WO2008046163A1 - §procédé de réduction du rapport de puissance de crête sur puissance moyenne dans des signaux à multiplexage par répartition orthogonale de la fréquence - Google Patents

§procédé de réduction du rapport de puissance de crête sur puissance moyenne dans des signaux à multiplexage par répartition orthogonale de la fréquence Download PDF

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WO2008046163A1
WO2008046163A1 PCT/AU2007/001604 AU2007001604W WO2008046163A1 WO 2008046163 A1 WO2008046163 A1 WO 2008046163A1 AU 2007001604 W AU2007001604 W AU 2007001604W WO 2008046163 A1 WO2008046163 A1 WO 2008046163A1
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papr
error
signal
ofdm
code
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PCT/AU2007/001604
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English (en)
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Alexander James Grant
Ismail Shakeel
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University Of South Australia
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Publication of WO2008046163A1 publication Critical patent/WO2008046163A1/fr

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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/26—Systems using multi-frequency codes
    • H04L27/2601—Multicarrier modulation systems
    • H04L27/2614—Peak power aspects
    • H04L27/2615—Reduction thereof using coding
    • H04L27/2617—Reduction thereof using coding using block codes

Definitions

  • This invention relates to the field of digital communications and in particular, to a method of reducing PAPR in multi-carrier signals.
  • Orthogonal Frequency Division Multiplexing is a bandwidth efficient multicarrier transmission technique for digital communications.
  • the fundamental principle of OFDM is to spread the data to be transmitted over a large number of subcarriers, where each subcarrier is modulated with a much lower data rate stream and the subcarriers are made orthogonal to each other.
  • OFDM Fast Fourier Transforms
  • OFDM has several advantages over single carrier systems in that OFDM is more robust to multipath induced intersymbol interference (ISI) and has high spectral efficiency. Despite these advantages, OFDM has some disadvantages that need to be addressed for its successful implementation.
  • a major disadvantage of OFDM is that it generates signals with large amplitude variations. This problem is known as the peak-to-average power ratio (PAPR) problem, which degrades system performance, reduces the efficiency of the high power amplifier (HPA) and also limits the dynamic range of the analogue-to-digital (A/D) and digital-to-analogue (D/ A) converters. These negative effects may outweigh all the potential benefits of OFDM transmission systems in many low-cost applications.
  • PAPR reduction techniques have been proposed during the last decade. These broadly fall into three areas, namely, signal distortion techniques, symbol scrambling techniques and coding techniques.
  • Signal distortion techniques are the most straightforward PAPR reduction methods. These techniques simply reduce or clip the high peak amplitudes of Hie OFDM before transmission. In general, these techniques do not require side information for recovering the transmitted sequence at the receiver. Another advantage of these techniques is their simplicity and low complexity. However, there are several disadvantages of these techniques which make these techniques less preferable than others. Firstly, these techniques introduce distortion noise which reduces the Bit Error Rate (BER) performance of the system. Secondly, some of these techniques introduce spectrum distortion (spectral regrowth) of the signal. The simplest example of a signal distortion technique is deliberate clipping, where peaks above a certain threshold are clipped.
  • Symbol scrambling techniques are a large group of distortionless techniques for reducing PAPR.
  • the basic idea of symbol scrambling is to generate a set of statistically independent OFDM symbols by scrambling the data sequence and selecting the OFDM symbol with smallest PAPR for transmission.
  • One of the most widely referred and studied symbol scrambling technique is selective mapping (SLM).
  • SLM selective mapping
  • the basic idea of this technique is to generate a set of independent candidate data blocks, all representing the original data block and selecting the candidate data block which gives the lowest PAPR for transmission.
  • the receiver has to know which candidate data block was used, which requires sending of side information along with the transmitted signal. Thus it is very important for the receiver to receive the side information correctly, since an error in the side information will result in losing the whole information block.
  • the two previous techniques discussed only focus on the reduction of the PAPR of the OFDM signal.
  • the third broad approach used is coding, which is another distortionless technique which not only reduces PAPR but also corrects errors.
  • coding techniques do not require the transmission of side information to the receiver. Further, the error correcting capability of this technique also improves the BER performance.
  • coding techniques typically significantly reduce the information rate of the system.
  • the basic approach to coding is to avoid transmitting codewords with high PAPR.
  • the simplest approach is to simply use a coding technique that excludes sequences with high PAPR such as one that maps sequence of length k to a sequence of length n, where the mapped sequence has a PAPR below some threshold.
  • An alternative coding approach is to transpose a code set to an equivalent code set in terms of error correction properties, but with reduced PAPR. The whole code set is transposed using an offset vector where the optimum offset vector corresponds to the vector with the minimum PAPR possible for the set.
  • the main advantage of this technique is that it provides both error correction and PAPR reduction. However, finding good codes and their offsets is very difficult and requires extensive calculations.
  • a method for reducing the peak-to-average-power ratio (PAPR) of an error coded signal having a bit sequence comprising: introducing at least one error in the error coded signal, such that the PAPR of the error coded signal with the introduced at least one error is less than the PAPR of the error coded signal.
  • PAPR peak-to-average-power ratio
  • a method wherein the step of introducing the at least one error comprises flipping at least one bit of the bit sequence.
  • a method further comprising determining which of the one or more bits to flip by calculating a PAPR contribution of the one or more bits and flipping the one or more bits that contribute the greatest PAPR to the signal.
  • a method further comprising flipping one or more bits until the PAPR does not reduce any further.
  • a method further comprising flipping one or more bits until the PAPR of the signal becomes equal to or less than a predetermined PAPR threshold.
  • a method wherein the step of calculating the PAPR contribution of the one or more bits comprises:
  • a method wherein the side information comprises information identifying to the receiver, the location of at least one of the one or more bits flipped.
  • a method wherein the error coded signal is coded with an error code that is not correctable by a receiver and wherein side information is transmitted to the receiver to allow the receiver to correct the error coded signal.
  • a method further comprising error coding an input signal with an error code to produce the error coded signal.
  • a method wherein the error code is a block code.
  • a method wherein the error code is a convolution code. In another aspect of the invention, a method wherein the error code is a trellis code.
  • a method wherein the error code is a turbo code.
  • a method wherein the error code is a low density parity check code.
