AS AN attractive technology for wireless communications,

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1 IEEE TRANSACTIONS ON BROADCASTING, VOL. 54, NO. 2, JUNE An Overview: Peak-to-Average Power Ratio Reduction Techniques for OFDM Signals Tao Jiang, Member, IEEE, and Yiyan Wu, Fellow, IEEE Abstract One of the challenging issues for Orthogonal Frequency Division Multiplexing (OFDM) system is its high Peak-to-Average Power Ratio (PAPR). In this paper, we review and analysis different OFDM PAPR reduction techniques, based on computational complexity, bandwidth expansion, spectral spillage and performance. We also discuss some methods of PAPR reduction for multiuser OFDM broadband communication systems. Index Terms Complementary cumulative distribution function (CCDF), high power amplifier (HPA), multiuser OFDM, OFDM, peak-to-average power ratio (PAPR). I. INTRODUCTION AS AN attractive technology for wireless communications, Orthogonal Frequency Division Multiplexing (OFDM), which is one of multi-carrier modulation (MCM) techniques, offers a considerable high spectral efficiency, multipath delay spread tolerance, immunity to the frequency selective fading channels and power efficiency [1], [2]. As a result, OFDM has been chosen for high data rate communications and has been widely deployed in many wireless communication standards such as Digital Video Broadcasting (DVB) and based mobile worldwide interoperability for microwave access (mobile WiMAX) based on OFDM access technology [3]. However, still some challenging issues remain unresolved in the design of the OFDM systems. One of the major problems is high Peak-to-Average Power Ratio (PAPR) of transmitted OFDM signals. Therefore, the OFDM receiver s detection efficiency is very sensitive to the nonlinear devices used in its signal processing loop, such as Digital-to-Analog Converter (DAC) and High Power Amplifier (HPA), which may severely impair system performance due to induced spectral regrowth and detection efficiency degradation. For example, most radio systems employ the HPA in the transmitter to obtain sufficient transmits power and the HPA is usually operated at or near the saturation region to achieve the maximum output power efficiency, and thus the memory-less nonlinear distortion due to high PAPR of the input signals will be introduced into the communication channels. If the HPA is not operated in linear region with large power back-off, it is impossible to keep the out-of-band power Manuscript received August 13, 2007; revised December 3, T. Jiang is with the Department of Electronic and Information Engineering, Huazhong University of Science and Technology, Wuhan , P. R. China ( Tao.Jiang@ieee.org). Y. Wu is with the Communications Research Center, Ottawa, ON K2H 8S2, Canada ( yiyan.wu@crc.ca). Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /TBC below the specified limits. This situation leads to very inefficient amplification and expensive transmitters. Therefore, it is important and necessary to research on the characteristics of the PAPR including its distribution and reduction in OFDM systems, in order to utilize the technical features of the OFDM. As one of characteristics of the PAPR, the distribution of PAPR, which bears stochastic characteristics in OFDM systems, often can be expressed in terms of Complementary Cumulative Distribution Function (CCDF). Recently, some researchers have reported on determination of the PAPR distribution based on different theoretics and hypotheses [4] [10]. Moreover, various approaches also have been proposed to reduce the PAPR including clipping [11] [14], coding schemes [15] [21], phase optimization [22], [23], nonlinear companding transforms [24] [29], Tone Reservation (TR) and Tone Injection (TI) [30], [31], constellation shaping [32] [34], Partial Transmission Sequence (PTS) and Selective Mapping (SLM) [35] [51] and other techniques such as pre-scrambles proposed in [52]. These schemes can mainly be categorized into signal scrambling techniques, such as block codes and PTS etc., and signal distortion techniques such as clipping. Although some techniques of PAPR reduction have been summarized in [53], it is still indeed needed to give a comprehensive review including some motivations of PAPR reductions, such as power saving, and to compare some typical methods of PAPR reduction through theoretical analysis and simulation results directly. An effective PAPR reduction technique should be given the best tradeoff between the capacity of PAPR reduction and transmission power, data rate loss, implementation complexity and Bit-Error-Ratio (BER) performance etc. In this paper, firstly we investigate the distribution of PAPR based on the characteristics of the OFDM signals. Then, we analyze five typical techniques of PAPR reduction and propose the criteria of PAPR reduction in OFDM systems in details. Finally, we briefly discuss the issue of PAPR in some broadband communication systems correlative with OFDM technology, such as multiuser OFDM systems. II. CHARACTERISTICS OF OFDM SIGNALS Let a block of symbols is formed with each symbol modulating one of a set of subcarriers, where is the number of subcarriers. The subcarriers are chosen to be orthogonal, that is,, where and is the original symbol period. Therefore, the complex envelope of the transmitted OFDM signals can be written as (1) /$ IEEE

