Multicarrier Modulation actually divides the input signal in low rate parallel bit streams and uses these bit streams to perform the modulation for several carriers. It divides the complete input frequency band in N channels in such a way, no over lapping of the signal will be done. These N sub channels are frequency multiplexed and to modulate each channel a separate symbol is used. If some kind of overlapping occur over the signal it will cause the channel interference, so that the MCM is also responsible for the non-overlapping of the channels. But the utilization of the available spectrum is also a challenge for the OFDM systems. To manage along with inefficiency, one approach was proposed in 1960 that collect he MCM along with Frequency Division Multiplexing (FDM). It gives the frequency division with overlapping channels. OFDM provide the such kind of multicarrier transmission over the signal. Here the word orthogonal defines the relation between the frequencies of carrier in the system. To receive the signals in a MCM systems, some traditional filters and demodulators are spaced apart and in theses receivers, some guard bands are define between the carriers and the frequency domain. But inclusion of such bands in the system reduces the efficiency of the spectrum
Most of the problems of traditional MCM is been rectified by OFDM. It actually arrange the carriers in such a way that even in case of overlapping of the carriers, it will return the effective signal throughput without any carrier interference. And this is done only by selecting the carriers mathematically orthogonal. In OFDM systems, on the receiver side the translation of the carrier is performed to DC and then the integration of the signal is performed over a symbol period to get the raw data. OFDM waveforms can be generated using a Discrete Fourier Transform (DFT) at the transmitter and receiver for the modulation and demodulation [1]. For a long time, usage of OFDM in practical systems was limited. Main reasons for this limitation were the complexity of real time Fourier Transform and the linearity required in RF power amplifiers. Presently, OFDM is used for wideband data communications over mobile radio FM channels, High-bit-rate Digital Subscriber Lines (HDSL, 1.6Mbps), Asymmetric Digital Subscriber Lines (ADSL, up to 6Mbps), Very-high-speed Digital Subscriber Lines (VDSL, 100Mbps), Digital Audio Broadcasting (DAB), and High Definition Television (HDTV) terrestrial broadcasting.
1.2 ADVANTAGES OF OFDM
OFDM has many advantages over single carrier systems discussed below.
The implementation complexity of OFDM is significantly lower than that of a single carrier system with equalizer. When the transmission bandwidth exceeds coherence bandwidth of the channel, resultant distortion may cause intersymbol interference (ISI). Single carrier systems solve this problem by using a linear or nonlinear equalization. The problem with this approach is the complexity of effective equalization algorithms. OFDM systems divide available channel bandwidth into a number of subchannels. By selecting the subchannel bandwidth smaller than the coherence bandwidth of the frequency selective channel, the channel appears to be nearly flat and no equalization is needed.
Inserting a guard time at the beginning of OFDM symbol during which the symbol is cyclically extended, intersymbol interference (ISI) and intercarrier interference (ICI) can be completely eliminated, if the duration of guard period is properly chosen. This property of OFDM makes the single frequency networks possible. In single frequency networks, transmitters simultaneously broadcast at the same frequency, which causes intersymbol interference.
In slow time varying channels, it is possible to significantly enhance the capacity by adapting the data rate per subcarrier according to the signal-to-noise ratio (SNR) of that particular subcarrier. Another advantage of OFDM over single carrier systems is its robustness against narrowband interference because such interference affects only a small percentage of the subcarriers.
The most important disadvantage of OFDM systems is that highly linear RF amplifiers are needed [2]. An OFDM signal consists of a number of independently modulated subcarriers, which can give a large crest factor or Peak-to-Average Power Ratio (PAPR) when added up coherently. To average the signal power, The N Times power is added to N signals. The OFDM system has a high peak-to-average power ratio (PAPR) that can cause unwanted saturation in the power amplifiers. In order to avoid nonlinear distortion, highly linear amplifiers are required which cause a severe reduction in power efficiency. Several methods are explained in the literature in order to solve this problem.
