Phase Shift Keying & π/4 -Quadrature Phase Shift Keying
-
Upload
naveen-jakhar-its -
Category
Education
-
view
546 -
download
4
Transcript of Phase Shift Keying & π/4 -Quadrature Phase Shift Keying
![Page 1: Phase Shift Keying & π/4 -Quadrature Phase Shift Keying](https://reader036.fdocuments.in/reader036/viewer/2022081420/58a2ed961a28abc9648b6e79/html5/thumbnails/1.jpg)
1
Phase Shift Keying & π/4 -Quadrature Phase
Shift Keying Presentation by:
Naveen Jakhar, ITS
![Page 2: Phase Shift Keying & π/4 -Quadrature Phase Shift Keying](https://reader036.fdocuments.in/reader036/viewer/2022081420/58a2ed961a28abc9648b6e79/html5/thumbnails/2.jpg)
2
Topics covered in this presentation: Some basic definitions & concepts of digital communicationWhat is Phase Shift Keying(PSK) ?Binary Phase Shift Keying – BPSKBPSK transmitter & receiverAdvantages & Disadvantages of BPSKPi/4 – QPSKPi/4 – QPSK transmitter & receiverAdvantages of Pi/4- QPSK
![Page 3: Phase Shift Keying & π/4 -Quadrature Phase Shift Keying](https://reader036.fdocuments.in/reader036/viewer/2022081420/58a2ed961a28abc9648b6e79/html5/thumbnails/3.jpg)
3
Some basic concepts of Digital Communication:Information capacity: linear function of bandwidth and transmission
time i.e. where I is information capacity(bits per second)B is bandwidth (hertz)t is transmission time (sec) Shannon limit for information capacity
Where SNR is signal to noise power ratio (unit less quantity)
![Page 4: Phase Shift Keying & π/4 -Quadrature Phase Shift Keying](https://reader036.fdocuments.in/reader036/viewer/2022081420/58a2ed961a28abc9648b6e79/html5/thumbnails/4.jpg)
4
M-ary coding:
M-ary is a term derived from binaryM 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 or where N is number of necessary bits & M is number of conditions/combinations/levels
![Page 5: Phase Shift Keying & π/4 -Quadrature Phase Shift Keying](https://reader036.fdocuments.in/reader036/viewer/2022081420/58a2ed961a28abc9648b6e79/html5/thumbnails/5.jpg)
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 occurredBaud is a unit of transmission rate, modulation rate or symbol rate where is 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,, where is the bit rate in bits per second and B is the ideal Nyquist bandwidth.
![Page 6: Phase Shift Keying & π/4 -Quadrature Phase Shift Keying](https://reader036.fdocuments.in/reader036/viewer/2022081420/58a2ed961a28abc9648b6e79/html5/thumbnails/6.jpg)
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 or =>
where is channel capacity in bits per second, B is minimum Nyquist bandwidth and M is number of discrete signal or voltage levels , so Baud is also the bit rate divided by the number of bits encoded
into one signalling element
![Page 7: Phase Shift Keying & π/4 -Quadrature Phase Shift Keying](https://reader036.fdocuments.in/reader036/viewer/2022081420/58a2ed961a28abc9648b6e79/html5/thumbnails/7.jpg)
7
Phase Shift Keying (PSK): IntroductionPSK is a digital modulation scheme which conveys data by
changing/modulating the phase of the carrier signalPhase of carrier signal is varied in proportional to the information signalThe carrier signal is also called reference signalThe modulation is done by varying sine and cosine inputs at a precise
timePSK is often called angle modulated constant amplitude digital
modulationSimplest form of PSK is Binary phase shift keying (BPSK)
![Page 8: Phase Shift Keying & π/4 -Quadrature Phase Shift Keying](https://reader036.fdocuments.in/reader036/viewer/2022081420/58a2ed961a28abc9648b6e79/html5/thumbnails/8.jpg)
8
Binary Phase Shift Keying (BPSK):BPSK has values of N=1 and M=2, so two phases for the carrier are
possibleOne 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°
![Page 9: Phase Shift Keying & π/4 -Quadrature Phase Shift Keying](https://reader036.fdocuments.in/reader036/viewer/2022081420/58a2ed961a28abc9648b6e79/html5/thumbnails/9.jpg)