2 258 IEEE TRANSACTIONS ON BROADCASTING, VOL. 54, NO. 2, JUNE 2008 Fig. 1. Distribution of PAPR of OFDM signal samples oversampled by different L. where. Suppose that the input data streams is statistically independent and identically distributed (i.i.d.), i.e. the real part and imaginary part are uncorrelated and orthogonal. Therefore, based on the central limit theorem, when is considerably large, the distribution of both and approaches Gaussian distribution with zero mean and variance, where is the expected value of [27]. In other words, OFDM signals with large become Gaussian distributed with Probability Density Function (PDF) as [25] where is the variance of. Moreover, the Rayleigh nature of original OFDM signals amplitude can be gotten and its PDF can be expressed as [30] (2) where is the average power of and it can be computed in the frequency domain because Inverse Fast Fourier Transform (IFFT) is a (scaled) unitary transformation. 2) Discrete-time PAPR The PAPR of the discrete time sequences typically determines the complexity of the digital circuitry in terms of the number of bits necessary to achieve a desired signal to quantization noise for both the digital operation and the DAC. However, we are often more concerned with reducing the PAPR of the continuous-time signals in practice, since the cost and power dissipation of the analog components often dominate. To better approximate the PAPR of continuous-time OFDM signals, the OFDM signals samples are obtained by times oversampling. -times oversampled time-domain samples are -point IFFT of the data block with zero-padding. Therefore, the oversampled IFFT output can be expressed as where is the amplitude of OFDM signals. (3) (5) A. Baseband PAPR III. DEFINITION OF PAPR 1) Continuous-time PAPR In general, the PAPR of OFDM signals is defined as the ratio between the maximum instantaneous power and its average power Fig. 1 shows the distribution of the PAPR of the OFDM signals with and. As shown, the largest PAPR increase happens from to. However, the PAPR does not increase significantly after. It has shown that is sufficient to get accurate PAPR results [30]. The PAPR computed from the -times oversampled time domain OFDM signal samples can be defined as (6) (4) where denotes the expectation operator.

3 JIANG AND WU: OVERVIEW OF PEAK-TO-AVERAGE POWER RATIO REDUCTION TECHNIQUES FOR OFDM SIGNALS 259 B. Passband PAPR Note that, if is large, an OFDM system usually does not employ pulse shaping, since the power spectral density of the band-limited OFDM signal is approximately rectangular. Thus, the amplitude of OFDM RF signals can be expressed as where is the carrier frequency and. Therefore, the peak of RF signals is equivalent to that of the complex baseband signals. Moreover, the average power of the passband signal is Therefore, the passband PAPR is approximately twice the baseband PAPR, i.e. In this paper, we only consider the PAPR of the baseband OFDM signals. IV. MOTIVATION OF PAPR REDUCTION A. Nonlinear Characteristics of HPA and ADC Most radio systems employ the HPA in the transmitter to obtain sufficient transmission power. For the proposed of achieving the maximum output power efficiency, the HPA is usually operated at or near the saturation region. Moreover, the nonlinear characteristic of the HPA is very sensitive to the variation in signal amplitudes. However, the variation of OFDM signal amplitudes is very wide with high PAPR. Therefore, HPA will introduce inter-modulation between the different subcarriers and introduce additional interference into the systems due to high PAPR of OFDM signals. This additional interference leads to an increase in BER. In order to lessen the signal distortion and keep a low BER, it requires a linear work in its linear amplifier region with a large dynamic range. However, this linear amplifier has poor efficiency and is so expensive. Power efficiency is very necessary in wireless communication as it provides adequate area coverage, saves power consumption and allows small size terminals etc. It is therefore important to aim at a power efficient operation of the non-linear HPA with low back-off values and try to provide possible solutions to the interference problem brought about. Hence, a better solution is to try to prevent the occurrence of such interference by reducing the PAPR of the transmitted signal with some manipulations of the OFDM signal itself. Large PAPR also demands the DAC with enough dynamic range to accommodate the large peaks of the OFDM signals. (7) (8) (9) Although, a high precision DAC supports high PAPR with a reasonable amount of quantization noise, but it might be very expensive for a given sampling rate of the system. Whereas, a low-precision DAC would be cheaper, but its quantization noise will be significant, and as a result it reduces the signal Signal-to-Noise Ratio (SNR) when the dynamic range of DAC is increased to support high PAPR. Furthermore, OFDM signals show Gaussian distribution for large number of subcarriers, which means the peak signal quite rarely occur and uniform quantization by the ADCs is not desirable. If clipped, it will introduce in band distortion and out-of-band radiation (adjacent channel interference) into the communication systems. Therefore, the best solution is to reduce the PAPR before OFDM signals are transmitted into nonlinear HPA and DAC. B. Power Saving When a HPA have a high dynamic range, it exhibits poor power efficiency. It has been shown that PAPR reduction can significantly save the power, in which the net power saving is directly proportional to the desired average output power and it is highly dependent upon the clipping probability level [54]. Suppose that an ideal linear model for HPA, where linear amplification is achieved up to the saturation point, and thus we obtain (10) where is the HPA efficiency and it is defined as, where is the average of the output power and is the constant amount of power regardless of the input power. To illustrate the power inefficiency of a HPA in terms of the PAPR, we give an example of OFDM signals with 256 subcarriers and its CCDF has been shown in Fig. 1. In order to guarantee that probability of the clipped OFDM frames is less than 0.01%, we need to apply an input backoff (IBO) equivalent to the PAPR at the probability level, i.e. ( ), referring to Fig. 1, and thus the efficiency of HPA becomes. Therefore, so low efficiency is a strong motivation to reduce the PAPR in OFDM systems. V. DISTRIBUTION OF THE PAPR IN OFDM SYSTEMS