In this thesis various PAPR reduction techniques are discussed and simulated using MATLAB software and their performance is compared. This thesis is organized as follows.
Chapter 2 is a rather detailed overview of OFDM. Main equations are derived and applications of OFDM are discussed.
Chapter 3 discusses literature survey of PAPR reduction techniques.
Chapter 4 provides a deep insight into the PAPR problem by discussing the methods used in the literature. Each method with its advantages and disadvantages are discussed.
Chapter 5 a new scheme for PAPR reduction is suggested using radix 2 Discrete in Frequency (DIF) Fast Fourier Transform (FFT) with block diagram. Additionally, this chapter provides the simulated and numerical results obtained by algorithm implementation and system comparison.
Finally, Chapter 6 includes some concluding remarks.
Chapter 2
OVERVIEW OF OFDM
In this chapter, first the general structure of an OFDM system will be discussed. The second part will be about main techniques of OFDM. Finally, applications of OFDM will be examined.
2.1. GENERAL STRUCTURE OF OFDM
The basic principle of OFDM is to split a high rate input data stream into a number of lower rate streams that are transmitted simultaneously over a number of subcarriers [3]. Because the transmission rate is slower in parallel subcarriers, a frequency selective channel appears to be flat to each subcarrier. ISI is eliminated almost completely by adding a guard interval at the beginning of each OFDM symbol [4]. However, instead of using an empty guard time, this interval is filled with a cyclically extended version of the OFDM symbol. This method is used to avoid ICI.
OFDM is a special case of Multicarrier Modulation (MCM). In MCM, input data stream is divided into lower rate sub streams, and these sub streams are used to modulate several subcarriers. In general, the spacing between these subcarriers is large enough such that individual spectrum of subcarriers do not overlap. Therefore the receiver uses a band pass filter tuned to that subcarrier frequency in order to demodulate the signal. In OFDM, subcarrier spacing is kept at minimum, while still preserving the time domain orthogonality between subcarriers, even though the individual frequency spectrum may overlap. The minimum subcarrier spacing should equal to 1/T, where T is the symbol period.
2.1.1 OFDM Transmitter Structure
Figure 2.1 shows a basic OFDM transmitter structure. The serial input data stream is divided into frames of Nf bits. These Nf bits are arranged into N groups, Number Here of carriers are represented by N. The number of bits in each of the N groups determines the constellation size for that particular subcarrier. For example, if all the subcarriers are modulated by QPSK then each of the groups consists of 2 bits, if 16-QAM modulation is used each group contains 4 bits. This scheme is called as fixed loading. However, this is not the only way of distributing input bits among the subchannels. Nf bits could be divided among subcarriers according to the channel states. Therefore, one of the subcarriers can be modulated with 16-QAM whereas another one can be modulated with 32-QAM, etc. In this case, the former subcarrier consists of 4 bits and the latter subcarrier consists of 5 bits. This scheme is named as adaptive loading. Hence, OFDM can be considered as N independent QAM channels, each having a different QAM constellation but each operating at the same symbol rate 1/T. After signal mapping, N complex points are obtained.
Figure 2.1 Block Diagram of an OFDM Transmitter
These complex points are passed through an IDFT block. Cyclic prefix of length v is added to the IDFT output in order to combat with ICI and ISI. After Parallel-to- Serial conversion, windowing function is applied. The output is fed into a Digital- to-Analog converter operating at a frequency of N/T. Finally transmit filter is applied in order to provide necessary spectrum shaping before power amplification.
2.1.2 Mathematical System Model:
Let denote [D0, D1… DN-1] data symbols. Digital signal processing techniques, rather than frequency synthesizers, can be deployed to generate orthogonal sub-carriers [5]. The DFT as a linear transformation maps the complex data symbols [D0, D1… DN-1] to OFDM symbols [d0, d1… dN-1] such that
(2.1)
The linear mapping can be represented in matrix form as:
(2.2)
Where
(2.3)
and
(2.4)
is a symmetric and orthogonal matrix. After FFT, a cyclic pre/postfix of lengths k1 and k2 will be added to each block (OFDM symbol) followed by a pulse shaping block. Proper pulse shaping has an important effect in improving the performance of OFDM systems in the presence of some channel impairments. The output of this block is fed to a D/A at the rate of fs, and low-pass filtered. A basic representation of the equivalent complex baseband transmitted signal is
(2.5)
for
(2.6)
2.1.3 OFDM Receiver Structure
Figure 2.2 Block Diagram of an OFDM Receiver
Figure 2.2 gives the block diagram of an OFDM receiver.
