Chapter: Digital Modulation Techniques

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Introduction Digital ModulationDigital data needs to be carried on an

analog signal.A carrier signal (frequency fc)

performs the function of transporting the digital data in an analog waveform.

The analog carrier signal is manipulated to uniquely identify the digital data being carried.

• Mechanisms for Modulating Digital Data into Analog Signal is done by certain techniques.

Introduction Digital Modulation

Binary Phase Shift Keying (BPSK)• In BPSK the transmitted signal is a

sinusoid of fixed amplitude.• It has one fixed phase when data is at one

level and when the data is at the other level the phase is different by 180º.

• The transmitted signal is,

• In BPSK the data b(t) is a stream of binay digit. Then transmitted BPSK signal is given as,

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Binary Phase Shift Keying (BPSK)• The received signal has a,

• The output voltage vo(kTb) at the end of a bit interval extending from time (k-1)Tb to KTb is,

Spectrum of BPSK• The waveform b(t) is a NRZ binary

waveform whose power spectral density makes an excursion between

and , we have,

The Power Spectral density of the BPSK signal is,

sP

sP

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Geometrical Representation of BPSK• A BPSK signal can be represented in terms of

one orthonormal signal as

The BPSK signal can be drawn as,

Fig. Geometrical representation of BPSK Signal

The distance “d” between the signals,

Where Eb= PsTb is the energy contained in a bit duration.

tCosTtu b 01 /2

Differential Phase Shift Keying• DPSK is the modification of BPSK.• DPSK eliminates the ambiguity about whether

the demodulated data is inverted or not.• It also avoids the need to provide the

synchronous carrier required at the demodulator for detecting a BPSK signal.

• Fig. Generating a DPSK Signal• The data stream to be transmitted is d(t).

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Differential Phase Shift Keying Cont.• b(t) is applied to a balanced modulator

to which is applied the carrier The modulator output which is the transmitted signal is,

• When d(t) =0 the phase of the carrier does not change at the beginning of the bit interval.

• While when d(t) =1 there is a phase change of magnitude π.

tCosPs 02

Differential Phase Shift Keying Cont.

Fig. Method of recovering data from DPSK Signal

• The received signal and the received signal delayed by the time interval Tb are multiplied to a multiplier. The multiplier output is,

Differentially Encoded Phase Shift Keying• DPSK demodulator required a device which

operates at the carrier frequency and provides a delay Tb.

• DEPSK eliminates the need for such a piece of hardware.

• In DEPSK synchronous demodulation recovers the signal b(t) and the decoding of b(t) to generate d(t) is done at baseband.

• The transmitter of DEPSK is identical with DPSK.

Fig. Baseband decoder to obtain d(t) from b(t)

15Fig. Errors in Differentially Encoded PSK occurs in pair.

(a)

(b)

Differentially Encoded PSK (Cont.)• The signal b(t) is recovered in exactly

the same manner for a BPSK system.• DPSK there is a tendency for bit errors to

occur in pairs but that single bit errors are possible.

• In DEPSK errors always occur in pairs.

Quadrature Phase Shift Keying (QPSK)• PSK that uses phase shifts of 90º=π/2

rad ⇒ 4• Different signals generated, each

representing 2 bits.• advantage: higher data rate than in PSK

(2 bits per bit interval), while bandwidth occupancy remains the same.

• 4-PSK can easily be extended to 8-PSK, i.e. n-PSK

• higher rate PSK schemes are limited by the ability of equipment to distinguish small differences in phase.

Quadrature Phase Shift Keying (Cont.)

• Fig. Type D Flip Flop symbol

Fig. Flip Flop Characteristics

Quadrature Phase Shift Keying (Cont.)

Fig. An offset QPSK

Quadrature Phase Shift Keying (Cont.)• The transmitted output signal is given

by,

Quadrature Phase Shift Keying (Cont.)

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Quadrature Phase Shift Keying

Fig. QPSK Receiver

QPSK Signal Space Reprsentation (Cont.) • The four quadrature signal can be

represented as,

• These signals were represented in terms of two orthonormal signals,

• The QPSK signal vm(t) can be given as,

QPSK Signal Space Reprsentation (Cont.)

• Where T = 2Tb= Ts

QPSK Signal Space Reprsentation (Cont.)

Non-offset Quadrature Phase Shift Keying • An additional flip-flop is placed either

before even or odd flip-flop.• So in each transition time Tb for OQPSK

and 2Tb for QPSK.• One bit for OQPSK and two bit for QPSK

change for 1V to -1V.

Amplitude Shift Keying (ASK)In ASK, the two binary values are represented

by to different amplitudes of the carrier frequency.

The resulting modulated signal for one bit time is

Susceptible to noise.ASK is also called On-Off Keying.The simplest and most common form of operate

as a switch.Application: ASK is used to transmit digital data

over optical fiber.

0,0

1),2cos()(

binary

binarytfAts c

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Amplitude Shift Keying (Cont.)

Nbaud = baud ratefc = carrier frequency

• The bandwidth B of ASK is proportional to the signal rate S.