It is known that the CCDF of PAPR can be used to estimate the bounds for the minimum number of redundancy bits required to identify the PAPR sequences and evaluate the performance of any PAPR reduction schemes. We can also determine a proper output back-off of HPA to minimize the total degradation according to CCDF. Moreover, we can directly apply distribution of PAPR to calculate the BER and estimate achievable information rates. In practice, we usually adjust these design parameters jointly according to simulation results. Therefore, if we can use an analytical expression to accurately calculate the PAPR distribution for OFDM systems, it can greatly simplify the system design process. Therefore, it is of great importance to accurately identify PAPR distribution in OFDM systems. Recently, some upper and lower bounds of the PAPR, which is based on the Rayleigh distribution and Nyquist sampling rate, have been derived. In the OFDM system with M-Phase-Shift- Keying (MPSK) modulation, signal constellation has the same

4 260 IEEE TRANSACTIONS ON BROADCASTING, VOL. 54, NO. 2, JUNE 2008 amplitude level, and thus the power of each subcarrier is constant. Therefore, the PAPR of an MPSK-OFDM signal can be expressed as [30] (11) However, for the OFDM system with square M-Quadrature Amplitude Modulation (MQAM), signal constellation has varying signal power levels over different constellation points. When all the subcarriers have the same phase, the maximum of PAPR occurs. Therefore, according to the conclusion of [55], the upper bound of PAPR in MQAM-OFDM systems can be derived out (12) For a relatively large, the lower and upper bounds of the distribution of the PAPR have been proposed in [7], which were developed based on the previous works in conjunction with some approximations and parameters obtained through simulations. In [8], some bounds analysis has also been developed for both independent and dependent subcarriers in OFDM systems. For independent subcarriers, a generic path for bounding practical constellations was used and discussed. For dependent subcarriers, some theoretical bounds of distributions of the PAPR have been obtained in terms of the Euclidian distance distributions, in which the focus was mainly on binary codes, such as Bose-Chaudhuri-Hocquenghem (BCH) codes. However, the lower and upper bounds can offer little help in characterizing the distribution of the PAPR in practical OFDM systems. In fact, the accurate statistical distribution of the PAPR for generic OFDM system is what we want. When the number of the subcarriers is relatively small, the CCDF expression of the PAPR of OFDM signals can be written as [4] (13) However, (13) does not fit well in OFDM systems with a very large [4]. In [5], an empirical approximation expression of the CCDF of the PAPR in OFDM systems has been given as (14) It should be noted that (14) lacks theoretical justification and also yields some discrepancies with the simulation results for large, which has been proven in [6]. In [6], an analytical PAPR CCDF expression has been developed, which is based on the level-crossing rate approximation of the peak distribution along with the exact distribution, since the envelope of an OFDM signal can always be considered as an asymptotically Gaussian process in a band-limited OFDM system. In fact, the theoretical results obtained in [6] were based on the conditional probability of the peak distribution of the OFDM signals when the reference level is given. When the constraint provides a lower bound of, the effect on the accuracy of the PAPR distribution can be numerically evaluated. Indeed, for high, the conditional probability that the peak of the OFDM signals exceeds may be very small. In this case, the expression of the PAPR CCDF, as shown in [6], can be simplified as (15) The approximation of (15) can be made relatively accurate for a relatively large number of subcarriers by appropriately adjusting the reference level of the PAPR. If the range of the PAPR of interest is great, the distribution can be further simplified without loss of the accuracy. In [6], it also has been shown that the statistical distribution of the PAPR of the OFDM signals is not so sensitive to the increase of the number of subcarriers. In coded OFDM systems, it has been proven that the complex envelope of the coded OFDM signals can converge weakly to a Gaussian random process if the number of subcarriers goes to infinity [9]. In [9], a simple approximation of the CCDF of PAPR has been developed by employing the extreme value theory, and the expression can be written as (16) However, all the above mentioned the expressions of the CCDF have not been considered power distribution strategy in OFDM systems. Similarly, with the help of the extreme value theory for Chi-squared-2 process, a more accurate analytical expression of the CCDF of PAPR for adaptive OFDM systems with unequal power allocation to subcarriers has been derived in [10] (17) where if the subcarrier at DC is inactive, otherwise if the subcarrier at DC is active, in which denotes the number of active subcarriers (carrying information) and denotes the number of inactive subcarriers (idle). If the subcarrier at DC is nonzero, it is active subcarrier; otherwise it is inactive subcarrier. Thus, the number of the subcarriers should be equal to the sum of and. denotes the transmission power allocated to the -th subcarrier. VI. PAPR REDUCTION TECHNIQUES IN OFDM SYSTEMS In this section, we mainly discuss five typical techniques for PAPR reduction in OFDM systems. A. Clipping and Filtering The simplest and most widely used technique of PAPR reduction is to basically clip the parts of the signals that are outside the allowed region [11]. For example, using HPA with saturation level below the signal span will automatically cause the signal to be clipped. For amplitude clipping, that is where (18) is preset clipping level and it is a positive real number.

