Lecture 5: Digital Modulation Techniques

Modulation is the process of encoding information from a message source in a manner suitable for transmission.

The ultimate goal of a modulation technique is to transport the message signal through a radio channel with the best possible quality while occupying the least amount of radio spectrum.

Modulation

Modulation

Modulation may be done by varying the amplitude, phase, or frequency of a high frequency carrier in accordance with the amplitude of the message signal.

As such, there are 3 main types of digital modulation schemes Amplitude Shift Keying (ASK)

Frequency Shift Keying (FSK)

Phase Shift Keying (PSK)

Other modulation schemes can be derived from the 3 main schemes

IQ signal representation

In digital communications, modulation is often expressed in terms of I and Q.

This is a rectangular representation of the polar diagram. On a polar diagram, the I axis lies on the zero degree phase reference, and the Q axis is rotated by 90 degrees.

The signal vectors projection onto the I axis is its I component and the projection onto the Q axis is its Q component.

S = I + Q 2 2

j = tan -1 I

Q

Magnitude of Signal:

Phase of Signal:

I and Q components in a digital transmitter

The Q component is passed through a phase shifter to make the signal components orthogonal/in-quadrature to each other hence avoid interference.

The main advantage of I/Q modulation is the symmetric ease of combining independent signal components into a single composite signal and later splitting such a composite signal into its independent component parts.

This simplifies the design of digital radios

I and Q components in a digital transmitter

At the receiver, The composite input signal (in terms of magnitude and phase) is broken into an in-phase, I, and a quadrature, Q, component.

These two signal components are independent and orthogonal.

Amplitude Shift Keying (ASK)

Amplitude is changed in response to information. Bit 1 is transmitted by a signal of one particular amplitude and to transmit bit 0, we change the amplitude keeping frequency constant. (ex. On-Off Keying, OOK, which is a special form of ASK).

Baseband information sequence 0010110010

ASK(t) = s(t) sin(2p f t)

ASK demonstrates poor performance, as it is heavily affected by noise and interference.

Pulse shaping can be employed to remove spectral spreading

Frequency Shift Keying (FSK)

In FSK we change the frequency in response to information. One particular f1 for a bit 1 and another f0 for a bit 0.

FSK can be expanded to a M-ary scheme, employing multiple frequencies as different states

The bandwidth occupancy in FSK is dependent on the spacing of the two symbols. A frequency spacing of 0.5 times the symbol period is typically used.

Phase Shift Keying (PSK)

In PSK, we change the phase of the sinusoidal carrier. To transmit 0, we shift the phase of the sinusoidal by 180 degrees.

Binary Phase Shift Keying (BPSK) demonstrates better performance than ASK and FSK. PSK can be expanded to a M-ary scheme, employing multiple phases and amplitudes as different states.

Filtering can be employed to avoid spectral spreading.

PSK(t) = { sin (2p f t) for bit 1

sin (2p f t+p) for bit 0

Binary Phase Shift Keying (BPSK)

The phase of a constant amplitude carrier signal moves between 0 and 180 degrees.

On the I Q diagram,the I state has two different values.

There are two possible locations in the state diagram, so a

binary 0 or 1 can be sent.

(symbol rate = 1bit/symbol)

Expression Carrier I Bit Symbol Q

0 S1

1 S2

1

-1

0

0

(2Es/T ) cost

(2Es/T)cos(t+)

Es- Transmitted energy per bit which is given by Es=1/2 * Ac^2*T, Ac is the signal amplitude

Q

I

BPSK Modulator

11

Assume the random bit stream 0110110.

Next are shown the first few symbols

from this bit stream. The Q channel

for BPSK is 0 so ignore it. The

modulator assigns a certain symbol

to the I channel depending on the bit

to be sent.

Bit Symbol I Q

0 S1 -1 0

1 S2 1 0

1 S2 1 0

0 S1 -1 0

1 S2 1 0

1 S2 1 0

0 S1 -1 0

BPSK Modulator Contd

12

Now a carrier of frequency fc is used to create the packet of signal. In

order to create the correct modulated signal the carrier is multiplied with

the I channel amplitude values.

0 -1

1 1

1 1

0 -1

1 1

1 1

0 -1

s1

s2

s2

s1

s2

s2

s1

x cos(t) =

The first column contains the bits. These are mapped to amplitudes of the I

channels by the BPSK mapping rules. These are then multiplied by a

cosine wave which is held for symbol time T. This results in a packet of

analog signals called the symbol. The frequency of the cosine wave is

called carrier frequency.

