MODULATION SCHEMES IN COMMUNICATION

MARTIN MATOVUBSTE 06/U/5761/PSA 206006175

BSc. In Telecommunications Eng, Department of Electrical EngineeringFaculty of Technology, Makerere University

Kampala, Uganda

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Abstract- the characteristics, performance and resulting physical realization of a communication system are significantly affected by the choice of a modulation scheme. At the same time, the choice of a scheme depends on the physical characteristics of the channel, required levels of performance and target hardware trade-offs, therefore some schemes will prove a better fit than others. Consideration must be given to the required data rate, acceptable level of latency, available bandwidth, anticipated link budget and target hardware cost, size and current consumption. The objective of this paper is to review the key characteristics and salient features of the main analog and digital modulation schemes used, including consideration of the receiver and transmitter requirements.

INTRODUCTION

In telecommunications, modulation is the process of conveying a message signal, for example a digital bit stream or an analog audio signal, inside another signal that can be physically transmitted. [1] A device that performs modulation is a modulator and a device that performs the inverse operation of modulation is a demodulator (also detector). A device that can do both operations is a modem (short for "Modulator-Demodulator"). There are basically two methods for modulating- Analog and Digital techniques.

ANALOG MODULATION

In analog modulation, there is continuous modulation applied in response to the analog information signal. The aim of analog modulation is to transfer an analog baseband signal, for example an audio signal over an analog pass band channel. The common analog modulation techniques are: Amplitude and Angle Modulation.

A. AMPLITUDE MODULATION (AM)

For a sinusoid, Ac cos (2π fc t + φ0 ), where Ac is the (constant) amplitude, fc is the (constant) frequency in Hz and φ0 is the initial phase angle. Let the sinusoid be written as Ac cos[ θ(t) ] where θ(t)= 2π fct + φ0 . The condition that Ac is a function of the message signal m(t), gives rise to amplitude

modulation. This is a technique used majorly in electronic communication, most commonly for transmitting information via a radio carrier wave. In AM, a quantity called modulation depth, indicates by how much the modulated variable varies around its 'original' level. For AM, it relates to the variations in the carrier amplitude and is defined as:Where M and A were introduced above. So if h = 0.5, the carrier amplitude varies by 50% above and below its unmodulated level, and for h = 1.0 it varies by 100%.

Double-Sideband AM (DSB-AM)[2]

Since each sideband is equal in bandwidth to that of the modulating signal, Amplitude modulation that results in two sidebands and a carrier is often called double sideband amplitude modulation (DSB-AM). Amplitude modulation is inefficient in terms of power usage and much of it is wasted. At least two-thirds of the power is concentrated in the carrier signal, which carries no useful information; the remaining power is split between two identical sidebands, though only one of these is needed since they contain identical information.

Figure 1: The (2-sided) spectrum of an AM signal. [2]

To increase transmitter efficiency, the carrier can be removed from the AM signal. This produces a double-sideband suppressed-carrier (DSBSC) signal. A suppressed-carrier amplitude modulation scheme is three times more power-efficient than traditional DSB-AM. If the carrier is only partially suppressed, a double-sideband reduced-carrier (DSBRC) signal results. DSBSC and DSBRC signals need their carrier to be regenerated to be

demodulated using conventional techniques.

Single-Sideband AM (SSB-AM)[2]

This is a type of amplitude modulation that uses electrical power and bandwidth more efficiently. SSB was also used over long distance telephone lines, as part of a technique known as frequency-division multiplexing (FDM). This enabled many voice channels to be sent down a single physical

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circuit, for example in L-carrier. SSB allowed channels to be spaced just 4,000 Hz apart, while offering a speech bandwidth of nominally 300–3,400 Hz. Most often, the carrier is reduced or removed entirely, being referred as single sideband suppressed carrier (SSBSC).

Figure 2: The LSB spectrum is inverted compared to the baseband. For example, a 2 kHz baseband signal modulated

onto a 5 MHz carrier produces an SSB frequency of 5.002 MHz if USB is used or 4.998 MHz if LSB is used.

Vestigial sideband (VSB) [2]

A vestigial sideband is a sideband that has been only partly cut off or suppressed. Television broadcasts use this method if the video is transmitted in AM, due to the large bandwidth used. It may also be used in digital transmission, the Milgo 4400/48 modem (circa 1967) used vestigial sideband and phase-shift keying to provide 4800-bit/s transmission over a 1600 Hz channel. To conserve bandwidth, SSB would be desirable, but the video signal has significant low frequency content (average brightness) and has rectangular synchronizing pulses. The engineering compromise is vestigial sideband modulation since the full upper sideband of bandwidth W2 = 4 MHz is transmitted, but only W1 = 1.25 MHz of the lower sideband is transmitted, along with a carrier. This makes the system AM at low modulation frequencies and SSB at high modulation frequencies. The absence of the lower

sideband components at high frequencies must be compensated for, and this is done by the RF and IF filters.