5 JIANG AND WU: OVERVIEW OF PEAK-TO-AVERAGE POWER RATIO REDUCTION TECHNIQUES FOR OFDM SIGNALS 261 Generally, clipping is performed at the transmitter. However, the receiver need to estimate the clipping that has occurred and to compensate the received OFDM symbol accordingly. Typically, at most one clipping occurs per OFDM symbol, and thus the receiver has to estimate two parameters: location and size of the clip. However, it is difficult to get these information. Therefore, clipping method introduces both in band distortion and out of band radiation into OFDM signals, which degrades the system performance including BER and spectral efficiency. Filtering can reduce out of band radiation after clipping although it can not reduce in-band distortion. However, clipping may cause some peak regrowth so that the signal after clipping and filtering will exceed the clipping level at some points. To reduce peak regrowth, a repeated clipping-and-filtering operation can be used to obtain a desirable PAPR at a cost of computational complexity increase. As improved clipping methods, peak windowing schemes attempt to minimize the out of band radiation by using narrowband windows such as Gaussian window to attenuate peak signals. B. Coding Schemes When signals are added with the same phase, they produce a peak power, which is times the average power. Of course, not all code words result in a bad PAPR. Therefore, the good PAPR reduction can be obtain when some measures are taken to reduce the occurrence probability of the same phase of the signals, which is the key idea of the coding schemes. A simple block coding scheme was introduced by Jones et al.[15], and its basic idea is that mapping 3 bits data into 4 bits codeword by adding a Simple Odd Parity Code (SOBC) at the last bit across the channels. The main disadvantage of SOBC method is that it can reduce PAPR for a 4-bit codeword. Later, Wulich applied the Cyclic Coding (CC) to reduce the PAPR [56]. In 1998, Fragiacomo proposed an efficient Simple Block Code (SBC) to reduce the PAPR of OFDM signals [57]. However, it is concluded that SBC is not effective when the frame size is large. Subsequently, Complement Block Coding (CBC) and Modified Complement Block Coding (MCBC) schemes were proposed to reduce the PAPR without the restriction of frame size [20], [58]. CBC and MCBC are more attractive due to their flexibility on choosing the coding rate, frame size and low implementation complexity. CBC and MCBC utilize the complementary bits that are added to the original information bits to reduce the probability of the peak signals occurrence. To make comparisons, some results of the PAPR reduction obtained with different coding schemes have been shown in Table I, in which the number of subblock is 2 and the coding rate for MCBC. About 3-dB PAPR reduction can be obtained when coding rate by using CBC with long frame size. It is also shown that the PAPR reductions obtained with CBC when coding rate are almost the same as that when. In addition, when coding rate is 3/4, more than 3-dB more PAPR reduction can be obtained using MCBC than the other schemes with any frame size. The flexibility in coding rate choice and low complexity makes the proposed CBC and MCBC schemes attractive for OFDM systems with large frame sizes and high coding rates. TABLE I PAPR REDUCTION COMPARISON WITH DIFFERENT CODING SCHEMES In [59], [60], [62], authors used the Golay complementary sequences to achieve the PAPR reduction, in which more than 3-dB PAPR reduction had been obtained. Codes with error correcting capabilities has been proposed in [61] to achieve more lower PAPR for OFDM signals by determining the relationship of the cosets of Reed-Muller codes to Golay complementary sequences. While these block codes reduce PAPR, they also reduce the transmission rate, significantly for OFDM systems with large number of subcarriers. In fact, let be a code defined over an equal energy constellation, denotes the rate and denotes the length of the, respectively, then has possible codewords. Therefore, it is possible to compute the codewords with large PAPR by trying all the codewords of and computing the peaks of the corresponding signals at some selected time points. However, it is little hope for computing the PAPR of an arbitrary code when is large. Even if it is possible, the complexity is still too high. Based on this motivates, authors of [22] proposed a novel method of computation and reduction of the PAPR and it mainly introduced a specific phase shift to each coordinate of all possible codewords where phase shifts are independent of the codewords and known both to transceiver, then it can be freely obtained more 4.5-dB PAPR reduction by using the optimized phase shifts. From this viewpoint, we also consider the coding scheme of PAPR reduction as a special phase optimization. In summarization, the inherent error control capability and simplicity of implementation make coding method more promising for practical OFDM systems design. However, the main disadvantage of this method is the good performance of the PAPR reduction at the cost of coding rate loss. C. PTS and SLM In a typical OFDM system with PTS approach to reduce the PAPR, the input data block in is partitioned into disjoint subblocks, which are represented by the vectors [35] as shown in Fig. 2. Therefore, we can get (19) where with or 0. In general, for PTS scheme, the known subblock partitioning methods can be classified into three categories [35]: adjacent partition, interleaved partition and pseudo-

