A Piecewise Linear Companding Transform for PAPR Reduction of OFDM Signals With Companding Distortion Mitigation
Abstract
Companding is a well-known technique for the peakto- average power ratio (PAPR) reduction of orthogonal frequency division multiplexing (OFDM) signals. However, as companding transform is an extra operation after the modulation of OFDM signals, companding schemes reduce PAPR at the expense of increasing the bit error rate (BER). In this paper, a new piecewise linear companding scheme is proposed aiming at mitigating companding distortion. In the design of the companding transform, we study the theoretical characterization of companding distortion. It demonstrates that companding larger signals with smaller amplitude increments are more favorable in reducing companding distortion. Based on the analysis results, a new piecewise linear companding transform is proposed by clipping the signals with amplitudes over a given companded peak amplitude for peak power reduction, and linearly transforming the signals with amplitudes close to the given companded peak amplitude for power compensation. With the careful design of the companded peak amplitude and the linear transform scale, the proposed transform can achieve enhanced BER and power spectral density performance, while reducing PAPR effectively.
Index Terms—OFDM, PAPR, companding transform, companding distortion.
1. INTRODUCTION
ORTHOGONAL frequency division multiplexing (OFDM) is one of the most popular technologies in high speed wireless communication systems since the past few decades. However, despite the advantages, the inherent drawback of large envelope fluctuations of OFDM signals may cause serious performance degradation with nonlinear high power amplifier (HPA) at the transmitter.
Peak-to-average power ratio (PAPR) is widely used to characterize envelope fluctuations of OFDM signals by relating peak and mean power. Many PAPR reduction techniques have been proposed [1], [2], such as selective mapping (SLM) [3], partial transmit sequence (PTS) [4], tone reservation (TR) [5], tone injection (TI) [5], active constellation extension (ACE) [6], clipping [7] and companding [8]–[15]. Among these techniques, companding techniques have gained great attention due to their flexibility and low complexity.
In this paper, a new piecewise linear companding scheme is proposed aiming at mitigating companding distortion. In the design of the companding transform, we first investigate the theoretical characterization of the effects of companding distortion on BER. It is manifested that BER performance can be effectively improved by reducing companding distortion.
2. BLOCK DIAGRAM
3. BASIC OFDM SYSTEM
The block diagram of OFDM system is shown in fig.1.The input high data rate streams are converted into number of low data rate streams. This parallel stream is then modulated using QPSK or QAM modulation techniques, which is then applied as input to IFFT block producing OFDM samples. These samples are then converted into OFDM signal using Parallel-to-Serial converter (P/S).The signal is then encoded by adding Cyclic Prefix (CP) and is then transmitted over the channel. The reverse process is done at the receiver
4. LITERATURE SURVEY
(1) A new companding scheme is proposed to reduce PAPR by transforming the statistics of the companded signal into exponential distribution with adjustable parameters. The proposed scheme can enhance the bit error rate (BER) performance significantly by minimizing the companding distortion in the reduction of PAPR. Moreover, with the introduction of an inflexion point and transform parameters, the proposed scheme can offer more flexibility in the PAPR reduction, and therefore achieves a better tradeoff among the PAPR reduction, BER and power spectral density (PSD) performance [1].
(2)In this study, a novel phase offset-based partial transmit sequence (PTS) scheme is proposed to reduce the peak-to-average power ratio (PAPR) in Alamouti coded multi-input-multi-output orthogonal frequency division multiplexing systems, and its key idea is that different phase rotation sequences are multiplied by their corresponding phase offsets at the transmitter. Moreover, a minimum Euclidean distance decoder is proposed to recover the phase rotation sequences at the receiver [2].
(3) In this study, a new peak-to-average power ratio (PAPR) reduction scheme for orthogonal frequencydivision multiplexing (OFDM) is proposed based on the selected mapping (SLM) scheme. The proposed SLM scheme generates alternative OFDM signal sequences by cyclically shifting the connections in each subblock at an intermediate stage of inverse fast Fourier transform (IFFT). Compared with the conventional SLM scheme, the proposed SLM scheme achieves similar PAPR reduction performance with much lower computational complexity and no bit error rate degradation. The performance of the proposed SLM scheme is analysed mathematically and verified through numerical analysis [3].
(4) In this paper, a peak-to-average-ratio (PAPR) reduction scheme based on a weighted orthogonal frequency-division multiplexing (OFDM) signal is proposed to reduce the PAPR without distortion in removing the weight at the receiver side. In the proposed scheme, a weight is imposed on each discrete OFDM signal via a certain kind of a bandlimited signal, and an OFDM signal formed with the weighted discrete data is then considered before a high power amplifier (HPA), whereas the original signal can be recovered completely at the receiver side. Meanwhile, the time duration needed to transmit the weighted OFDM signal is the same as the time duration for the original OFDM signal. The effectiveness of the proposed scheme is evaluated with computer simulations. According to numerical results, the PAPR of the weighted OFDM signal is smaller than that of the clipping and filtering (C&F) method, and the bit-error-rate (BER) performance of the weighted OFDM system is improved compared with the C&F method. Here, the proposed method is simpler than the C&F method
(5) In the last decades, many solutions have been proposed to cope with high Peak-to-Average Power Ratio (PAPR) of OFDM communication systems. We focus here on signals whose spectrum's amplitude respects a fix spectrum mask. We first build a framework based on Set Theoretic Estimation that offers many tools to reduce the PAPR down to the 3dB lower bound. By means of this framework, we then propose new algorithms that address the PAPR problem with a convergence time drastically lower than any of the previously used algorithms. [4].