The receiver implements inverse operations of the transmitter. Received signal is passed through a receive filter at pass band and an Analog-to-Digital converter operating at a frequency of N/T. After these down converting and sampling operations, cyclic prefix is removed from the signal and a DFT operation is performed on the resultant complex points in order to demodulate the subcarriers. Subcarrier decoder converts obtained complex points to the corresponding bit stream.
2.2 OFDM DESIGN ISSUES
There are certain key factors needed to taken under serious consideration when developing and designing OFDM system.
2.2.1 Useful symbol duration
The size of symbol or length of symbol in respect of time effect the number of carriers and spacing between them. It is helpful in measuring latency etc. Larger symbol duration is helpful in accommodation delay profile of channel and cause increment number of subcarrier, reduces subcarrier spacing and higher the FFT size. There may arise issue of subcarrier offset and instability of OFDM symbol. Subcarrier spacing and number of carriers depend up on application and requirement. In mobile environment due to Doppler shift subcarrier spacing is chosen to be large [1].
2.2.2 Number of Carriers
Number of subcarrier chosen depends up on channel bandwidth, data rate, through put requirements and territory (ruler, urban etc). If number of carriers is N then it would be reciprocal of duration of symbol in time T i.e.
(2.7)
Selection of number of carrier depends on FFT size supported by FFT module. For higher number of carrier there would be higher number of complex point processing by FFT.
2.2.3 Modulation scheme
It is one of the advantage of OFDM that different modulation scheme can be applied to each sub channel depends on channel condition, data rate, robustness, throughput and channel bandwidth. There could be different modulation scheme applied specified by complex number i.e. QPSK, 16 QAM, 64 QAM . Modulation to each sub channel can be made adaptive after getting information and estimation of channel at transmitter.
OFDM LIMITATIONS
The following are the limitations of OFDM
2.3.1 Sensitivity to Phase Noise
In [6], power spectrum density of an oscillator signal with phase noise is modeled by a Lorentzian spectrum, which is equal to the squared magnitude of a first order low pass filter transfer function. The single sided spectrum is given by
(2.8)
In (2.8), f1 is the 3 dB line width of the oscillator signal and fc is the carrier frequency. Phase noise has two main effects. First, the phase noise results in attenuation and rotation of the received signal. Second and more important effect is the ICI, because phase noise changes the 1/T separation between subcarriers in the frequency domain. The degradation in SNR caused by phase noise is given as
(2.9)
where β is the 3 dB one sided bandwidth of the power spectrum density of the carrier, T is the symbol period and Es/ N0 is the symbol-to-noise energy ratio. From (2.9), it is seen that phase noise degradation is proportional with the ratio of subcarrier bandwidth (β) and the subcarrier spacing (1/T). It can be seen from [6] that, for a negligible SNR degradation of less than 0.1 dB, the 3 dB phase noise bandwidth has to be about 0.1 to 0.01 percent of the subcarrier spacing, depending on the modulation. For example, if 64 QAM modulations is used in an OFDM system with a subcarrier spacing of 300 kHz, the 3 dB bandwidth should be 30 Hz at most.
2.3.2 Sensitivity to Frequency Offset
As stated in [6], the degradation in SNR caused by a frequency offset which is small relative to subcarrier spacing can be approximated as
(2.10)
As shown in [6], for a negligible degradation of about 0.1 dB, maximum tolerable frequency offset is less than 1% of subcarrier frequency. For example, for an OFDM system at a carrier frequency of 5 GHz and a subcarrier spacing of 300 kHz, the oscillator accuracy needs to be 3 kHz or 0.6 ppm. Initial frequency error of a low cost oscillator will not meet this requirement. Therefore, a frequency synchronization technique has to be applied before the FFT block of the receiver.