6 262 IEEE TRANSACTIONS ON BROADCASTING, VOL. 54, NO. 2, JUNE 2008 Fig. 2. Block diagram of PTS technique. Fig. 3. Block diagram of SLM technique. random partition. Then, the subblocks are transformed into time-domain partial transmit sequences (20) These partial sequences are independently rotated by phase factors. The objective is to optimally combine the subblocks to obtain the timedomain OFDM signals with the lowest PAPR (21) Therefore, there are two important issues should be solved in PTS: high computational complexity for searching the optimal phase factors and the overhead of the optimal phase factors as side information needed to be transmitted to receiver for the correct decoding of the transmitted bit sequence. Suppose that there are phase angles to be allowed, thus can has the possibility of different values. Therefore, there are alternative representations for an OFDM symbol. To reduce the searching complexity and avoid/reduce the usage of side information, many extensions of PTS have been developed recently [63] [67]. In [66], authors proposed a novel scheme, which is based on a nonlinear optimization approach named as simulated annealing, to search the optimal combination of phase factors with low complexity. In general, PTS needs IFFT operations for each data block, and the number of the required side information bits is, where denotes the smallest integer that does not exceed. Similarly, in SLM, the input data sequences are multiplied by each of the phase sequences to generate alternative input symbol sequences. Each of these alternative input data sequences is made the IFFT operation, and then the one with the lowest PAPR is selected for transmission [51]. A block diagram of the SLM technique is depicted in Fig. 3. Each data block is multiplied by different phase factors, each of length,, resulting in different data blocks. Thus, the vth phase sequence after multiplied is. Therefore, OFDM signals becomes as (22) where,. Among the data blocks, only one with the lowest PAPR is selected for transmission and the corresponding selected phase factors also should be transmitted to receiver as side information. For implementation of SLM OFDM systems, the SLM technique needs IFFT operation and the number of required bits as side information is for each data block. Therefore, the ability of PAPR reduction in SLM depends on the number of phase factors and the design of the phase factors. Some extension of SLM also have been proposed to reduce the computational complexity and number of the bits for side information transmission [36]. For example,

7 JIANG AND WU: OVERVIEW OF PEAK-TO-AVERAGE POWER RATIO REDUCTION TECHNIQUES FOR OFDM SIGNALS 263 Fig. 4. The spectrums of original OFDM signals and companded signals. an SLM scheme without explicit side information was proposed in [68]. Although PTS and SLM are important probabilistic schemes for PAPR reduction, it was already known that SLM can produce multiple time domain OFDM signals that are asymptotically independent, whereas the alternative OFDM signals generated by PTS are interdependent. PTS divides the frequency vector into some subblocks before applying the phase transformation. Therefore, some of the complexity of the serval full IFFT operations can be avoided in PTS, so that it is more advantageous than SLM if the amount of computational complexity is limited [69]. Also it is demonstrated that the PAPR reduction in PTS performs better than that of SLM. However, the required bits of the side information in PTS is larger than that of SLM. D. Nonlinear Companding Transforms One of the most attractive schemes is nonlinear companding transform due to its good system performance including PAPR reduction and BER, low implementation complexity and no bandwidth expansion. The first nonlinear companding transform is the -law companding, which is based on the speech processing algorithm -law, and it has shown better performance than that of clipping method [24]. -law mainly focuses on enlarging signals with small amplitude and keeping peak signals unchanged, and thus it increase the average power of the transmitted signals and possibly results in exceeding the saturation region of HPA to make the system performance worse. In fact, the nonlinear companding transform is also an especial clipping scheme. The differences between the clipping and nonlinear companding transform can be summarized as: 1) Clipping method deliberately clips large signals when the amplitude of the original OFDM signals is larger than the given threshold, and thus the clipped signals can not be recovered at the receiver. However, nonlinear companding transforms compand original OFDM signals using the strict monotone increasing function. Therefore, the companded signals at the transmitter can be recovered correctly through the corresponding inversion of the nonlinear transform function at the receiver; 2) Nonlinear companding transforms enlarge the small signals while compressing the large signals to increase the immunity of small signals from noise, whereas clipping method does not change the small signals. Therefore, clipping method suffers from three major problems: in-band distortion, out-of-band radiation and peak regrowth after digital analog conversion. As a result, the system performance degradation due to the clipping may not be optimistic. However, nonlinear companding transforms can operate well with good BER performance while keeping good PAPR reduction [70]. The design criteria of nonlinear companding transform has also been