Phase Modulation 1

PHASE MODULATION
Frequency modulation requires the oscillator frequency to deviate both above and below the carrier frequency. During the process of frequency modulation, the peaks of each successive cycle in the modulated waveform occur at times other than they would if the carrier were unmodulated. This is actually an incidental phase shift that takes place along with the frequency shift in fm. Just the opposite action takes place in phase modulation. The af signal is applied to a PHASE MODULATOR in pm. The resultant wave from the phase modulator shifts in phase, as illustrated in figure 2-17. Notice that the time period of each successive cycle varies in the modulated wave according to the audio-wave variation. Since frequency is a function of time period per cycle, we can see that such a phase shift in the carrier will cause its frequency to change. The frequency change in fm is vital, but in pm it is merely incidental. The amount of frequency change has nothing to do with the resultant modulated wave shape in pm. At this point the comparison of fm to pm may seem a little hazy, but it will clear up as we progress.
Figure 2-17. - Phase modulation.

Let's review some voltage phase relationships. Look at figure 2-18 and compare the three voltages (A, B, and C). Since voltage A begins its cycle and reaches its peak before voltage B, it is said to lead voltage B. Voltage C, on the other hand, lags voltage B by 30 degrees. In phase modulation the phase of the carrier is caused to shift at the rate of the af modulating signal. In figure 2-19, note that the unmodulated carrier has constant phase, amplitude, and frequency. The dotted wave shape represents the modulated carrier. Notice that the phase on the second peak leads the phase of the unmodulated carrier. On the third peak the shift is even greater; however, on-the fourth peak, the peaks begin to realign phase with each other. These relationships represent the effect of 1/2 cycle of an af modulating signal. On the negative alternation of the af intelligence, the phase of the carrier would lag and the peaks would occur at times later than they would in the unmodulated carrier.

Figure 2-18. - Phase relationships.

Figure 2-19. - Carrier with and without modulation.

The presentation of these two waves together does not mean that we transmit a modulated wave together with an unmodulated carrier. The two waveforms were drawn together only to show how a modulated wave looks when compared to an unmodulated wave.
Now that you have seen the phase and frequency shifts in both fm and pm, let's find out exactly how they differ. First, only the phase shift is important in pm. It is proportional to the af modulating signal. To visualize this relationship, refer to the wave shapes shown in figure 2-20. Study the composition of the fm and pm waves carefully as they are modulated with the modulating wave shape. Notice that in fm, the carrier frequency deviates when the modulating wave changes polarity. With each alternation of the modulating wave, the carrier advances or retards in frequency and remains at the new frequency for the duration of that cycle. In pm you can see that between one alternation and the next, the carrier phase must change, and the frequency shift that occurs does so only during the transition time; the frequency then returns to its normal rate. Note in the pm wave that the frequency shift occurs only when the modulating wave is changing polarity. The frequency during the constant amplitude portion of each alternation is the REST FREQUENCY.
Figure 2-20. - Pm versus fm.

The relationship, in pm, of the modulating af to the change in the phase shift is easy to see once you understand AM and fm principles. Again, we can establish two clear-cut rules of phase modulation:
AMOUNT OF PHASE SHIFT IS PROPORTIONAL TO THE AMPLITUDE OF THE MODULATING SIGNAL.
(If a 10-volt signal causes a phase shift of 20 degrees, then a 20-volt signal causes a phase shift of 40 degrees.)
RATE OF PHASE SHIFT IS PROPORTIONAL TO THE FREQUENCY OF THE MODULATING SIGNAL.
(If the carrier were modulated with a 1-kilohertz tone, the carrier would advance and retard in phase 1,000 times each second.)
Phase modulation is also similar to frequency modulation in the number of sidebands that exist within the modulated wave and the spacing between sidebands. Phase modulation will also produce an infinite number of sideband frequencies. The spacing between these sidebands will be equal to the frequency of the modulating signal. However, one factor is very different in phase modulation; that is, the distribution of power in pm sidebands is not similar to that in fm sidebands, as will be explained in the next section.
Modulation Index
Recall from frequency modulation that modulation index is used to calculate the number of significant sidebands existing in the waveform. The higher the modulation index, the greater the number of sideband pairs. The modulation index is the ratio between the amount of oscillator deviation and the frequency of the modulating signal:

In frequency modulation, we saw that as the frequency of the modulating signal increased (assuming the deviation remained constant) the number of significant sideband pairs decreased. This is shown in views (A) and (B) of figure 2-21. Notice that although the total number of significant sidebands decreases with a higher frequency-modulating signal, the sidebands spread out relative to each other; the total bandwidth increases.
Figure 2-21. - Fm versus pm spectrum distribution.