2.3.3 Peak-to-Average Power Ratio (PAPR)
Amplitude of the OFDM signal has an almost Rayleigh distribution and exhibits strong fluctuations. Therefore, the resultant Peak-to-Average Power Ratio (PAPR) can be rather high. In the worst case, PAPR of an OFDM system with N subchannels may reach up to a value of N. High PAPR value has some disadvantages for practical implementations and needs to be reduced to an acceptable level. In the literature various methods are proposed for the purpose of PAPR reduction [7]. Next chapter deals with PAPR problem and the existing solutions in more detail.
2.4 CHANNEL MODELS
The communications channel is the physical medium connecting the transmitter to receiver. Wired telephone, wireless phones, optical fiber are examples of communication channels. An accurate and appropriate modeling of the radio channel is crucial in order to predict the performance of wireless radio systems. A narrow band model is based on predicted mean signal level and some assumptions about the envelope fading statistics. The assumption is necessary due to the limited bandwidth of the signal being sent through the channel. For this reason, a narrow band channel is usually called flat fading channel. However, in wide band channels, the signal fading caused by time dispersion varies as a function of frequency and the channel model is usually called frequency selective fading. Early Binary symmetric channel (BSC) model was described by Wozencraft and Jacobs in 1967. This channel was memory less channel. Bello presented a channel using a tapped delay line representation that is based on knowledge of the correlation properties of the channel in 1963. In the literature; Stein, Schwartz and Bennett used a deterministic characterization of the channel and then introduced dynamics into the model to describe the time varying fading channel in 1996 [8].
The modeling of channel has been continuing research to recent days. The modeling of the multiple-input and multiple-output (MIMO) channel has attracted attention, because it offers significant increases in data throughput without additional bandwidth or transmits power [9]. In this section we introduce the Additive White Gaussian Noise (AWGN) channel and Rayleigh fading channel.
2.4.1 Additive White Gaussian Noise (AWGN) Channel
The simplest channel model in wireless commutations is the well known Additive White Gaussian Noise (AWGN) model. The mathematical expression of the AWGN channel as follows in Figure 2.3
Y(t)=X(t)+N(t) (2.11)
where, X(t) is the transmitted signal and plus N(t) is the white Gaussian Noise.
Figure 2.3 AWGN channel
AWGN channel is considered as an important reference or benchmark model for comparing the performance evaluation of communication systems and modulation formats. However, when the signal travels from transmitter to receive via multiple propagation paths then a practical fading channel model must be used to model the propagation environment. There are some factors affecting fading including multipath propagation, speed of surrounding objects, speed of the mobile, the transmission symbol duration and the transmission bandwidth of the signal.
2.4.2 Rayleigh fading channel
Multipath is the propagation phenomenon that results in radio signal reaching the receiver antennas via multiple propagation paths. There are many causes of multipath fading including atmospheric ducting, refraction, reflection from terrestrial objects such as buildings and mountains, etc. The most harmful fading channel is the Rayleigh fading model which was first introduced by Bell Lab in 1970s. It is a statistical model of the communication channel to represent the effects of a propagation environment on a radio signal. A statistical Rayleigh fading model is the simplest fading channel model. A Rayleigh fading channel is viewed as a model when a radio signal passes through communication channel that varies power of signal according to Rayleigh distribution. Note that when there is no dominant propagation along a Line-of-Sight (LOS) between transmitter and receiver, Rayleigh fading is most applicable. Rician fading is more applicable when there is a dominant LOS component. Rayleigh fading model performs as reasonable channel model when there are many objects (such as building and mountain) in the propagation environment which scatter the radio signal before it arrives at the receiver.
2.5. APPLICATIONS OF OFDM
OFDM is used as the transmission technique in digital audio and television broadcasting applications, and in wireless LAN applications. This section describes the main applications of OFDM.