  • PAPR peak-to-average
  • a method of determining the peak-to- average-power ratio (PAPR) of an error coded signal having a bit sequence comprising:
  • a transmitter for use in a multi-carrier communications system configured to perform the any of the preceding methods
  • a multicarrier communications system comprising the above transmitter.
  • BER Bit Error Rate
  • PAPR Peak-to-Average-Power Ratio
  • FIGURE 1 - is a block diagram of a typical OFDM system
  • FIGURE 2 - is a block diagram of an OFDM Modulator
  • FIGURE 3 - is a block diagram of an encoder according to an aspect of the present invention
  • FIGURE 4 - shows a graph of PAPR CCDF for QPSK modulation
  • FIGURE 5 - shows a graph of PAPR CCDF for 16QAM modulation
  • FIGURE 6 - shows a graph of CCDF Comparison for QPSK modulation
  • FIGURE 7 - shows a graph of CCDF Comparison for 16QAM modulation
  • FIGURE 8 - shows a graph of the probability that encoding algorithm will generate an E vector with weight W 0 ;
  • FIGURE 9 - shows a graph of the BER performance
  • FIGURE 10 - shows one example of an architecture for an OFDM transmitter according to an aspect of the present invention
  • FIGURE 11 - shows an alternative architecture of an OFDM transmitter according to an aspect of the present invention.
  • FIGURE 12 - shows an OFDM communications system using side information.
  • the present invention relates to a method for controlling the peak-to-average-power Ratio (PAPR) of a signal.
  • PAPR peak-to-average-power Ratio
  • an embodiment of the invention to perform error correction and a reduction of the PAPR of an OFDM signals will now be described.
  • this embodiment is in no way limiting, and that the invention may be applied more generally to the field of digital communications, or wherever it is desirable to reduce the PAPR of a sequence of bits.
  • the data symbols are transmitted sequentially, with the frequency spectrum of each symbol allowed to occupy the entire available bandwidth.
  • the available bandwidth is divided into N non-overlapping sub-channels.
  • Each subcarrier is modulated with a different symbol from the data sequence.
  • the N modulated subcarriers are frequency division multiplexed.
  • the subcarriers are made orthogonal
  • the subcarrier spacing is usually kept small compared with title coherence bandwidth of the channel.
  • Figure 1 shows a typical OFDM transmitter 100.
  • An input data stream (110) of length k is fed into the coder (120), which outputs a codeword of length n .
  • the symbols in the coded word are then mapped onto a suitable signal constellation by signal mapper (130).
  • Examples of typical constellations used include Binary Phase Shift Keying (BPSK), Quadrature Phase Shift Keying (QPSK) and M-Quadrature Amplitude Modulation (MQAM).
  • BPSK Binary Phase Shift Keying
  • QPSK Quadrature Phase Shift Keying
  • MQAM M-Quadrature Amplitude Modulation
  • the output parallel stream from S/P converter undergoes an N -point inverse fast Fourier transform (IFFT) (150) and is then converted back to serial form for transmission (160).
  • IFFT inverse fast Fourier transform
  • This signal is not alone sufficient for reliable transmission as there is always the possibility that channel distortion may cause interference between neighbouring symbols of the OFDM signal.
  • This type of interference is commonly known as inter-symbol interference (ISI).
  • ISI inter-symbol interference
  • OFDM systems add a cyclic prefix (CP) to the time domain signal (170).
  • CP also helps to reduce inter-carrier interference (ICI) by maintaining orthogonality of the signal.
  • D/ A Digital to Analog
  • the analog output is lowpass filtered and modulated to the desired carrier frequency (180).
  • the output radio frequency (RF) signal (186) is amplified by passing through the High Power Amplifier (HPA) (190) to transmit across the channel (192).
  • HPA High Power Amplifier
  • the received signal (210) is demodulated to baseband, filtered, sampled (220) and the inverse process of the transmitter is performed. This involves removing the CP(230), performing a serial to parallel conversion (240), a N-point fast f ourier transform (FFT) (250) followed by conversion back to a serial form (260) for signal demapping (270).
  • FFT fast f ourier transform
  • the demapped signal is then passed through the decoder (280) to produce the output data stream (290).
  • the continuous-time baseband representation of an OFDM signal is where j — V-T .
  • T denotes the symbol period and ⁇ X m ⁇ J 0 are the data symbols drawn from a finite modulation signal set.
  • the baseband modulation is done in the digital domain using an oversampled version of x(t) given by
  • L vN m o where L is the oversampling factor.
  • the case L > 1 corresponds to oversampling. It can be seen that the sequence can be interpreted as the IDFT of the OFDM data block X with N(L-I) zero padding.
  • the spectrum of the OFDM signal is the superposition of N separate signals at N frequencies separated by the signalling rate. Each signal has the spectrum of the form sin(40 with nulls at the centre of the other sub-carriers.
  • the peak-to-average power ratio is a measure of the level of amplitude variation of a signal.
  • a large PAPR corresponds to a large amplitude variation of the signal.
  • PAPR has no negative effects on the OFDM signal.
  • Figure 2 shows the block diagram of an OFDM modulator.
  • the serial to parallel converter (140) produces ⁇ symbols, X 1 (141, 142, and 143) from a signal constellation, which modulates the / th subcarrier.
  • IDFT is used to implement the OFDM modulation function (151, 152, 153, 154, 155, 156).
  • the ⁇ subcarrier sinusoids (157, 158, 159) are summed together (160) and the CP is added (160) to produce an output signal (172).
  • the peak amplitude of the signal can reach as high as N due to constructive interference between the sinusoids.
  • the PAPR of the signal in equation (4) is defined as
  • the distribution of PAPR values is commonly described using the complementary cumulative distribution function (CCDF).
  • CCDF of the PAPR represents the probability that the PAPR of a data block exceeds a given threshold z . That is,
  • QPSK quaternary phase shift keying
  • a signal with a larger PAPR value requires a wide linear region of the amplifier (160 in Figure 1) to avoid signal distortion.
  • power amplifiers with wide linear range that can handle large signal peaks can be highly power consuming, making the amplifier very inefficient.
  • the operating point of an amplifier is given by the back-off.