In phase modulation the oscillator does not deviate, and the power in the sidebands is a function of the amplitude of the modulating signal. Therefore, two signals, one at 5 kilohertz and the other at 10 kilohertz, used to modulate a carrier would have the same sideband power distribution. However, the 10-kilohertz sidebands would be farther apart, as shown in views (C) and (D) of figure 2-21. When compared to fm, the bandwidth of the pm transmitted signal is greatly increased as the frequency of the modulating signal is increased. Read More..

Phase Modulation 2

Phase modulation basics

Before looking at phase modulation it is first necessary to look at phase itself. A radio frequency signal consists of an oscillating carrier in the form of a sine wave is the basis of the signal. The instantaneous amplitude follows this curve moving positive and then negative, returning to the start point after one complete cycle - it follows the curve of the sine wave. This can also be represented by the movement of a point around a circle, the phase at any given point being the angle between the start point and the point on the waveform as shown.

Phase modulation works by modulating the phase of the signal, i.e. changing the rate at which the point moves around the circle. This changes the phase of the signal from what it would have been if no modulation was applied. In other words the speed of rotation around the circle is modulated about the mean value. To achieve this it is necessary to change the frequency of the signal for a short time. In other words when phase modulation is applied to a signal there are frequency changes and vice versa. Phase and frequency are inseparably linked as phase is the integral of frequency. Frequency modulation can be changed to phase modulation by simply adding a CR network to the modulating signal that integrates the modulating signal. As such the information regarding sidebands, bandwidth and the like also hold true for phase modulation as they do for frequency modulation, bearing in mind their relationship.

Forms of phase modulation

Although phase modulation is used for some analogue transmissions, it is far more widely used as a digital form of modulation where it switches between different phases. This is known as phase shift keying, PSK, and there are many flavours of this. It is even possible to combine phase shift keying and amplitude keying in a form of modulation known as quadrature amplitude modulation, QAM.

The list below gives some of the forms of phase shift keying that are used:

• PM - Phase Modulation
• PSK - Phase Shift Keying
• BPSK - Binary Phase Shift Keying
• QPSK - Quadrature Phase Shift Keying
• 8 PSK - 8 Point Phase Shift Keying
• 16 PSK - 16 Point Phase Shift Keying
• QAM - Quadrature Amplitude Modulation
• 16 QAM - 16 Point Quadrature Amplitude Modulation
• 64 QAM - 64 Point Quadrature Amplitude Modulation
• MSK - Minimum Shift Keying
• GMSK - Gaussian filtered Minimum Shift Keying

These are just some of the major forms of phase modulation that are widely used in radio communications applications today. With today's highly software adaptable radio communications systems, it is possible to change between the different types of modulation to best meet the prevailing conditions.

Overview

Phase modulation, PM, is widely used in today's radio communications scene, with phase shift keying being widely used for digital modulation and data transmission. It is used in all forms of radio communications from cellular technology to Wi-Fi, WiMAX, radio broadcasting of digital audio and TV, and many more forms of transmission.

communications. PSK, phase shift keying enables data to be carried on a radio communications signal in a more efficient manner than Frequency Shift Keying, FSK, and some other forms of modulation.

With more forms of communications transferring from analogue formats to digital formats, data communications is growing in importance, and along with it the various forms of modulation that can be used to carry data.

There are several flavours of phase shift keying, PSK that are available for use. Each form has its own advantages and disadvantages, and a choice of the optimum format has to be made for each radio communications system that is designed. To make the right choice it is necessary to have a knowledge and understanding of the way in which PSK works.

