• International Journal of Technology (IJTech)
  • Vol 12, No 2 (2021)

Maximal Minimum Hamming Distance Codes for Embedding SI in a Data based BSLM Scheme for PAPR Reduction in OFDM

Maximal Minimum Hamming Distance Codes for Embedding SI in a Data based BSLM Scheme for PAPR Reduction in OFDM

Title: Maximal Minimum Hamming Distance Codes for Embedding SI in a Data based BSLM Scheme for PAPR Reduction in OFDM
Adnan Haider Yusef Sa'd, Hisham Haider Yusef Saad, Aeizaal Azman Abd Wahab

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Cite this article as:
Sa'd, A.H.Y., Saad, H.H.Y., Abd Wahab, A.A., 2021. Maximal Minimum Hamming Distance Codes for Embedding SI in a Data based BSLM Scheme for PAPR Reduction in OFDM. International Journal of Technology. Volume 12(2), pp. 412-421

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Adnan Haider Yusef Sa'd 1. Faculty of Computer and IT, Al-Razi University, Sana'a, Yemen 2. School of Electrical & Electronic Engineering, Universiti Sains Malaysia, Penang 14300, Malaysia
Hisham Haider Yusef Saad Faculty of Computer and IT, Al-Razi University, Sana'a, Yemen
Aeizaal Azman Abd Wahab School of Electrical & Electronic Engineering, Universiti Sains Malaysia, Penang 14300, Malaysia
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Abstract
Maximal Minimum Hamming Distance Codes for Embedding SI in a Data based BSLM Scheme for PAPR Reduction in OFDM

The bi-orthogonal codes for embedding Side-Information (SI) in data-based blind SLM (BSLM) proposed in Joo et al. (2012) produce better bit error rate (BER) and SI error rate (SIER) performance compared to binary codes. However, the authors do not provide details for code generation; instead, they list some codes with a length of  and a minimum Hamming distance of . The suggested bi-orthogonal code does not work for any value of the maximum iteration number  other than . Therefore, this paper proposes two algorithms for generating  codes for any value of . The proposed methods maintain the normalized minimum Hamming distance between generated codes to . However, the second proposed algorithm, which works in the case of , is also able to only consider codes with a maximum Hamming distance, allowing it to improve SIER performance. Thus, the second proposed algorithm improves SIER performance by up to 1 dB at Eb/No=3dB. Furthermore, the proposed algorithms are able to generate a multiple set of  codes that deliver same performance.

Blind SLM; OFDM; PAPR; Side Information; SLM

Introduction

Orthogonal frequency division multiplexing (OFDM) is a transmission technique with a high data-transmission rate and can cope with severe channel conditions. Moreover, unlike other techniques that utilize parallelism for increasing transmission speed, the orthogonal nature of OFDM uses bandwidth more efficiently. OFDM has been adopted by many standards for its advantages over other techniques, such as single carrier or frequency division multiplexing (FDM). Examples of well-known standards include DSL, 802.11a, WiFi-Max, and LTE (Han and Lee, 2005; Jiang and Wu, 2008; Rahmatallah and Mohan, 2013).

Thanks to advances in digital signal processing (DSP) technology, OFDM has become more widely applicable and popular. However, OFDM suffers from the major problem of having high signal peaks. The high peaks problem, often called the high peak-to-average power ratio (PAPR) problem, is a result of the summation of multiple subcarrier signals due to the existence of a parallelism concept in transmission. The high peaks of an OFDM signal cannot be amplified linearly using a normal power amplifier (PA); doing so corrupts the signal, as there are high peaks in the non?linear region of PA. Thus, as using normal PA with OFDM introduces in-band and out-band radiation, OFDM requires a very complex PA design to maintain linearity. Mathematically, PAPR is calculated as follows:

 


where  is the th sample of OFDM time domain signal , and  denotes expectation.

Many methods have been proposed to alleviate the high PAPR problem; each one has advantages and disadvantages. Examples of PAPR reduction techniques found in the literature are clipping (Juwono et al., 2013), partial transmit sequence (PTS) (Müller et al., 1997; Müller and Huber, 1997), selected mapping (SLM) (Müller et al., 1997; Sa'd and Wahab, 2019), tone injection (TI) (Wattanasuwakull and Benjapolakul, 2005), tone reservation (TR) (Park et al., 2003), interleaving (Rahmatallah and Mohan, 2013), and hybrid (Jones et al., 1994; Wang and Chen, 2014; Sa’d et al., 2016; Wahab and Sa’d, 2017; Liang et al., 2019).

SLM is a well-known distortion-less PAPR reduction technique; however, it requires sending side information (SI) for the receiver to be able to retrieve the original signal. To solve this problem, many blind SLM (BSLM) schemes have been proposed in the literature (Jayalath and Tellambura, 2002; Pezeshk and Khalaj, 2002; Baxley and Zhou, 2005; Jayalath and Tellambura, 2005; Han et al., 2006; Chen and Zhou, 2006;Alsusa and Yang, 2008; Han et al., 2008; Joo et al., 2009; Le Goff et al., 2009; Hong et al., 2010; Park et al., 2011;Li et al., 2011; Badran and El-Helw, 2011;Eom et al., 2012; Joo et al., 2012; El-Helw et al., 2012; Hong et al., 2013; Ji and Ren, 2013; Elhelw and Badran, 2015; Ji et al., 2015; Yoon et al., 2018; Goel and Sidhu, 2020). BSLM, in general, embeds SI in an OFDM signal by utilizing noise margins instead of dedicated subcarriers to eliminate data rate waste due to SI. While there are different types of BSLM, the data-based BSLM proposed in Joo et al. (2012) can maintain a similar PAPR and an almost similar BER as conventional SLM without manipulating or imposing restrictions on channel estimation methods, providing that the number of subcarriers of OFDM is not very small. SI is embedded onto the phase of data subcarriers by making a unique and distinguished phase disparity between all the possible iterations of data manipulation, and this is done over all data subcarriers. To improve SI error rate (SIER) performance, phase disparity forms are constructed using a biorthogonal vector with a code length of . However, the work in Joo et al. (2012) lacks the generalization of constructing biorthogonal codes for any  value. Therefore, in this paper, we propose a systematic way of generating  SI embedding-codes that fulfill the general and important condition of having a normalized minimum Hamming distance of at least 0.5.

        This paper is organized as follows. Section 2 explains the data?based BSLM in Joo et al. (2012). Section 3 discusses SI embedding-code generation and explains the proposed maximal Hamming distance code generation method. Finally, a conclusion is drawn in Section 4.

Conclusion

    Two new algorithms were proposed for generating maximal Hamming distance codes of  for embedding SI. The proposed algorithms generalize the construction of SI embedding codes for any value of . The codes produced using the algorithms proposed here and the biorthogonal codes used in Joo et al. (2012) have similar SIER performance for , since they all have a normalized minimum distance of . However, for  Algorithm 2 proposed here produces better SIER performance.

Acknowledgement

    This research was supported partially by Research University Grant, Universiti Sains Malaysia (1001/PELECT/8014160).

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