given in [70]. Since the distribution of the original OFDM signals has been known, such as Rayleigh distribution of the OFDM amplitudes written in (3), we can obtain the nonlinear companding transform function through theoretical analysis and derivation according to the desirable distribution of the companded OFDM signals. For example, we transform the amplitude of the original OFDM signals into the desirable distribution with its PDF,. Therefore, the nonlinear transform function can be derived as (23) Obviously, this nonlinear companding transform of (23) belongs to the exponential companding scheme. Based on this design criteria, two types of nonlinear companding transform, which are based on error function and exponential function, respectively, have been proposed in [25], [27]. It is well-known that original OFDM signals have a very sharp, rectangular-like power spectrum as shown in Fig. 4. This good property will be affected by the PAPR reduction schemes, e.g. slower spectrum roll-off, more spectrum side-lobes, and higher adjacent channel interference. Many PAPR reduction

8 264 IEEE TRANSACTIONS ON BROADCASTING, VOL. 54, NO. 2, JUNE 2008 Fig. 5. Block diagram of TR/TI approaches for PAPR reduction. schemes cause spectrum side-lobes generation, but the nonlinear companding transforms cause less spectrum side-lobes. As seen in Fig. 4, error and exponential companding transforms have much less impact on the original power spectrum comparing to the -law companding scheme. It is the major reason that the error and exponential companding schemes not only enlarge the small amplitude signals but also compress the large amplitude signals, while maintain the average power unchanged by properly choosing parameters, which can increase the immunity of small amplitude signals from noise. However, the -law companding transform increases the average power level and therefore requires a larger linear operation region in HPA. Nonlinear companding transform is a type of nonlinear process that may lead to significant distortion and performance loss by companding noise. Companding noise can be defined that the noises are caused by the peak regrowth after DAC to generate in-band distortion and out-band noise, by the excessive channel noises magnified after inverse nonlinear companding transform etc. For out-of-band noise, it needs to be filtered and oversampled. For in-band distortion and channel noises magnified, they need to iterative estimation. Unlike Additive White Gaussian Noise (AWGN), companding noise is generated by a process known and that can be recreated at the receiver, and subsequently be removed. In [28], the framework of an iterative receiver has been proposed to eliminate commanding noise for companded and filtered OFDM system. E. TR and TI TR and TI are two efficient techniques to reduce the PAPR of OFDM signals [30]. Fig. 5 describes the block diagram of TR and TI, in which the key idea is that both transmitter and receiver reserve a subset of tones for generating PAPR reduction signals. Note that these tones are not used for data transmission. In TR, the objective is to find the time domain signal to be added to the original time domain signal to reduce the PAPR. Let denote complex symbols for tone reservation at reserved tones. Thus, the data vector changes to after tone reservation processing, and this results in a new modulated OFDM signals as (24) where. Therefore, the main aim of the TR is to find out the proper to make the vector with low PAPR. To find the value of, we must solve a convex optimization problem that can easily be cast as a linear programming problem. Similarly, TI also uses an additive correction to optimize in (24). The basic idea of TI is to extend the constellation and thus the same data point corresponds to multiple possible constellation points. One option is to replicate the original shaded constellation into serval alternative ones. Therefore, is a translation vector such that. Note that TI needs not require the extra side information and the receiver only needs to know how to map the redundant constellations on the original one. An alternative strategy is to move the constellation points by applying an FFT on the clipped time signals, and the same operations are repeated till all the constellation points are within specified boundaries and the PAPR specification of the time signal is satisfied [71]. Some modifications of TI have been proposed to obtain good performance including PAPR reduction and low complexity [72]. The TI technique is more problematic than the TR technique since the injected signal occupies the frequency band as the information bearing signals. Moreover, the alternative constellation points in TI technique have an increased energy and the implementation complexity increases for the computation the optimal translation vector. VII. CRITERIA OF THE PAPR REDUCTION IN OFDM SYSTEMS As above analyzed, we find most of existing solutions still have some drawbacks and the obvious one is the trade-off between PAPR reduction and some factors such as bandwidth. The criteria of the PAPR reduction is to find the approach that it can reduce PAPR largely and at the same time it can keep the good performance in terms of the following factors as possible. 1) High capability of PAPR reduction: It is primary factor to be considered in selecting the PAPR reduction technique with as few harmful side effects such as in-band distortion and out-of-band radiation. 