This presentation covers: Some basic definitions & concepts of digital communication What is Phase Shift Keying(PSK) ? Binary Phase Shift Keying – BPSK BPSK transmitter & receiver Advantages & Disadvantages of BPSK Pi/4 – QPSK Pi/4 – QPSK transmitter & receiver Advantages of Pi/4- QPSK

1. Phase Shift Keying &
π/4 -Quadrature Phase Shift
Keying
Presentation by:
Naveen Jakhar, ITS
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2. Topics covered in this presentation:
 Some basic definitions & concepts of digital communication
What is Phase Shift Keying(PSK) ?
Binary Phase Shift Keying – BPSK
BPSK transmitter & receiver
Advantages & Disadvantages of BPSK
Pi/4 – QPSK
Pi/4 – QPSK transmitter & receiver
Advantages of Pi/4- QPSK
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3. Some basic concepts of Digital Communication:
Information capacity: linear function of bandwidth and transmission
time i.e. 𝐼 ∝ 𝐵 × 𝑡
where I is information capacity(bits per second)
B is bandwidth (hertz)
t is transmission time (sec)
 Shannon limit for information capacity
𝐼 = 𝐵 log2(1 + 𝑆𝑁𝑅)
Where SNR is signal to noise power ratio (unit less quantity)
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4. M-ary coding:
M-ary is a term derived from binary
M represents a digit that corresponds to the number of conditions,
levels, or combinations possible for a given number of binary
variables, for e.g. a digital signal with four possible conditions (voltage
levels, frequencies, phases) is an M-ary system where M = 4
Number of bits necessary to produce a given number of conditions is
expressed mathematically as 𝑁 = log2 𝑀 or 2 𝑁 = 𝑀 where N is
number of necessary bits & M is number of
conditions/combinations/levels
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5. Baud and Minimum bandwidth:
Baud or symbols per second- 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
𝐵𝑎𝑢𝑑 =
1
𝑡 𝑠
where 𝑡 𝑠is time of one signalling element (seconds)
Minimum theoretical bandwidth necessary to propagate a signal is
called the minimum Nyquist bandwidth or minimum Nyquist
frequency. Thus,𝑓𝑏 = 𝐵, where 𝑓𝑏 is the bit rate in bits per second
and B is the ideal Nyquist bandwidth.
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6. Baud and Minimum bandwidth: continued ….
 The relationship between bandwidth and bit rate also applies to the
opposite situation. For a given bandwidth (B), the highest theoretical
bit rate is 2B.
Using multilevel signalling, the Nyquist formula for channel capacity
is 𝑓𝑏 = 𝐵log2 𝑀 or 𝑓𝑏 = 𝐵 × 𝑁 => 𝐵 =
𝑓 𝑏
𝑁
where 𝑓𝑏 is channel capacity in bits per second, B is minimum Nyquist
bandwidth and M is number of discrete signal or voltage levels
𝐵𝑎𝑢𝑑 =
𝑓 𝑏
𝑁
, so Baud is also the bit rate divided by the number of bits
encoded into one signalling element
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7. Phase Shift Keying (PSK): Introduction
PSK is a digital modulation scheme which conveys data by
changing/modulating the phase of the carrier signal
Phase of carrier signal is varied in proportional to the information
signal
The carrier signal is also called reference signal
The modulation is done by varying sine and cosine inputs at a precise
time
PSK is often called angle modulated constant amplitude digital
modulation
Simplest form of PSK is Binary phase shift keying (BPSK)
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8. Binary Phase Shift Keying (BPSK):
BPSK has values of N=1 and M=2, so two phases for the carrier are
possible
One phase represents a logic 1 and the other phase represents a logic