  • the input back-off (IBO) of an amplifier can defined by
  • signals can be left to pass through an amplifier which cannot handle high peaks.
  • the signal from the output of the power amplifier will be distorted causing a reduction of the error performance of the system.
  • this clipping effect of the signal will also result in higher order harmonics that spill over the out-of-band spectrum.
  • the power amplifier operates most efficiently when operating near its saturation region. Input signals with low peak-to-average power ratio (PAPR) will enable the amplifier to operate near saturation. Amplifier saturation is an example of nonlinear effects which significantly distorts the original signal.
  • PAPR peak-to-average power ratio
  • FIG. 3 A block diagram of one embodiment of the error correction and PAPR reduction method is shown in Figure 3.
  • the input message sequence m (310) of k bits (312, 314, 316) is first passed to the standard block coder (320).
  • the standard block coder uses a standard block code C ⁇ n, k, t) with generator matrix G to produce the coded output word U of n bits(322, 324, 326, 328) where t is the error correcting capability of the code (number of bits).
  • the coded word is passed to the PAPR coder (330) which maps the coded word onto a low PAPR word 340 of k bits (332, 334, 336, 338).
  • the proposed coding technique is expressed as an optimisation problem in equation (13). Given an integer W 1 W ⁇ t , find the error pattern E e .F 2 " for min
  • the problem in ((13)) is a constrained discrete optimisation problem and can be solved using an optimisation technique or other suitable techniques.
  • Another aspect of the present invention provides for a PAPR encoding algorithm as follows:
  • INPUT Message sequence m , encoding function f e (m), an integer W , W ⁇ t and t is the error correcting capability of the code.
  • Step l: U f ⁇ (m)
  • Step 4 Update U with the flipped sequence.
  • Step 6 If no PAPR reduction is observed, or if the observed PAPR reaches a predetermined threshold, go to Step 9.
  • the coded message sequence U is obtained using U — mG .
  • a comparison as to the value of the calculated PAPR may be made to a preset threshold.
  • the threshold would be set so as to provide as much PAPR reduction as possible, at the expense of the error correction.
  • the error correction is paramount, and the PAPR problem is less important.
  • the threshold will be set so as to perform a minimal amount of PAPR reduction, if any, to maintain the error correction capability as high as possible.
  • step 3 the complexity of this algorithm largely depends on step 3. At each iteration ⁇ , this step computes a total of n IDFTs. However, a closer investigation of this step shows that the mathematical operations between IDFT computations are highly repetitive.
  • Step 3 can be simplified as follows.
  • the matrix representation of the OFDM signal in equation (5) can be given by,
  • Equation (14) can also be expressed as equation (16) where the vector x can be obtained by summing all columns of matrix M.
  • the vector x in (15) is the IDFT of the unflipped sequence XJ , which is computed only once for each iteration ⁇ .
  • Generation of matrix M does not require any additional computations, as it can be obtained during the computation of x.
  • M can be updated by replacing the column M j with - M 1 , where j is the flipped bit position of iteration ⁇ -1.
  • the simplification given in equation (17) significantly reduces the computational load of the proposed algorithm. Similar simplifications can be obtained for other modulation schemes.
  • Step 3 Modulate U to obtained X according to BPSK modulation
  • Step 6 Obtain M (equation 14) from Step 4
  • CCDF Pr(PAPR > z )
  • BER bit error rate
  • the PAPR of a signal exceeds 11.6dB for 0.01% (Le. 1 in 10000) of the transmitted OFDM symbols, (i.e. 0.01% of PAPR is 11.6dB).
  • the 0.01% PAPR of the OFDM signal coded with the proposed algorithm is around 6.5dB for both systems. This corresponds to a PAPR reduction of 5.IdB over the uncoded OFDM system.
  • Figures 6 and 7 compares the PAPR reduction performance of the algorithm with the selective mapping technique (SLM).
  • SLM selective mapping technique
  • the variable P of the SLM technique is the number of pseudo-random representations generated for PAPR comparison. To generate P representations, P IDFTs have to be computed. The simulated results show the proposed algorithm performs better than the SLM technique. The largest performance difference is observed at higher percentages of PAPR (i.e. > 0.1% PAPR).
  • the code C has a variable error correcting capability T , (t-W) ⁇ T ⁇ t .
  • t is the error correcting capability of the code C .
  • the variable T depends on the weight of E vector, w(£).
  • a PAPR code C is normally denoted using the parameters (n,k,t, ⁇ ) where ⁇ is the PAPR of the code defined by,
  • PAPR ⁇ 7 max ⁇ PAPR(c) ⁇ , ⁇ /c e C - (18)
  • Pr(Ai > ⁇ ) P (20) where P « 0.
  • the PAPR reduced code C generated by the proposed algorithm can be described using the parameters (n,k,T, ⁇ ,N ), where ⁇ (in dB) is a measure of PAPR of the code given in ((2O)) and N is the number of subcarriers.
  • BCH Ray-Chaudhuri Hocquenghem
  • the signal distortions due to the nonlinear amplifier can be modelled using a solid state power amplifier (SSPA) described by,
  • the nonlinear gain f[A(t)] is referred to as the AM/ AM conversion characteristics.
  • A(t) is the amplitude of the input signal
  • a ms ⁇ is the maximum output amplitude
  • the parameter p controls the smoothness of the transition from the linear region to the saturation region.
  • p was set at 2 and the input back-off at OdB.
  • AWGN additive white Gaussian noise
  • An algebraic hard- decision decoder of the standard block code C is then used to decode the transmitted information.
  • This code is also equivalent to (378,162,8,6.3,95) on GF(2) .
  • the BER performance of the code is compared with uncoded OFDM system, SLM and the system coded with C .
  • C is the Reed-Solomon code (63,27,18) on GF (2 6 ) which has a higher error correcting capability than C .
  • the BER performance results show that the PAPR reduced code performed much better than the code C .
  • BER results for the uncoded system and the C -coded OFDM system show an error floor, which is removed by using the PAPR reduced code.
  • the ordinary SLM technique requires perfect side information for retrieving transmitted information at the receiver. Ideal side information at the receiver was assumed for all SLM simulations. BER performance of SLM show an error floor for all simulations conducted. As expected, the proposed method which is designed to correct errors as well as reduce PAPR, performed much better than the SLM.
