Probability distribution analysis of M-QAM-modulated OFDM symbol and reconstruction of distorted data
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RESEARCH
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Probability distribution analysis of M-QAMmodulated OFDM symbol and reconstruction of distorted data Hyunseuk Yoo*, Frédéric Guilloud and Ramesh Pyndiah
Abstract It is usually assumed that N samples of the time domain orthogonal frequency division multiplexing (OFDM) symbols have an identical Gaussian probability distribution (PD) in the real and imaginary parts. In this article, we analyze the exact PD of M-QAM/OFDM symbols with N subcarriers. We show the general expression of the characteristic function of the time domain samples of M-QAM/OFDM symbols. As an example, theoretical discrete PD for both QPSK and 16-QAM cases is derived. The discrete nature of these distributions is used to reconstruct the distorted OFDM symbols due to deliberate clipping or amplification close to saturation. Simulation results show that the data reconstruction process can effectively lower the error floor level. Keywords: OFDM, discrete probability distribution, M-QAM, nonlinear amplifier, data reconstruction.
1 Introduction A significant drawback of orthogonal frequency division multiplexing (OFDM)-based systems is their high peakto-average power ratio (PAPR) at the transmitter, requiring the use of a highly linear amplifier which leads to low power efficiency. For reasonable power efficiency, the OFDM signal power level should be close to the nonlinear area of the amplifier, going through nonlinear distortions and degrading the error performance. The distortion can be introduced for two main reasons: nonlinear amplifier [1,2] and/or deliberate clipping [3]. For the first case, if an OFDM symbol is amplified in the saturation area of an amplifier, its data recovery is not possible. For the second case, deliberate clipping makes an intentional noise which falls both in-band and out-of-band. In-band distortion results in an error performance degradation, while out-of-band radiation reduces spectral efficiency. Filtering methods can reduce out-of-band radiation, but also introduces peak regrowth of OFDM signals and increases the overall system impulse response [4,5]. Several approaches have been investigated for mitigating the clipping noise with an amount of computational
complexity, such as iterative methods [6-10] and an oversampling method [11]. It is usually assumed that the time domain samples of OFDM symbols are complex Gaussian distributed, which is a very good approximation if the number of subcarriers is large enough. Furthermore, it is theoretically proved in [12,13] that a bandlimited uncoded OFDM symbol converges weakly to a Gaussian random process as the number of subcarriers goes to infinity. In this article, we derive the discrete Probability Distribution (PD) of the time domain samples of M-QAM/ OFDM symbols with a limited number of subcarriers. The discrete PD can be used to reconstruct distorted OFDM symbols. We focus on the in-band distortion which can be caused when OFDM symbols are amplified in the saturation area or when deliberate clipping is used to reduce the PAPR [3]. Note that the c
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