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

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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

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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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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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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

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9 System Model
9SISO-OFDM case
9MIMO-OFDM case
9 Conclusions
OUTLINE
Outline

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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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6
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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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.

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9 System Model
9SISO-OFDM case
9MIMO-OFDM case
9 Conclusions
OUTLINE
Outline

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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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¾ why we use this discrete-time approach for CCDF computation :
9
the simulation tools are implemented in discrete-time,
computation in continuous-time is too complex as closed-form expression,
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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9 System Model
9SISO-OFDM case
9MIMO-OFDM case
9 Conclusions
OUTLINE
Outline

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PAPR Analysis in MIMO-OFDM-AWGN Channel
¾The received signal is :
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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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¾ Then, the CCDF of the PAPR of the continuous received signal is
approximately given by
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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.

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9 System Model
9SISO-OFDM case
9MIMO-OFDM case
9 Conclusions
OUTLINE
Outline

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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
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¾The pdf of
After development, we find
¾The distribution function of is then expressed as :
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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 :
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¾Then, the CCDF of the PAPR of the continuous received signal can be
approximated by
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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
16

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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 :
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¾The CCDF of the PAPR of the continuous signal in the case of
can be approximated by :
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¾The CCDF of the PAPR of the continuous signal in the case of
can be approximated by :
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¾CCDFs of the PAPR of the received signal in SISO, MIMO(2,2)
and MIMO(4,4) (flat Rayleigh fading channel), SNR=10dB

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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

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9 System Model
9SISO-OFDM case
9MIMO-OFDM case
9 Conclusions
OUTLINE
Outline

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Conclusions
The influence of AWGN and flat Rayleigh fading channel
on the PAPR distribution in MIMO-OFDM systems has been
analyzed
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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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Basel Rihawi - Influence des canaux Gaussien et de Rayleigh sur la distribution du PAPR dans les systèmes MIMO-OFDM

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

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