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Hybrid SLM-PTS for PAPR Reduction in MIMO-OFDM

Mohamed M. Zahra 1, Ibrahim F. Tarrad 2, Mohamed Mounir 3
  1. Assistant professor, Dept. of ECE, Faculty of Engineering, Al Azhar University, Cairo, Egypt
  2. Lecturer, Dept. of ECE, Faculty of Engineering, Al Azhar University, Cairo, Egypt
  3. M.Sc. Student, Dept. of ECE, Faculty of Engineering, Al Azhar University, Cairo, Egypt
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Abstract

Multiple-Input Multiple-Output Orthogonal Frequency Division Multiplexing (MIMO-OFDM) is a promising candidate for 4G broadband wireless communications. However, MIMO-OFDM inherited the problem of high Peak-to-Average Power Ratio (PAPR) from OFDM. Many PAPR reduction techniques were developed in last two decades to reduce the PAPR of OFDM, among them Partial Transmit Sequence (PTS) and Selected Mapping (SLM) show a highly successful PAPR reduction performance. In literature there are three well known approaches for extending SLM and PTS to MIMO-OFDM namely ordinary (oSLM/oPTS), simplified (sSLM/sPTS), and directed (dSLM/dPTS). Hybrid SLM-PTS techniques combine SLM and PTS in four different ways to reduce the required computational complexity lower than both SLM and PTS. Here, we will show the performance of applying ordinary and simplified approaches on the Hybrid SLM-PTS techniques in MIMO-OFDM system. Also, we will investigate the possibility of applying directed approach to Hybrid SLM-PTS techniques by means of proposed approach that combining dSLM and dPTS in one approach.

Keywords
MIMO, OFDM, PAPR, SLM, PTS.