9
Binary Phase Shift Keying (BPSK): continued ….. Any carrier signal is s(t) = A cos (2πt +θ) where θ is the phaseFor BPSK, we have θ=0 or θ=π, separated by 180 degreesSo, the BPSK signals become A m(t)cos (2πt +θ) 0 ≤ t ≤ T, for 1 and 0 ≤ t ≤ T, for 0where A is a constant, is the carrier frequency and T is the bit duration The signal has a power means
![Page 10: Phase Shift Keying & π/4 -Quadrature Phase Shift Keying](https://reader036.fdocuments.in/reader036/viewer/2022081420/58a2ed961a28abc9648b6e79/html5/thumbnails/10.jpg)
10
Binary Phase Shift Keying (BPSK): continued …..So, the signals becomes where E=P*T is the energy contained in a bit duration. are the orthonormal functions with unit energy in a bit
duration
![Page 11: Phase Shift Keying & π/4 -Quadrature Phase Shift Keying](https://reader036.fdocuments.in/reader036/viewer/2022081420/58a2ed961a28abc9648b6e79/html5/thumbnails/11.jpg)
11
BPSK Constellation Diagram Constellation points are drawn on a 2 dimensional complex co-ordinate system 0 ≤ t ≤ T 0 ≤ t ≤ T
![Page 12: Phase Shift Keying & π/4 -Quadrature Phase Shift Keying](https://reader036.fdocuments.in/reader036/viewer/2022081420/58a2ed961a28abc9648b6e79/html5/thumbnails/12.jpg)
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)
signalImportant components of a BPSK transmitter are : Balanced
modulator, level converter, Band pass filter and Reference Carrier Oscillator
Balanced modulator acts as a phase reversing switchAnother name of Balanced modulator is Balanced Ring modulator
![Page 13: Phase Shift Keying & π/4 -Quadrature Phase Shift Keying](https://reader036.fdocuments.in/reader036/viewer/2022081420/58a2ed961a28abc9648b6e79/html5/thumbnails/13.jpg)
13
BPSK transmitter diagram:
![Page 14: Phase Shift Keying & π/4 -Quadrature Phase Shift Keying](https://reader036.fdocuments.in/reader036/viewer/2022081420/58a2ed961a28abc9648b6e79/html5/thumbnails/14.jpg)
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 dataFor the balanced modulator to operate properly, the digital input
voltage must be much greater than the peak carrier voltage
![Page 15: Phase Shift Keying & π/4 -Quadrature Phase Shift Keying](https://reader036.fdocuments.in/reader036/viewer/2022081420/58a2ed961a28abc9648b6e79/html5/thumbnails/15.jpg)
15
BPSK Balanced Ring Modulator Function: When the binary input logic is 1 When the binary input logic is 0
![Page 16: Phase Shift Keying & π/4 -Quadrature Phase Shift Keying](https://reader036.fdocuments.in/reader036/viewer/2022081420/58a2ed961a28abc9648b6e79/html5/thumbnails/16.jpg)
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
![Page 17: Phase Shift Keying & π/4 -Quadrature Phase Shift Keying](https://reader036.fdocuments.in/reader036/viewer/2022081420/58a2ed961a28abc9648b6e79/html5/thumbnails/17.jpg)
17
BPSK Receiver: Input signal to receiver maybe + or - 𝑡 𝑡The 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
![Page 18: Phase Shift Keying & π/4 -Quadrature Phase Shift Keying](https://reader036.fdocuments.in/reader036/viewer/2022081420/58a2ed961a28abc9648b6e79/html5/thumbnails/18.jpg)
18
BPSK Receiver output: For a BPSK input signal of + (logic 1), the output of the balanced 𝑡
modulator is:output = ( )( ) = 𝑡 𝑡Now = 0.5(1 – 𝑡 ) = 0.5 - 0.5 𝑡output = + 0.5 V = logic 1 filtered out
![Page 19: Phase Shift Keying & π/4 -Quadrature Phase Shift Keying](https://reader036.fdocuments.in/reader036/viewer/2022081420/58a2ed961a28abc9648b6e79/html5/thumbnails/19.jpg)
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 between the points on the constellation diagram
BPSK requires half the transmission energy for the same bit error rate as in FSK and ASK
DisadvantagesCostly 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
![Page 20: Phase Shift Keying & π/4 -Quadrature Phase Shift Keying](https://reader036.fdocuments.in/reader036/viewer/2022081420/58a2ed961a28abc9648b6e79/html5/thumbnails/20.jpg)
