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Dar es Salaam Institute of Technology (DIT)

ETU 07123

Introduction to Communication Systems

Ally, J

jumannea@gmail.com

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Digital Modulation

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Digital Encoding In a digital communication system, the first step is to convert the

information into a bit stream of ones and zeros. Then the bit stream has to be represented as an electrical signal.

The electrical signal representation has to be chosen carefully for the following reasons: The electrical representation decides the bandwidth requirement. The electrical representation helps in clocking— the beginning and

ending of each bit. Error detection can be built into the signal representation. Noise immunity can be increased by a good electrical

representation. The complexity of the decoder can be decreased. The encoding scheme should be chosen keeping in view.

bandwidth requirement, clocking, error detection capability, noise immunity, and complexity of the decoder.

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Signaling FormatSignaling format can be divided into the following categories: Unipolar nonreturn-to-zero (NRZ) signaling Symbol 1 is represented by transmitting a pulse of constant amplitude for the entire duration of the bit interval, and symbol 0 is represented by no pulse. Bipolar nonreturn-to-zero (NRZ) signaling Symbol 1 and 0 are represented by pulses of equal positive and negative amplitudes. Unipolar return-to-zero (RZ) signaling Symbol 1 is represented by a positive pulse that returns to zero before the end of the bit interval, and symbol 0 is represented by the absence of pulse. Bipolar return-to-zero (RZ) signaling Positive and negative pulses of equal amplitude are used for symbol 1 and 0, respectively. In either case, the pulse return to 0 before the end of the bit interval. Alternate Mark Inversion (AMI) RZ signaling Positive and negative pulses are used for symbol 1, and no pulse is used for symbol 0. Manchester Encoding Symbol 1 is represented by a positive pulse followed by a negative pulse, with both pulses being of equal amplitude and half-bit duration; for symbol 0, the polarities of these are reversed.

Binary Signaling Format

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Introduction to Digital Modulation Digital modulation is the process by which digital symbols are transformed

into waveforms that are compatible with the characteristics of the channel.

In the case of base-band modulation, these waveforms usually takes the form of shaped pulses.

In the case of band-pass modulation the shaped pulses modulate a sinusoid called a carrier wave, or simply a carrier; for radio transmission the carrier is converted to an electromagnetic (EM) field for propagation to the desired destination.

Band-pass signal can transmit more than one signal on a single channel by assigning different frequencies to different signals.

Block Diagram of a Generic Digital Communication System

A/D converterChannel encoder

Source encoder

Modulator

Channel

D/A converterSourcedecoder

Channeldecoder

Demodulator

Analoginformation

Analogoutput

Noise, interference, fading

Digitaloutput

Digitalinformation

Transmitter

Receiver

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Digital Modulation Techniques Digital modulation technique used to transmit binary

data over a band-pass communication channel with fixed frequency limits set by the channel.

The notions involved in the generation of digital-modulated waves are basically the same as those described for analog-modulated waves.

With a binary modulation technique, the modulation process corresponds to switching or keying the amplitude, frequency, or phase of the carrier between either of two possible values corresponding to binary symbol 0 and 1.

This results in three basic signaling techniques, namely, amplitude-shift keying (ASK), frequency-shift keying (FSK), and phase-shift keying (PSK).

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ASK, PSK, and FSK Amplitude Shift Keying (ASK)

Phase Shift Keying (PSK)

Frequency Shift Keying

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1 0 1 1

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Binary Phase-Shift Keying (PSK) In a coherent binary PSK system, the pair of signals s1(t) and s2(t)

used to represent binary symbols 1 and 0, respectively, is defined by

where and Eb is the transmitted signal energy per bit. in the case of binary PSK, there is only one basis function of unit

energy, namely,

Then we may express the transmitted signals s1(t) and s2(t) in terms of as follows:

and

bTt 0

t1

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Generation of Coherent Binary PSK Signals To generate a binary PSK signal, we represent the input binary

sequence in polar form with symbols 1 and 0 represented by constant amplitude levels of and respectively.

The resulting binary wave and a sinusoidal carrier , are applied to a product modulator.

The carrier and the timing pulses used to generate the binary wave are usually extracted from a common master clock. The desired PSK wave is obtained at the modulator output.

bEbE

t1

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Detection of Coherent Binary PSK Signals To detect the original binary sequence of Is and Os, we apply the

noisy PSK signal x(t) (at the channel output) to a correlator, which is also supplied with a locally generated coherent reference signal

The correlator output, x1,is compared with a threshold of zero volts.

