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BINARY PHASE SHIFT

KEYING (BPSK)


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DIGITAL MODULATION TECHNIQUES

There are basically two types of transmission of digital signals

1. Baseband data transmission :The digital data is transmitted over the channel

directly. There is no carrier or any modulation. This is suitable for transmission over

short distances

2. Passband data transmission: The digital data modulates high frequencysinusoidal carrier. It is suitable for transmission over long distances.

TYPES OF PASS BAND MODULATION:

The digital data can modulate can phase frequency , or amplitude of carrier. This gives

rise to three basic techniques

Phase shift keying (PSK)Frequency shift keying (FSK)

Amplitude shift keying (ASK)

Introduction


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Figure 6.2Functional model of pass-band data transmission system.

Receiver side (blocks described in detail p.326-327) detector

signal transmission decoder; reverses the operationsperformed in the transmitter;


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PSK (PHASE SHIFT KEYING)

Phase Shift Keying (PSK) Phase of carrier is varied to represent 1 or 0

Peak amplitude and frequency remain constant

Phase remains constant during each bit duration


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Forms of phase shift keying

PSK - Phase Shift Keying

1. BPSK - Binary ( 2 point ) Phase Shift Keying

2. QPSKQuadrature (4 point ) Phase Shift Keying

3. 8 PSK - 8 Point Phase Shift Keying




These are just some of the major forms of phase shift keying, PSK,

In general the higher order forms of modulation allow higher datarates to be carried within a given bandwidth.


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Binary phase-shift keying (BPSK)

BPSK is the simplest form of phase shift keying (PSK). Ituses two phases which are separated by 180 and so

can also be termed 2-PSK. It does not particularly matter

exactly where the constellation points are positioned, and

in this figure they are shown on the real axis, at 0 and

180.

AdvantagesThe distance between the signal point is great, then the error rate of BPSK is less


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BPSK Generation Scheme

A sinusoidal waveform is multiplied by the input bit stream.

Each time the bit stream changes sign (by crossing zero level), the

phase of the PSK signal also changes.


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BPSK ( 2 - PSK)

2-PSK: only 2 phase values are used, each for 1 or 0

Only phase is varied to represent 1 or 0


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6.3 Coherent Phase Shift Keying

- Binary Phase Shift Keying (BPSK)

In a coherent binary PSK the pair of signals

used to represent binary 0 and 1 are defined

as:

1

2( ) cos(2 ) (6.8)b

c

b

Es t f t

T

2 2 2( ) cos(2 ) cos(2 ) (6.9)b b

c c

b b

E Es t f t f tT T

transmitted energy

per bit

duration of one bit

fc=nc/Tb


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So the transmitted signals can be expressed as:

1

2( ) cos(2 ), 0 (6.10)c b

bt f t t T T

1 1( ) ( ), 0 (6.11)b bs t E t t T

The equations (6.8) and (6.9) represent antipodal signalssinusoidal

signals that differ only in a relative phase shift of 180 degrees.

In BPSK there is onlyone

basis function

of unit energy expressed as:

2 1( ) ( ), 0 (6.12)b bs t E t t T


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A coherent BPSK system can be characterized

by having a signal space that is onedimensional (N= 1), with signal constellationconsisting of two message points (M = 2)

The coordinates of the message points are:

11 1 1

0

( ) ( )

(6.13)

bT

b

s s t t dt

E

21 2 10

( ) ( )

(6.14)

bT

b

s s t t dt

E


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Figure 6.3Signal-space diagram for coherent binary PSK system. The waveforms depicting the

transmitted signals s1(t) and s2(t), displayed in the inserts, assume nc2.