  • Table 3 shows a comparison of the PAPR reduction performance with the typical performance of several other techniques.
  • 0.1% PAPR gain refers to the amount of PAPR reduction achieved over the uncoded OFDM system at the 0.1 %
  • the above embodiment and associated figures describe an efficient method for joint error correction and PAPR reduction of OFDM signals.
  • the input OFDM signal is first coded using a standard coding method, and this code is converted to a PAPR reduced code.
  • the method adds single bit errors (in a bit by bit fashion) to the coded codeword with the aim of reducing its PAPR.
  • the embodiment described above describes a method for both error correction and PAPR reduction of OFDM signals. This process of adding an error pattern to the coded signal does not affect the code rate, and thus the code rate of PAPR reduced code is simply that of the encoding method used.
  • the PAPR reduction and BER performance of the algorithm were investigated and compared with other systems.
  • the CCDF results show that this algorithm gives PAPR reductions of more than 4.8dB over uncoded OFDM systems with 128 and 256 subcarriers.
  • the proposed method drastically improves the BER performance of the system, as the proposed method reduces PAPR as well as corrects errors resulting from amplifier nonlinearity and channel noise.
  • the simulated results also show that the PAPR reduction performance of proposed algorithm is comparable with other well known PAPR reduction techniques such as SLM. These benefits give improved system performance.
  • the PAPR reduced BCH code (511, 277) which has a code rate of 0.54, can correct at least 16 bit errors and gives a PAPR reduction of more than 4.8dB over the uncoded OFDM system with 256 QPSK subcarriers.
  • Figure 10 shows one example of an architecture of an OFDM transmitter 100.
  • One example of an OFDM transmitter incorporating an aspect of the present invention is the same structure as the transmitter shown in Figure 1, where like elements are labelled accordingly.
  • additional block 122 is disposed after the error coder or encoder 120.
  • Transmitter 100 as shown in Figure 10 may be provided as an integrated circuit chip, or any other suitable embodiment, such as commercially available OFDM transmitter chips provided by companies such as Aetheros and Broadcom.
  • one type of chipset is the 802.11 chipset.
  • Figure 11 shows one example of a system architecture for use with an aspect of the present invention. Shown is a block diagram illustrating the position of the PAPR reduction algorithm of one aspect of the present invention within a general OFDM transmitter 400. Input data 410 containing a plurality of information bits is input to coder 420 to have an error code applied thereto, as previously described. It will be appreciated that while the PAPR coder 330 as shown in Figure 3 was located directly after the block coder, this is not essential. Other forms of processing 430 ( Figure 11) may be applied to the post-coded signal, including, but not limited to, interleaving, scrambling, puncturing, or other encoding steps. The PAPR reduction block 440 ( Figure 11) may then be introduced anywhere prior to modulation.
  • Figure 12 shows an OFDM communications system 500 with transmitter 510 and receiver 520.
  • the OFDM signal is processed as described above, but using an error code that is not correctable by receiver 520.
  • This signal is transmitted from antenna 511 of transmitter 510 to antenna 521 of receiver 520, together with side information 530.
  • the side information 530 provides the receiver, and in particular, the decoder (not shown) of the receiver with sufficient information to decode the coded signal.
  • more single bit errors could be made than code is capable of correcting, that is W > t.
  • Side information could then be transmitted to specifying the locations of at least n e of the single bit errors. The receiver can then use this side information to remove the extra bit errors, thus enabling the decoding method to decode the message.
  • All of the above embodiments include the use of an encoding method. It is to be understood that this includes the use of codes with code rates of 1. Thus the method could be applied to an uncoded message, or a message in which the encoding method simply rearranges bits order.
  • OFDM Orthogonal Frequency Division Multiplexing
  • Orthogonal Frequency Division Multiplexing is a bandwidth efficient multi- carrier transmission technique for digital communications.
  • the basic idea of OFDM is to spread the data to be transmitted over a large number of subcarriers, where each subcarrier is modulated with a much lower data rate stream.
  • the subcarriers are made orthogonal to each other.
  • OFDM technology was first used commercially in Digital Audio Broadcasting (DAB). In 1994, OFDM was included in European DAB as well as in Digital Video Broadcasting (DVB) standards [3, 4]. DAB services were introduced to UK and Sweden in 1995. In the same year, DVB and High-Definition Television (HDTV) terrestrial Chapter 5: Joint Error Correction and PAPR Reduction of OFDM Signals
  • Wireless Local Area Network such as IEEE 802.11a [6]
  • OFDM has been adopted in wireline applications such as Asymmetric Digital Subscriber Lines (ADSL) [7].
  • ADSL Asymmetric Digital Subscriber Lines
  • WiMAX broadband wireless access
  • the data symbols are transmitted sequentially, with the frequency spectrum of each symbol allowed to occupy the entire available bandwidth.
  • the available bandwidth is divided into N non-overlapping sub-channels.
  • Each subcarrier is modulated with a different symbol from the data sequence.
  • the N modulated subcarriers are frequency division multiplexed.
  • the N subcarriers possess the frequencies / m , given by:
  • ⁇ / f ⁇ /N and / ⁇ denotes entire bandwidth.
  • the subcarriers are made orthogonal to each other by carefully selecting the frequency spacing. In practical OFDM systems, the subcarrier spacing is usually kept small compared to the coherence bandwidth of the channel.
  • Figure 1.1 shows a typical OFDM transmitter. The basic operations of the blocks shown in this figure are briefly described below.
  • An input data stream of length A is fed into the encoder, which outputs a codeword of length n.
  • the symbols in the encoded word are then mapped onto a suitable signal constellation. Examples Chapter 5: Joint Error Correction and PAPR Reduction of OFDM Signals
  • Figure 1.1 Block diagram of a typical coded OFDM system.
  • Chapter 5 Joint Error Correction and PAPR Reduction of OFDM Signals
  • ISI inter-symbol interference
  • OFDM systems add a cyclic prefix (CP) to the time domain signal.
  • CP also helps to reduce inter-carrier interference (ICI) by maintaining orthogonality of the subcarriers.
  • the signal After adding CP, the signal is passed through the digital-to-analog (D /A) converter as shown in Figure 1.1.
  • the analog output is lowpass filtered and modulated to the desired carrier frequency.