2) Low average power: Although it also can reduce PAPR through average power of the original signals increase, it requires a larger linear operation region in HPA and thus resulting in the degradation of BER performance. 3) Low implementation complexity: Generally, complexity techniques exhibit better ability of PAPR reduction. However, in practice, both time and hardware requirements for the PAPR reduction should be minimal. 4) No bandwidth expansion: The bandwidth is a rare resource in systems. The bandwidth expansion directly results in the data code rate loss due to side information (such as the phase factors in PTS and complementary bits in CBC). Moreover, when the side information are received in error unless some ways of protection such as channel coding employed. Therefore, when channel coding is used, the loss in data rate is increased further due to side information. Therefore, the loss in bandwidth due to side information should be avoided or at least be kept minimal. 5) No BER performance degradation: The aim of PAPR reduction is to obtain better system performance including BER than that of the original OFDM system. Therefore, all the methods, which have an increase in BER at the receiver, should be paid more attention in practice. Moreover, if the side information is received in error at the receiver, which may also result in whole erroneous data frame and thus the BER performance is reduced. 6) Without additional power needed: The design of a wireless system should always take into consideration the efficiency

9 JIANG AND WU: OVERVIEW OF PEAK-TO-AVERAGE POWER RATIO REDUCTION TECHNIQUES FOR OFDM SIGNALS 265 Fig. 6. Comparisons of CCDF based on different PAPR reductions. of power. If an operation of the technique which reduces the PAPR need more additional power, it degrades the BER performance when the transmitted signals are normalized back to the original power signal. 7) No spectral spillage: Any PAPR reduction techniques can not destroy OFDM attractive technical features such as immunity to the multipath fading. Therefore, the spectral spillage should be avoided in the PAPR reduction. 8) Other factors: It also should be paid more attention on the effect of the nonlinear devices used in signal processing loop in the transmitter such as DACs, mixers and HPAs since the PAPR reduction mainly avoid nonlinear distortion due to these memory-less devices introducing into the communication channels. At the same time, the cost of these nonlinear devices is also the important factor to design the PAPR reduction scheme. We consider a typical OFDM system with 256 subcarriers (namely ) and 16-QAM constellation in which oversampled OFDM sequences with the oversampling rate of 4 are used to analyze PAPR reduction and BER performance based on different schemes as shown in the following figures. The preset clipping level has been selected to 80% of the maximum of the original OFDM symbols in the clipping scheme and the number of the reserved tone is 20 in TR scheme. For PTS scheme, the rotation vectors belong to the set and the number of the subblocks is 16. Therefore, the searches is for each optimal PTS. Note that, for PTS and TR schemes, all the side information have not been submitted to the receiver. For nonlinear companding transform, the error companding is that proposed in [25], and the exponential companding is based on (23). As shown in Fig. 6, different curves of the CCDF have been given for random original OFDM symbols generated and different PAPR reduction schemes. From Fig. 6, it is very clear that all schemes can reduce the PAPR largely in OFDM system. However, their performances of the PAPR reduction are different. For example, when, the PAPRs are 2.6 db, 4.5 db, 6.6 db, 6.8 db, 6.9 db and 11.7 db for the exponential companding, error companding, PTS, TR, clipping scheme and original OFDM signals, respectively. Obviously, the signals companded by the nonlinear companding transform with exponential function can reduce the PAPR largest and the PAPR reduction of the clipping scheme is the smallest among these typical methods. Although clipping scheme can improve its performance of the PAPR reduction through reducing its preset clipping level A. However, the performance of the BER will be degraded largely when its preset clipping level is reduced [73]. Fig. 7 depicts the performance of BER versus SNR of actual OFDM signals with PAPR reduction based on different schemes over the AWGN channel, in which the typical HPA of the Solid State Power Amplifier (SSPA) has been considered. Note that SSPA produces no phase distortion and only the AM/AM conversion [25]. In Fig. 7, the performance bounds are obtained by ignoring the effect of SSPA and directly transmitting the original OFDM signals through the AWGN channels. Generally speaking, the performances of the BER with different PAPR reduction schemes have some degradation from Fig. 7. Specifically, to achieve a BER of, the minimum required SNR is 13.8 db (performance bound). The required SNRs under the exponential companding, PTS, TR, error companding and clipping schemes are 14.9 db, 15.7 db, 16.6 db, 17.5 db and 25.6 db, respectively. Therefore, an efficient PAPR reduction should be the lowest possible value of PAPR while keeping a minimal level BER. In Table II, we summarize the five typical PAPR reduction techniques based on the theoretical analysis and simulation results. VIII. PAPR REDUCTION FOR MULTIUSER OFDM SYSTEMS Recently, multiuser OFDM also has received much attention due to its applicability to high speed wireless multiple access