If x1 > 0, the receiver decides in favor of symbol 1. On the other hand, if x1 < 0, it decides in favor of symbol 0. If x1 is exactly zero, the receiver makes a random guess in favor of 0 or 1.

t1

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Binary Frequency-shift Keying (FSK) In a binary FSK system, symbols 1 and 0 are distinguished from

each other by transmitting one of two sinusoidal waves that differ in frequency by a fixed amount. A typical pair of sinusoidal waves is described by

where i = 1,2, and Eb is the transmitted signal energy per bit

Thus symbol 1 is represented by s1(t) and symbol 0 by s2(t). We therefore deduce that the most useful form for the set of

orthonormal basis functions is

Thus, unlike coherent binary PSK, a coherent binary FSK system is characterized by having a signal space that is two-dimensional. The two message point are:

and

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Generation of Coherent Binary FSK Signals To generate a binary FSK signal, the incoming binary data sequence is first

applied to an on-off level encoder, at the output of which symbol 1 is represented by a constant amplitude of volts and symbol 0 is represented by zero volts.

When we have symbol 1 at the input, the oscillator with frequency f1 in the upper channel is switched on while the oscillator with frequency f2 in the lower channel is switched off, with the result that frequency f1 is transmitted.

For symbol 0 at the input, the oscillator in the upper channel is switched off and the oscillator in the lower channel is switched on, with the result that frequency f2 is transmitted.

bE

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Detection of Coherent Binary FSK Signals To detect the original binary sequence given the noisy received

signal x(t), we may use the receiver which consists of two correlators with a common input, which are supplied with locally generated coherent reference signals and

The correlator outputs are then subtracted, one from the other, and the resulting difference y, is compared with a threshold of zero volts. If y > 0, the receiver decides in favor of 1. On the other hand, if y < 0, it decides in favor of 0. If y is exactly zero, the receiver makes a random guess in favor of 1 or 0.

t1 t2

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Generation and Detection of Coherent ASK Signals

To generate an ASK wave, we apply the incoming binary data (represented in unipolar form) and the sinusoidal carrier to a product modulator. The resulting output provides the desired ASK wave.

ProductModulator

Binary waveIn

Unipolar form m(t)

Carrier wave

Binary ASK waves(t)

tfT

Ec

b

b 2cos2

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QuadriPhase Shift Keying (QPSK) The provision of reliable performance, exemplified by a very low probability of

error, is one important goal in the design of a digital communication system. Another important goal is the efficient utilization of channel bandwidth.

The coherent QPSK is an example of the efficient utilization of channel bandwidth.

In quadriphase-shift keying (QPSK), as with binary PSK, information carried by the transmitted signal is contained in the phase. In particular, the phase of the carrier takes on one of four equally spaced values, such as π/4, 3π/4, 5π/4, and 7π/4. its transmitted signal is

where i = 1, 2, 3, 4; E is the transmitted signal energy per symbol, and T is the symbol duration. Each possible value of the phase corresponds to a unique dibit. Thus, for example, we may choose the foregoing set of phase values to represent the Gray-encoded set of dibits: 10,00,01, and 11, where only a single bit is changed from one dibit to the next.

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Signal-Space of QPSK We redefine the transmitted signal si(t) for the interval in the

equivalent form:

where i = 1,2,3,4. we can make the following observations: There are two orthonormal basis functions, Ф1(t) and Ф2(t) contained

in the expansion of si(t).

There are four message points, and the associated signal vectors are defined by

Tt 0

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Signal-space characterization of QPSK

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Generation of Coherent QPSK Signals The incoming binary data sequence is first transformed into polar

form by a nonreturn-to-zero level encoder. Thus, symbols 1 and 0 are represented by and respectively.

This binary wave is next divided by means of a demultiplexer into two separate binary waves consisting of the odd- and even numbered input bits.

bE bE

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Detection of Coherent QPSK Signals The QPSK receiver consists of a pair of correlators with a common input

and supplied with a locally generated pair of coherent reference signals Ф1(t) and Ф2(t).

The correlator outputs x1 and x2, produced in response to the received signal x(t), are each compared with a threshold of zero.

Finally, these two binary sequences at the in-phase and quadrature channel outputs are combined in a multiplexer to reproduce the original binary sequence at the transmitter input with the minimum probability of symbol error in an AWGN channel.

8-PSK Transmitter With 8-PSK, three bits are encoded, forming tribits and producing

eight different output phases. With 8-PSK, n=3, M=8, and there are eight possible output phases.

The incoming serial bit stream enters the bit splitter, where it is converted to a parallel, three channel output (the I or in-phase channel, the Q or in-quadrature channel, and the C or control channel.

The bit rate in each of the three channel is fb/3. The bits in the I and C channels enter the I channel 2-to-4-level

converter, and the bits in the Q and channels enter the Q channel 2-to-4-level converter. Essentially, the 2-to-4-level converters are parallel-input Digital-to-Analog Converters (DAC).

