International Scholarly Research Notices

Volume 2016, Article ID 8506986, 8 pages

http://dx.doi.org/10.1155/2016/8506986

## Estimation of Cyclic Shift with Delayed Correlation and Matched Filtering in Time Domain Cyclic-SLM for PAPR Reduction

Department of Electronics and Electrical Engineering, Keio University, 3-14-1 Hiyoshi, Kohoku, Yokohama, Kanagawa 223-8522, Japan

Received 30 May 2016; Revised 23 August 2016; Accepted 6 September 2016

Academic Editor: Pierpaolo D’Urso

Copyright © 2016 Panca Dewi Pamungkasari and Yukitoshi Sanada. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Time domain cyclic-selective mapping (TDC-SLM) reduces the peak-to-average power ratio (PAPR) in OFDM systems while the amounts of cyclic shifts are required to recover the transmitted signal in a receiver. One of the critical issues of the SLM scheme is sending the side information (SI) which reduces the throughputs in wireless OFDM systems. The proposed scheme implements delayed correlation and matched filtering (DC-MF) to estimate the amounts of the cyclic shifts in the receiver. In the proposed scheme, the DC-MF is placed after the frequency domain equalization (FDE) to improve the accuracy of cyclic shift estimation. The accuracy rate of the propose scheme reaches 100% at = 5 dB and the bit error rate (BER) improves by 0.2 dB as compared with the conventional TDC-SLM. The BER performance of the proposed scheme is also better than that of the conventional TDC-SLM even though a nonlinear high power amplifier is assumed.

#### 1. Introduction

Orthogonal frequency division multiplexing (OFDM) is multicarrier modulation which provides reliable high speed data rate because of its high spectral efficiency and its robustness against multipath fading channel. One of the significant problems of the OFDM signal is its high peak-to-average power ratio (PAPR) that requires wide range linearity in a power amplifier (PA). The high PAPR may drive a power amplifier into the saturation region, create interference among subcarriers, and corrupt the spectrum of the signal [1–3]. Some schemes for reducing PAPR have been available, for example, coding, filtering and clipping, and phase manipulation (selective mapping and partial transmit sequences).

Selective mapping (SLM) is one of the popular PAPR reduction schemes without signal distortion. SLM is a probabilistic scheme where signal candidates (SCs) are generated by multiplying the original signal sequence and the phase sequence. The SC with the lowest PAPR is chosen for transmission. In SLM, side information (SI) is needed at a receiver side to recover the transmitted signal. The SI is usually transmitted as a set of bits for every OFDM symbol and channel coding is required to protect it from a harsh channel. It involves the reduction of throughputs in wireless OFDM systems. Moreover, SLM has large computational complexity because it requires several inverse discrete Fourier transform (IDFT) operations and it makes the restrictions in implementation. A lower-complexity SLM scheme has also been proposed to solve this problem [4–15].

Many schemes have been proposed to exclude the SI [9–16]. The scheme in [9] makes the difference between the average energies of the extended and nonextended symbols to recover the SI at the receiver. As a consequence, higher order modulation symbols would influence the accuracy of SI detection. The scheme in [10] realizes semiblind SI detection in the SLM. However, this scheme requires embedding the SI in transmit symbols. In the scheme presented in [11], time domain cyclic-SLM with delayed correlation (DC) is applied to reduce a PAPR and to estimate the amount of a cyclic shift at the receiver without SI transmission. Nevertheless, there is a tradeoff between the amount of PAPR reduction and the BER. The method in [12] has been proposed to further reduce the PAPR of the abovementioned scheme. It uses matched filtering (MF) with a Barker sequence to estimate the amounts of cyclic shifts. One of the causes of the estimation error is multipath components. These components mislead the outputs of the DC-MF.

In this paper, time domain cyclic-SLM (TDC-SLM) without SI transmission is proposed. The proposed time domain cyclic-SLM (TDC-SLM) places the DC-MF after frequency domain equalization (FDE) to remove multipath components in a received signal. At a transmitter side, a transmit signal is generated by the summation of an original signal and signals with cyclic shifts. At a receiver side the amounts of the cyclic shifts are detected by using the DC-MF. In this proposed scheme, intervals between the cyclic shifts are designed so that the receiver can distinguish the cyclic shifts and multipath delays with the use of the MF. However, multipath components still deteriorate the accuracy rate of cyclic shift estimation since they generate additional peaks at the outputs of the DC-MF. By using the proposed scheme, the accuracy rate then improves and the bit error rate (BER) reduces as compared to that of the conventional TDC-SLM and DC-MF in [12].

The rest of this paper is organized as follows. Section 1 contains the introduction. Section 2 explains system models including the OFDM symbol structure, time domain cyclic-selective mapping, channel estimation and frequency domain equalization, and the proposed cyclic shift estimation scheme. In Section 3 the performance results of the proposed scheme are presented and finally Section 4 concludes this paper.

#### 2. System Model

##### 2.1. OFDM Symbol

The discrete OFDM signal in time domain can be written aswhere is the time index, is the data symbol on the th subcarrier, denotes the subcarrier index, and is the number of the subcarriers. The OFDM signal can also be defined as a vector .

In order to mitigate the intersymbol interference, a guard interval (GI) is needed. The GI can be obtained by copying the last part of the OFDM signal and adding it to the beginning of the signal.where is the length of the GI.

##### 2.2. Time Domain Cyclic-Selective Mapping

In the TDC-SLM scheme, a signal on each branch is generated by applying a cyclic shift to the original signal. The block diagram of the TDC-SLM scheme is shown in Figure 1. The cyclically shifted signal in the TDC-SLM is given aswhere is the OFDM signal in the time domain at the time index of , is the GI length, is the SC that is generated by cyclically shifting the OFDM signal by , is the amount of the cyclic shift for the th SC, and , where is an integer [11, 12]. The resolution of the cyclic shifts, , has to be large enough for accurate estimation of the cyclic shifts in a receiver.