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

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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
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
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
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
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
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
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
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.
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
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
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 :
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
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
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.
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
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
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
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
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
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
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
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
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
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
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
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
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
28. TITRE Séminaire SCEE jeudi 1 mars