With two input bits, four output voltages are possible. I-channel and Q-channel truth tables are as follows:

C

I C Output

0 00 11 01 1

-0.541 V -1.307 V +0.541 V +1.307V

CQ Output

0 00 11 01 1

-1.307 V -0.541 V +1.307 V +0.541 V

8-PSK Modulator2-to-4-level converter

Product Modulator

Product Modulator

2-to-4-level converter

Reference oscillator

BPF

BPF

Linearsummer

Q CI BPFInputdata

I Channel

Q Channel

C

C

3bf

3bf

3bf

bf

PAM

PAM

Converter

8-PSKoutput

90

tfc2sin

tfc2cos

Binaryinput

8-PSKOutputphase

Q I C

0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 0

-112.5o

-157.5o

-67.5o

-22.5o

+112.5o

+157.5o

+67.5o

+22.5o

8-PSK Receiver The power splitter directs the input 8-PSK signal to the I and Q

product detectors and the carrier recovery circuit. The carrier recovery circuit reproduces the original reference

oscillator signal. The incoming 8-PSK signal is mixed with the recovered carrier

in the I product detector and with a quadrature carrier in the Q product detector.

The output of the product detectors are 4-level PAM signals that are fed to the 4-to-2 level Analog-to-Digital Converters (ADCs).

The outputs from the Q channel 4-to-2-level converter are the I and C bits, whereas the outputs from the Q channel 4-to-2-level converter are the Q and bits.

The parallel-to-serial logic circuit converts the I/C and Q/ bit pairs to serial I, Q, and C output data streams.

CC

8-PSK Demodulator

BPFPowersplitter

Carrierrecovery

Productdetector

Productdetector

Analog-to-Digital

converter

Analog-to-Digital

converter

Q I C

Clockrecovery

90

tf c2sin

tf c2cos

I channel

Q channel

8-PSKinput

4-level PAM

4-level PAM

I

C

Q

C

Parallel-to-serialconverter

QICOutputData bits

Quadrature Amplitude Modulation (QAM) 8-QAM is an M-ary encoding technique where

M=8. Unlike 8-PSK, the output signal from an 8-QAM modulator is not a constant-amplitude signal.

Only difference between the 8-QAM transmitter and the 8-PSK transmitter is the omission of the inverter between the C channel and the Q product modulator.

The incoming data are divided into groups of three bits (tribits): the I, Q, and C bit streams, each with a bit rate equal to 1/3 of the incoming data rate.

The I and Q bits determine the polarity of the PAM signal at the output of the 2-to-4-level converters, and the C channel determines the magnitude.

Because the C bit is fed uninverted to both the I and the Q channel 2-to-4-level converters, the magnitudes of the I and Q PAM signal are always equal.

Their polarities depend on the logic condition of the I and Q bits, therefore, may be different.

I/Q C Output

0 00 11 01 1

-0.541 V -1.307 V +0.541 V +1.307V

8-QAM Truth Table 2-4 level converter

8-QAM Truth Tableand phase

Binaryinput

8-QAM output

Q I C Amplitude Phase

0 0 00 0 10 1 00 1 11 0 01 0 11 1 01 1 1

0.765 V -135o

1.848 V -135o

0.765 V -45o

1.848 V -45o

0.765 V +135o

1.848 V +135o

0.765 V +45o

1.848 V +45o

8-QAM Transmitter

2-to-4-level converter

Product Modulator

Product Modulator

2-to-4-level converter

Reference oscillator

BPF

BPF

Linearsummer

Q CI BPF

I Channel

Q Channel

3bf

3bf

3bf

bf

PAM

PAM

90

tfc2sin

tfc2cos

CInputdata

8-QAMoutput

8-QAM Receiver An 8-QAM receiver is almost identical to the 8-PSK

receiver. The differences are the PAM levels at the output of the

product detectors and the binary signals at the output of the Analog-to-Digital Converters.

Because there are two transmit amplitudes possible with 8-QAM that are different from those achievable with 8-PSK, the four demodulated PAM levels in 8-QAM are different from those in 8-PSK.

Therefore the conversion factor for the Analog-to-Digital Converters must also be different.

With 8-QAM the binary output signals from the I channel ADC are the I and C bits, and the binary output signals from the Q channel ADC are the Q and C bits.

16-QAM 16-QAM is an M-ary system where M=16. The input data are acted in

groups of four (24=16). As with 8-QAM, both the phase and the amplitude of the transmit carrier are varied.

The input binary data are divided into four channels: I, I’, Q, and Q’. The bit rate in each channel is fb/4 of the input bit rate.

