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    Quadrature Amplitude Modulation (QAM)

    Uploaded by

    Fahad Rizwan
    This document describes the implementation of a QAM transmitter and demodulator. A QAM transmitter takes two PAM signals, shifts them to the same carrier frequency with a 90 degree phase offset, and sums them. A QAM demodulator recovers the transmitted symbols by using a Hilbert transform filter to generate the complex envelope, then downconverting with the carrier. Carrier offset causes rotation of the QAM constellation rather than just scaling as with PAM.

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    Attribution Non-Commercial (BY-NC)
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    Quadrature Amplitude Modulation (QAM)

    Uploaded by

    Fahad Rizwan
    123 views17 pages
    This document describes the implementation of a QAM transmitter and demodulator. A QAM transmitter takes two PAM signals, shifts them to the same carrier frequency with a 90 degree phase offset, and sums them. A QAM demodulator recovers the transmitted symbols by using a Hilbert transform filter to generate the complex envelope, then downconverting with the carrier. Carrier offset causes rotation of the QAM constellation rather than just scaling as with PAM.

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    Lecture q Am

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    This document describes the implementation of a QAM transmitter and demodulator. A QAM transmitter takes two PAM signals, shifts them to the same carrier frequency with a 90 degree phase offset, and sums them. A QAM demodulator recovers the transmitted symbols by using a Hilbert transform filter to generate the complex envelope, then downconverting with the carrier. Carrier offset causes rotation of the QAM constellation rather than just scaling as with PAM.

    Copyright:

    Attribution Non-Commercial (BY-NC)
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    123 views17 pages

    Quadrature Amplitude Modulation (QAM)

    Uploaded by

    Fahad Rizwan
    This document describes the implementation of a QAM transmitter and demodulator. A QAM transmitter takes two PAM signals, shifts them to the same carrier frequency with a 90 degree phase offset, and sums them. A QAM demodulator recovers the transmitted symbols by using a Hilbert transform filter to generate the complex envelope, then downconverting with the carrier. Carrier offset causes rotation of the QAM constellation rather than just scaling as with PAM.

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    Quadrature Amplitude Modulation (QAM) PAM signals occupy twice the bandwidth required for the baseband Transmit

    two PAM signals using carriers of the same frequency but in phase and quadrature

    Demodulation:

    QAM Transmitter Implementation


    QAM is widely used method for transmitting digital data over bandpass channels A basic QAM transmitter Inphase component
    an dn 1
    Impulse Modulator

    a*(t)

    Serial to Parallel

    Map to Constellation Point

    Pulse Shaping Filter

    a(t)

    +
    sin wct s(t)

    gT(t)
    Impulse Modulator

    b*(t)

    bn

    Pulse Shaping Filter

    b(t)

    quadrature component

    gT(t)

    cos wct

    Using complex notation


    s (t ) = a (t ) cos wc t b(t )sin wc t s + (t ) =

    s (t ) = {s+ (t )} which is the preenvelope of QAM


    jwc t

    (ak + jbk )gT (t kT )e

    s + (t ) =

    (ck e jwc kT ) gT (t kT )e jwc (t kT )

    Complex Symbols
    Quadriphase-Shift Keying (QPSK)
    4-QAM Transmitted signal is contained in the phase
    imaginary imaginary

    real

    real

    M-ary PSK
    QPSK is a special case of M-ary PSK, where the phase of the carrier takes on one of M possible values
    imaginary

    real

    Pulse Shaping Filters


    The real pulse shaping filter response Let where This filter is a bandpass filter with the frequency response

    gT (t )
    h(t ) = gT (t )e jwc t = hI (t ) + jhQ (t )
    hI (t ) = gT (t ) cos wc t hQ (t ) = gT (t )sin wc t

    H ( w) = GT ( w wc )

    Transmitted Sequences
    Modulated sequences before passband shaping
    ' ak = {ck e jwc kT } = ak cos wc kT bk sin wc kT

    bk' = {ck e jwc kT } = ak sin wc kT + bk cos wc kT


    Using these definitions

    s (t ) = {s+ (t )} =

    k =

    a hI (t kT ) b h (t kT )
    ' k ' k Q

    Advantage: computational savings

    Ideal QAM Demodulation


    Exact knowledge of the carrier and symbol clock phases and frequencies Apply the Hilbert Transform of the received signal to generate the pre-envelope s+(t)

    s(t ) = s+ (t )e jwc t =

    k =

    (ak + jbk ) gT (t kT )

    If gT(t) has no intersymbol interference, we get exactly the transmitted symbol

    s (nT ) = an + jbn

    QAM Demodulation
    QAM demodulator using the complex envelope
    e-jwct
    s(t)

    Receive Filter

    Hilbert Transform Filter

    Second Method
    Based on a pair of DSBSC-AM coherent demodulators a(t)
    LPF s(t) 2coswct LPF -2sinwct b(t)

    In DSP implementations, Hilbert transform method is popular because


    It only requires single filter 2wc terms are automatically cancelled

    QAM Front-End Subsystems


    Automatic gain control
    Full scale usage of A/D and avoid clipping No need to implement AGC in your project

    The Carrier detect subsystem


    Determine if a QAM signal is present at the receiver This power estimate can be easily formed by averaging the squared ADC output samples r(n):

    You can select c as a number slightly less than 1, i.e, 0.9. When the power estimate p(n) exceeds a predetermined threshold for a period of time, a received QAM signal is declared to be present.

    Carrier Detect
    Determine a threshold value by inspecting your power estimate. The following figure shows the portion of received QAM signal and the power estimate average.

    Frame Synchronization
    Assume that the receiver knows marker symbols (say, 10 complex symbols, m(n)) Assume that s(k) is the output of your QAM demodulator. Note that s(k) and m(n) are complex. Of course, in DSP you define complex numbers by keeping real and imaginary parts in different buffers.

    Frame Synchronization
    Correlation, Peak=

    Peakindex=max(abs(Peak)) Note that Peak is complex quantity

    Initial Phase Correction


    Defining ej=peak/abs(peak), then, the phase shift on s(n) which is the output of QAM demodulator can be corrected as x(k)=s(index+k-1)e-j

    Switch to QAM Modulation


    You can proceed with hilbert transform filtering and complex downconversion by setting your receiver pointer to the beginning of your input buffer. First the receiver is on and transmitter is off Transmitter starts with marker and PN sequence, both complex When transmitter starts, carrier detect will switch to QAM downconversion

    Carrier Offset Impairment for QAM


    Received QAM signal After Hilbert transform, we can form Complex demodulator ej2fct+j) Obtain m1(t) as the real part

    Carrier Offset Impairment for QAM


    For PAM signaling carrier offset causes scaling with cosine of the phase offset For QAM signaling carrier offset causes rotation of the constellation by the carrier offset
    -

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