INTRODUCTION
The modern day phenomenon of increased thirst for more information and the explosive growth of new multimedia wireless applications have resulted in an increased demand for technologies that support very high speed transmission rates, mobility and efficiently utilize the available spectrum and network resources. Orthogonal Frequency Division Multiplexing (OFDM) is one of the best solutions to achieve this goal and it offers a promising choice for future high speed data rate systems [1]. 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 impulse noise, power efficiency and eliminates the need for equalizers, while efficient hardware implementation can be realized using fast Fourier transform (FFT) techniques[2-3]. Multiple-Input Multiple-Output (MIMO) is known to boost capacity. For high data rate transmission, the multipath characteristic of the environment causes the MIMO channel to be frequency-selective. OFDM can transform such a frequency-selective MIMO channel into a set of parallel frequency-flat MIMO channels, and therefore decrease receiver complexity. The combination of the two powerful techniques, MIMO and OFDM, is very attractive, and has become a most a promising candidate for 4G broadband wireless communications [4]. However, one main disadvantage of MIMO-OFDM is that the signals transmitted on different antennas might have large Peak-to-Average Power Ratio (PAPR), Since MIMO-OFDM system is based on OFDM, it will also suffers from the problem of inherent high PAPR [5]. This phenomenon results from that in the time domain, an OFDM signal is the superposition of many narrowband subcarriers. At certain time instances, the peak amplitude of the signal is large and at the other times is small, that is, the peak power of the signal is substantially larger than the average power of the signal. When a high PAPR OFDM signal passes through a nonlinear device, it may cause in-band distortion and undesired spectral spreading. Thus, handling occasional large peaks leads to low power efficiency and then increases the cost of the RF power amplifier. Therefore, how to find a solution to reduce high PAPR effectively is one of the most important implementation issues in OFDM communications [6-7]. There has been a significant amount of research devoted to the development of PAR reduction algorithms for OFDM. But, in general PAPR reduction techniques achieve PAPR reduction at the expense of transmit signal power increase, bit error rate (BER) increase, data rate loss, computational complexity increase [3]. Selected Mapping (SLM) and Partial Transmit Sequence (PTS) schemes are widely studied techniques because they show good PAPR reduction performance without BER degradation, by optimal using of redundancy bits. However, they require many Inverse Fast Fourier Transforms (IFFTs), which cause high computational complexity, and need to transmit the Side Information (SI), delivering which phase rotation vector was used [8]. Recently different hybrid schemes combine PTS and SLM aim to reduce the computational complexity or obtain a better PAPR reduction performance compared with conventional PTS.
In this paper, Hybrid SLM-PTS techniques introduced in a general form which make them capable to be used with any number of sub-blokes, overstep being restricted to two sub-blokes as in [6] and [7]. Extension of Hybrid SLM-PTS techniques to MIMO-OFDM is proposed in this paper, ordinary and simplified approaches used to implement Hybrid SLM-PTS techniques in MIMO-OFDM systems, done in the same way as it done in [9] for conventional PTS or SLM. whereas ordinary approach applies PTS or SLM individually to each antenna in MIMO-OFDM, simplified approach on other hand, applies them concurrently. But, neither ordinary nor simplified indeed use the potential of MIMO transmission for PAR reduction. In MIMO communication, data rate or diversity order can be improved by exploiting the spatial dimension. In the same spirit, treating the parallel transmit signals jointly, PAR reduction can be improved by “reallocate the peak power over the antennas” [10]. With this spirit two approaches presented in [10-11] called directed SLM (dSLM) and directed PTS (dPTS) utilize the potential of MIMO transmission in PAPR reduction. Also in this paper, a suggested technique for combining dSLM and dPTS as a directed Hybrid SLM-PTS technique is presented here. Whereas Hybrid SLM-PTS techniques are themselves a combination between SLM and PTS. The rest of this paper is organized as follows: Section II, the related works are presented. Section III provides a brief description of the MIMO-OFDM system model and PAPR equation. Section IV reviews conventional SLM and conventional PTS for single antenna systems. Hybrid SLM-PTS techniques for PAPR reduction are reviewed and generalized in Section V. The extensions of Hybrid SLM-PTS techniques to MIMO-OFDM systems are given in Section VI. In Section VII, simulation results are given and the PAPR reduction performance of the three possible extension approaches per each one of the four Hybrid SLM-PTS techniques to MIMO-OFDM system is compared for different numbers of transmitting antennas. Finally, Section VIII is the conclusion.

RELATED WORK
Many PAPR reduction techniques have been proposed in the literature. These techniques can be broadly classified into three main categories: Signal distortion techniques, multiple signalling and probabilistic techniques, and coding techniques [1]. Clipping and filtering [12-13], windowing [14], peak cancellation [15], tone reservation (TR) [16] and Companding [17], are all belong to signal distortion techniques, where the PAPR reduced by distorting the transmitted OFDM signal before it passes through the power amplifier, this will brought errors to the system. On other hand, coding schemes such as block coding [18], LDPC coding [19] or turbo coding [20], whose always use to correct errors in the communication systems, are also have the capability to reduce the PAPR. Multiple signal representation and probabilistic techniques, include Selective mapping (SLM) [21], partial transmit sequence (PTS) [22], interleaving [23], tone injection (TI) [16], Dummy Sequence Insertion (DSI) [24], and active constellation extension (ACE) [25], in which several candidate signals are generated and the one with the minimum PAPR is selected for transmission. Among these techniques PTS and SLM are highly successful PAPR reduction techniques. However, the highly computational complexities of both techniques limit their PAPR reduction capability. To reduce the required number of IFFTs (computational complexity) and obtain a significant PAPR reduction performance in OFDM systems, a Hybrid SLM-PTS algorithm combining SLM and PTS was firstly given in [26] known as Conventional Hybrid (CH). Other Hybrid methods such as Additional Hybrid (AH), Switching Hybrid (SH) were introduced in [6], a Modified Hybrid algorithm (MH) combining AH with SH schemes is also proposed in [6]. Moreover one of these techniques (MH) combines with Dummy Sequence Insertion (DSI) in [7] to produce (DH) technique. In MIMO-OFDM systems, a straightforward way for PAPR reduction is to apply existing algorithms separately on each transmit antenna. It is effective to reduce PAPR, but requires high complexity and large amount SI [5]. A first extension of SLM and PTS to MIMO-OFDM was given in [9]. It applies SLM or PTS to each antenna in MIMOOFDM individually, this procedure called ordinary SLM (oSLM) or ordinary PTS (oPTS) respectively. Another approach proposed by Baek et al. in [9] aims to reduce number of SI bits called simplified SLM (sSLM) or simplified PTS (sPTS).
But, neither ordinary nor simplified indeed use the potential of MIMO transmission for PAR reduction. In [10] directed SLM (dSLM) was the first approach utilizes the potential of MIMO transmission in reducing the PAPR, after that "directed" approach was applied to PTS in [11] leaded directed PTS (dPTS).

