Promising modulation methods in broadband data transmission systems. Radio communication How many information symbols does each qpsk signal contain?

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 simple 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

Direct sequence pulse phase modulated (DSSS/PPM) wideband 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 trademark, which uses Frequency Hopping technology, QPSK modulation in conjunction with 16QAM. In contrast to the generally accepted FSK frequency modulation in this case, this 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.

Quadrature modulation and its characteristics (QPSK, QAM)

Consider quadrature phase shift keying (QPSK). The original data stream dk(t)=d0, d1, d2,… consists of bipolar pulses, i.e. dk take the values ​​+1 or -1 (Fig. 3.5.a)), representing a binary one and a binary zero. This pulse flow is divided into an in-phase flow dI(t) and a quadrature flow - dQ(t), as shown in Fig. 3.5.b).

dI(t)=d0, d2, d4,… (even bits)

dQ(t)=d1, d3, d5,… (odd bits)

A convenient orthogonal implementation of a QPSK signal can be obtained using amplitude modulation of in-phase and quadrature flows on sine and cosine functions of the carrier.

Using trigonometric identities, s(t) can be represented in the following form: s(t)=cos(2рf0t+у(t)). The QPSK modulator shown in Fig. 3.5.c), uses the sum of the sine and cosine terms. The pulse stream dI(t) is used to amplitude modulate (with amplitude +1 or -1) the cosine wave.

This is equivalent to shifting the phase of the cosine wave by 0 or p; therefore, the result is a BPSK signal. Similarly, the pulse stream dQ(t) modulates the sine wave, which produces a BPSK signal orthogonal to the previous one. By summing these two orthogonal carrier components, a QPSK signal is obtained. The value u(t) will correspond to one of four possible combinations of dI(t) and dQ(t) in the expression for s(t): u(t)=00, ±900 or 1800; the resulting signal vectors are shown in the signal space in Fig. 3.6. Since cos(2pf0t) and sin(2pf0t) are orthogonal, the two BPSK signals can be detected separately. QPSK has a number of advantages over BPSK: because with QPSK modulation, one pulse transmits two bits, then the data transfer rate is doubled, or at the same data transfer rate as in the BPSK scheme, half the frequency band is used; and also increases noise immunity, because The pulses are twice as long and therefore more powerful than BPSK pulses.

Rice. 3.5.

Rice. 3.6.

Quadrature amplitude modulation (KAM, QAM) can be considered a logical continuation of QPSK, since the QAM signal also consists of two independent amplitude-modulated carriers.

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. 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 (in-phase and quadrature):

s(t)=A(t)cos(шt + ц(t))=x(t)sinоt + y(t)cosоt, where

x(t)=A(t)(-sinс(t)),y(t)=A(t)cosс(t)

Such discrete modulation (manipulation) is carried out over two channels, on carriers shifted by 900 relative to each other, i.e. located in quadrature (hence the name).

Let us explain the operation of the quadrature circuit using the example of generating four-phase PM (PM-4) signals (Fig. 3.7).

Rice. 3.7.

Rice. 3.8. 16

The original sequence of binary symbols of duration T is divided, using a shift register, into odd pulses y, which are fed into the quadrature channel (cosсht), and even pulses - x, fed into the in-phase channel (sinхt). Both sequences of pulses are supplied to the inputs of the corresponding manipulated pulse shapers, at the outputs of which sequences of bipolar pulses x(t) and y(t) with an amplitude ±Um and a duration of 2T are formed. Pulses x(t) and y(t) arrive at the inputs of channel multipliers, at the outputs of which two-phase (0, p) PM oscillations are formed. After summation, they form an FM-4 signal.

In Fig. 3.8. shows a two-dimensional signal space and a set of signal vectors modulated by hex QAM and represented by dots that are arranged in a rectangular array.

