (QPSK) to increase the information rate when transmitting wideband signals in the 2.4 GHz range, information transmission rates of up to 11 Mbit/s can be achieved, taking into account the limitations , imposed by the FCC for operation in this range. Since broadband signals are expected to be transmitted without obtaining a spectrum license, the characteristics of the signals are limited to reduce mutual interference.

These modulation types are various forms of M-ary orthogonal modulation (MOK), pulse phase modulation (PPM), quadrature amplitude modulation (QAM). Broadband also includes signals received by simultaneous operation of several parallel channels separated by frequency (FDMA) and/or time (TDMA). Depending on the specific conditions, one or another type of modulation is selected.

Selecting the modulation type

The main task of any communication system is to transfer information from the message source to the consumer in the most economical way. Therefore, a type of modulation is chosen that minimizes the effect of interference and distortion, thereby achieving maximum information speed and minimum error rate. The modulation types under consideration were selected according to several criteria: resistance to multipath propagation; interference; number of available channels; power amplifier linearity requirements; achievable transmission range and complexity of implementation.

DSSS modulation

Most of the modulation types presented in this review are based on direct sequence wideband signals (DSSS), the classic wideband signals. In systems with DSSS, expanding the signal spectrum by several times makes it possible to reduce the spectral power density of the signal by the same amount. Spreading the spectrum is typically accomplished by multiplying a relatively narrowband data signal by a wideband spreading signal. The spreading signal or spreading code is often called a noise-like code, or PN(pseudonoise) code. The principle of the described spectrum expansion is shown in Fig. 1.

Bit period - period of the information bit
Chip period - chip tracking period
Data signal - data
PN-code - noise-like code
Coded signal - broadband signal
DSSS/MOK modulation

Wideband direct sequence signals with M-ary orthogonal modulation (or MOK modulation for short) have been known for a long time, but are quite difficult to implement on analog components. Using digital microcircuits, today it is possible to use the unique properties of this modulation.

A variation of MOK is M-ary biorthogonal modulation (MBOK). An increase in information speed is achieved by simultaneously using several orthogonal PN codes while maintaining the same chip repetition rate and spectrum shape. MBOK modulation effectively uses spectrum energy, that is, it has a fairly high ratio of transmission speed to signal energy. It is resistant to interference and multipath propagation.

From the one shown in Fig. 2 of the MBOK modulation scheme together with QPSK, it can be seen that the PN code is selected from M-orthogonal vectors in accordance with the control data byte. Since the I and Q channels are orthogonal, they can be MBOKed simultaneously. In biorthogonal modulation, inverted vectors are also used, which allows increasing the information speed. The most widely used set of truly orthogonal Walsh vectors with a vector dimension divisible by 2. Thus, using a system of Walsh vectors with a vector dimension of 8 and QPSK as PN codes, with a repetition rate of 11 megachips per second in full compliance with the IEEE 802.11 standard, it is possible to transmit 8 bits per channel symbol, resulting in a channel speed of 1.375 megasymbols per second and an information speed of 11 Mbit/s.

Modulation makes it quite easy to organize joint work with broadband systems operating at standard chip speeds and using only QPSK. In this case, the frame header is transmitted at a speed 8 times lower (in each specific case), which allows a slower system to correctly perceive this header. Then the data transfer speed increases.
1. Input data
2. Scrambler
3. Multiplexer 1:8
4. Select one of 8 Walsh functions
5. Select one of 8 Walsh functions
6. I-channel output
7. Q-channel output

Theoretically, MBOK has a slightly lower error rate (BER) compared to BPSK for the same Eb/N0 ratio (due to its encoding properties), making it the most energy efficient modulation. In BPSK each bit is processed independently of the other, in MBOK the character is recognized. If it is recognized incorrectly, this does not mean that all the bits of this symbol were received incorrectly. Thus, the probability of receiving an erroneous symbol is not equal to the probability of receiving an erroneous bit.

The MBOK spectrum of modulated signals corresponds to that established in the IEEE 802.11 standard. Currently, Aironet Wireless Communications, Inc. offers wireless bridges for Ethernet and Token Ring networks using DSSS/MBOK technology and transmitting information over the air at speeds up to 4 Mbit/s.

Multipath immunity depends on the Eb/N0 ratio and signal phase distortion. Numerical simulations of the transmission of broadband MBOK signals carried out by Harris Semiconductor engineers inside buildings have confirmed that such signals are quite robust to these interfering factors1. See: Andren C. 11 MBps Modulation Techniques // Harris Semiconductor Newsletter. 05/05/98.