  • the output radio frequency (RF) signal is amplified by passing it through the High Power Amplifier (HPA) to transmit across the channel.
  • HPA High Power Amplifier
  • the received signal is demodulated to baseband, filtered, sampled and the inverse process of the transmitter are performed.
  • the FFT and A/D in the receiver represent the fast Fourier transform and analog-to-digital converter respectively.
  • the baseband modulation is done in the digital domain using an oversampled version of x(t) given by:
  • L is the oversampling factor.
  • the case L > 1 corresponds to oversampling. It can be seen 604
  • the spectrum of the OFDM signal is the superposition of N separate signals at N frequencies separated by the signalling rate. Each signal has the spectrum of the form sin(fc/)// with nulls at the center of the other subcarriers.
  • OFDM has several advantages over other transmission systems. Due to this, OFDM has found important applications in broadcasting and wireless local area networks (WLA ⁇ ). OFDM is also considered as a potential transmission scheme for the fourth generation mobile communication systems. Some of the important advantages of OFDM are summarised below:
  • OFDM has some disadvantages that need to be addressed for its successful implementation.
  • Major disadvantages of OFDM are summarised below:
  • Peak-to-average power ratio is a measure of the level of amplitude variation of a signal.
  • a large PAPR corresponds to a large amplitude variation of the signal.
  • PAPR has no negative effects on the OFDM signal.
  • Figure 1.2 shows the block diagram of an OFDM modulator.
  • Xi denotes the symbol (from a signal constellation) which modulates the ith subcarrier.
  • the PAPR of the signal (1.2) is defined as [13]: max lrzr(t)P
  • PAPR peak-to average power ratio
  • PAP peak-to-average power
  • CF crest factor
  • the implementation of the OFDM transceiver system requires the use of one or more power amplifiers at the output stage of the transmitter.
  • Amplifiers have a certain linear region, beyond which there is a saturation region where the output power does not increase even if the input power increases substantially.
  • a signal with a larger PAPR value requires a wider linear region of the amplifier to avoid signal distortions [17].
  • power amplifiers with wider linear range that can handle large signal peaks can be highly power consuming, making the amplifier very inefficient. In mobile applications, this may reduce the battery lifetime.
  • the signals are left to pass through an amplifier which cannot handle high peaks, the signal from its output will get distorted, causing a reduction of system performance. This distortion effect will also result in higher order harmonics that spill over the out-of-band spectrum.
  • the power amplifier is most efficient when operating near its saturation region. Input signals with low PAPR will enable the amplifier to operate near saturation [17].
  • nonlinear models can be divided into two categories, namely memoryless models and models with memory.
  • Non-linearities are usually restricted to devices such as non-linear amplifiers and transducers in communication systems [18].
  • the conventionally used model for these devices is a bandpass memoryless model, where the output signal of the device depends on the envelope of its input.
  • the relationship between the input and the output of the nonlinear device eg. an amplifier
  • Chapter 5 Joint Error Correction and PAPR Reduction of OFDM Signals
  • the AM/AM and AM/PM models are referred to as a bandpass nonlinearity because the signal (1.9) has only frequency components around /o and not around harmonic frequencies.
  • the two functions (/[A(t)] and g[ ⁇ (t)]) do not depend on the carrier frequency.
  • Amplifiers commonly used in communication systems can be divided into two types, namely; the solid state power amplifier (SSPA) and the travelling wave tube amplifier (TWTA) [20-23].
  • SSPA solid state power amplifier
  • TWTA amplifiers are used commonly in satellite transponders, while SSPA is more common in mobile transmitters. These two types of amplifiers are considerably different in their AM/AM and AM/PM characteristics.
  • SSPA solid state power amplifier
  • TWTA travelling wave tube amplifier
  • the AM/AM and AM/PM conversion characteristics for the SSPA transmitter can Chapter 5: Joint Error Correction and PAPR Reduction of OFDM Signals
  • An ideal soft limiter(SL) physically represents the ideal SSPA amplifier characteristics. As the smoothing parameter p of SSPA model goes to infinity, the characteristics of the SSPA will become that of the ideal SL.
  • the SL can be modelled as:
  • A/D and D/A converters with very large dynamic ranges.
  • the cost of A/D and D/A converters can depend on the size of their dynamic range.
  • a large dynamic range is often required to achieve high precision of the signal. Lack of precision will result in quantization errors during A/D conversions at the receiver.
  • the PAPR of an OFDM signal is always less than or equal to 101og 10 ( ⁇ T) dB, where N is the number of subcarriers. This means the PAPR value of an OFDM signal in a system with 128 subcarriers can be as high as 21 dB. However, it can be observed Chapter 5: Joint Error Correction and PAPR Reduction of OFDM Signals
  • Figure 1.4 Envelope power of all possible data words of length four. OFDM system with BPSK modulation and four subcarriers.
  • the distribution of PAPR values is commonly described using the complementary cumulative distribution function (CCDF).
  • the CCDF of the PAPR represents the probability that the PAPR of a data block exceeds a given 4
  • the CCDF curves for number of carriers, N — 16, 32, 64 and 128, obtained by simulation, are shown in Figure 1.5.
  • An oversampling rate of 4 and quaternary phase shift keying (QPSK) are used in the simulation. Apart from QPSK, there are several other modulation schemes that can be used.
  • the statistical distribution of PAPR is largely independent of the signal constellation and also the CCDF does not significantly improve for sampling rates above 4 [15].
  • Figure 1.5 CCDF for N QPSK subcarriers.
  • CDF cumulative distribution function
  • the CDF of the amplitude of a signal sample can be expressed as:
  • an expression for CDF of the PAPR can be derived as:
  • CCDF of the PAPR is:
  • the expression (1.20) is an empirical approximation of PAPR and differs as much as 1 dB from the actual PAPR distribution of x(t). The small discrepancy is due to the fact that the expression (1.20) assumes the samples to be independent and uncorrelated. However, this is not true when oversampling is used.
  • Several attempts have been made to determine a more accurate distribution of PAPR [9, 13, 24-27]. The first such attempt, reported in [9], is simply a modification of the expression (1.20). The modified expression is:
  • PAPR reduction techniques have been proposed during the last few years. Most of these techniques can be broadly divided into three categories. These are signal distortion techniques, symbol scrambling techniques and coding techniques. In this section, a review of some of the most common signal distortion and symbol scrambling techniques are reviewed. A discussion of the coding techniques will be presented in the next section.