Quadrature AM (QAM) [2]

This is both an analog and a digital modulation scheme. It conveys two analog message signals, or two digital bit streams, by modulating the amplitudes of two carrier waves, using the AM analog modulation scheme or amplitude-shift keying (ASK) digital modulation scheme. These two waves, usually sinusoids, are out of phase with each other by 90° and are thus called quadrature carriers or components — hence the name of scheme. In the digital QAM case, a finite number of at least two phases and at least two amplitudes are used. PSK modulators are often designed using the QAM principle, but are not considered as QAM since the amplitude of the modulated carrier signal is constant.

Analog QAMWhen transmitting two signals by modulating them with QAM, the transmitted signal will be of the form:

Where I(t) and Q(t) are the modulating signals and f0

is the carrier frequency. At the receiver, these two modulating signals can be demodulated using a coherent demodulator. Such a receiver multiplies the received signal separately with both a cosine and sine signal to produce the received estimates of I(t) and Q(t) respectively. Because of the orthogonality property of the carrier signals, it is possible to detect the modulating signals independently.In the ideal case I(t) is demodulated by multiplying the transmitted signal with a cosine signal:

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Figure 3: Analog QAM

Digital QAMLike all modulation schemes, QAM conveys data by changing some aspect of a carrier signal, in response to a data signal. In the case of QAM, the amplitude of two waves, 90 degrees out-of-phase with each other (in quadrature) are changed (modulated or keyed) to represent the data signal. Amplitude modulating two carriers in quadrature can be equivalently viewed as both amplitude modulating and phase modulating a single carrier. Phase modulation (analog PM) and phase-shift keying (digital PSK) can be regarded as a special case of QAM, where the magnitude of the modulating signal is a constant, with only the phase varying. This can also be extended to frequency modulation (FM) and frequency-shift keying (FSK), for these can be regarded as a special case of phase modulation.

B. ANGLE MODULATION [3]

Consider a sinusoid, Ac cos (2π fc t + φ0 ), where Ac is the (constant) amplitude, fc is the (constant) frequency in Hz and φ0 is the initial phase angle. Let the sinusoid be written as Ac cos[ θ(t) ] where θ(t)= 2π fct + φ0 . When Ac is a constant but θ(t), instead of being equal to 2πfc t + φ0 , is a function of m(t) . This leads to what is known as the angle modulated signal. Two important cases of angle modulation are Frequency Modulation (FM) and Phase modulation (PM).

FREQUENCY MODULATION (FM)Consider the case where fi (t) is a function of m(t) ; that is, fi(t) = fc+ kf m(t) or

kf is a constant, which we will identify shortly. A frequency modulated signal s(t) is described in the time domain by

kf is termed as the frequency sensitivity of the modulator with the units Hz/volt. As with other modulation indices, this quantity indicates by how much the modulated variable varies around its unmodulated level. It relates to the variations in the frequency of the carrier signal:

where is the highest frequency component

present in the modulating signal xm(t), and is the Peak frequency-deviation, i.e the maximum deviation of the instantaneous frequency from the carrier frequency. If , the modulation is called narrowband FM, and its bandwidth is approximately . If , the modulation is called wideband FM and its bandwidth is approximately . While wideband FM uses more bandwidth, it can improve signal-to-noise ratio significantly. With a tone-modulated FM wave, if the modulation frequency is held constant and the modulation index is increased, the bandwidth of the FM signal increases, but the spacing between spectra stays the same. A rule of thumb, Carson's rule states that nearly all (~98%) of the power of a frequency-modulated signal lies within a bandwidth of

where ,as defined above, is the peak deviation of the instantaneous frequency

from the center carrier frequency .

PHASE MODULATION (PM)For PM, θi (t ) is given by The term 2πfct is the angle of the unmodulated carrier and the constant kp is the phase sensitivity of the modulator with the units, radians per volt. the phase modulated wave s(t) can be written as

PM is not very widely used for radio transmissions because it tends to require more complex receiving hardware thus presenting problems in determining whether, for example, the signal has changed phase by +180° or -180°.