Phase Shift Keying, PSK, basics

Like any form of shift keying, there are defined states or points that are used for signalling the data bits. The basic form of binary phase shift keying is known as Binary Phase Shift Keying (BPSK) or it is occasionally called Phase Reversal Keying (PRK). A digital signal alternating between +1 and -1 (or 1 and 0) will create phase reversals, i.e. 180 degree phase shifts as the data shifts state.

Binary phase shift keying, BPSK

The problem with phase shift keying is that the receiver cannot know the exact phase of the transmitted signal to determine whether it is in a mark or space condition. This would not be possible even if the transmitter and receiver clocks were accurately linked because the path length would determine the exact phase of the received signal. To overcome this problem PSK systems use a differential method for encoding the data onto the carrier. This is accomplished, for example, by making a change in phase equal to a one, and no phase change equal to a zero. Further improvements can be made upon this basic system and a number of other types of phase shift keying have been developed. One simple improvement can be made by making a change in phase by 90 degrees in one direction for a one, and 90 degrees the other way for a zero. This retains the 180 degree phase reversal between one and zero states, but gives a distinct change for a zero. In a basic system not using this process it may be possible to loose synchronisation if a long series of zeros are sent. This is because the phase will not change state for this occurrence.

There are many variations on the basic idea of phase shift keying. Each one has its own advantages and disadvantages enabling system designers to choose the one most applicable for any given circumstances. Other common forms include QPSK (Quadrature phase shift keying) where four phase states are used, each at 90 degrees to the other, 8-PSK where there are eight states and so forth.

PSK constellation diagrams

It is often convenient to represent a phase shift keyed signal, and sometimes other types of signal using a phasor or constellation diagram. Using this scheme, the phase of the signal is represented by the angle around the circle, and the amplitude by the distance from the origin or centre of the circle. In this way the can be signal resolved into quadrature components representing the sine or I for In-phase component and the cosine for the quadrature component. Most phase shift keyed systems use a constant amplitude and therefore points appear on one circle with a constant amplitude and the changes in state being represented by movement around the circle. For binary shift keying using phase reversals the two points appear at opposite points on the circle. Other forms of phase shift keying may use different points on the circle and there will be more points on the circle.

Constellation diagram for BPSK

When plotted using test equipment errors may be seen from the ideal positions on the phase diagram. These errors may appear as the result of inaccuracies in the modulator and transmission and reception equipment, or as noise that enters the system. It can be imagined that if the position of the real measurement when compared to the ideal position becomes too large, then data errors will appear as the receiving demodulator is unable to correctly detect the intended position of the point around the circle.

Constellation diagram for QPSK

Using a constellation view of the signal enables quick fault finding in a system. If the problem is related to phase, the constellation will spread around the circle. If the problem is related to magnitude, the constellation will spread off the circle, either towards or away from the origin. These graphical techniques assist in isolating problems much faster than when using other techniques.

QPSK is used for the forward link form the base station to the mobile in the IS-95 cellular system and uses the absolute phase position to represent the symbols. There are four phase decision points, and when transitioning from one state to another, it is possible to pass through the circle's origin, indicating minimum magnitude.

On the reverse link from mobile to base station, O-QPSK is used to prevent transitions through the origin. Consider the components that make up any particular vector on the constellation diagram as X and Y components. Normally, both of these components would transition simultaneously, causing the vector to move through the origin. In O-QPSK, one component is delayed, so the vector will move down first, and then over, thus avoiding moving through the origin, and simplifying the radio's design. A constellation diagram will show the accuracy of the modulation.

Forms of phase shift keying

Although phase modulation is used for some analogue transmissions, it is far more widely used as a digital form of modulation where it switches between different phases. This is known as phase shift keying, PSK, and there are many flavours of this. It is even possible to combine phase shift keying and amplitude keying in a form of modulation known as quadrature amplitude modulation, QAM.