(6) High peak-to-average power ratio (PAPR) of the transmitted signal is one of the limitations to employing orthogonal frequency division multiplexing (OFDM) system. In this paper, we propose a new nonlinear companding algorithm that transforms the OFDM signals into the desirable statistics form defined by a linear piecewise function. By introducing the variable slopes and an inflexion point in the target probability density function, more flexibility in the companding form and an effective trade-off between the PAPR and bit error rate performances can be achieved. A theoretical performance study for this algorithm is presented and closed-form expressions regarding the achievable transform gain and signal attenuation factor are provided. We also investigate the selection criteria of transform parameters focusing on its robustness and overall performance aspects.
4. PROPOSED METHOD
When the initial signal is companded with a given peak amplitude Ac, the proposed companding scheme shown in Fig.5 clips the signals with amplitudes over Ac for peak power reduction, and linearly transforms the signals with amplitudes close to Ac for power compensation. Then, the companding function of the proposed companding scheme is
(1)
Where sgn(x is the sign function.
Consequently, the decompounding function at the receiver is
(2)
It is obvious that the proposed companding transform is specified by parameters andk.Acis the peak amplitude of the companded signals. As the average signal power is maintained constant, then according to the definition of PAPR in (3), the PAPR value of the proposed scheme that can be achieved theoretically is determined by . With a preset theoretical PAPR value, can be determined as = PAPR. With determined, parameters andkcan be obtained by solving.
With acceptable manipulation, are often simplified into a equation about k. the details of the manipulation are shown in Appendix. With the premise of keeping the typical signal power constant, k has to be a positive real number smaller than one. Besides, to limit the peak amplitude of the distended signals not larger than, ks hould not be a negative real number. Therefore, k is confined to the interval (0,1).
5. SOFTWARE AND HARDWARE REQUIREMENTS
Operating system : Windows XP/7.
Coding Language: MATLAB
Tool:MATLAB R 2012
SYSTEM REQUIREMENTS:
HARDWARE REQUIREMENTS:
System: Pentium IV 2.4 GHz.
Hard Disk : 40 GB.
Floppy Drive: 1.44 Mb.
Monitor: 15 VGA Colour.
Mouse: Logitech.
Ram: 512 Mb.
6. CONCLUSION
In this paper, a new piecewise linear companding scheme is proposed aiming at mitigating companding distortion to enhance the BER performance. Based on the theoretical analysis of the BER performance in terms of companding distortion, we get the general design criteria for companding transform that companding transform should avoid unnecessary compression and expand larger signals with smaller amplitude increments. Based on the design criteria, we propose a new piecewise linear companding scheme. By carefully designing the companding parameters, the proposed scheme can effectively reduce companding distortion. Simulation results verify that the proposed piecewise linear companding scheme can achieve enhanced BER and PSD performance, while reducing PAPR effectively.
REFERENCES
[1] MeixiaHu, Yongzhao Li, Yi Liu, Hailin Zhang, Parameter-adjustable piecewise exponential companding scheme for peak-to-average power ratio reduction in orthogonal frequency division multiplexing systems, Published in IET Communications, Received on 21st March 2014, doi: 10.1049/iet-com.2013.0226
[2] Peak-to-average power ratio reduction in alamouti multi-input-multi-output orthogonal frequency division multiplexing systems without side information using phase offset based-partial transmit sequence scheme, Tao Jiang, Chunxing Ni ; Lili Guan ; QiQi March 27 2014,10.1049/iet-com.2013.0812
[3] Low-complexity selected mapping scheme using cyclic-shifted inverse fast Fourier transform for peak-to-average power ratio reduction in orthogonal frequency division multiplexing systems, Kee-Hoon Kim, Hyun-Bae Jeon ; Jong-Seon No ; Dong-Joon Shin 2013
[4] A Weighted OFDM Signal Scheme for Peak-to-Average Power Ratio Reduction of OFDM Signals Chang Eon Shin, Kyung Soo Rim, and Youngok Kim; 2013
[5] Using Set Theoretic Estimation to Address the PAPR Problem of Spectrum-Constrained Signals; Fumat, G. ; Zoubir, A. ; Fournier-Prunaret, D., 2012
[6] Nonlinear Companding Transform for Reduction of Peak-to-Average Power Ratio in OFDM Systems; Yong Wang, JianhuaGe, Lihua Wang, Jing Li, and Bo Ai; 2012