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Figure 4: An example of FM, showing the modulating, or message, signal, xm(t), superimposed on the carrier wave, xc(t)

Figure 5(a): An example of phase modulation, diagram shows the modulating signal superimposed on the carrier wave [4]

Figure 5(b): diagram shows the resulting phase-modulated signal. [4]

The modulation index relates to the variations in the phase of the carrier signal: where Δθ is the peak phase deviation. For a single large sinusoidal signal, PM is similar to FM, and its bandwidth is approximately where fM = ωm / 2π and h is the modulation index defined below. This is also known as Carson's Rule for PM.

DIGITAL MODULATION

In digital modulation, an analog carrier signal is modulated by a digital bit stream with the aim of transfering a bit over an analog pass band channel. These are the most fundamental digital modulation techniques; PSK (uses a defined number of phases), FSK (uses a finite number of frequencies), ASK (uses a defined number of amplitudes), QAM (uses finite

number of at least two phases, and at least two amplitudes). Now the details-

A. PHASE SHIFT-KEYED (PSK)

PSK is achieved by modulating the phase. This can be achieved simply by defining a relative phase shift from the carrier, usually equi-distant for each required state. The resulting signal will, probably, not be constant amplitude and not be very spectrally efficient due to the rapid phase discontinuities. Phase modulation requires coherent generation and as such if an I-Q modulation technique is employed this filtering can be performed at baseband. PSK can be further classified as discussed below.

I. BINARY-PSK (BPSK)[5]

This is the simplest form of phase modulation. With binary (two level) phase modulation, the carrier phase has only two states, +/- π/2. The transition from a one to a zero, or vice versa, will result in the modulated signal crossing the origin of the constellation diagram resulting in 100% AM. Figure 6(a) below shows the theoretical spectra of a 1 Mbits BPSK signal with no additional filtering. Figure 6(a): Theoretical BPSK

Several techniques are employed in real systems to improve the spectral efficiency. One such method is to employ Raised Cosine filtering. figure 6(b) below shows the improved spectral efficiency achieved by applying a raised cosine filter with b=0.5 to the baseband modulating signals.

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Figure 6(b): Raised Cosine BPSK β=0.5

One potentially undesirable feature of BPSK that the application of a raised cosine filter will not improve is the 100% AM. Further hybrid versions of BPSK are used in real systems that combine constant amplitude modulation with phase modulation. One such example would be Constant Amplitude ‘50%’ BPSK, generated with shaped I and Q vectors designed to rotate the phase around the unit circle between the two constellation points. For a 010 data sequence the trajectory spends 25% of the time travelling from one point to other, 50% of the time at the required point and 25% of the time returning.

The resulting carrier phase shift is shown in figure 7 below.

Figure 7: Constant Amplitude ‘50%’ BPSK.

II. QUADRATURE-PSK (QPSK) [5]

QPSK uses four points on the constellation diagram, equispaced around a circle. Higher order modulation schemes, such as QPSK, are often used in preference to BPSK when improved spectral efficiency is required. QPSK utilizes four constellation points, as shown in figure 8 below, each representing two bits of data. Again as with BPSK the use of trajectory shaping (raised cosine, root raised cosine etc) will yield an improved spectral efficiency, although one of the principle disadvantages of QPSK, like BPSK, is the potential to cross the origin, hence generating 100% AM.

Figure 8: Constellation points for QPSK. π/4–QPSK This final variant of QPSK uses two identical constellations which are rotated by 45° (π / 4 rads) with respect to one another. Usually, either, the even or odd symbols are used to select points from one of the constellations and the other symbols select points from the other constellation. This reduces the phase-shifts from a maximum of 180°, but only to a maximum of 135° and so the amplitude fluctuations of π / 4–QPSK are between OQPSK and non-offset QPSK. One property this modulation scheme possesses is that the modulated signal does not pass through the origin. This lowers the dynamical range of fluctuations in the signal which is desirable when engineering communications signals. On the other hand, π / 4–QPSK lend itself to easy demodulation and have been adopted for use in, for example, TDMA cellular telephone systems.

Figure 9: Constellation points for π/4-QPSK. Offset-QPSK (OQPSK) As previously discussed the potential for a 180o

phase shift in QPSK results in the requirement for better linearity in the Power Amplifiers (PA) and the potential for spectral re-growth due to the 100% AM. O-QPSK reduces this tendency by adding a time delay of one bit period (half a symbol) in the Q-arm of the modulator. The result is that the phase of the carrier is modulated every bit (depending on the data), not every other bit as for QPSK, hence the phase trajectory never approaches the origin. The ability of the modulated signal to demonstrate a

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phase shift of 180o is thus removed. The shaping of the phase trajectory between constellation points is typically implemented with a raised cosine filter to improve the spectral efficiency. Due to the similarities between QPSK and O-QPSK similar signal spectra and probability of error are achieved. O-QPSK is utilized in the North American IS-95 CDMA cellular system for the link from the mobile to the base station.