The list below gives some of the more commonly used forms of phase shift keying, PSK, and related forms of modulation that are used:

• PSK - Phase Shift Keying
• BPSK - Binary Phase Shift Keying
• QPSK - Quadrature Phase Shift Keying
• O-QPSK - Offset Quadrature Phase Shift Keying
• 8 PSK - 8 Point Phase Shift Keying
• 16 PSK - 16 Point Phase Shift Keying
• QAM - Quadrature Amplitude Modulation
• 16 QAM - 16 Point Quadrature Amplitude Modulation
• 64 QAM - 64 Point Quadrature Amplitude Modulation
• MSK - Minimum Shift Keying
• GMSK - Gaussian filtered Minimum Shift Keying

These are just some of the major forms of phase shift keying, PSK, that are widely used in radio communications applications today. Each form of phase shift keying has its own advantages and disadvantages. In general the higher order forms of modulation allow higher data rates to be carried within a given bandwidth. However the downside is that the higher data rates require a better signal to noise ratio before the error rates start to rise and this counteracts any improvements in data rate performance. In view of this balance many radio communications systems are able to dynamically choose the form of modulation depending upon the prevailing conditions and requirements.

Overview

Phase shift keying, PSK, is a particularly important form of modulation these days. With most of the traffic on the newer radio communications systems and radio communications links being carried as data and using forms of phase shift keying, PSK, it is of particular importance.

Reason for Minimum Shift Keying, MSK

It is found that binary data consisting of sharp transitions between "one" and "zero" states and vice versa potentially creates signals that have sidebands extending out a long way from the carrier, and this creates problems for many radio communications systems, as any sidebands outside the allowed bandwidth cause interference to adjacent channels and any radio communications links that may be using them.

Minimum Shift Keying, MSK basics

The problem can be overcome in part by filtering the signal, but is found that the transitions in the data become progressively less sharp as the level of filtering is increased and the bandwidth reduced. To overcome this problem GMSK is often used and this is based on Minimum Shift Keying, MSK modulation. The advantage of which is what is known as a continuous phase scheme. Here there are no phase discontinuities because the frequency changes occur at the carrier zero crossing points.

When looking at a plot of a signal using MSK modulation, it can be seen that the modulating data signal changes the frequency of the signal and there are no phase discontinuities. This arises as a result of the unique factor of MSK that the frequency difference between the logical one and logical zero states is always equal to half the data rate. This can be expressed in terms of the modulation index, and it is always equal to 0.5.

Signal using MSK modulation

GMSK basics

GMSK modulation is based on MSK, which is itself a form of phase shift keying. One of the problems with standard forms of PSK is that sidebands extend out from the carrier. To overcome this, MSK and its derivative GMSK can be used.

MSK and also GMSK modulation are what is known as a continuous phase scheme. Here there are no phase discontinuities because the frequency changes occur at the carrier zero crossing points. This arises as a result of the unique factor of MSK that the frequency difference between the logical one and logical zero states is always equal to half the data rate. This can be expressed in terms of the modulation index, and it is always equal to 0.5.

Signal using MSK modulation

A plot of the spectrum of an MSK signal shows sidebands extending well beyond a bandwidth equal to the data rate. This can be reduced by passing the modulating signal through a low pass filter prior to applying it to the carrier. The requirements for the filter are that it should have a sharp cut-off, narrow bandwidth and its impulse response should show no overshoot. The ideal filter is known as a Gaussian filter which has a Gaussian shaped response to an impulse and no ringing. In this way the basic MSK signal is converted to GMSK modulation.

Spectral density of MSK and GMSK signals

Generating GMSK modulation

There are two main ways in which GMSK modulation can be generated. The most obvious way is to filter the modulating signal using a Gaussian filter and then apply this to a frequency modulator where the modulation index is set to 0.5. This method is very simple and straightforward but it has the drawback that the modulation index must exactly equal 0.5. In practice this analogue method is not suitable because component tolerances drift and cannot be set exactly.

Generating GMSK using a Gaussian filter and VCO

A second method is more widely used. Here what is known as a quadrature modulator is used. The term quadrature means that the phase of a signal is in quadrature or 90 degrees to another one. The quadrature modulator uses one signal that is said to be in-phase and another that is in quadrature to this. In view of the in-phase and quadrature elements this type of modulator is often said to be an I-Q modulator. Using this type of modulator the modulation index can be maintained at exactly 0.5 without the need for any settings or adjustments. This makes it much easier to use, and capable of providing the required level of performance without the need for adjustments. For demodulation the technique can be used in reverse.