Quadrature PSK (QPSK) Quadrature PSK (QPSK) is used extensively in applications including

CDMA cellular networks, Iridium and DVB-S (digital video broadcasting-satellite)

Quadrature means that the signal shifts between phase states which are separated by 90 degrees.

Quadrature Phase Shift Keying is effectively two independent BPSK systems (I and Q), and therefore exhibits the same performance but twice the bandwidth efficiency

Mapping rules for QPSK

14

315 10 S4

225 11 S3

135 01 S2

45 00 S1

Q I Carrier signal Phase (deg.)

Expression Bits Symbol

2Es cos(t+/4)

1

2

1

2

1

2

1

2

1

2

1

2

1

2

1

2

2Es sin(t+3/4)

2Es cos(t+3/4)

2Es sin(t+/4)

Constellation diagram of QPSK

In the constellation diagram, each adjacent symbol only differs by one bit.

QPSK can encode two bits per symbol hence may be used either to double the data rate compared to a BPSK system while maintaining the bandwidth of the signal or to maintain the data-rate of BPSK but halve the bandwidth needed.

This is used in the cellular CDMA (Code Division Multiple Access) system for the reverse (mobile to base) link.

In QPSK, the I and Q bit streams are switched at the same time. The symbol clocks, or the I and Q digital signal clocks, are synchronized.

However, in OQPSK, the I and Q bit streams are offset in their relative alignment by one bit period (one half of a symbol period) as shown in the diagram.

Since the transitions of I and Q are offset, at any given time only one of the two bit streams can change values. This creates a different constellation, even though there are still just two I/Q values. This has power efficiency advantages.

Offset QPSK (OQPSK)

Offset QPSK (OQPSK)

The spectral efficiency is the same with two I states and two Q states. The reduced amplitude variations (perhaps 3 dB for OQPSK, versus 30 to 40 dB for QPSK) allow a more power-efficient, less linear RF power amplifier to be used.

Disadvantages of Offset QPSK (OQPSK)

OQPSK introduces a delay of half a symbol into the demodulation process. In other words, using OQPSK increases the temporal efficiency of normal QPSK.

This is due to the reason that the in phase and quadrature phase components of the OQPSK cannot be simultaneously zero. Hence, the range of the fluctuations in the signal is smaller. An additional disadvantage is that the quiescient power is

nonzero, which may be a design issue in devices targeted for low power applications.

Minimum shift keying (MSK) is a special type of continuous phase-frequency shift keying (CPFSK) with a modulation index, h=0.5, which corresponds to the minimum frequency spacing that allows two FSK signals to be coherently orthogonal.

As such, minimum shift keying implies the minimum frequency separation (i.e. bandwidth) that allows orthogonal detection.

Binary data may consist of sharp transitions between 1" and 0" states and vice-versa, which may potentially create signals that have sidebands extending out of the carrier bandwidth.

This may create problems for many radio communications systems, as any sidebands extending outwards from the main carrier bandwidth cause interference to the adjacent channels.

Minimum Shift Keying (MSK)

MSK modulation ensures that the modulating data signal changes the frequency of the signal with 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 (0.5) the data rate. This can be expressed in terms of the modulation index, and it is always equal to 0.5.

Minimum Shift Keying (MSK)

In a traditional FSK modulation system with frequency f0 and f1 and used to transmit message m=0 and m=1 over period Tb second. The respective message symbols are given by;

Assuming that f0>f1>0, and if we choose frequencies such that in each time interval TB, there is an integer number of periods Tb, then;

Where k0 and k1 are integers.

Minimum Shift Keying (MSK)

In MSK, f0 and f1 are chosen such that there is an integer number of periods, Tb to ensure signal continuity.

Minimum Shift Keying (MSK)

Fig 1. Discontinuous signal

Fig 2. Discontinuous phase signal Fig 3. Continuous phase

signal

Minimum Shift Keying (MSK)

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MSK can be derived from OQPSK by making one further change OQPSK I

and Q channels use square root-raised cosine pulses. For MSK, change the

pulse shape to a half-cycle sinusoid.

MSK pulse and carrier for a 1 bit MSK pulse and carrier for a 0 bit

The carrier signal expression for MSK is:

Red curve = Carrier signal Blue curve = MSK pulse shape Black curve = multiplication of the pulse shape and the carrier giving the modulated carrier. The underlined portion of the mathematical expression for MSK is the half-sinusoid pulse shape.