Note that the frequency fcis chosen to ensure that each transmitted bit contains an integer

number of cycles..

message point

corresponding to

s1

message point

corresponding to

s2

ncis an integer such thTsymbol = nc/Tbit


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Error Probability of Binary PSK

Decision rule: based on the maximum l ikelihooddecis ion algor i thm /ru lewhich in this case meansthat we have to choose the message point closest tothe received signal point

observation v ector x l ies in region Ziif

the Euclid ean distanc e ||x-sk| | is minim um for k = i

For BPSK: N= 1, space is divided into two areas(fig.6.3) the set of points closest to message point 1 at +E1/2

the set of points closest to message point 2 atE1/2


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The decision rule is simply to decide that signal s1(t) (i.e.

binary 1) was transmitted if the received signal point falls

in region Z1, and decide that signal s2(t) (i.e. binarysymbol 0) was transmitted if the received signal falls in

region Z2.

Two kinds of errors are possible due to noise:

sent s1(t), received signal point falls in Z2 sent s2(t), received signal point falls in Z1

This can be expressed as: Zi: 0 < x1<

and the observed element is expressed as a function of

the received signal x(t) as:

1 1

0

( ) ( ) (6.15)bT

x x t t dt


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So,

In Ch.5 it was deduced that memory-less AWGN

channels, the observation elements Xiare Gaussian

RV with mean si jand variance N0/2.

The conditional probability density function that xj

(signal sjwas received providing miwas sent) is given

by:

2

100

1 1

( / ) exp[ ( ) ]jx j i ijf x m x sNN


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When we substitute for the case of BPSK

1

2

1 1 21

00

2

1

00

1 1( / 0) exp[ ( ) ]

1 1exp[ ( ) ] (6.16)

x

b

f x x sNN

x ENN

1

2

10 1 1 1 1

00 00

1 1( / 0) exp[ ( ) ] (6.17)x bf x dx x E dx

NN

Then the conditional probability of the receiver

in favor of 1 provided 0 was transmitted is:


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Considering an error of the second kind: signal space is symmetric about the origin

p01is the same as p10

Average probability of symbol error or the biterror rate for coherent BPSK is:

0

1( ) (6.20)

2

be

EP erfc

N

So increasing the sign al energy per bi tmakes the po ints - and move

far ther apart which correspond to reduc ing

the error pro babi l i ty.


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Generation and Detection of Coherent

BPSK Signals

Transmitter side: Need to represent the binary sequence 0 and 1 in

polar form with constant amplitudes, respectivelyand + (po lar non-return -to-zero NRZ -encoding).

Carrier wave is with frequency fc=(nc/Tb)

Required BPSK modulated signal is at the output ofthe product modulator.

Receiver side noisy PSK is fed to a correlator with locally generated

reference signal

correlator output is compared to a threshold of 0 voltsin the decision device


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Figure 6.4Block diagrams for (a) binary PSK transmitter and (b)

coherent binary PSK receiver.


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Quadrature phase-shift keying (QPSK)

4-PSK

QPSK can encode two bits per symbol. Analysis shows thatthis may be used either to double the data rate comparedto a BPSK system while maintaining the bandwidth of thesignal or to maintain the data-rate of BPSK but halve the

bandwidth needed. May utilize four variations of phase shift by 90 degrees

Each phase shift represents 2 bits ;technique isreferred to as 4-PSK

Allows data transmission two times as fast as 2-PSK


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4 -PSK


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QPSK versus BPSK

BPSK modulation results in 1 symbol/Hz, where QPSK modulation

results in 2 symbols/Hz).

As a result, the spectrum of QPSK is narrower than that of BPSK.

The main lobe of QPSK is half the width of the BPSK spectrum

mainlobe.

The probabilities of bit error for BPSK and QPSK are equal, butQPSK can support twice the data rate that BPSK can.

Higher orders of PSK can be designed (8-PSK, 16-PSK, etc.), but

there is a tradeoff (higher required power or higher BER).