0. As the input digital signal changes state (i.e., 1 -> 0 or 0 -> 1), the
phase of the output carrier shifts between two angles that are
separated by 180°
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9. Binary Phase Shift Keying (BPSK): continued …..
 Any carrier signal is s(t) = A cos (2π𝑓𝑐t +θ) where θ is the phase
For BPSK, we have θ=0 or θ=π, separated by 180 degrees
So, the BPSK signals become A m(t)cos (2π𝑓𝑐t +θ)
𝑣1 𝑡 = Acos2π𝑓𝑐 𝑡 0 ≤ t ≤ T, for 1 and
𝑣2 𝑡 = −Acos2π𝑓𝑐 𝑡 0 ≤ t ≤ T, for 0
where A is a constant, 𝑓𝑐is the carrier frequency and T is the bit
duration
 The signal has a power 𝑃 =
𝐴2
2
means 𝐴 = 2𝑃
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10. Binary Phase Shift Keying (BPSK): continued …..
So, the signals 𝑣1,2 𝑡 = ±Acos2π𝑓𝑐 𝑡 becomes
𝑣1,2 𝑡 = ± 2𝑃cos2π𝑓𝑐 𝑡
= ± 𝑃𝑇
2
𝑇
cos2π𝑓𝑐 𝑡
= ± 𝐸
2
𝑇
cos2π𝑓𝑐 𝑡
where E=P*T is the energy contained in a bit duration.
ᶲ1,2 𝑡 = ±
2
𝑇
cos2π𝑓𝑐 𝑡 are the orthonormal functions with unit
energy in a bit duration
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11. BPSK Constellation Diagram
 Constellation points are drawn on a
2 dimensional complex co-ordinate
system
ᶲ1 𝑡 =
2
𝑇
cos2π𝑓𝑐 𝑡 0 ≤ t ≤ T
ᶲ2 𝑡 = −
2
𝑇
sin2π𝑓𝑐 𝑡 0 ≤ t ≤ T
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12. BPSK transmitter:
Other names for BPSK are phase reversal keying (PRK) and biphase
modulation
BPSK is a form of square-wave modulation of a continuous wave (CW)
signal
Important components of a BPSK transmitter are : Balanced
modulator, level converter, Band pass filter and Reference Carrier
Oscillator
Balanced modulator acts as a phase reversing switch
Another name of Balanced modulator is Balanced Ring modulator
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13. BPSK transmitter diagram:
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14. BPSK Balanced Ring Modulator:
The balanced modulator has two inputs: (1) a carrier which is in
phase with the reference oscillator and (2) the binary digital data
For the balanced modulator to operate properly, the digital input
voltage must be much greater than the peak carrier voltage
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15. BPSK Balanced Ring Modulator Function:
When the binary input logic is 1 When the binary input logic is 0
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16. Output of a BPSK waveform:
Logic 1 input produces an analog output signal with a 0°phase angle,
and a logic 0 input produces an analog output signal with a 180°
phase angle
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17. BPSK Receiver:
Input signal to receiver maybe +𝑠𝑖𝑛𝜔𝑐 𝑡 or - 𝑠𝑖𝑛𝜔𝑐 𝑡
The coherent carrier recovery circuit detects and regenerates a
carrier signal that is both frequency and phase coherent with the
original transmit carrier
The balanced modulator is a product detector; the output is the
product of the two inputs (the BPSK signal and the recovered carrier)
The low-pass filter (LPF) separates the recovered binary data from
the complex demodulated signal
Coherent BPSK requires that the reference signal at the receiver to be
synchronized in phase and frequency with the received signal
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18. BPSK Receiver output:
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For a BPSK input signal of +𝑠𝑖𝑛𝜔𝑐 𝑡 (logic 1), the output of the
balanced modulator is:
output = (𝑠𝑖𝑛𝜔𝑐 𝑡 )(𝑠𝑖𝑛𝜔𝑐 𝑡 ) = 𝑠𝑖𝑛2
𝑤𝑐 𝑡
Now 𝑠𝑖𝑛2 𝑤𝑐 𝑡 = 0.5(1 –𝑐𝑜𝑠2𝜔𝑐 𝑡 ) = 0.5 - 0.5 𝑐𝑜𝑠2𝜔𝑐 𝑡
output = + 0.5 V = logic 1
filtered out