  • Signal distortion techniques are the most straightforward PAPR reduction methods. These techniques simply reduce or clip the high peak amplitudes of the OFDM before transmission. In general, these techniques do not require side information to recover the transmitted sequence at the receiver. Another advantage of these techniques is their simplicity and low complexity. However, there are several disadvantages which make these techniques less preferable than others. Firstly, signal distortion techniques introduce distortion noise which reduces the BER performance of the system. Secondly, some of these techniques introduce spectrum distortion (spectral regrowth) of the signal. The simplest distortion technique is clipping [28-31], where the peaks are clipped above a certain threshold z, according to:
  • the peak windowing approach is more spectrally efficient.
  • a window is applied to the region where there exist large peaks.
  • the signal is multiplied by the window function in such a way that the signal peaks fall at the center of the window.
  • window functions There are several window functions that could be used. The most common window functions are Hamming and Kaiser windows.
  • Companding technique [36] is another important distortion technique for reducing PAPR.
  • the companding technique (which refers to compressing and expanding) was initially used to expand the dynamic range of D/A converters. This technique was later adopted for PAPR reduction in OFDM signals.
  • Companding uses a compressing function F(-) at the transmitter. This function is applied to signal x before transmission, so that the dynamic range of the compressed signal F(x) is less than the input signal x.
  • F(-) Upon receiving the signal y, the receiver attempts to approximate the transmitted signal x, by applying an expanding function (i.e. F "1 ⁇ )) on the received signal y.
  • x F ⁇ 1 (y).
  • Companding has similar drawbacks as the amplitude clipping technique.
  • symbol scrambling is to generate a set of statistically independent OFDM symbols, by scrambling the data sequence and selecting the OFDM symbol with the smallest PAPR for transmission. While there exists a number of scrambling techniques [14, 37-39], the selective mapping (SLM) [38] and the partial transmit sequences (PTS) [39] are the most cited and studied techniques. These two techniques are quite similar in many ways. The main difference between these techniques is that the SLM applies an independent rotation to each subcarrier, while the PTS applies a scrambling sequence to a group of subcarriers. Chapter 5: Joint Error Correction and PAPR Reduction of OFDM Signals
  • Figure 1.6 shows the block diagram of the SLM technique. This technique gen-
  • Figure 1.6 Block diagram of the SLM technique.
  • the candidate data block which gives the lowest PAPR is then selected for transmission.
  • the U candidate data block are generated using U distinct vectors defined as:
  • each of the U OFDM frequency-domain sequences is transformed into a time-domain signal using IDFT.
  • the PAPR of each signal is calculated and the one with the lowest PAPR is selected for transmission.
  • the receiver has to know which vector u was used with the transmitted signal.
  • a straightforward method is to send the number u as side information to the receiver, which would require log 2 (C/) bits. Using the side information, Chapter 5: Joint Error Correction and PAPR Reduction of OFDM Signals
  • Figure 1.7 Block diagram of the PTS technique.
  • X is first partitioned into M disjoint sub-blocks, s0 that,
  • the IDFT output of each sub-block is then multiplied by an optimised sequence of phase constants such that the PAPR of the combined signal is minimised.
  • the phase constants are drawn from a finite set with I elements.
  • the complexity of this technique increases exponentially with M and L Similar to SLM scheme, this technique also requires perfect side information to recover the transmitted signal correctly. The side information allows the receiver to distinguish £ M different mappings. This would require up to M log 2 £ bits.
  • PAPR techniques include the tone reservation [44] and constellation shaping techniques [44, 45].
  • tone reservation technique uses a small set of subcarriers to reduce the PAPR of the signal. These subcarriers are reserved for this purpose and do not send any information.
  • constellation shaping schemes PAPR reduction is achieved by reshaping the signal constellation.
  • coding techniques aims to reduce PAPR as well as simultaneously correct errors.
  • the coding technique does not require side information to be transmitted to the receiver.
  • the error correcting capability of this technique also improves the BER performance.
  • coding techniques significantly reduce the information rate of the system.
  • Table 1.3 Examples of codes and their offset vectors.
  • the PAPR of a code C is defined as:
  • PAPR ⁇ max ⁇ PAPR(c) ⁇ , Vc G C- (1.28)
  • a PAPR code C be denoted using the parameters (n, k, t, ⁇ ) where n is the codeword length, k is the dimension, t is the error correcting capability and ⁇ is the PAPR of the code.
  • ⁇ (-) is the Kronecker delta function
  • p x ⁇ k is the aperiodic auto-correlation of the sequence x given by:
  • the code rate of the first order Reed-Muller codes is (m + l)/2 m . This code rate vanishes rapidly for n > 32, as depicted in Figure 1.8.
  • the code rate of RM(1, 6) which has a codeword length of only 128 bits is 0.06.
  • Many OFDM systems require from 8 to 8192 subcarriers.
  • PAPR codes are constructed by selecting a set of words which have low PAPR properties. Codes constructed in this manner always face a fundamental tradeoff between PAPR and code rate. If a word has low PAPR, it is likely that its neighbouring words too will have relatively low PAPR values. A code with good PAPR reduction properties can be constructed using these words. However, for the code to correct errors, adequate distance between the words has to be maintained. Chapter 5: Joint Error Correction and PAPR Reduction of OFDM Signals
  • an encoding technique for joint error correction and PAPR reduction of OFDM signals is proposed.
  • the proposed technique uses a standard block code for error correction and achieves PAPR reduction at the expense of lower error correcting capability of the block code used.
  • This technique is first expressed as an optimisation problem and a computationally efficient suboptimal algorithm for solving this problem is then proposed.
  • the proposed technique has the following advantages over some of the other coding techniques:
  • Codewords obtained from the encoder is decoded using the standard decoder of the block code used.
  • the block diagram of the proposed encoder is shown in Figure 1.9.
  • the input message sequence m of k bits is first encoded using a standard block code C (n, k,t) Chapter 5: Joint Error Correction and PAPR Reduction of OFDM Signals
  • w(E) is the Hamming weight of E.