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BPSK VS QPSK


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Reliable performance

Very low probability of error Efficient utilization of channel bandwidth

Sending more then one bit in a symbol

Quadriphase-shift keying (QPSK) - example of quadrature-carrier multiplexing Information is carried in the phase Phase can take one of four equally spaced values/4, 3/4,

5/4, 7/4

We assume gray encoding (10, 00, 01, 11)

Transmitted signal is defined as:

2 cos[2 (2 1) ], 0( ) (6.23)4

0,

ci

E f t i t Ts t T

elsewhere

6.3 Coherent Phase Shift Keying - QPSK


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Signal-Space Diagram of QPSK

From 6.23 we can redefine the transmitted signalusing a trigonometric identity:

From this representation we can use Gram-

Schmidt Orthogonal Procedure to create the

signal-space diagram for this signal. It allows us to find the orthogonal basis

functions used for the signal-space

representation.

2 2( ) cos[(2 1) ]cos(2 ) sin[(2 1) ]sin(2 ) (6.24)

4 4i c c

E Es t i f t i f t

T T


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In our case there exist two or thogonal bas is

funct ionsin the expansion of s

i(t). These are

1(t) and 2(t), defined by a pair of quadraturecarriers:

Based on these representations we can makethe following two important observations:

1

2( ) cos(2 ), 0 (6.25)ct f t t T

T

2

2( ) sin(2 ), 0 (6.26)ct f t t T

T


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There are 4 message points and the associated

vectors are defined by:

Values are summarized in Table 6.1

Conclusion:

QPSK has a two -dimension al s ignal cons tel lat ion(N = 2) and four message points(M = 4).

As binary PSK, QPSK has minimum average energy

cos[(2 1) ]4

, 1, 2, 3, 4 (6.27)

sin[(2 1) ]4

i

E i

s i

E i


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Figure 6.6

Signal-space diagram of coherent QPSK system.


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8-PSK

In this we Vary signal by shifts of 45degrees; each shift may then representthree bits (tri-bit) and send data threetimes as fast

C ll i ( Ph S )


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Constellation (or Phase-State)Diagram


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Comparison b/w 4-psk and 8-psk


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M-PSK (Circular Constellations)

16-PSK

an

bn4-PSK

M-PSK ( 16 - PSK) constellations

Tradeoffs

Higher-order modulations (M large) are mo re spectra l ly

eff ic ientbut less power eff ic ient (i .e. BER hig her).

M-QAM is more spectrally efficient than M-PSK but

also more sensitive to system nonlinearities.


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BER and Eb/No

The rate at which bits are corrupted beyond the capacity to reconstruct them

is called the BER (Bit Error Rate).

A BER of less than 1 in 100,000 bits is generally desired for an average

satellite communications channel (also referred to as a BER of 10-5).

For some types of data, an even smaller BER is desired (10-7).

The BER is directly dependent on the Eb/No, which is the Bit Energy-to-

Noise Density ratio.

Since the noise density present on the channel is difficult to control, this

basically means that BER can be reduced through using a higher powered

signal, or by controlling other parameters to increase the energy transmitted

per bit.

As the following chart shows, the BER will decrease (i.e., fewer errors)if the Eb/No increases.


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Higher Eb/No Reduces the BER


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Bandwidth vs. Power Efficiency

Bandwidth vs. Power Efficiency

MPSK:


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Bandwidth of M-PSK


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Advantages and Disadvantages

Advantages

1. BPSK produce less errors as compared to ASK2. More efficient use of bandwidth means higher data rate is possible

Disadvantages

More complex detection process than ASK and FSK

Rapid amplituded change between symbols due to phase discontinuty

QPSK AND BPSK::::

1. In QPSK higher data rate as compared to BPSK

2. For the same bit error rate the band width required by QPSK is reduced to

half than BPSK


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APPLICATIONS

IN SATELLITE COMMUNICATIONwireless LAN

biometric passports

Bluetooth

CDMA systemDVB-S

Cable modems

Video conferencing

Cellular phone system and other forms of digital

communication system over an RF

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