10 266 IEEE TRANSACTIONS ON BROADCASTING, VOL. 54, NO. 2, JUNE 2008 Fig. 7. Comparisons of BER based on different PAPR reductions. TABLE II COMPARISON OF DIFFERENT PAPR REDUCTION TECHNOLOGIES communication systems. In multiuser OFDM system, data streams from multiple users are orthogonally multiplexed onto the downlink and uplink subchannels. In a multiuser OFDM system, a group of carriers is assigned for each user with adaptive modulation, bit and power allocation. Obviously, the characteristics including distribution of the PAPR for each user in uplink multiuser OFDM is the same as that of the PAPR in single user OFDM system since the data of each user will be transmitted to channels independently in uplink multiuser OFDM system. Therefore, the PAPR can be reduced according to these schemes mentioned above in the uplink multiuser OFDM systems. However, the characteristics of the PAPR in downlink multiuser OFDM is different from that of the PAPR in single user OFDM system since the data composed from different users will be transmitted to channels successively in downlink multiuser OFDM system. Therefore, the PAPR reduction is more complicated in an downlink than that in OFDM uplink in multiuser OFDM systems. If downlink PAPR reduction is achieved by some approaches which have been designed for OFDM, each user has to process the whole data frame and then demodulate the assigned subcarriers to extract their own information. Thus, it introduces additional processing for each user at the receiver. Therefore, we mainly describe some modifications of PAPR reduction techniques for the downlink multiuser OFDM systems. 1) PTS/SLM for PAPR reduction in multiuser OFDM systems: PTS and SLM techniques can easily be modified for PAPR reduction in downlink of multiuser OFDM systems. For PTS, subcarriers assigned to one user are grouped into one or more subblocks, and then PTS can be applied to subblocks for all users. As side information, the selected phase factor for each subblock can be embedded into the pre-reserved subcarrier in each subblock. Note that, the pre-reserved subcarrier does not undergo the phase rotation in each subblock. Similarly, some of the subcarriers can be used to transmit side information when the modified SLM is applied to reduce the PAPR for multiuser OFDM systems. All users use the information carried by these subcarriers to obtain the phase sequence is used at the transmitter, and thus the data for each user can be recovered correctly. 2) TR for PAPR reduction in multiuser OFDM systems: In the TR technique for multiuser OFDM systems, the symbols in peak reduction subcarriers are optimized for the whole data frame in both amplitude and phase. At the same time, some peak reduction subcarriers are assigned to each user in the TR for PAPR reduction. IX. CONCLUSIONS OFDM is a very attractive technique for wireless communications due to its spectrum efficiency and channel robustness.

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Broadcasting, vol. 49, no. 3, pp , Sept [73] J. Armstrong, Peak-to-average reduction for OFDM by repeated clipping and frequency domain filtering, IEEE Electron Letters, vol. 38, no. 5, pp , May Tao Jiang (M) received the B.S. and M.S. degrees in applied geophysics from China University of Geosciences, Wuhan, P. R. China, in 1997 and 2000, respectively, and the Ph.D. degree in information and communication engineering from Huazhong University of Science and Technology, Wuhan, P. R. China, in April Then, he joined the Brunel University, UK. In Oct. 2006, he moved to the University of Michigan, USA. He is now with the Department of Electronics and Information Engineering, Huazhong University of Science and Technology, Wuhan, , P. R. China. He has authored or co-authored over 40 technical papers in major journals and conferences and five books/chapters in the areas of communications. His current research interests include the areas of wireless communications and corresponding signal processing, especially for OFDM, UWB and MIMO systems, cooperative networks, cognitive radio and wireless sensor networks. He serves on the editorial boards of some international journals, such as Wiley of Wireless Communications and Mobile Computing (WCMC), and as a Technical Program Committee Member for some major international conferences, including IEEE Globecom, ICC, VTC and Chinacom. Dr. Jiang is a Member of IEEE Communication Society and IEEE Broadcasting Society. Yiyan Wu (Fellow) received the B.S. degree from Beijing University of Posts and Telecommunications, and M.S. and Ph.D. degrees in electrical engineering from Carleton University, Ottawa, Canada, in 1986 and 1990, respectively. After graduation, he worked at Telesat Canada as a senior satellite communication systems Engineer. In 1992, He joined Communications Research Center Canada (CRC) and now is a Principle Research Scientist. His research interests include broadband multimedia communications, digital broadcasting and communication systems engineering. He is an IEEE Fellow, an adjunct professor of Carleton University, Ottawa, Canada; Shanghai Jiaotung University; and Beijing University of Posts and Telecommunications, China. He is a member of IEEE Broadcast Technology Society Administrative Committee, and a member of the ATSC Board of Directors, representing IEEE. He is the Editor-in-Chief of the IEEE TRANSACTIONS ON BROADCASTING. He has more than 200 publications and received many technical awards for his contribution to the research and development of digital broadcasting and broadband multimedia communications.