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Phase Shift Keying & π/4 -Quadrature Phase Shift Keying

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Phase Shift Keying & π/4 -Quadrature Phase Shift Keying Presentation by: Naveen Jakhar, ITS 1
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Page 1: Phase Shift Keying & π/4 -Quadrature Phase Shift Keying

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Phase Shift Keying & π/4 -Quadrature Phase

Shift Keying Presentation by:

Naveen Jakhar, ITS

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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

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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)

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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

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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.

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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

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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)

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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°

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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

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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

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BPSK Constellation Diagram Constellation points are drawn on a 2 dimensional complex co-ordinate system 0 ≤ t ≤ T 0 ≤ t ≤ T

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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

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BPSK transmitter diagram:

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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

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BPSK Balanced Ring Modulator Function: When the binary input logic is 1 When the binary input logic is 0

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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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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

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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

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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

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Applications of BPSK: BPSK is widely used for wireless LANs, RFID and Bluetooth

communicationBPSK is used in radio communications due to robust BER

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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

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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

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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).

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

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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

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Constellation Diagram for π/4 QPSK:

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QPSK Transmission Technique:

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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

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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)

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π/4 QPSK FM Discriminator Detection

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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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Thank YouAn efficient Telecommunications network is the

foundation upon which an information society is built


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