Figure 10(a): OQPSK, Signal doesn't cross zero, because only one bit of the symbol is changed at a time

Figure 10(b): Difference of the phase between QPSK and OQPSK

B. FREQUENCY MODULATION (FSK)

A frequency modulation scheme in which digital information is transmitted through discrete frequency changes of a carrier wave. FSK has the advantage of being very simple to generate, simple to demodulate and due to the constant amplitude can utilize a non-linear PA. Significant disadvantages, however, are the poor spectral efficiency and BER performance. This precludes its use in this basic form from cellular and even cordless systems.

I. BINARY-FSK (BFSK) [6]

The simplest FSK is binary FSK (BFSK). BFSK literally implies using a pair of discrete frequencies to transmit binary (0s and 1s) information. With this scheme, the "1" is called the mark frequency and the "0" is called the space frequency. The time domain of an FSK modulated carrier is illustrated in the figures to the right.

Figure 11: Binary (2 level) FSK modulation. [3]

II. MINIMUM SHIFT KEYEING (MSK)[5]

Minimum Shift Keying is FSK with a modulation index of 0.5. Therefore the carrier phase of an MSK signal will be advanced or retarded 900

over the course of each bit period to represent either a one or a zero. Due to this exact phase relationship MSK can be considered as eitherphase or frequency modulation. The result of this exact phase relationship is that MSK can’t practically be generated with a voltage controlled oscillator and a digital waveform. Instead an I-Q modulation technique, as for PSK, is usually implemented. Gaussian Minimum Shift Keyed (GMSK)A variant of MSK that is employed by some cellular systems (including GSM) is Gaussian Minimum Shift Keying. GMSK can also be viewed as either frequency or phase modulation. The phase of the carrier is advanced or retarded up to 90o over the course of a bit period depending on the data pattern, although the rate of change of phase is limited with a Gaussian response. The result is the dependence on the Bandwidth Time product (BT), the achieved phase change over the bit may fall short of 90o. This will obviously have an impact on the BER, although the advantage of this scheme is the improved bandwidth efficiency. The extent of this shaping can clearly be seen from the 'eye' diagrams in figures below for BT=0.3, BT=0.5 and BT=1.

Figure 12: Eye Diagrams for GMSK with BT=0.3 (up), BT=0.5 (centre) and BT=1 (down).

III. AMPLITUDE SHIFT KEYING (ASK) [6]

It is a form of modulation that represents digital data as variations in the amplitude of a carrier wave. Like AM, ASK is also linear and sensitive to atmospheric noise, distortions, propagation conditions on different routes in PSTN, etc. Both ASK modulation and demodulation processes are relatively inexpensive. The ASK technique is also commonly used to transmit digital data over optical fiber. For

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LED transmitters, binary 1 is represented by a short pulse of light and binary 0 by the absence of light. Binary-ASK (B-ASK) [7]

A binary amplitude-shift keying (BASK) signal can be defined by equation (1)…......s(t) = A m(t) cos(2πfct), 0 < t < T where A is a constant, m(t) = 1 or 0, fc is the carrier frequency, and T is the bit duration. It has a power P = A2/2, so that A = √2P. Thus equation (1) can bewhere E = PT is the energy contained in a bit

duration. If we take Φ1(t) = √2/T (cos(2pfc t))as the orthonormal basis function, the applicable signal space or constellation diagram of the BASK signals

M-ary Amplitude-Shift Keying (M-ASK) [7]

An M-ary amplitude-shift keying (M-ASK) signal can be defined by equation (2) below,

Where Ai = A[2i - (M - 1)] for i = 0, 1, ..., M - 1 and M > 4. Here, A is a constant; fc is the carrier frequency, and T is the symbol duration. The signal has a power , so that , Thus equation (2) can be written as

where Ei = PiT is the energy of s(t) contained in a symbol duration for i = 0, 1, ..., M - 1.

CONCLUSION

Clearly, the various modulation techniques have been analyzed with focus on their behavior, advantages, and disadvantages with a follow up on where they find suitable application. The objective of this academic paper therefore has been achieved.

REFERENCES

1. http://www.wikipedia.com/ modulation2. http://www.wikipedia.com/ Single-sideband_modulation.htm3. Indian institute of Technology, Mandras- Principles of

Communication by Prof. V. Venkata Rao4. http://www.wikipedia.com/Phase_modulation.htm5. Introduction to Digital modulation schemes by Geoff Smithson6. http://en.wikipedia.org/wiki/Amplitude-shift_keying7. http://www.elec.mq.edu.au/~cl/files_pdf/elec321/lect_mask.pdf

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