  • the problem (1.32) is a constrained discrete optimisation problem and can be solved using an optimisation technique.
  • finding the optimum solution for this problem can be computationally very Chapter 5: Joint Error Correction and PAPR Reduction of OFDM Signals
  • INPUT Message sequence m, generator matrix G of a block code C(n, k, t), an integer W, W ⁇ t.
  • step 3 The complexity of this algorithm largely depends on step 3.
  • a brute-force method of computing this step would require n PAPR evaluations to locate the bit position which corresponds to the largest PAPR reduction.
  • Each PAPR evaluation would require an IDFT computation.
  • step 3 would require a total of n IDFTs.
  • a closer investigation of this step shows that the mathematical operations between each IDFT computation are highly repetitive.
  • a simplification of step 3 is presented below.
  • the OFDM signal x was expressed in (1.4) as
  • the vector x in (1.35) is the IDFT of the unflipped sequence U, which is computed only once for each iteration £.
  • Generation of the matrix M does not require any additional computations, as it can be obtained during the computation of x.
  • M can be updated by replacing the column M 3 - with -M 7 -, where j is the flipped bit position of iteration £-1.
  • the simplification given in (1.35) significantly reduces the computational load of the proposed algorithm. Similar simplifications can be obtained for other modulation schemes.
  • Chapter 5 Joint Error Correction and PAPR Reduction of OFDM Signals
  • Simulations are performed to evaluate the performance of the proposed algorithm.
  • the simulations are carried out for OFDM systems with different values of N with different modulation schemes.
  • Figures 1.10, 1.11, 1.12 and 1.13 show the CCDFs of PAPR for the proposed encoding algorithm. In general, the closer the CCDF curve to the vertical axis, the better its PAPR reduction performance.
  • Figures 1.10 and 1.11 are obtained for 64 and 128 subcarriers with QPSK modulation respectively and Figures 1.12 and 1.13 are obtained for 64 and 128 subcarriers with 16QAM modulation. From these figures, it can be seen that, the PAPR reduction increases with the value of W . However, a limit is observed after which no significant reduction is achieved. For the OFDM systems with 128 subcarriers, this limit is 12. For the uncoded OFDM systems with 128 subcarriers, the PAPR of a signal exceeds 11.6 dB for 0.01% (i.e. 1 in 10000) of the transmitted OFDM symbols. At the same probability (i.e.
  • the PAPR of the OFDM signal encoded with the proposed algorithm is about 6.5 dB for systems with 128 subcarriers. This corresponds to a PAPR reduction of 5.1 dB over the uncoded OFDM system.
  • PAPR reduction performance of the proposed algorithm for various OFDM system configurations are shown in Table 1.5.
  • 0.1% PAPR gain refers to the amount of PAPR reduction achieved over the uncoded OFDM system at the 0.1% PAPR level in the CCDF plot.
  • Table 1.5 PAPR reduction performance of the proposed algorithm.
  • the code C has a variable error correcting capability T, (t — W) ⁇ T ⁇ t.
  • t is the error correcting capability of the code G.
  • the variable T depends on the weight of E vector, w(E).
  • a PAPR code C is normally denoted using the parameters (n, k, t, 77), where ⁇ is the PAPR of the code.
  • the PAPR ⁇ of C defined in (1.28), is one of the most important parameters used to design PAPR codes.
  • the definition (1.28) can Chapter 5: Joint Error Correction and PAPR Reduction of OFDM Signals
  • the code C obtained from the proposed encoder can be described using the parameters (n, k, T, ⁇ , N), where ⁇ (in dB) is a measure of PAPR of the code defined in (1.37) and N is the number of subcarriers.
  • Table 1.6 Examples of PAPR reduced codes derived from standard BCH codes.
  • the BER performance of the OFDM system with the proposed encoder is evaluated by computer simulations.
  • An SSPA model described in (1.12) is adopted to simulate signal distortions due to the non-linear amplifier.
  • the smoothing constant p of the SSPA is set at 2.
  • amplifier nonlinearities cause spectral leakage and performance degradation of the system.
  • the input back-off is increased.
  • the efficiency of the amplifier and the operational range of the system reduces with an increase in input back-off.
  • an input back-off of 0 dB is used. It is assumed that the OFDM signal is passed through the SSPA amplifier and then through a channel corrupted by additive white Gaussian noise (AWGN).
  • AWGN additive white Gaussian noise
  • n is a complex Gaussian noise vector with mean zero and s is the output from the amplifier.
  • s is the output from the amplifier.
  • Figures 1.15 and 1.16 show BER performance of some of the codes obtained from the proposed encoder.
  • the PAPR reduced codes obtained are compared with both
  • the variable U of the SLM technique is the number of signal representations generated for comparison. To generate U representations, U IDFTs have to be computed. The results show that a large number of representations (i.e higher value of U) are required to attain the same PAPR reduction performance of the proposed algorithm. Results presented in Figures 1.17 and 1.18 show that the proposed algorithm performs better than the SLM technique. The largest performance difference is observed at higher percentages of PAPR (i.e. > 0.1% PAPR). In general, for small values of U, the complexity of the proposed algorithm is higher Chapter 5: Joint Error Correction and PAPR Reduction of OFDM Signals
  • Figure 1.19 and 1.20 show the comparison of the BER performance of the proposed algorithm with the SLM.
  • the ordinary SLM technique requires perfect side information to retrieve the transmitted information at the receiver. Ideal side information at the receiver is assumed for all simulations carried out for SLM. Even with ideal side information, the BER performance of SLM shows an error floor for all simulations conducted.
  • the proposed algorithm which is designed to correct errors as well as reduce PAPR, performs much better than the SLM.
  • Table 1.7 shows a comparison of the PAPR reduction performance with Chapter 5: Joint Error Correction and PAPR Reduction of OFDM Signals
  • 0.1% PAPR gain refers to the amount of PAPR reduction achieved over the uncoded OFDM system, at 0.1% PAPR level in the CCDF plot.
  • the results shown in the table are approximate and are taken from the reference quoted. Further, some of these results may not necessary be the optimum performance for the technique. Nevertheless, the results presented in the table show that the PAPR reduction performance of the proposed algorithm is comparable with the best techniques in the table.