2.5.1. Digital Audio Broadcasting (DAB)
DAB is the successor of current analog audio broadcasting based on AM and FM and offers improved sound quality, comparable to that of CD quality, new data services and a higher spectrum efficiency. DAB was standardized in 1995 by the European Telecommunications Standards Institute (ETSI) as the first standard to use OFDM [10]. DAB OFDM parameters are specified in table 2.1.
2.5.2. Terrestrial Digital Video Broadcasting
Terrestrial Digital Video Broadcasting (DVB) standardized in 1997 uses OFDM with two possible modes, using 1705 and 6817 subcarriers, respectively [11]. These modes are referred to us 2k and 8k modes, which correspond to the sizes of IFFT and FFT blocks used in multicarrier modulation and demodulation. The symbol period of 8k system is about 896 μs, while the guard time may have four different values between 28 to 224 μs. The corresponding values for the 2k system are four times smaller. At the DVB-T transmitter, the input data is divided into groups of 188 bytes, which are scrambled and coded by an outer shortened (204,188) Reed-Solomon (RS) code over GF(256). This code can correct up to 8 byte errors in a frame of 204 bytes. The coded bits are then interleaved and then coded again by a rate ½ convolutional code, with a constraint length of 7. The coding rate can be increased for higher throughput by puncturing to 2/3, 3/4, 5/6 or 7/8. The encoded bits are then interleaved by an inner interleaver and then mapped onto QPSK, 16 QAM or 64 QAM symbols.
The receiver side employs coherent detection of QAM signals which requires the estimation of channel effects. This is accomplished by using pilot subcarriers. For the 8k mode, in each symbol there are 768 pilots, so 6048 subcarriers are allocated to data traffic. The 2k mode has 192 pilots and 1512 data subcarriers. The position of pilots varies from symbol to symbol with a pattern that repeats after 4 OFDM symbols. The pilots allow the receiver to estimate the channel both in frequency and time.
2.5.3 Magic WAND
The Magic WAND (Wireless ATM Network Demonstrator) project was a part of European ACTS (Advanced Communications Technology and Servers) program [12]. The Magic WAND consortium members implemented a prototype wireless ATM network based on OFDM. This prototype had a large impact on standardization activities in the 5 GHz band. The wireless ATM application based on OFDM forms the basis for the standardization of the HYPERLAN type II Physical layer. The main parameters of the WAND physical layer number of subcarriers is 16, with a guard time of 400 ns. With this guard time, rms delay spreads up to 100 ns are completely tolerated without employing equalization. While this is sufficient for most of the office buildings, a realistic product would require more delay spread robustness in order to cover large office buildings and factory halls. The parameters for magic WAND are considered as , the subcarrier modulation is 8 PSK with a symbol rate of 13.3 Msymbols/s, yielding a raw data rate of 40 Mbps. The rate ½ complementary coding reduces the net rate to 20 Mbps. The subcarrier spacing is 1.25 MHz, which gives a total bandwidth of 20 MHz. The packet preamble is 8.4 μs in duration and consists of one OFDM symbol, repeated 7 times. This preamble is used for packet detection, automatic gain control, frequency offset estimation, symbol timing and channel estimation. Transmission is done on half-slots, which consists of 9 OFDM symbols, carrying 27 bytes. An ATM cell is mapped on two consecutive half-slots, which form a full-slot. Of the 54 bytes carried on one fullslot, 53 bytes are allocated to ATM cell traffic and remaining 1 byte is reserved for physical layer control signaling.
2.5.4. IEEE 802.11
The IEEE standard of 802.11 should not be confused with these two standards 802.11 and 802.11x because the 802.11 standard defining wireless local area network (WLAN) while the other 802.11x standard defines the port based network [13]. The IEEE accepts the standard of 802.11 for air interface between patrons wirelessly connected either by the subscriber with the base station or in other words like between two wireless subscribers in 1997 . So some of the IEEE standard 802.11 define the wireless local area network (WLANs) and become the developing base for further enhancement and improvement in data rate for derived standards of 802.11. It uses the Frequency Hoping Spread Spectrum (FHSS) and Direct sequence Spread Spectrum (DSSP), and supports throughput of 1 or 2 Mbps in 2.4 GHz band .
