Evaluation of performance improvement capabilities of PAPR-reducing methods Marc Deumal †, Ali Behravan *, Thomas Eriksson ‡ and Joan Lluís Pijoan † † Department of Communications and Signal Theory La Salle School of Engineering, Ramon Llull University, Barcelona, Spain * Qamcom Technology, Göteborg, Sweden ‡ Department of Signals and Systems, Chalmers University of Technology, Göteborg, Sweden

Outline Introduction Theoretical analysis –OFDM system performance in NL environments –Peak-to-average power ratio Considerations on PAPR-reduction Performance of the PAPR-reduced signals Conclusions

Introduction OFDM is a powerful modulation technique being used in many new and emerging broadband communication systems. –Advantages: Robustness against frequency selective fading and time dispersion. Transmission rates close to capacity can be achieved. Low computational complexity implementation (FFT). –Drawbacks: Sensitivity to frequency offset. Sensitivity to nonlinear amplification. Compensation techniques for nonlinear effects –Linearization (digital predistortion). –Peak-to-average power ratio (PAPR) reduction. –Post-processing.

Introduction PAPR-reduction techniques: –Varying PAPR-reduction capabilities, power, bandwidth and complexity requirements. –The performance of a system employing these techniques has not been fully analyzed PAPR is a very well known measure of the envelope fluctuations of a MC signal –Used as figure of merit. –The problem of reducing the envelope fluctuations has turned to reducing PAPR. In this paper we... –present a quantitative study of PAPR and NL distortion –simulate an OFDM-system employing some of these techniques Motivation: evaluate the performance improvement capabilities of PAPR- reducing methods.

Theoretical analysis of PAPR and system performance An OFDM signal can be expressed as If the OFDM signal is sampled at, the complex samples can be described as Orthogonal Frequency Division Multiplexing

Theoretical analysis of PAPR and system performance Peak-to-average power ratio Let be the m-th OFDM symbol, then its PAPR is defined as The CCDF of the PAPR of a non- oversampled OFDM signal is CCDF of PAPR increases with the number of subcarriers in the OFDM system. –It is widely believed that the more subcarriers are used in a OFDM system, the worse the distortion caused by the nonlinearity will be.

Theoretical analysis of PAPR and system performance In-band and out-of-band distortion If N is large enough, the OFDM signal can be approximated as a complex Gaussian distributed random variable. Thus its envelope is Rayleigh distributed NL Bussgang theorem where the variance of the real and imaginary parts of the signal is In particular if,then An interesting result is that the output of a NL with Gaussian input (OFDM) can be written as:

Theoretical analysis of PAPR and system performance In-band and out-of-band distortion (cont.) attenuation and rotation: compensated at the rx. distortion: in the frequency domain: with is the out-of-band radiation introduces an in-band noise that increases the error probability Both the distortion term and α are independent of N. The envelope of the OFDM signal is also independent of N.

Considerations on PAPR reduction In order to improve the system performance, PAPR should predict the amount of distortion introduced by the nonlinearity –PAPR increases with the number of subcarriers in the OFDM signal. –The distortion term and the uniform attenuation and rotation of the constellation only depend on the back-off. The effect of a nonlinearity to an OFDM signal is not clearly related to its PAPR The effective energy per bit at the input of the nonlinearity is where E o is the average energy of the signal at the input of the nonlinearity, K is the number of bits per symbol and η p is the power efficiency. –There will only be a a BER performance improvement when the effect of reducing the in-band distortion becomes noticeable and more important than the loss of power efficiency. –This is not taken into account in the majority of the PAPR reducing methods.

Performance of the PAPR-reduced signals In ACE, at each OFDM block, some of the outer signal constellation points are extended towards outside of the constellation such that the PAPR of the resulting block is reduced Active Constellation Extension (ACE) Advantages: ×Drawbacks: –It is transparent to receiver. –There is no loss of data rate. –No side information is required. –The increase in the average energy per bit might be higher than the NL distortion reduction. –The larger the constellation size is the lower the number of extensible points will be.

Performance of the PAPR-reduced signals Active Constellation Extension (ACE) Bit Error RatePower Spectral DensityPSD rectangular window

Performance of the PAPR-reduced signals TR consists on reducing the PAPR by reserving a few tones (PRT) within the transmitted bandwidth and assign them the appropriate values Tone Reservation (TR) Advantages: ×Drawbacks: –No distortion is introduced to the data bearing tones –No side information is required. –Increase in the average energy per bit which might reduce the BER performance improvement. –Loss of spectral efficiency due to tone reservation

Performance of the PAPR-reduced signals Tone Reservation (TR) Bit Error RatePower Spectral Density 4.3% of the subcarriers are reserved for PAPR-reduction

Performance of the PAPR-reduced signals In SLM, from the original data block several candidate data blocks are generated and the one with lowest PAPR is transmitted. At the receiver the reverse operation is performed to recover the original data block. Selected Mapping (SLM) Advantage: No distortion is introduced ×Drawback: It requires transmitting bits of side information per OFDM symbol » It is crucial that the side information is received without errors. » The side information has to be heavily protected. SLM has a complexity of U IFFT operations and U complex vector multiplications. The amount of PAPR reduction depends on U and the design of the phase sequences.

Performance of the PAPR-reduced signals Selected Mapping (SLM) Bit Error RatePower Spectral Density U=8 phase sequences are used

Performance of the PAPR-reduced signals The original data block is partitioned into V disjoint subblocks. The subcarriers in each subblock are rotated by the same phase factor such the PAPR of the combination is minimized. At the receiver the reverse operation is performed to recover the original data block. Partial Transmit Sequences (PTS) Advantage: No distortion is introduced ×Drawback: It requires transmitting bits of side information per OFDM symbol. » It is crucial that the side information is received without errors. » The side information has to be heavily protected. PTS has a complexity of V IFFT operations, complex vector multiplications and complex vector sums. The amount of PAPR reduction depends on V, W and the subblock partitioning.

Performance of the PAPR-reduced signals Partial Transmit Sequences (PTS) Bit Error RatePower Spectral Density V=3 subblocks and W=4 phase factors are used

Conclusions In this paper we presented a quantitative study of both the PAPR and the performance of an OFDM system when a NL is present. PAPR-reduction is meant to decrease the distortion introduced by the NL. –We showed that the effect of a NL on an OFDM signal is not clearly related to its PAPR. –In some recent contributions other measures of the envelope fluctuations have been proposed. The cubic metric [Motorola,TechReport,2005] relies on the fact that major distortion is caused by the third order intermodulation product. The variance of the instantaneous power [Behravan,VTC,2006] directly reduces the envelope fluctuations We also compared the BER performance and the PSD of a conventional OFDM with that of a PAPR-reduced OFDM system. –Spectral spreading is reduced when applying PAPR-reduction. –BER performance improvement only occurs when the effect of reducing the in- band distortion is more important than the loss of power efficiency.

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High power amplifiers Baseband model: HPA Operating point: –Input back-off: –Output back-off:

High power amplifiers We assume that predistortion is done at the transmitter side –The idea of predistortion is to modify the input signal of the HPA so that the output is as close as possible to the linearly amplified input signal –The AM/AM and AM/PM characteristics of the PD satisfy: –After combining the PD and the NL we obtain a SL: PDHPA