The I channel, Q channel and 16-QAM Modulator truth tables:

I I’ Output

0 00 11 01 1

-0.22 V-0.821 V+0.22 V

+0.821 V

Q Q’ Output

0 00 11 01 1

-0.22 V-0.821 V+0.22 V+0.821 V

Binary input 16-QAM output

Q Q’ I I’

0 0 0 00 0 0 10 0 1 00 0 1 10 1 0 00 1 0 10 1 1 00 1 1 11 0 0 01 0 0 11 0 1 01 0 1 11 1 0 01 1 0 11 1 1 01 1 1 0

0.311 V -135o

0.850 V -165o

0.311 V -45o

0.850 V -15o

0.850 V -105o 1.161 V -135o

0.850 V -75o

1.161 V -45o

0.311 V +135o

0.850 V +165o

0.311 V +45o

0.850 V +15o

0.850 V +105o

1.161 V +135o

0.850 V +75o

1.161 V +45o

16-QAM Transmitter

2-to-4-level converter

BalanceModulator

Balance Modulator

2-to-4-level converter

Reference oscillator

Linearsummer

Q I BPF

90

tfc2sin

tfc2cos

BinaryInputdata

16-QAMoutput

Q’ I’

Bit splitter

Q’

I’

Q

I

fb/4fb/4

fb/4fb/4

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Baud and Minimum Bandwidth Baud is a term that is often misunderstood and

commonly confused with bit rate (bps) Bit rate is the rate of change of a digital information

signal, which is usually binary. Baud is the rate of change of a signal on the

transmission medium after encoding and modulation have occurred.

Baud is a unit of transmission rate, modulation rate, or symbol rate and therefore, the terms symbols per second and baud are often used interchangeably.

Mathematically, baud is the reciprocal of the time of one output signaling element, and a signaling element may represent several information bits.

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Probability of Error and Bit Error Rate Probability of Error P(e) and Bit error Rate (BER) are

often used interchangeably, although in practice they do have slightly different meanings.

P(e) is a theoretical (mathematical) expectation of the bit error rate for a given system, OR P(e) is the probability of the detector making an incorrect decision.

BER is an empirical (historical) record of a system’s actual bit error performance.

For example, if a system has a P(e) of 10-5, this means that mathematically you can expect one bit error in every 100,000 bits transmitted (1/10-5 = 1/100,000). If a system has a BER of 10-5, this means that in past performance there was one bit error for every 100,000 bits transmitted.

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Probability of Error and Bit Error Rate (2) Probability of error is a function of the carrier-to-noise power ratio

(or, the average energy per bit-to-noise power density ratio) and the number of possible encoding conditions used.

Carrier-to-noise power ratio is the ratio of the average carrier power to the thermal noise power.

C(dBm)=10log(C(watts)/0.001) Thermal noise power is expressed mathematically as

N = KTB (watts)where, N = thermal noise power (watts)

K = Boltzman’s proportionality constant (1.38X10-23 J/K)

T = temperature (kelvin)

B = Bandwidth (hertz) Mathematically, the carrier-to-noise power ratio is

C/N = C/KTB (unitless ratio) or C/N (dB) = 10log(C/N) = C(dBm)-N(dBm)

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Probability of Error and Bit Error Rate (3) Energy per bit is the energy of a single bit of information

Eb = CTb (J/bit) or Eb = C/fb (J/bit)

where, Eb = energy of a single bit (joules per bit)

Tb = time of a single bit (seconds)

C = carrier power (watts) Noise power density is the thermal noise power normalized to a

1-Hz bandwidth. Mathematically, noise power density is given by

No = N/B (W/Hz) or No = KTB/B = KT (W/Hz)

The energy per bit-to-noise power density ratio is given byEb/ No = (C/fb)/(N/B) = (C/N) X (B/fb) or Eb/ No(dB) = 10log(C/N)-10log(B/fb)

where, Eb/ No = energy per bit-to-noise power density ratio

C/N = carrier-to-noise power ratio

B/fb = noise bandwidth-to-bit rate ratio

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Error Performance Error Probability of Binary PSK is given by

Error Probability of QPSK is given by

Error Probability of coherent binary FSK is given by

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Error Performance (2) Error Probability of noncoherent binary FSK is given by

Error Probability of coherent binary ASK is given by

Error Probability of noncoherent binary ASK is given by

Error Probability for M-QAM, where M=2k and k is even

o

b

N

EerfcPe

2

1

2

1

o

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N

EPe

4exp

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1

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N

EPe

2exp

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LLogQ

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2

2

1

ML

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Goals of the designer to Digital Communications To maximize transmission bit rate, R.

To minimize probability of error, Pe. To minimize required power or equivalently, to

minimize required bit energy to noise power spectral density Eb/No.

To minimize required system bandwidth, W. To maximize system utilization, that is to provide

reliable service for a maximum number of users with minimum delay and with maximum resistance to interference.

To minimize system complexity, computational load, and system cost.

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