In Fig. Figure 3 shows graphs of the probability of receiving an erroneous data frame (PER) as a function of distance at a radiated signal power of 15 dB/MW (for 5.5 Mbit/s - 20 dB/MW), obtained as a result of numerical simulation, for various information data rates.

Simulation shows that with an increase in Es/N0, required for reliable symbol recognition, PER increases significantly under conditions of strong signal reflection. To eliminate this, coordinated reception by multiple antennas can be used. In Fig. Figure 4 shows the results for this case. For an optimal matched reception, the PER will be equal to the square of the PER of the uncoordinated reception. When considering Fig. 3 and 4, it is necessary to remember that with PER=15% the actual loss in information speed will be 30% due to the need to retransmit failed packets.

A prerequisite for using QPSK in conjunction with MBOK is coherent signal processing. In practice, this is achieved by receiving the frame preamble and header using BPSK to set up a phase feedback loop. However, all this, as well as the use of serial correlators for coherent signal processing, increases the complexity of the demodulator.

CCSK modulation

Wideband M-ary orthogonal cyclic code sequence (CCSK) signals are easier to demodulate than MBOK because only one PN code is used. This type of modulation occurs due to a temporal shift in the correlation peak within a symbol. Using Barker's code of length 11 and a speed of 1 megasymbol per second, it is possible to shift the peak to one of eight positions. The remaining 3 positions do not allow them to be used to increase information speed. In this way, three information bits can be transmitted per symbol. By adding BPSK, you can transmit one more information bit per symbol, that is, 4 in total. As a result, using QPSK we get 8 information bits per channel symbol.

The main problem with PPM and CCSK is sensitivity to multipath propagation when the delay between signal reflections exceeds the duration of the PN code. Therefore, these types of modulations are difficult to use indoors with such reflections. CCSK is fairly easy to demodulate and requires only a slight increase in complexity from a traditional modulator/demodulator circuit. The CCSK scheme is similar to the MBOK modulation scheme together with QPSK (see Fig. 2), only instead of a block for selecting one of the 8 Walsh functions there is a word shift block.

DSSS/PPM modulation

Wideband direct sequence pulse phase modulated (DSSS/PPM) signals are a type of signal that is a further development of direct sequence spread spectrum signals.

The idea of ​​pulse phase modulation for conventional wideband signals is that an increase in information speed is obtained by changing the time interval between correlation peaks of successive symbols. Modulation was invented by Rajeev Krishnamoorthy and Israel Bar-David at Bell Labs in the Netherlands.

Current modulation implementations make it possible to determine eight time positions of correlation pulses in the symbol interval (within the PN sequence interval). If this technology is applied independently on the I- and Q-channels in DQPSK, then 64 (8x8) different information states are obtained. Combining phase modulation with DQPSK modulation, which provides two different states in the I channel and two different states in the Q channel, 256 (64x2x2) states are obtained, which is equivalent to 8 information bits per symbol.

DSSS/QAM modulation

Direct sequence quadrature amplitude modulation (DSSS/QAM) wideband signals can be thought of as classic wideband DQPSK modulated signals, in which information is also transmitted through a change in amplitude. By applying two-level amplitude modulation and DQPSK, 4 different states are obtained in the I channel and 4 different states in the Q channel. The modulated signal can also be subjected to pulse phase modulation, which will increase the information speed.

One of the limitations of using DSSS/QAM is that signals with such modulation are quite sensitive to multipath propagation. Also, due to the use of both phase and amplitude modulation, the Eb/N0 ratio is increased to obtain the same BER value as for MBOK.

To reduce sensitivity to distortion, you can use an equalizer. But its use is undesirable for two reasons.

Firstly, it is necessary to increase the sequence of symbols that adjusts the equalizer, which in turn increases the length of the preamble. Secondly, adding an equalizer will increase the cost of the system as a whole.

Additional quadrature modulation can also be used in systems with Frequency Hopping. Thus, WaveAccess has released a modem with the Jaguar brand, which uses Frequency Hopping technology, QPSK modulation in conjunction with 16QAM. In contrast to the generally accepted frequency modulation in this case, FSK allows for a real data transfer rate of 2.2 Mbit/s. WaveAccess engineers believe that the use of DSSS technology with higher speeds (up to 10 Mbit/s) is impractical due to the short transmission range (no more than 100 m).