From Fig. 3.8. it can be seen that the distance between signal vectors in the signal space with QAM is greater than with QPSK, therefore, QAM is more noise-resistant compared to QPSK,

Consider an opening loop power control (less accurate). The mobile station, after being turned on, searches for a signal from the base station. After synchronizing the mobile station using this signal, its power is measured and the power of the transmitted signal required to ensure a connection with the base station is calculated. Calculations are based on the fact that the sum of the expected power levels of the emitted signal and the power of the received signal must be constant and equal to 73 dB. If the received signal level is, for example, 85 dB, then the radiated power level should be ± 12 dB. This process is repeated every 20 ms, but it still does not provide the desired power control accuracy since the forward and return channels operate in different frequency ranges (45 MHz frequency spacing) and therefore have different levels of propagation attenuation and are differently susceptible to interference.

Let's consider the process of power regulation in a closed loop. The power control mechanism allows you to precisely adjust the power of the transmitted signal. The base station constantly evaluates the probability of error in each received signal. If it exceeds a software-defined threshold, then the base station commands the corresponding mobile station to increase the radiation power. Adjustment is carried out in 1 dB steps. This process is repeated every 1.25 ms. The goal of this control process is to ensure that each mobile station emits the minimum signal power that is sufficient to provide acceptable speech quality. Due to the fact that all mobile stations emit signals of the power necessary for normal operation, and no more; their mutual influence is minimized, and the subscriber capacity of the system increases.

Mobile stations must provide output power control over a wide dynamic range - up to 85 dB.

6.2.12. QPSK signal generation

CDMA IS-95 system uses quadrature phase shift keying

(QPSK – Quadrature Phase-shift Keying) base and shifted QPSK in mobile

ny stations. In this case, information is extracted by analyzing the change in the phase of the signal, so the phase stability of the system is a critical factor in ensuring a minimum probability of errors in messages. The use of shifted QPSK makes it possible to reduce the requirements for the linearity of the mobile station's power amplifier, since the amplitude of the output signal with this type of modulation changes much less. Before interference can be suppressed by digital signal processing techniques, it must pass through the receiver's high-frequency path without saturating the low-noise wideband amplifier (LNA) and mixer. This

forces system designers to seek a balance between the dynamic and noise characteristics of the receiver.

With quadrature phase shift keying, two bits correspond to 4 phase values ​​of the emitted signal, depending on the values ​​of these bits (Fig. 6.39), that is, one phase value can transmit the value of 2 bits at once.

Rice. 6.39. Diagram of phase values ​​for QPSK modulation

The data stream is divided into even and odd bits (Fig. 6.40). Further, the process proceeds in parallel in the in-phase and quadrature channels. After conversion to NRZ (non-return-to-zero) the encoder produces a bipolar signal (Fig. 6.41). The signal is then modulated using two orthogonal functions. After summing the signals of the two channels, we obtain a quadrature modulated (QPSK) signal.

Rice. 6.40. QPSK signal generation scheme

Rice. 6.41. Code without return to zero

The modulated time domain signal is shown in Fig. 6.42 and is a short segment of a random bit sequence. The figure shows fragments of a sine and cosine wave used in the in-phase and quadrature channels. The bit sequence used in the figure is: 1 1 0 0 0 1 1 0, which is divided into a sequence of even and odd bits. The total QPSK signal is shown below.

Rice. 6.42. QPSK signal in time domain

On the receiving side, the reverse process occurs (Fig. 6.43). Each channel uses a matched filter. The detector of the corresponding channel uses the relative value of the threshold to make a decision: 0 or 1 is accepted. The analysis proceeds through frames corresponding to the transmission time of one symbol.

Mobile stations use offset quadrature modulation (OQPSK – Offset QPSK). In one of the channels, the bit sequence is delayed for a time corresponding to half the duration of the transmitted symbol. In this case, the components of the in-phase and quadrature channels never change their phase shift simultaneously (Fig. 6.44). The maximum phase jump is 90 degrees. This makes signal amplitude fluctuations much smaller. This effect

there the signal is much smaller. This effect is clearly visible when compared with QPSK modulation with the same bit sequence (Fig. 6.42).

Rice. 6.43. Demodulation of QPSK signal in the receiver

Rice. 6.44. OQPSK signal in time domain

Transmission of messages in the IS-95 standard is carried out in frames. The reception principles used make it possible to analyze errors in each information frame. If the number of errors exceeds the acceptable level, leading to unacceptable degradation of speech quality, this frame is erased

(frame erasure).