20
Applications of BPSK: BPSK is widely used for wireless LANs, RFID and Bluetooth
communicationBPSK is used in radio communications due to robust BER
![Page 21: Phase Shift Keying & π/4 -Quadrature Phase Shift Keying](https://reader036.fdocuments.in/reader036/viewer/2022081420/58a2ed961a28abc9648b6e79/html5/thumbnails/21.jpg)
21
Other types of Phase Shift Keying: QPSK - Quadrature Phase Shift Keying π/4-QPSK - Quadrature Phase Shift KeyingO-QPSK - Offset Quadrature Phase Shift Keying8 PSK - 8 Point Phase Shift Keying16 PSK - 16 Point Phase Shift KeyingQAM - Quadrature Amplitude Modulation16 QAM - 16 Point Quadrature Amplitude Modulation64 QAM - 64 Point Quadrature Amplitude Modulation
![Page 22: Phase Shift Keying & π/4 -Quadrature Phase Shift Keying](https://reader036.fdocuments.in/reader036/viewer/2022081420/58a2ed961a28abc9648b6e79/html5/thumbnails/22.jpg)
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 valuesSymbol: 00 01 11 10
The QPSK signal is given by, s(t) = cos (2πt +(i-1) π/2) 0 ≤ t ≤ T, i=1,2,3,4
![Page 23: Phase Shift Keying & π/4 -Quadrature Phase Shift Keying](https://reader036.fdocuments.in/reader036/viewer/2022081420/58a2ed961a28abc9648b6e79/html5/thumbnails/23.jpg)
23
QPSK Constellation Diagram
Now we have two basic functionsEs = 2 Eb since 2 bits are transmitted per symbolI = in-phase component from sI(t).Q = quadrature component that is sQ(t).
![Page 24: Phase Shift Keying & π/4 -Quadrature Phase Shift Keying](https://reader036.fdocuments.in/reader036/viewer/2022081420/58a2ed961a28abc9648b6e79/html5/thumbnails/24.jpg)
24
QPSK Bit Error Rate: BER is related to the distance between constellation points
![Page 25: Phase Shift Keying & π/4 -Quadrature Phase Shift Keying](https://reader036.fdocuments.in/reader036/viewer/2022081420/58a2ed961a28abc9648b6e79/html5/thumbnails/25.jpg)
25
π/4 -QPSK : 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
![Page 26: Phase Shift Keying & π/4 -Quadrature Phase Shift Keying](https://reader036.fdocuments.in/reader036/viewer/2022081420/58a2ed961a28abc9648b6e79/html5/thumbnails/26.jpg)
26
Constellation Diagram for π/4 QPSK:
![Page 27: Phase Shift Keying & π/4 -Quadrature Phase Shift Keying](https://reader036.fdocuments.in/reader036/viewer/2022081420/58a2ed961a28abc9648b6e79/html5/thumbnails/27.jpg)
27
QPSK Transmission Technique:
![Page 28: Phase Shift Keying & π/4 -Quadrature Phase Shift Keying](https://reader036.fdocuments.in/reader036/viewer/2022081420/58a2ed961a28abc9648b6e79/html5/thumbnails/28.jpg)
28
π/4 QPSK phase components: Ik k = Ik-1 k - Qk-1 k
Qk k = Ik-1 k + Qk-1 k
where,
k = k -1 + k
k and k -1 are the phases of the kth and (k-1)st symbolsThe phase shift k is related to the input symbols mik and mqk
![Page 29: Phase Shift Keying & π/4 -Quadrature Phase Shift Keying](https://reader036.fdocuments.in/reader036/viewer/2022081420/58a2ed961a28abc9648b6e79/html5/thumbnails/29.jpg)
29
π/4 QPSK mathematical analysis: The waveform is represented by:
S(t)= I(t) cos – Q(t) 𝑡 𝑡where,Ik p(t - kTs - Ts /2) = k p(t - kTs - Ts /2) Qk p(t - kTs - Ts /2) = k p(t - kTs - Ts /2)
![Page 30: Phase Shift Keying & π/4 -Quadrature Phase Shift Keying](https://reader036.fdocuments.in/reader036/viewer/2022081420/58a2ed961a28abc9648b6e79/html5/thumbnails/30.jpg)
30
π/4 QPSK FM Discriminator Detection
![Page 31: Phase Shift Keying & π/4 -Quadrature Phase Shift Keying](https://reader036.fdocuments.in/reader036/viewer/2022081420/58a2ed961a28abc9648b6e79/html5/thumbnails/31.jpg)
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
![Page 32: Phase Shift Keying & π/4 -Quadrature Phase Shift Keying](https://reader036.fdocuments.in/reader036/viewer/2022081420/58a2ed961a28abc9648b6e79/html5/thumbnails/32.jpg)
32
Thank YouAn efficient Telecommunications network is the
foundation upon which an information society is built