Elsevier

Physical Communication

Volume 8, September 2013, Pages 47-55
Physical Communication

Full length article
Statistical distributions of instantaneous power and peak-to-average power ratio for single-carrier FDMA systems

https://doi.org/10.1016/j.phycom.2012.10.003Get rights and content

Abstract

This paper analyzes the distributions of instantaneous power and peak-to-average power ratio (PAPR) for single-carrier frequency-division multiple-access (SC-FDMA) signals, where localized FDMA (LFDMA) and interleaved FDMA (IFDMA), as well as a block-interleaved FDMA (B-IFDMA) are considered as a part of the discrete Fourier transform (DFT)-precoded orthogonal frequency-division multiple access (OFDMA) systems adopted in the recent mobile communications standard. Comparisons of analytical and simulation results show a good match in terms of both the measures, which confirms the validity of the analytical framework developed in this work.

Introduction

One of the well-known advantages of the single-carrier frequency division multiple access (SC-FDMA) signaling over the orthogonal frequency-division multiple access (OFDMA) is its waveform with lower peak-to-average power ratio (PAPR), which is inherited from the single-carrier nature of the generated signals despite its use of the inverse discrete Fourier transform (IDFT) at the transmitter similar to OFDMA  [1], [2]. This can be generally achieved by the use of preprocessing based on the orthogonal matrix known as a discrete Fourier transform (DFT) precoding  [3]. The reduction of PAPR translates to the improvement of power amplifier (PA) efficiency and is thus desirable for battery-driven wireless terminals. The statistical property of signal dynamic range of SC-FDMA signal is thus of primary interest upon designing PA architectures.

There have been several variations of SC-FDMA proposed in the literature. Among them, the localized FDMA (LFDMA) and interleaved FDMA (IFDMA)  [1] are the two most studied systems. In addition, as an extension of LFDMA and IFDMA, the block-interleaved FDMA (B-IFDMA) has been also proposed in the literature mainly due to its improved frequency diversity property compared to LFDMA  [4]. It has been shown, however, that the B-IFDMA signal tends to have higher dynamic range compared to those of LFDMA and IFDMA through extensive simulation study  [5].

Despite its practical importance, the theoretical studies on dynamic range of SC-FDMA signals are rather scarce [6], [2]. In  [7], we have developed an approach for calculating an approximate distribution of the instantaneous power for LFDMA and IFDMA signals, but to the best of the author’s knowledge, only the simulation studies have been conducted for the signal dynamic range analysis of general B-IFDMA systems and no rigorous theoretical justification has been provided to the fact that B-IFDMA signal has higher dynamic range than LFDMA.

In the orthogonal frequency-division multiplexing (OFDM) literature, PAPR is often adopted as a measure of signal dynamic range where it is defined as a maximum peak level of the instantaneous power for a given OFDM symbol. The PAPR is thus considered as a random variable that is determined by each OFDM symbol pattern and its distribution is of major concern (e.g.,  [8], [9]). Since SC-FDMA is a block transmission similar to OFDM, the knowledge of distribution of PAPR in addition to that of instantaneous power is helpful when we make a comparison between SC-FDMA and OFDM signals.

Given the above background, in this paper, we attempt to theoretically analyze the statistical distribution of the general B-IFDMA signal in terms of both instantaneous power and PAPR. Specifically, we first develop a mathematical description for SC-FDMA with main focus on the general B-IFDMA system. Based on this model, we derive an analytical expression for the statistical property of the instantaneous power for B-IFDMA signals. Using this instantaneous power model, we further establish a statistical expression for PAPR of the B-IFDMA signals that enables one to numerically calculate their distribution.

This paper is organized as follows. In Section  2, we review the mathematical models of LFDMA and IFDMA signals and extend them to B-IFDMA signals. Their instantaneous power distribution is analyzed in Section  3, followed by the PAPR analysis in Section  4. Finally, concluding remarks are presented in Section  5.

Section snippets

SC-FDMA signal model

This section describes the SC-FDMA system model considered in this paper and formulates mathematical model of its baseband signal waveform.

Instantaneous power distribution

In this section, we derive an expression for the instantaneous power of B-IFDMA signals as an extension of LFDMA and IFDMA, which has been derived in  [7]. Note that with sufficient oversampling, the distribution of instantaneous power for LFDMA and IFDMA is identical. On the other hand, we will see that B-IFDMA tends to suffer from higher dynamic range as confirmed by the simulation studies in  [5].

Peak-to-average power ratio analysis

In the literature of OFDM, the statistical distribution of PAPR is often used as an indicator of severity of signal dynamic range. Since the OFDM and SC-FDMA signals are based on block transmission, the PAPR, denoted by ζ in what follows, is defined block-wise (symbol-wise): ζ=maxl{0,1,,JM1}pl. Note that in (31), it is implicitly assumed that the average power is unity, i.e., E{pl}=E{|s̃l|2}=1. For a given sample index l,pl is a random variable and thus ζ itself is a random variable that

Conclusions

We have analyzed the distributions of instantaneous power and PAPR for a general B-IFDMA system. The accuracy of the analytical results has been confirmed by Monte-Carlo simulations. It has been shown through numerical calculations that the dynamic range of B-IFDMA can be considerably increased compared to conventional LFDMA or IFDMA when the block spreading factor is moderate. Therefore, when one employs B-IFDMA, a more careful consideration for a power amplifier back-off operation should be

Acknowledgment

This work was supported in part by MEXT KAKENHI23686058.

Hideki Ochiai received the B.E. degree in Communication Engineering from Osaka University, Osaka, Japan, in 1996, and the M.E. and Ph.D. degrees in Information and Communication Engineering from the University of Tokyo, Tokyo, Japan, in 1998 and 2001, respectively.

From 1994 to 1995, he was with the Department of Electrical Engineering, University of California, Los Angeles (UCLA), CA, under the scholarship of the Ministry of Education, Science, and Culture. From 2001 to 2003, he was a Research

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Hideki Ochiai received the B.E. degree in Communication Engineering from Osaka University, Osaka, Japan, in 1996, and the M.E. and Ph.D. degrees in Information and Communication Engineering from the University of Tokyo, Tokyo, Japan, in 1998 and 2001, respectively.

From 1994 to 1995, he was with the Department of Electrical Engineering, University of California, Los Angeles (UCLA), CA, under the scholarship of the Ministry of Education, Science, and Culture. From 2001 to 2003, he was a Research Associate at the Department of Information and Communication Engineering, the University of Electro-Communications, Tokyo, Japan. Since April 2003, he has been with the Department of Electrical and Computer Engineering, Yokohama National University, Yokohama, Japan, where he is an Associate Professor. From 2003 to 2004, he was a Visiting Scientist at the Division of Engineering and Applied Sciences, Harvard University, Cambridge, MA.

Dr. Ochiai served as an Editor for IEEE Transactions on Wireless Communications from 2007 to 2011. Since 2011, he has served as an Editor for IEEE Wireless Communications Letters.

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