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Basel Rihawi - Influence des canaux Gaussien et de Rayleigh sur la distribution du PAPR dans les systèmes MIMO-OFDM

SCEE Team
March 01, 2007

Basel Rihawi - Influence des canaux Gaussien et de Rayleigh sur la distribution du PAPR dans les systèmes MIMO-OFDM

SCEE Team

March 01, 2007
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  1. TITRE
    Séminaire SCEE jeudi 1 mars
    Influence des canaux Gaussien et de Rayleigh
    sur la distribution du PAPR dans les
    systèmes MIMO-OFDM
    Basel RIHAWI
    IETR
    Supélec, Équipe SCEE
    Jeudi 1 Mars 2007 – Séminaire SCEE

    View Slide

  2. TITRE
    Séminaire SCEE jeudi 1 mars
    2
    Introduction
    ¾ MIMO-OFDM is one of the technologies in the fourth generation
    wireless communication
    9 It provides a significant capacity gain in wireless channels
    9 High spectral efficiency
    9 Robustness against frequency-selective fading channel
    ¾ MIMO-OFDM system takes advantage of both OFDM technology
    and spatial diversity obtained by STBC

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  3. TITRE
    Séminaire SCEE jeudi 1 mars
    ¾ One key drawback of OFDM is its large PAPR which is a measure
    of the amplitude fluctuations of the signal
    ¾ Instantaneous power of transmitted signal will exhibit large peaks
    when subcarriers have phases that constructively align at certain
    instants of time
    ¾ The large PAPR make it difficult to pass thru the PA and LNA
    ¾ Peaks can saturate the amplifier resulting in clipping of signal peaks
    and distortion in signal
    Introduction
    3

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  4. TITRE
    Séminaire SCEE jeudi 1 mars
    Outline
    9 OFDM signal and PAPR definitions
    9 System Model
    9 PAPR Analysis in MIMO-OFDM-AWGN Channel
    9 PAPR Analysis in flat Rayleigh fading channel
    9The flat Rayleigh fading channel model
    9SISO-OFDM case
    9MIMO-OFDM case
    9 Conclusions
    OUTLINE
    4

    View Slide

  5. TITRE
    Séminaire SCEE jeudi 1 mars
    9 OFDM signal and PAPR definitions
    9 System Model
    9 PAPR Analysis in MIMO-OFDM-AWGN Channel
    9 PAPR Analysis in flat Rayleigh fading channel
    9The flat Rayleigh fading channel model
    9SISO-OFDM case
    9MIMO-OFDM case
    9 Conclusions
    OUTLINE
    Outline

    View Slide

  6. TITRE
    Séminaire SCEE jeudi 1 mars
    OFDM signal and PAPR definitions
    5
    ¾ Analog OFDM complex envelope
    ¾ Real transmitted signal
    ¾ The baseband modulation is done in the digital domain using an
    oversampled version of given by

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  7. TITRE
    Séminaire SCEE jeudi 1 mars
    6
    OFDM signal and PAPR definitions
    ¾ Complex time-domain samples of the OFDM signal are approximately Gaussian
    distributed due to the statistical independence of carriers (central-limit theorem).
    This means that there can be some very high peaks present in the signal those can
    be quantified by the PAPR (for signals RF) which is defined by
    ¾ In a classical OFDM context, the CCDF of PAPR of the sampled baseband signal
    is approximately given by
    ¾ To evaluate the PAPR from a statistical point of view, the complementary cumulative
    distribution function (CCDF) of PAPR is used to quantify the probability of exceeding a
    given threshold . It is defined by
    this last equation is a very good approximation of the PAPR distribution of
    but differs as much as one dB from the PAPR distribution of

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  8. TITRE
    Séminaire SCEE jeudi 1 mars
    7
    OFDM signal and PAPR definitions
    ¾ One of the attempts to determine the PAPR distribution of
    came from [1]
    The 2.8 value has been obtained by simulations, where the PAPR
    of approaches the PAPR of for large L. In practice L=4
    is enough to detect the presence of continuous-time peaks with
    satisfactory precision.
    [1] R. Van Nee and A. de Wild, "Reducing the peak-to-average power ratio of OFDM,"
    Proc. IEEE Vehicular Technology Conference, vol. 3, pp. 2072-2076, 1998.