Block diagram of I-Q modulator used to create GMSK

Advantages of GMSK modulation

there are several advantages to the use of GMSK modulation for a radio communications system. One is obviously the improved spectral efficiency when compared to other phase shift keyed modes.

A further advantage of GMSK is that it can be amplified by a non-linear amplifier and remain undistorted This is because there are no elements of the signal that are carried as amplitude variations. This advantage is of particular importance when using small portable transmitters, such as those required by cellular technology. Non-linear amplifiers are more efficient in terms of the DC power input from the power rails that they convert into a radio frequency signal. This means that the power consumption for a given output is much less, and this results in lower levels of battery consumption; a very important factor for cell phones.

A further advantage of GMSK modulation again arises from the fact that none of the information is carried as amplitude variations. This means that is immune to amplitude variations and therefore more resilient to noise, than some other forms of modulation, because most noise is mainly amplitude based.

GMSK highlights

GMSK modulation is a highly successful form of modulation, being used in GSM cellular technology, and as a result, its use is particularly widespread. It is also used in other radio communications applications because of its advantages in terms of spectral efficiency, resilience to noise and its ability to allow the use of efficient transmitter final amplifiers. Even though other radio communications systems utilise other forms of modulation, GMSk is an ideal choice for many applications.

Analogue and digital QAM

Quadrature amplitude modulation, QAM may exist in what may be termed either analogue or digital formats. The analogue versions of QAM are typically used to allow multiple analogue signals to be carried on a single carrier. For example it is used in PAL and NTSC television systems, where the different channels provided by QAM enable it to carry the components of chroma or colour information. In radio applications a system known as C-QUAM is used for AM stereo radio. Here the different channels enable the two channels required for stereo to be carried on the single carrier.
Digital formats of QAM are often referred to as "Quantised QAM" and they are being increasingly used for data communications often within radio communications systems. Radio communications systems ranging from cellular technology through wireless systems including WiMAX, and Wi-Fi 802.11 use a variety of forms of QAM, and the use of QAM will only increase within the field of radio communications.

Digital / Quantised QAM basics

Quadrature amplitude modulation, QAM, when used for digital transmission for radio communications applications is able to carry higher data rates than ordinary amplitude modulated schemes and phase modulated schemes. As with phase shift keying, etc, the number of points at which the signal can rest, i.e. the number of points on the constellation is indicated in the modulation format description, e.g. 16QAM uses a 16 point constellation.
When using QAM, the constellation points are normally arranged in a square grid with equal vertical and horizontal spacing and as a result the most common forms of QAM use a constellation with the number of points equal to a power of 2 i.e. 2, 4, 8, 16 . . . .
By using higher order modulation formats, i.e. more points on the constellation, it is possible to transmit more bits per symbol. However the points are closer together and they are therefore more susceptible to noise and data errors.
To provide an example of how QAM operates, the table below provides the bit sequences, and the associated amplitude and phase states. From this it can be seen that a continuous bit stream may be grouped into threes and represented as a sequence of eight permissible states.

Bit sequence	Amplitude	Phase (degrees)
000	1/2	0 (0°)
000	1	0 (0°)
010	1/2	π/2 (90°)
011	1	πi/2 (90°)
100	1/2	π (180°)
101	1	π (180°)
110	1/2	3πi/2 (270°)
111	1	3π/2 (270°)

Bit sequences, amplitudes and phases for 8-QAM Phase modulation can be considered as a special form of QAM where the amplitude remains constant and only the phase is changed. By doing this the number of possible combinations is halved.

QAM advantages and disadvantages

Although QAM appears to increase the efficiency of transmission for radio communications systems by utilising both amplitude and phase variations, it has a number of drawbacks. The first is that it is more susceptible to noise because the states are closer together so that a lower level of noise is needed to move the signal to a different decision point. Receivers for use with phase or frequency modulation are both able to use limiting amplifiers that are able to remove any amplitude noise and thereby improve the noise reliance. This is not the case with QAM.
The second limitation is also associated with the amplitude component of the signal. When a phase or frequency modulated signal is amplified in a radio transmitter, there is no need to use linear amplifiers, whereas when using QAM that contains an amplitude component, linearity must be maintained. Unfortunately linear amplifiers are less efficient and consume more power, and this makes them less attractive for mobile applications.