GMSK is a modification of MSK scheme. A pre-modulation filter is used to reduce the bandwidth of a baseband pulse train prior to modulation. The filter limits the instantaneous frequency variations of the MSK signal resulting to a signal with much narrower bandwidth.

However, pre-filtering may cause intersymbol interference (ISI) of the signal pulses due to smearing effect. Therefore, in GMSK applications, there is always a trade-off between power efficiency and bandwidth efficiency.

Gaussian Minimum Shift Keying (GMSK)

Method 1

Involves the use of a Gaussian low-pass filter to filter the modulating signal before being passed through a frequency modulator with modulation index set at 0.5.

This method is very simple to implement. However, it is very difficult to accurately maintain modulation index of the FM at 0.5.

Generation of GMSK modulation

Method 2

Involves the use of a quadrature modulator that use a 90 degrees phase-shifter to ensure that the I-Q signal components are orthogonal.

The modulation index can be accurately maintained at 0.5 without the need for adjustments. This makes this method more preferred

Generation of GMSK modulation

Higher spectral efficiency

Allows the use of non-linear amplifiers without causing any form of signal distortion No amplitude variations on the signal

A GMSK signal is immune to noise interference as a result of amplitude variations

Applications of GMSK

Mobile communication systems such as;

GSM

Digital European Cordless Telephone (DECT)

Cellular Digital Packet Data (CDPD)

Digital Communications System (DCS1800) in Europe

GSM-based Personal Communications System (PCS1900) in the US

Advantages of GMSK modulation

A M-ary symbol can be realized by grouping m consecutive binary bits together. As such, the number of possible modulating symbols is M=2m and the symbol period (duration) is T= m.Tb

The objective is to improve system data rate without increasing bandwidth by increasing the number of bits per symbol. However, they are more prone to noise effects

8-PSK

For 8PSK, m=3 and there are 8 possible phase shifts (at intervals of45 degrees) which allow 3 bits to be transmitted per each symbol. The signal constellation diagram is as follows;

Multi-level (M-ary) modulation schemes

8-PSK

16 PSK transmits 4 bits per symbol

16-PSK

In order to increase the distance between points in the signal constellation, another option is to modulate both the amplitude and the phase. This is called Quadrature Amplitude Modulation (QAM).

Quadrature Amplitude Modulation (QAM)

QAM signals can be extended to much higher bit rates .

64-QAM and 256-QAM are common in cable modems, satellites, and high-speed fixed broadband wireless.

8 QAM

Applications of digital modulation schemes

Modulation scheme Application

MSK, GMSK GSM, CDPD

BPSK Deep space telemetry, cable modems

QPSK, /4 DQPSK Satellite, CDMA, NADC, TETRA, PHS, PDC, LMDS, DVB-S, cable (return path), cable modems, TFTS

0QPSK CDMA, satellite

FSK, GFSK DECT, paging, RAM mobile data, AMPS, ERMES, land mobile, public safety

8PSK Satellite, aircraft, telemetry pilots for monitoring broadband video systems

16 QAM

Microwave digital radio, MMDS

32 QAM Terrestrial microwave, DVB-T

64 QAM DVB-C, modems

256 QAM Modems, DVB-C Europe

Refers to a measure of how fast data can be transmitted over a given bandwidth.

It is measured in bits per second per hertz (bps/Hz).

Spectral Efficiency

Typical Spectral Efficiency values

Refers to the ratio of the number of bit errors to the number of bits transmitted

The channel signal-to-noise (S/N) also affects the spectral efficiency of the system.

The larger the amount noise present (lower S/N ratio), the greater the number of bit errors.

Generally, the basic modulation schemes (BPSK, QPSK) have a higher immunity to noise that the more complex constellations.

Bit Error Rate (BER)

For error free communication, the capacity of a system which uses an Additive White Gaussian Noise (AWGN) channel can be expressed as follows;

fb/W = log2(1 + Ebfb/W) Shannon-Hartley Capacity Theorem

where fb = Capacity (bits per second)

W = bandwidth of the modulating baseband signal (Hz)

Eb = energy per bit

= noise power density (watts/Hz)

thus Ebfb = total signal power

W = total noise power

fb /W = bandwidth efficiency (bits per second per Hz)

Shannon Hartley Capacity Theorem