    View Slide

  9. TITRE
    Séminaire SCEE jeudi 1 mars
    9 OFDM signal and PAPR definitions
    9 System Model
    9 PAPR Analysis in MIMO-OFDM-AWGN Channel
    9 PAPR Analysis in flat Rayleigh fading channel
    9The flat Rayleigh fading channel model
    9SISO-OFDM case
    9MIMO-OFDM case
    9 Conclusions
    OUTLINE
    Outline

    View Slide

  10. TITRE
    Séminaire SCEE jeudi 1 mars
    System Model
    ‰ MIMO-OFDM systems based on Alamouti diversity scheme
    ¾The Alamouti space-Time coding MIMO :
    8
    ¾ the computation of the CCDF of the PAPR at the receiver is
    considered and is approximated using a discrete-time CCDF, which is
    obtained from the samples of the received signal.
    OFDM
    Modulator
    data
    mapping space–time
    encoder
    DAC
    DAC
    HPA LNA
    LNA
    OFDM
    Modulator
    DAC
    DAC
    HPA
    MIMO
    channel

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  11. TITRE
    Séminaire SCEE jeudi 1 mars
    ¾ why we use this discrete-time approach for CCDF computation :
    9
    ƒ the simulation tools are implemented in discrete-time,
    ƒ computation in continuous-time is too complex as closed-form expression,
    ƒ when an oversampling rate of four times the Nyquist rate is used, it closely
    approximates continuous-time CCDF of the PAPR.
    ¾ The signal at one of the transmitting antenna is :
    Each discrete-time sample of the transmitted signals and follows a
    Gaussian law with zero mean and variance .
    System Model
    ¾ Their pdf is of the form :

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  12. TITRE
    Séminaire SCEE jeudi 1 mars
    9 OFDM signal and PAPR definitions
    9 System Model
    9 PAPR Analysis in MIMO-OFDM-AWGN Channel
    9 PAPR Analysis in flat Rayleigh fading channel
    9The flat Rayleigh fading channel model
    9SISO-OFDM case
    9MIMO-OFDM case
    9 Conclusions
    OUTLINE
    Outline

    View Slide

  13. TITRE
    Séminaire SCEE jeudi 1 mars
    PAPR Analysis in MIMO-OFDM-AWGN Channel
    ¾The received signal is :
    10
    ¾ By considering the pdf of any sample of is then :
    ¾Then, we can obtain the cumulative distribution function of
    by integrating (1) as

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  14. TITRE
    Séminaire SCEE jeudi 1 mars
    ¾ Then, the CCDF of the PAPR of the continuous received signal is
    approximately given by
    11
    PAPR Analysis in MIMO-OFDM-AWGN Channel
    This result can be generalized : in a Gaussian channel context and for MIMO-OFDM
    systems, the transmitted and received signals at each of transmitting and receiving
    antennas respectively all follow Gaussian laws. The consequence is that the Gaussian
    channel does not influence the PAPR distribution of the received signals, whatever the
    signal to noise ratio value is.
    CCDFs of the PAPR of RF received signal .
    These curves are obtained by the simulation
    of 10^5 symbols with N=1024 subcarriers
    modulated with a 4-QAM. The signal-to-
    noise ratio is equal to 10dB. We set the
    oversampling factor L=4.

    View Slide

  15. TITRE
    Séminaire SCEE jeudi 1 mars
    9 OFDM signal and PAPR definitions
    9 System Model
    9 PAPR Analysis in MIMO-OFDM-AWGN Channel
    9 PAPR Analysis in flat Rayleigh fading channel
    9The flat Rayleigh fading channel model
    9SISO-OFDM case
    9MIMO-OFDM case
    9 Conclusions
    OUTLINE
    Outline

    View Slide

  16. TITRE
    Séminaire SCEE jeudi 1 mars
    PAPR Analysis in flat Rayleigh fading channel
    ‰ The flat Rayleigh fading channel model
    ¾ On a flat Rayleigh fading channel, all signal frequencies are attenuated by the same
    factor. For any discrete-time sample, the received signal can be written as :
    ‰ SISO-OFDM case
    data
    mapping OFDM
    modulator
    Rayleigh
    Channel
    HPA
    LO
    LNA
    DAC
    12