  • ETSI Radio Broadcasting Systems
  • DAB Digital Audio Broadcasting
  • ETSI Digital Video Broadcasting (DVB); Framing, Structure, Channel Coding and Modulation for digital Terrestrial Television. EN 300 744 Vl.5.1, November 2004.
  • N OFDM
  • T denotes the symbol peof high-speed transmission scheme suitable for digiriod
  • the L-oversampled version OFDM has several advantages over the single carrier of x(t) is given by systems such as its robustness against multipath fading JV-I and high spectral efficiency.
  • the PAPR of an OFDM sigtechnique is the selective mapping (SLM) [3].
  • Coding [4] nal is always less than or equal to 101og 10 (JV) dB. This is another distortionless technique which not only remeans the PAPR value of an OFDM signal in a system Jerusalem PAPR but also corrects errors. with 128 subcarriers can be as high as 2IdB.
  • the distribution of PAPR values is commonly delimited to be used only with M-ary Phase Shift Keying scribed using the complementary cumulative distribu(MPSK) modulations.
  • the CCDF of the PAPR repder the use of Reed-Muller codes in practical OFDM resents the probability that the PAPR of a data block systems is their low code rate.
  • the code rate vanexceeds a given threshold z. That is, ishes rapidly for n > 32.
  • the code rate of RM(1,6) which has a codeword length of only 128 bits
  • a signal with a larger PAPR value requires a wider linear region of the amplifier to avoid signal distortion.
  • the proposed coding technique is expressed as an However, power amplifiers with wider linear range that optimisation problem in (7). can handle large signal peaks can be highly power consuming, making the amplifier very inefficient.
  • the operLet C (n, k, t) be a standard block code with generaating point of an amplifier is given by the back-off. High tor matrix G, length n, dimension k and error correcting back-offs move the operating point of the amplifier to capability t. Given an information sequence m of length the linear region, which reduces the effects of nonlin- k and an integer W, W ⁇ t, find error pattern E e F ⁇ earities.
  • the input back-off (IBO) of an amplifier can for defined by min
  • the optimisation optimisation large number for this A comparable in PAPR reduction
  • QPSK Quadrature Phase Shift Keying
  • 16QAM 16-Quadrature Amplitude Modulation
  • a PAPR code C is normally denoted using the parameters (n, k ) 4, ⁇ ) where ⁇ is the PAPR of the code defined by,
  • the PAPR of a signal exceeds 11.6dB for 0.01% (i.e. 1 in 10000) of the transmitted OFDM symbols, (i.e. 0.01% of PAPR is 11.6dB).
  • the 0.01% PAPR of the OFDM signal encoded with the proposed algorithm is around 6.5dB for both systems. This corresponds to a PAPR reduction of 5.IdB over the uncoded OFDM system.
  • the 0.01% PAPR of the encoded OFDM signal were found to be 7.2dB
  • the ordinary SLM technique requires perfect side information for retrieving transmitted information at the receiver. Ideal side information at the receiver was assumed for all SLM simulations. BER performance of SLM show an error floor for all simulations conducted. As expected, the proposed algorithm which is designed to correct errors as well as reduced PAPR, performed much better than the SLM.
  • Figure 5 BER performance of PAPR reduced code OFDM signals.
  • mance of the algorithm were investigated and compared with other systems. The results showed that this algorithm gave PAPR reductions of more than 4.8dB over amplifier described by, uncoded OFDM systems with 128 and 256 subcarri-
  • the proposed algorithm reduces PAPR as well as corrects errors occurred due to amplifier nonlinearity and channel noise.
  • the simulated results also showed that where the nonlinear gain /
  • A(t) is the ampliis comparable with other well known PAPR reduction tude of the input signal,
  • a max is the maximum output techniques such as SLM. amplitude and the parameter p controls the smoothness of the transition from the linear region to the saturaREFERENCES .H. Han, J. K. Lee, "An Overview of Peak-to-Aver tion region.
  • p was [ 1 ] S age Power Ratio Reduction Techniques for Multicarrier Transmission," set at 2 and the input back-off at OdB. It is assumed IEEE Wireless Commumcatwns, pp. 56-65, April 20Q5. that the OFDM signal is passed through the SSPA am[2] X. Li and L.J. Cimini, Jr., "Effect of Clipping and Filtering on plifier and then through a channel corrupted by additive the Performance of OFDM," IEEE Communication letters, white Gaussian noise (AWGN).
  • the received vector r vol. 2, pp. 131-133, May 1998. is given by, [3] R. Bauml, R. Fisher, and J.
  • Figure 5 shows the BER performance of the PAPR tio of Multicarrier Transmission Scheme," Electromcs Letters, reduced Reed-Solomon (RS) code (63,27,8,6.3,95) on vol. 30, pp. 2098-2099, December 1994.
  • GF(2 ⁇ ) on an OFDM system with 95 16QAM subcar- [8] A.E. Jones and T.A. Wilkinson, "Combined coding For error riers. This code is also equivalent to (378,162,8,6.3,95) control and Increased Robustness to System Nonlinearities in OFDM," Vehicular Technology Conference, 1996. Mobile on GF(2).
  • the BER performance of the code is comTechnology for the Human Race, IEEE 46th, vol. 2, pp.
  • C is the Reed-Solomon [9] K. G. Paterson, "Generalized Reed-Muller codes and Power code (63,27,18) on GF(2 ⁇ ) which has a higher error corControl in OFDM Modulation," IEEE Trans. Information recting capability than C.
  • the BER perforTheory vol. 46, pp. 104-120, January 2000.

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Abstract

L'invention concerne un procédé, un dispositif et un système de réduction du rapport de puissance de crête sur puissance moyenne (PAPR) d'un signal codé d'erreur. Le procédé consiste à introduire au moins une erreur dans le signal codé d'erreur de telle manière que le rapport de puissance de crête sur puissance moyenne du signal codé d'erreur à erreur introduite est inférieur au rapport de puissance de crête sur puissance moyenne du signal codé d'erreur.
PCT/AU2007/001604 2006-10-20 2007-10-22 §procédé de réduction du rapport de puissance de crête sur puissance moyenne dans des signaux à multiplexage par répartition orthogonale de la fréquence WO2008046163A1 (fr)

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