B = (1+d)S• “d” is due to modulation and filtering,

lies between 0 and 1.

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Amplitude Shift Keying (Cont.)

We have an available bandwidth of 100 kHz which spans from 200 to 300 kHz. What are the carrier frequency and the bit rate if we modulated our data by using ASK with d = 1?SolutionThe middle of the bandwidth is located at 250 kHz. This means that our carrier frequency can be at fc = 250 kHz. We can use the formula for bandwidth to find the bit rate (with d = 1 and r = 1).

Example 3

Given a BW of 10,000 Hz (1000 – 12,000 Hz), draw the full-duplex ASK diagram of the system. Find the carriers and the BWs in each direction. Assume there is no gap between the bands in 2 directions

Solution:BW for each direction = 10,000/2 = 5000 HzThe carrier frequencies can be chosen at the middle of the bandsfc(forward) = 1000 + 5000/2 = 3,500Hzfc(backward) = 11,000 - 5000/2 = 8,500Hz

Example 4

• The digital data stream changes the frequency of the carrier signal, fc.

• frequency of carrier signal is varied to represent binary 1 or 0

• Amplitude and phase is not changeable. • Advant: FSK is less susceptible to errors than

ASK –specific frequency changes over a number of intervals, so voltage (noise) spikes can be ignored

• Disadvantage: FSK spectrum is 2 x ASK spectrum.

• application: over voice lines, in high-freq. radio transmission, etc. 36

Frequency Shift Keying (FSK)

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BFSK Generator

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Receiver for a BFSK signal

• In BFSK the binary data waveform d(t) generates a binary signal,

• Here d(t) = +1 or -1 corresponds to the logic 1 and 0 of the data waveform.

BFSK Spectrum• In terms of the variable pH and pL, The BFSK Signal

is,

• In the BPSK case b(t) is bipolar i.e. it alternates between +1 and -1. pH and pL as a sum of constant and a bipolar variable, that is,

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Geometrical Representation of Orthogonal FSKAn orthogonal BFSK can be generated

with the suitable selection of the frequencies of the unit vector, with m and n integers.

The vector u1 and u2 are the mth and nth harmonics of the fundamental frequencies fb.

The frequency fH and fL in the BFSK are selected to be with (m > n)

The corresponding signal vectors are,

The distance between the signal end points is,

Signal space representation of orthogonal BFSK

Geometrical Representation of non-orthogonal FSKWhen two FSK signals sH(t) and sL(t)

are not-orthogonal. Let us represent the higher frequency

signal sH(t) as,

Now represent the lower frequency signal sL(t) as,

Fig. Signal Space representation for SH(t) and SL(t) are not orthogonal

Geometrical Representation of non-orthogonal FSKThe distance separating sH(t) and sL(t)

is,

when the two signals are not orthogonal we have to evaluate S11, S12 and S22.

Geometrical Representation of non-orthogonal FSKWe are using the previous eq. &

getting,

The distance separating sH(t) and sL(t) is,

Now simplifying the equation we get,

The final result is then,

If then the optimum distance dopt

• It uses “two-dimensional” signaling.• Original information stream is split into two

sequences that consist of odd and even symbols, e.g. Bk and Ak

• Ak sequence (in-phase comp.) is modulated by Cos(2πfct), Bk sequence (quadrature-phase comp.) is modulated by Sin(2πfct).

• Composite signal is sent through the channel Ak

Cos(2πfct)+ Bk Sin(2πfct).50

Quadrature Amplitude Modulation (QAM)

• Adv: data rate = 2 bit per interval

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Quadrature Amplitude Modulation (QAM)

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Quadrature Amplitude Modulation (QAM)

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Quadrature Amplitude Modulation (QAM)

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16-QAM Constellation

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• It is also known as correlative coding and partial response signalling.

• It basically introduce controlled inter-symbol interference (ISI) in data stream.

• So encoding a binary bit stream by duobinary enoding effects a reduction of max. freq. than max. req. of unencoded data stream.

• So bandwidth reduces by using duobinary signalling.

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Duobinary Encoding

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• The waveform vD(k) is therefore,

• The inverter output is The differential encoder (called precoder ) output is,

• The input I2 = b(k-1). So that the inverter output d(k) is,

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Duobinary Encoding (Correlative coding)

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Spectrum of Duobinary Encoding

Find the minimum BW for an FSK signal transmitting at 2000 bps. The transmission mode is half-duplex and the carriers must be separated by 3,000 Hz

Solution:BW = baud rate + (fc1 –fc0)

The baud rate is the same as the bit rate

BW = 2000 + 3000 =5000 Hz

Example 5

Find the max bit rates for an FSK signal if the BW of the medium is 12,000 Hz and the difference between the carriers must be at least 2000 Hz. Transmission is in full-duplex mode.

Solution:BW = baud rate + (fc1 –fc0)The BW for each direction is 6000 Hz Baud rate = 6000 –2000 = 4000 Baud rate = bit rateBit rate = 4000 bps

Example 6