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  17. TITRE
    Séminaire SCEE jeudi 1 mars
    ¾The pdf of
    After development, we find
    ¾The distribution function of is then expressed as :
    PAPR Analysis in flat Rayleigh fading channel
    13

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  18. TITRE
    Séminaire SCEE jeudi 1 mars
    ¾Considering then we obtain
    denotes the complementary error function
    ¾Thanks to the independence of the N samples, the probability that none of them
    exceeds can be simplified as :
    PAPR Analysis in flat Rayleigh fading channel
    14

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  19. TITRE
    Séminaire SCEE jeudi 1 mars
    ¾Then, the CCDF of the PAPR of the continuous received signal can be
    approximated by
    PAPR Analysis in flat Rayleigh fading channel
    15

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  20. TITRE
    Séminaire SCEE jeudi 1 mars
    ¾CCDFs of the PAPR of received signal in the case of AWGN channel. These
    curves are obtained by the simulation of 10^5 symbols with N=1024 subcarriers
    modulated with a 4-QAM. SNR=10dB. L=4. RF, SISO
    PAPR Analysis in flat Rayleigh fading channel
    16

    View Slide

  21. TITRE
    Séminaire SCEE jeudi 1 mars
    ‰ MIMO-OFDM case
    ¾Now, we analyze the CCDF of the PAPR of the signal in a two-antenna
    MIMO-OFDM system . From the figure (MIMO-OFDM), a received sample of
    the signal can be expressed as :
    ¾The pdf of can be written as :
    17
    PAPR Analysis in flat Rayleigh fading channel

    View Slide

  22. TITRE
    Séminaire SCEE jeudi 1 mars
    ¾The CCDF of the PAPR of the continuous signal in the case of
    can be approximated by :
    18
    PAPR Analysis in flat Rayleigh fading channel

    View Slide

  23. TITRE
    Séminaire SCEE jeudi 1 mars
    ¾The CCDF of the PAPR of the continuous signal in the case of
    can be approximated by :
    19
    PAPR Analysis in flat Rayleigh fading channel

    View Slide

  24. TITRE
    Séminaire SCEE jeudi 1 mars
    20
    PAPR Analysis in flat Rayleigh fading channel
    ¾CCDFs of the PAPR of the received signal in SISO, MIMO(2,2)
    and MIMO(4,4) (flat Rayleigh fading channel), SNR=10dB

    View Slide

  25. TITRE
    Séminaire SCEE jeudi 1 mars
    21
    PAPR Analysis in flat Rayleigh fading channel
    ¾Comparisons of the CCDFs of the PAPR (theoretical and
    simulation) of the received signal in MIMO(2,2) (flat Rayleigh fading
    channel) for several values of SNR

    View Slide

  26. TITRE
    Séminaire SCEE jeudi 1 mars
    9 OFDM signal and PAPR definitions
    9 System Model
    9 PAPR Analysis in MIMO-OFDM-AWGN Channel
    9 PAPR Analysis in flat Rayleigh fading channel
    9The flat Rayleigh fading channel model
    9SISO-OFDM case
    9MIMO-OFDM case
    9 Conclusions
    OUTLINE
    Outline

    View Slide

  27. TITRE
    Séminaire SCEE jeudi 1 mars
    Conclusions
    ‰ The influence of AWGN and flat Rayleigh fading channel
    on the PAPR distribution in MIMO-OFDM systems has been
    analyzed
    22
    ‰ The received signal at any receiving antenna of MIMO-OFDM
    systems have a PAPR distribution equal to that of transmitted
    signals in the case of Gaussian channel
    ‰ In the flat Rayleigh fading channel, the PAPR is more than
    that of the Gaussian channel
    ‰ The PAPR in MIMO-OFDM is less than that in SISO-OFDM
    systems, and it decreases with the number of transmitting
    antennas in the case of flat Rayleigh fading channel

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  28. TITRE
    Séminaire SCEE jeudi 1 mars

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