QAM comparison with other modes

As there are advantages and disadvantages of using QAM it is necessary to compare QAM with other modes before making a decision about the optimum mode. Some radio communications systems dynamically change the modulation scheme dependent upon the link conditions and requirements - signal level, noise, data rate required, etc.
The table below compares various forms of modulation:

Modulation	Bits per symbol	Error margin		Complexity
OOK	1	1/2	0.5	Low
BPSK	1	1	1	Medium
QPSK	1	1 / √2	0.71	Medium
16 QAM	4	√2 / 6	0.23	High
64QAM	6	&radic / 14	0.1	High

Summary of types of modulation with data capacities

QAM summary

When choosing the form of modulation to use for a radio communications system, it is necessary to take account of all its attributes to assess whether it is suitable. QAM, Quadrature Amplitude Modulation is being used increasingly because of the increased data rate it offers compared to some of the simpler amplitude or phase only formats. Also adaptive systems are being used to use QAM when conditions are suitable, enabling high data rates to be transmitted over the radio communications link.

QAM, Quadrature amplitude modulation is widely used in many digital data radio communications and data communications applications. A variety of forms of QAM are available and some of the more common forms include 16 QAM, 32 QAM, 64 QAM, 128 QAM, and 256 QAM. Here the figures refer to the number of points on the constellation, i.e. the number of distinct states that can exist.
The various flavours of QAM may be used when data-rates beyond those offered by 8-PSK are required by a radio communications system. This is because QAM achieves a greater distance between adjacent points in the I-Q plane by distributing the points more evenly. And in this way the points on the constellation are more distinct and data errors are reduced. While it is possible to transmit more bits per symbol, if the energy of the constellation is to remain the same, the points on the constellation must be closer together and the transmission becomes more susceptible to noise. This results in a higher bit error rate than for the lower order QAM variants. In this way there is a balance between obtaining the higher data rates and maintaining an acceptable bit error rate for any radio communications system.

QAM applications

QAM is in many radio communications and data delivery applications. However some specific variants of QAM are used in some specific applications and standards.
For domestic broadcast applications for example, 64 QAM and 256 QAM are often used in digital cable television and cable modem applications. In the UK, 16 QAM and 64 QAM are currently used for digital terrestrial television using DVB - Digital Video Broadcasting. In the US, 64 QAM and 256 QAM are the mandated modulation schemes for digital cable as standardised by the SCTE in the standard ANSI/SCTE 07 2000.
In addition to this, variants of QAM are also used for many wireless and cellular technology applications.

Constellation diagrams for QAM

The constellation diagrams show the different positions for the states within different forms of QAM, quadrature amplitude modulation. As the order of the modulation increases, so does the number of points on the QAM constellation diagram.
The diagrams below show constellation diagrams for a variety of formats of modulation:

QAM bits per symbol

The advantage of using QAM is that it is a higher order form of modulation and as a result it is able to carry more bits of information per symbol. By selecting a higher order format of QAM, the data rate of a link can be increased.
The table below gives a summary of the bit rates of different forms of QAM and PSK.

Modulation	Bits per symbol	Symbol Rate
BPSK	1	1 x bit rate
QPSK	2	1/2 bit rate
8PSK	3	1/3 bit rate
16QAM	4	1/4 bit rate
32QAM	5	1/5 bit rate
64QAM	6	1/6 bit rate

QAM noise margin

While higher order modulation rates are able to offer much faster data rates and higher levels of spectral efficiency for the radio communications system, this comes at a price. The higher order modulation schemes are considerably less resilient to noise and interference.
As a result of this, many radio communications systems now use dynamic adaptive modulation techniques. They sense the channel conditions and adapt the modulation scheme to obtain the highest data rate for the given conditions. As signal to noise ratios decrease errors will increase along with re-sends of the data, thereby slowing throughput. By reverting to a lower order modulation scheme the link can be made more reliable with fewer data errors and re-sends. Read More..