SYSTEM MODEL AND PAPR DESCRIPTION
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HYBRID SLM-PTS TECHNIQUES FOR SINGLE ANTENNA SYSTEMS
A. Conventional Hybrid (CH)
Conventional hybrid (CH) method was the first hybrid technique that combines PTS and SLM, introduced by Pushkarev in [26] it reduce the required computational complexity less than that required by the conventional PTS for the same amount of redundancy .The original OFDM symbol S (the antenna index μ is suppressed in this section) is multiplied with the U phase rotation sequences, and then each of the new OFDM symbols are partitioned into V pairwise disjoints sub-blocks. Those OFDM sub-block values are calculated by each optimization block in each PTS blocks. This can be written as
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B. Additional Hybrid (AH)
PAPR reduction is improved in CH scheme, by generating a large number of alternative OFDM signal sequences without increasing the number of IFFTs to avoid high computational complexity [7]. AH scheme introduced by Hong Chou et al. In [6] combines CH scheme [26] with modified SLM scheme [27] to produce number of alternative signal representations more than CH using the same number of IFFTs , the excess alternative OFDM signal sequences are generated by the linear combination of the sub-block signals from different PTS blocks after IFFTs operations. Using the linear property of Fourier transform, the linear combination of these sequences can be obtained by:
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MIMO EXTENSION OF HYBRID SLM-PTS TECHNIQUES
A. Ordinary and Simplified Hybrid SLM-PTS Techniques
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antennas is selected. Consequently, number of required side information bits, for these four simplified approaches will the same as (16), (20), (22) and (23) respectively (SI bits will be transmitted from one transmitting antenna, while each receiving antenna will receive the same information bits by means of receiver diversity [9] ). However, no complexity reduction is achieved as still NTUV IFFTs operations have to be calculated.
B. Directed Hybrid SLM-PTS Techniques
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SIMULATION AND RESULTS
In this section we compare the PAPR reduction performance of the three different approaches ordinary, simplified and directed per each one of the Hybrid SLM-PTS techniques in a MIMO-OFDM system for different numbers of antennas. Simulation parameters are listed in Table 1.
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In Fig. 1(a), we compare the CCDF in case of no PAPR reduction with that of ordinary, simplified, and directed CH. The plot shows the behavior for a different number of transmit antennas ( NT = 2 , 4 ,8). Also as a reference the results for a single antenna system are also given (gray solid for no PAR reduction and gray dotted for CH with I = 8). Compared to the situation with no PAR reduction, the three CH approaches are able to reduce the PAPR significantly. Evidently, simplified approach sCH performs worse than ordinary approach oCH as less combination of the weighting factors are utilized. However, both reduction schemes perform worse than CH in the single antenna case and for an increasing number of transmit antennas NT the results get even worse. This reflects the fact that simplified and ordinary approaches are just a simple application of single antenna PAPR reduction techniques to a Multiantenna transmitter.
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In contrast to that, the directed approach is able to exploit the multiple transmit antennas; dCH always outperforms single antenna CH and the performance gets even better for increasing NT .this is obvious from Fig. 1(a),where dCH reduce the PAPR by 0.2 dB , 0.52 dB ,0.70 dB lower than oCH in case of 2,4,8 antennas respectively at 0.1% CCDF
In Fig. 1(b), Fig. 1(c), and Fig. 1(d) we do the same thing as in Fig. 1(a), but with AH, SH, and MH respectively. In Fig. 1(b), all of the three AH approaches are able to reduce the PAPR significantly. However, no one of them outperforms single antenna AH. In contrast to dCH, PAPR reduction performance of dAH gets worse for an increasing number of transmit antennas NT, due to the losses in the total number of PTS Blocks. In addition to that, dAH introduces PAPR reduction performance comparable to that of oAH or with non noticeable improvement. However, number of required SI bits will be larger than oAH. Thus, in MIMO-OFDM systems that will use AH technique, oAH will be the best choice.
In Fig. 1(c), PAPR reduction performance of dSH gets worse for an increasing number of transmit antennas NT, also it is worse than oSH approach for any number of antennas NT due to the losses in the total number of PTS Blocks. Thus, oSH approach will be the best choice for SH technique. The same thing can be noted for MH technique, shown in Fig. 1(d), oMH approach is the best choice.
Finally, from previous simulations and analysis, presented in this paper, we can say that, directed approach needed to be applied to Hybrid SLM-PTS techniques for exploiting the potential of MIMO transmission as in dPTS and dSLM. Applying dSLM approach only or dPTS approach only to Hybrid SLM-PTS techniques; degrade the PAPR reduction performance of Hybrid SLM-PTS techniques worse than ordinary approaches if they were used. Combining dPTS and dSLM in one approach is proposed in this paper. Results showed that, among the four directed approaches of the Hybrid SLM-PTS techniques (dCH, dAH, dSH, and dMH), only dCH approach which perform better than ordinary approach oCH. Others directed Hybrid SLM-PTS approaches (i.e. dAH, dSH, and dMH) have a performance worse than or at best equal to ordinary approaches (i.e. oAH, oSH, and oMH), with larger number of SI bits than ordinary approaches, of course.