OCDM modulation

Wideband signals produced by multiplexing multiple Orthogonal Code Division Multiplex (OCDM) signals use multiple wideband channels simultaneously on the same frequency.

Channels are separated by using orthogonal PN codes. Sharp has announced a 10-megabit modem built using this technology. In fact, 16 channels with 16-chip orthogonal codes are transmitted simultaneously. BPSK is applied in each channel, then the channels are summed using an analog method.

Data Mux - input data multiplexer

BPSK - block phase modulation

Spread - direct sequence spread spectrum block

Sum - output adder

OFDM modulation

Wideband signals, obtained by multiplexing several broadband signals with orthogonal frequency division multiplex (OFDM), represent the simultaneous transmission of phase-modulated signals on different carrier frequencies. Modulation is described in MIL-STD 188C. One of its advantages is its high resistance to gaps in the spectrum resulting from multipath attenuation. Narrowband attenuation may exclude one or more carriers. A reliable connection is ensured by distributing the symbol energy over several frequencies.

This exceeds the spectral efficiency of a similar QPSK system by 2.5 times. There are ready-made microcircuits that implement OFDM modulation. In particular, Motorola produces the MC92308 OFDM demodulator and the MC92309 "front-end" OFDM chip. The diagram of a typical OFDM modulator is shown in Fig. 6.

Data mux - input data multiplexer

Channel - frequency channel

BPSK - block phase modulation

Sum - frequency channel adder

Conclusion

The comparison table shows the ratings of each modulation type according to various criteria and the final rating. A lower score corresponds to a better score. Quadrature amplitude modulation is taken for comparison only.

During the review, various types of modulations that had unacceptable assessment values ​​for various indicators were discarded. For example, wideband signals with 16-position phase modulation (PSK) - due to poor resistance to interference, very wideband signals - due to restrictions on the length of the frequency range and the need to have at least three channels for the joint operation of nearby radio networks.

Among the considered types of broadband modulation, the most interesting is M-ary biorthogonal modulation - MBOK.

In conclusion, I would like to note modulation, which was not included in a series of experiments carried out by Harris Semiconductor engineers. We are talking about filtered QPSK modulation (Filtered Quadrature Phase Shift Keying - FQPSK). This modulation was developed by Professor Kamilo Feher from the University of California and patented jointly with Didcom, Inc.

To obtain FQPSK, nonlinear filtering of the signal spectrum is used in the transmitter with its subsequent restoration in the receiver. As a result, the FQPSK spectrum occupies approximately half the area compared to the QPSK spectrum, all other parameters being equal. In addition, the PER (packet error rate) of FQPSK is 10-2-10-4 better than that of GMSK. GSMK is Gaussian frequency modulation, used particularly in the GSM digital cellular communications standard. The new modulation has been sufficiently appreciated and used in their products by such companies as EIP Microwave, Lockheed Martin, L-3 Communications, as well as NASA.

It is impossible to say unequivocally what kind of modulation will be used in broadband in the 21st century. Every year the amount of information in the world is growing, therefore, more and more information will be transmitted through communication channels. Since the frequency spectrum is a unique natural resource, the requirements for the spectrum used by the transmission system will continuously increase. Therefore, the choice of the most effective modulation method when developing broadband continues to be one of the most important issues.

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, by applying noise-resistant coding, the area covered by a mobile communication system can be more accurately planned.

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 . The multiplier inputs can be supplied with input bit streams directly in NRZ code. such a modulator is shown in Figure 2.

Since in this case 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.

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.

The Nyquist filter can only be implemented using digital technology, so in the circuit shown in Figure 4, 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. The signal in the graph appears continuous due to the fairly high sampling frequency.

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.

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.

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.

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 minimal frequency spacing makes it possible to reduce the frequency 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.

Literature:

1. "Design of radio receiving devices" ed. A.P. Sivers - M.: "Higher School" 1976 p. 6
2. Palshkov V.V. "Radio receiving devices" - M.: "Radio and Communications" 1984 p. 32

Along with the article "Four-position phase modulation (QPSK)" read:

http://site/UGFSvSPS/modul/DQPSK/

http://site/UGFSvSPS/modul/BPSK/

http://site/UGFSvSPS/modul/GMSK/

http://site/UGFSvSPS/modul/FFSK/

• 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 refer to 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.

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

The figure shows 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. This coding method 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:

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.