19. Advantages and Disadvantages of BPSK:
Advantages
The bit error rate is least in case
of BPSK due to the presence of a
spacing of 2 𝐸 between the
points on the constellation
diagram
BPSK requires half the
transmission energy for the
same bit error rate as in FSK and
ASK
Disadvantages
Costly due to use of Costas
square loop or Costas PLL in
coherent demodulation
The abrupt change of phase in
time domain is an impulse
function which requires infinite
bandwidth for transmission in
frequency domain
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20. Applications of BPSK:
BPSK is widely used for wireless LANs, RFID and Bluetooth
communication
BPSK is used in radio communications due to robust BER
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21. Other types of Phase Shift Keying:
QPSK - Quadrature Phase Shift Keying
π/4-QPSK - Quadrature Phase Shift Keying
O-QPSK - Offset Quadrature Phase Shift Keying
8 PSK - 8 Point Phase Shift Keying
16 PSK - 16 Point Phase Shift Keying
QAM - Quadrature Amplitude Modulation
16 QAM - 16 Point Quadrature Amplitude Modulation
64 QAM - 64 Point Quadrature Amplitude Modulation
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22. QPSK- Quadrature Phase Shift Keying
 Four different phase states in one symbol period
 Two bits of information are transmitted in each symbol
 Twice the bandwidth efficiency of the BPSK
Phase: 0 π/2 π 3π/2 → possible phase values
Symbol: 00 01 11 10
The QPSK signal is given by, s(t) =
2Es
𝑇
cos (2π𝑓𝑐t +(i-1) π/2)
0 ≤ t ≤ T, i=1,2,3,4
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23. QPSK Constellation Diagram
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Now we have two basic functions
Es = 2 Eb since 2 bits are transmitted per symbol
I = in-phase component from sI(t).
Q = quadrature component that is sQ(t).

24. QPSK Bit Error Rate:
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BER is related to the distance between constellation points

25. π/4 -QPSK :
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 In π/4 QPSK, the maximum phase change is limited to ± 135o , as
compared to 180o for QPSK
 Hence the signal preserves the constant envelop property better
than the band limited QPSK
 This can be demodulated in a coherent or non-coherent fashion
thereby, simplifying the receiver design greatly
 In presence of multipath spread and fading, π/4 QPSK is found to
perform better

26. Constellation Diagram for π/4 QPSK:
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27. QPSK Transmission Technique:
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28. π/4 QPSK phase components:
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Ik = 𝑐𝑜𝑠θk = Ik-1 𝑐𝑜𝑠ϕk - Qk-1 𝑠𝑖𝑛ϕk
Qk = 𝑠𝑖𝑛θk = Ik-1 𝑠𝑖𝑛ϕk + Qk-1 𝑐𝑜𝑠ϕk
where,
Θk = θk -1 + ϕk
θk and θk -1 are the phases of the kth and (k-1)st symbols
The phase shift ϕk is related to the input symbols mik and mqk

29. π/4 QPSK mathematical analysis:
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The waveform is represented by:
S(t)= I(t) cos𝜔𝑐 𝑡 – Q(t) 𝑠𝑖𝑛𝜔𝑐 𝑡
where,
I 𝑡 = 𝑘=0
𝑁−1
𝐼k p(t - kTs - Ts /2) = 𝑘=0
𝑁−1
𝑐𝑜𝑠Ɵk p(t - kTs - Ts /2)
Q 𝑡 = 𝑘=0
𝑁−1
𝑄k p(t - kTs - Ts /2) = 𝑘=0
𝑁−1
𝑠𝑖𝑛Ɵk p(t - kTs - Ts /2)

30. π/4 QPSK FM Discriminator Detection
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31. Advantages of π/4- QPSK:
 Among all MPSK schemes, QPSK is the most-often-used scheme
since it does not suffer from BER degradation while the bandwidth
efficiency is increased
In the presence of the multipath spread and fading conditions, pi/4
QPSK performs the best
Signal is demodulated in coherent and non-coherent fashion and
hence the design of the receiver is simple
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32. Thank You
An efficient Telecommunications network is the
foundation
upon which an information society is built
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