CONCLUSION
Hybrid SLM-PTS techniques used to provide the same (or better) PAPR reduction performance as PTS or SLM with less number of IFFTs. ordinary, simplified, and directed are three different approaches for using PTS or SLM in reducing the PAPR of MIMO-OFDM systems. Likewise, this approaches used to apply Hybrid SLM-PTS techniques to MIMO-OFDM systems, in this paper. Appling ordinary and simplified is a straightforward procedure similar to that in PTS or SLM. However, neither ordinary nor simplified indeed use the potential of MIMO transmission for PAPR reduction, only directed approach which can exploit the potential of MIMO transmission. Take in consideration that, any Hybrid SLM-PTS technique composed of PTS and SLM. directed approach combining dSLM and dPTS in one adequate approach is proposed in this paper. But, unfortunately only dCH which performs better than oCH, while the others directed approaches (i.e. dAH, dSH, and dMH) perform worse than ordinary approaches (i.e. oAH, oSH, and oMH).
This is illustrated in Fig. 1. Fig. 1(a) shows that dCH is better than oCH, sCH and also single antenna CH, in addition of enhancing PAPR reduction performance with the increase in the number of antennas. On other hand, Fig. 1(b), show that single antenna AH is better than oAH, sAH and dAH, although dAH uses the potential of MIMO, it only better than sAH, but has a performance similar to oAH. While ordinary approach shows a PAPR reduction performance better than simplified and directed approaches in SH and MH techniques, this is shown in Fig. 1(c) and Fig. 1(d) respectively whose also show that directed approach is unfortunately worse than ordinary approach and single antenna in SH and MH techniques.
To sum up, proposed directed approach is suggested to be used only with CH, while ordinary approach is the best choice for the others Hybrid SLM-PTS techniques. However, if we are concerned with reducing the required number of SI bits, Simplified approach will be the best choice for all the Hybrid SLM-PTS techniques.

References