The IEEE Standard 802.11a is developing form of primary standard 802.11 which defines the wireless local area network (WLANs). They use the multicarrier scheme of Orthogonal Frequency Division Multiplexing (OFDM) encoding technique and support the high data rate up to 54-Mbps in the unlicensed 5 GHz band over the short range communication. And the IEEE Standard 802.11b is derived again from 802.11 which are referred to as Wi-Fi and it is approved in 1999. And its specification allows 11Mbps transmission in its indoor distance of different several dozen to several hundred feet and its outdoor distance of several tens of miles in 2.4 GHz band which is used only in DSSS, data communication and comparable to Ethernet [... The IEEE Standard 802.11e provide the best Quality of Services (QoS) to local area networks (LANs), which is supported by 802.11a and 802.11b it exists backward compatibility with previous standards and supports (QoS) and multimedia to the services provided by IEEE 802.11b and IEEE 802.11a.
The IEEE standard 802,11g defines throughput of 54 Mbps for a short range distance, which is used for data communication in wireless LANs in a band of 2.4 GHz . The IEEE standard 802.11n is meant for high data rate up to 5 times higher than the data rate of 802.11g by implication of spatial multiplexing and spatial diversity through different types of coding schemes and by increasing the number of antennas at the transmitter side and also by increasing the number of antennas at the receiver side (MIMO).
2.5.5 IEEE 802.16
The IEEE standard 802.16-2001 was completed in October 2001 and published on 8th April 2002. This defines the Wireless MANâ„¢ air interface specification for the wireless metropolitan area networks (MANs). The Wireless MANâ„¢ air interface network provides the MAN broadband wireless access under certain standards of development and implantation [5-6]. The IEEE standard 802.16 defines the gateway for 3G to 4G technology, and it mainly considers the wireless broadband fix and mobile that uses the architecture of a single point to multipoint (PMP) and mainly refers to evaluation of WiMAX technology. It acts as a major tool to link business organization and home etc to back pull of Telecommunication network in a world wirelessly with complete quality of services (QoS) [14].
This fundamentally design allows the enhancement in wireless MAN networking protocol to exchange information directly with the other individual (user) eventually supports the development of different technologies for nomadic and mobile users . Let us consider any systems in home for instance laptop, computer, PDAs etc is connected with a base station via external home receiver likely using different physical layers, but the design of wireless MAN MAC support the connection of Base Station with the individual user with all QoS, 802.16 fully supports the TDM data transmission, IP and VoIP connectivity, it enables the high data rate in both direction means (Uploading and downloading between Base Station & Subscriber) of up to 30 miles of distance .
There are Several other standards belongs to the family of IEEE 802.16 is given below IEEE 802.16a specifies Mesh Deployment, IEEE 802.16b specified increased Tech Spectrum, IEEE 802.16c defines Technical Standardization, IEEE 802.16d for System Profiles, IEEE 802.16e- specifies Network Standardization, IEEE 802.16f-High Speed Signals. This standard defines the multiple physical layer support by using MAC layer , address to two different frequency ranges i.e. licensed band 10 to 66 GHz, and 2GHz to 11 GHz licensed and licensed exempt band . In frequency band 10 to 66 GHz widely available throughout in the world, due to short wave length introduce challenges to deployment. IEEE 802.16a defines the support of air interface for lower frequency bands include licensed exempt and licensed spectra of 2-11 GHz, comparatively provide the low data rate and can be exchange data with scores of home individual or small to medium enterprise users in less cost, and thus make orientation to provide the services to individual customer.
