2 Modulation

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  • Modulation

    Evan Everett and Michael WuELEC 433 - Spring 2013

  • Questions from Lab 1?

  • Modulation

    Goal: overlay data onto carrier signal (sinusoid)

    Sinusoids have two very accessible parameters

    Modulate amplitude and phase

    x(t) = A sin(t + )

    DataModulation

    Carrier

    10100

  • Modulation

    Goal: overlay data onto carrier signal (sinusoid)

    Sinusoids have two very accessible parameters

    Modulate amplitude and phase

    DataModulation

    10100

    Why not? 1) Interference avoidance2) High freq small antennas

  • Signal Representation: Phasor

    Polar : Amplitude & Phase

    Rectangular : In-phase (I) & Quadrature (Q)

    Phase

    Amplitude

    0

    /2

    -/2

    I Re[x]

    QIm[x]

    x(t) = A sin(t + ) x(t) = I cos(t) +Q sin(t)

    I = A sin() Q = A cos()

  • Signal Representation

    Rectangular (I,Q) form suggests a practical implementation

    cos(t)

    sin(t)

    I

    Q

    90

    I cos(t) +Q sin(t)

    I Re[x]

    QIm[x]

    Modulation = mapping data bits to (I,Q) values

    10100

  • Digital Modulation

    Maps bits to complex values (I/Q) (focus of the Lab 3)

    Complex modulated values are called symbols

    Set of symbols is called constellation or alphabet

    # of symbols in constellation is modulation order, M

    M-order constellation can encode ______ bits per symbol

    [10][01]

    [11][00]

  • Digital Modulation

    Maps bits to complex values (I/Q) (focus of the Lab 2)

    Complex modulated values are called symbols

    Set of symbols is called constellation or alphabet

    # of symbols in constellation is modulation order, M

    M-order constellation can encode log2(M) bits per symbol

    [10][01]

    [11][00]

  • Phase Shift Keying (PSK)

    Encodes information only in phase

    Constant power envelope

    Pros: no need to recover amplitude, no need for linear amplifier

    Con: wastes amplitude dimension

    BPSK (M =2) QPSK (M =4) 8-PSK (M =8)

    [1][0]

    [01][00]

    [11][10]

    [000][001]

  • Encodes information in both amplitude and phase

    (I,Q) grid

    Quadrature Amplitude Modulation (QAM)

    M

    M

    4-QAM 16-QAM 64-QAM

    802.11b 802.11g/n 802.11ac

    16-QAM 64-QAM 256-QAM

    Common in wideband systems:

  • Bit-to-Symbol Mapping Confusing with neighbor is most likely error

    Best to minimize bit-difference between neighbors

    Gray Coding

    Neighboring symbols differ by only one bit

    Extra performance at zero cost (this is rare!)

    [10][01]

    [11][00]

    [11][01]

    [10][00]

    Natural-codedQPSK

    Gray-codedQPSK

  • Tradeoff: Rate vs. Error Probability

    By increasing modulation order, M, we get:

    More data in same bandwidth :)

    Lower noise tolerance (i.e. higher error probability) :(

    Therefore, SNR dictates feasible constellation size

  • QPSK: 2 bits/symbol

    I

    Q

  • QPSK: 2 bits/symbol

    I

    Q

  • 16-QAM: 4 bits/symbol

    I

    Q

  • 64-QAM: 6 bits/symbol

    I

    Q

  • 1E-09

    1E-08

    1E-07

    1E-06

    1E-05

    1E-04

    1E-03

    1E-02

    1E-01

    1E+00

    0 2 4 6 8 10 12 14 16 18

    BER

    BPSKQPSK8-PSK16-QAM64-QAM

    Eb/N0 (dB)

    Bit error rate (BER) vs. SNR per bit (Eb/N0)