The error rate or “bit erasure rate” is uniquely related to the ratio of the energy of the information symbol to the spectral noise density Eo/No. In Fig. Figure 6.45 shows the dependence of the probability of error in a frame (Prob. Frame Error) on the value of the Eo/No ratio for the forward and reverse channels, taking into account modulation, coding and interleaving.

As the number of active subscribers in a cell increases due to mutual interference, the Eo/No ratio decreases and the error rate increases. In this regard, different companies adopt their own acceptable error rates. For example, Motorola considers an error rate of 1% acceptable for CDMA IS-95, which corresponds, taking into account fading, to a ratio of Eo/No = 7 - 8 dB. At the same time, the throughput of IS-95 systems is on average 15 times higher than the throughput of analog AMPS systems.

Qualcomm takes 3% as the acceptable error rate. This is one of the reasons why Qualcomm claims that CDMA IS-95 has 20 to 30 times the capacity of analog AMPS.

The ratio Eo/No = 7 - 8 dB and the permissible error rate of 1% allows you to organize 60 active channels per three-sector cell. The dependence of the number of active communication channels (TCN) for the reverse channel on the value of the Eo/No ratio for a 3-sector cell is shown in Fig. 6.46.

Fig.6.45. Dependence of the probability of error in a frame on the signal level

• 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, the I component changes at the beginning of the symbol and the Q component changes after half the symbol (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.

Digital phase modulation is a versatile and widely used method for wireless transmission of 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. It's not surprising that we can also represent digital data using 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, the receiver will have difficulty distinguishing a symbol with a 90° phase offset from a symbol with a 91° phase offset. We have a 360° phase range to work with, so the maximum difference between the phases of logic one and logic 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 logical state and leaving it in its original state in response to another logical state.

To take the next step, we remember that multiplying a sine wave by negative one is the same as inverting it. This leads to the possibility of implementing BPSK using the following basic hardware configuration:

Basic scheme for receiving a BPSK signal

However, this circuit can easily result in high-slope transitions in the carrier waveform: if a transition between logic states occurs while the carrier signal is at its maximum value, the carrier signal voltage must quickly transition to its minimum value.

High slope in the BPSK waveform when changing the logical state of the baseband signal

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

If we enhance the above implementation with two additional functions, we can provide smooth transitions between characters. First, we need to ensure that the period of the digital bit is equal to one or more full periods of the carrier signal. Secondly, 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 symbol, which is what we are used to. Everything we've discussed about digital modulation assumes that the carrier signal changes depending on whether the digital voltage is logic low or high, and the receiver recreates the digital data by interpreting each symbol as a 0 or a 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 in which the voltage is at one extreme level or another, so that the voltage always represents a single digital bit. But the radio signal is not digital; rather, we use analog signals to transmit digital data, and it is perfectly acceptable to design a system in which analog signals are encoded and interpreted so that one character represents two (or more) bits.

The advantage of QPSK is the higher data rate: if we keep the same symbol duration, we can double the data 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 there is less separation between possible values. This is a reasonable assumption, but if you look at their math, it turns out that the error probabilities are actually very similar.)

Options

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

Phase jumps

Standard QPSK modulation ensures that transitions between symbols occur with a high slope; Since phase jumps can be ±90°, we cannot use the approach described for the 180° phase jumps produced by BPSK modulation.

This problem can be mitigated by using one of two variants of QPSK. Offset QPSK, 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 an advantage in reducing phase discontinuities, but π/4-QPSK wins because it is compatible with differential coding (discussed below).

Another way to solve problems with gaps between characters is to implement additional signal processing that creates smoother transitions between characters. This approach is included in a modulation scheme called minimum shift keying (MSK) frequency modulation, as well as an improvement to MSK known as Gaussian MSK.

Differential coding

Another complication is that demodulating PSK signals is more difficult than FSK signals. Frequency is "absolute" in the sense that changes in frequency can always be interpreted by analyzing changes in the signal over time. Phase, however, is relative in the sense that it does not have a universal reference point - the transmitter generates phase changes relative to one point in time, and the receiver can interpret phase changes relative 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, 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 an option 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 specific phase shift relative to 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 transmitter.