The intention of the standard is to enable vendors to manufacture the interoperable equipments in order to ensure the interoperability between the vendors. The WiMAX forum was created in June 2001 to ensure and enhance the interoperability of the standard. The WiMAX forum functionality is similar to the Wi-Fi forum, which have the standard to business organizations and manufacturers to ensure the standard of equipment interoperability to the IEEE 802.11. The WiMAX forum provides the certification answer testing essential to ensure vendor equipment interoperability up to the standard of IEEE 802.16 .
Chapter 3
LITERATURE SURVEY
Orthogonal Frequency Division Multiplexing (OFDM) has become the technology of choice for next generation wireless and wireline digital communication systems because of its high speed data rates, high spectral efficiency, high quality service and robustness against narrow band interference and frequency selective fading [15-17]. OFDM removes Inter Symbol Interference (ISI) by inserting a Guard Interval (GI) using a Cyclic Prefix (CP) and moderates the frequency selectivity of the Multi Path (MP) channel with a simple equalizer [18]. OFDM is widely adopted in various communication standards as discussed previously.
The Peak to Average Power Ratio (PAPR) is still one of the major drawbacks in the transmitted OFDM signal [19]. For zero distortion of the OFDM signal, the RF High Power Amplifier (HPA) must not only operate in its linear region but also with sufficient back-off. Thus, HPA with a large dynamic range are required for OFDM systems. These amplifiers are very expensive and are major cost components. Thus, if we reduce the PAPR it not only means that we are reducing the cost of OFDM system and reducing the complexity of A/D and D/A converters, but also increasing the transmit power, thus, for same range improving received SNR, or for the same SNR improving range.
The literature is replete with a large number of PAPR reduction techniques. Among them, schemes like constellation shaping [20], phase optimization [21], nonlinear companding transforms [22], Tone Reservation (TR) and Tone Injection (TI) [23, 24], clipping and filtering [25], Partial Transmit Sequence (PTS) [26], precoding based techniques [27-29], Selected Mapping (SLM) [30-32], Precoding based Selected Mapping (PSLM) [33], and phase modulation transform [34-36] are popular. The precoding based techniques, however, show great promise as they are simple linear techniques to implement.
Wang and Tellambura [25] proposed a soft clipping technique which preserves the phase and clips only the amplitude. They also put a lot of effort to characterize the performance and discover some properties to simplify the job. However, the PAPR gain is only estimated by simulations and is limited to a specific class of modulation technique.
Han and Lee [26] proposed a PAPR reduction technique based on Partial Transmit Sequence technique in which they divide the frequency bins into sub blocks and then they multiply each sub-block with a constant phase shift. Choosing the appropriate phase shift values reduces PAPR. The most critical part of this technique is to find out the optimal phase value combination and in this regard they also proposed a simplified search method and evaluated the performance of the proposed technique.
Min and Jeoti [28] presented a Zadoff-Chu precoding based PAPR reduction technique. This technique is efficient, signal independent, distortionless and it does not require any optimization algorithm. In addition, this precoding based PAPR reduction technique does not require power increase and side information to be sent for receiver.
Lim et al. [31] proposed a selected mapping (SLM) technique for PAPR reduction. In SLM scheme, an input symbol sequence is multiplied by each of phase rotation vectors to generate alternative input symbol sequences. Then alternative input symbol sequences are inverse fast Fourier transformed (IFFTed) and the one with the minimum PAPR is selected for transmission. SLM and PTS schemes require many IFFTs, which causes high computational complexity.
Liang and Ouyang [32] also proposed a low complexity an SLM technique in which they rotate the bins by one of the phase sequences and then select the sequence with lower PAPR for transmissions. The main emphasis of the paper is on method of generating the time domain results and IFFT is not performed on every possible phase rotation.
Han and Lee [37] and Jiang and Wu [38] presented an excellent survey of PAPR reduction techniques like clipping and filtering, coding, PTS, SLM, interleaving, TR, TI and ACE. In addition they also provide mathematical analysis of the distribution of PAPR in OFDM systems.
Boyd and Popovic [39-40] shown that the use of Golay Complementary Sequences as code words restricts the PAPR of the OFDM signal to at most 3dB.
