Chapter 5 Digital Modulation Systems Multilevel Modulated Bandpass Signalling Representation in the I-Q Plane MPSK and QPSK QAM PSD of MPSK, QPSK and QAM Huseyin Bilgekul EEE 461 Communication Systems II Department of Electrical and Electronic Engineering Eastern Mediterranean University

Digital Modulation Carrier signal: Ac cos (2pfct + θ) Modulation: m(t) Modulated signal: Ac (t) cos (2pfc(t) t + θ(t))  m(t); discrete Vary Vary amplitude frequency & phase Variations are discrete!!!!! Binary OOK BPSK DPSK FSK Multilevel QPSK MPSK QAM

Multilevel Modulated Bandpass Signaling Digital inputs with more than two levels are allowed on the transmitter output Multilevel Digital Transmission System Digital-to- analog converter l bits Transmitter Binary input R bits/sec M=2l – level multilevel signal Modulated output Multilevel signals can be generated by using a digital to analog converter (DAC). Multilevel signaling reduces the bandwidth requirement.

Signal Vector Representation s(t) = Ac(t) cos (2pfct + θ(t)) Q fixed!!! θ = 90 S t = t Magnitude Phase t = 0 0 degrees I θ = 0 I-Q Plane

Signal Changes: Representation in the I-Q plane Magnitude Change Phase Change S2 Q Q S1 S1 S2 I I I-Q Diagrams or Constellations S1 S2 I Q Magnitude & Phase Changes

M-ary Phase Shift Keying If the transmitter is a PM transmitter with an M-level digital modulation signal, M-ary phase-shift keying (MPSK) is generated The complex envelope is given by The phase θ(t) is permitted to have only ‘M’ values 4 level M-ary signaling Binary Seq. DAC Value PSK Phases 00 -3V 01 -1V 900 10 +1V 1800 11 +3V 2700 When M=4, the resulting signal is called Quadrature Phase Shift Keying (QPSK)

Quadrature Phase Shift Keying (QPSK) θ g(t) Imaginary (Quadrature) Real (In phase) θi g(t) Imaginary (Quadrature) (In phase) Real π/4 -QPSK QPSK

M-ary Phase Shift Keying MPSK signal can also be generated using two quadrature carriers modulated by the x and y components of the complex envelope Where the permitted values of x and y are for the permitted phase angles θi , I = 1, 2, … M

QPSK signal

π/4 - QPSK signal p/4 Ts 0 0 0 1 1 0 1 1 Binary sequence 0 0 0 1 1 0 1 1 Binary sequence 4 – psk signal I Q 10 11 00 01 p/4 Gray Code

M-ary Phase Shift Keying (MPSK) Q I Octophase I-Q Constellation MPSK signal constellation (permitted values of the complex envelope)

Quadrature Amplitude Modulation (QAM) QAM signal constellations are not restricted to having signaling points only on the circle of radius Ac (This is unlike M-PSK) The general QAM signal Where the complex envelope is With and where (xn,yn) denotes one of the permitted values of (xi,yi) during the symbol time that is centered on

Quadrature Amplitude Modulation (QAM) I-Q Constellation 16 symbol QAM constellation (four symbols per dimension)

OPSK & π/4 QPSK Offset Quadrature Phase-Shift Keying (OQPSK) is M=4 PSK in which allowed data transition times for the I and Q components are offset by a ½ symbol period A π/4 Quadrature Phase-shift Keying (π/4 QPSK) signal is generated by alternating between two QPSK constellations that are rotated by π/4 with respect to each other

PSD for MPSK, QAM, OQPSK, and π/4 QPSK The complex envelope is given by The rectangular symbol pulse Ts – Symbol period Baud rate And its fourier transform where PSD for the complex envelope of MPSK or QAM is where C – variance of cn

PSD for complex envelope of MPSK, QAM Observations : The PSD of MPSK or QAM is obtained by translating the PSD to the carrier frequency For l =1  PSD for BPSK For l =2  PSD for QPSK, OQPSK … PSD for complex envelope of the bandpass multilevel signal is same as the PSD of baseband multilevel signals

llustrating the Gray encoding of the four quadrants and dibits in each quadrant for the V.32 modem. The dashed arrows illustrate the 90° rotational invariance.

(a) Signal constellation of V. 32 modem using nonredundant coding (a) Signal constellation of V.32 modem using nonredundant coding. (b) Signal constellation of V.32 modem using trellis coding.

Quarter-superconstellation of V. 34 modem with 240 signal points Quarter-superconstellation of V.34 modem with 240 signal points. The full superconstellation is obtained by combining the rotated versions of these points by 0, 90, 180, and 270 degrees. (Taken from Forney et al., 1996)

Decision Regions * * QPSK BPSK Imag Imag A Real A Real x x x x x * x * A x x Real x Received signal points without error Transmitted signal point Received signal points with error

Decision Regions and Noise Effects What if the noise is not symmetric? Adds a bias onto the signals Asymmetric distribution Decision surface moves over Imag x x x x p(n) A Real x Noise Amplitude

QAM Decision Regions Sketch the decision regions for QAM16 Assume uniform noise Assume that you sent a “1101” symbol, what range should the in-phase and quadrature components be in? What do you decide if: (1.9,-1) is received? (2.1,-1) is received due to noise?