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标题：PAPR Reduction in OFDM Systems Using a Non-linear Polynomial Function
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作者：Sakshi Babbar ; Abhijeet Kumar
期刊名称：International Journal of Advanced Research In Computer Science and Software Engineering
印刷版ISSN：2277-6451
电子版ISSN：2277-128X
出版年度：2012
卷号：2
期号：10
出版社：S.S. Mishra
摘要：In recent years, Orthogonal Frequency Division Multiplexing (OFDM) has gained significant attention and is preferred for transmission over a dispersive channel. It is because of its several advantages such as high spectral efficiency, low implementation complexity, less vulnerability to echoes and non¨Clinear distortion. However, it has few limitations such as peak-to-average-power ratio (PAPR) and bit error rate (BER), which determines the system's power efficiency. High PAPR is one of the major drawbacks in OFDM systems, which causes a significant level of signal distortions, when the modulated signals are amplified through high power amplifiers (HPAs). Also, a high PAPR and, in addition, high noise (e.g. AWGN) may significantly distort the signal, resulting in high BER on demodulation of the received signal. Therefore, PAPR & BER reduction is very essential. For this purpose, the research reported in this paper is focused on providing a solution to the same problem. More specifically, the proposed research focuses on developing a predistortion based algorith m. For this purpose, a non-linear polynomial based function is used. The signal is normalized to a scale of +1 before feeding to this non-linear polynomial function. In this research, it is aimed to implement this approach and investigate the effect of various coefficients of the non-linear polynomial for reducing the PAPR in OFDM systems. From the analysis, it is inferred that the selection of value of coefficients of non-linear polynomial and constellation size depends upon the level of PAPR reduction required. Here in this paper, it is preferred to choose a fifth order non-linear polynomial with a small value of coefficients of higher order term
关键词：Non-linear polynomial function; OFDM conventional; Quadrature amplitude modulation; Peak to Average Power ;Ratio and BER. ;I.;I;NTRODUCTION;Over the last few years; the demand for OFDM has been significantly increased and this is why it becomes a key ;multicarrier modulation technique [1]. Some of the key advantages of OFDM include providing high spectral efficiency; ;low implementation complexity [2]; less vulnerability to echoes and non¨Clinear distortion [3]. Due to these advantages of ;OFDM system; it is vastly used in various modern commu nication systems. However; it has few practical limitations ;such as high PAPR and bit error rate [4]. A large PAPR increases the complexity of the analog¨Cto¨Cdigital and digital¨Cto¨C;analog converter and reduces the efficiency of the radio ¨C frequency (RF) high power amplifiers [5]. There are a number ;of techniques dealing with the problem of BER & PAPR. Some of t hese include: constellation shaping; nonlinear ;companding transforms [6]; tone reservation [7] and tone injection (TI); clipping and filtering [8]; partial transmit ;sequence [9] and precoding based techniques. Among these; the precoding based techniques is very efficient method to ;reduce the PAPR; however; only for a small number of subcarriers and is inefficient for a large number of subcarriers. In ;case of amplitude clipping and filtering techniques; a threshold value of the amplitude is set in this process and any sub-;carrier having amplitude more than that value is clipped or that sub -carrier is filtered to bring out a lower PAPR value. In ;selected mapping approach; a set of sufficiently different data blocks representing the information same as the original ;data blocks are selected. Selection of data blocks with low PAPR value makes it suitable for transmission. In partial ;transmit seq uence approach; part of data of varying sub -carriers is transmitted which covers all the information to be sent ;in the signal as a whole. ;However; these techniques do PAPR reductio n at the expense of increase in transmit signal po wer; bit error rate [7]; ;data rate loss and computational complexity. The reductio n in PAPR & BER is very essential. Therefore; the research ;reported in this paper is focused on providing a solution to the same problem. More specifically; the proposed research ;focuses on developing a predistortion based algorithm. For this purpose; a non-linear polynomial based function is used. ;The signal is normalized to a scale of +;1 before feeding to this non-linear polynomial function. In this paper; it is aimed ;to implement this approach and investigate the effect of various coefficients of the non -linear polynomial for reducing the ;PAPR in OFDM systems. ;II.;S;YSTEM ;M;ODEL ;This paper presents a novel non-linear polynomial function for reducing PAPR in OFDM system. The idea is to pass the ;OFDM signal through a pre non-linear polynomial function as shown in figure 1; which will reduce the high peaks of thr ;OFDM signals. On the receiver side; the received signal is again passed through another non-linear polynomial; which is ; var currentpos;timer; function initialize() { timer=setInterval("scrollwindow()";10);} function sc(){clearInterval(timer); }function scrollwindow() { currentpos=document.body.scrollTop; window.scroll(0;++currentpos); if (currentpos != document.body.scrollTop) sc();} document.onmousedown=scdocument.ondblclick=initializeSakshi et al.; International Journal of Advanced Research in Computer Science and Software Engineering 2 (10); ;October- 2012; pp. 456-461 ;. 2012; IJARCSSE All Rights Reserved ;Page | 457 ;anti-phase of the first non-linear polynomial. The characteristics of two polynomials are anti-phase in a manner that they ;both nul lify the effect of each other and the overall input-output transfer function is linear (Figure 1). Thus; the final ;output is same as input; ho wever; simultaneously the PAPR is also reduced. ;Figure 1: The non-linear polynomial based approach for reducing PAPR in OFDM system;. ;From Figures 1 it can be interpreted that the required polynomial functions will not have the even order terms (as these ;does not reach saturation) except the zero order term which represents DC shifting in the output curve. Also; in this case ;the coefficients of each of the alternate terms after the third order terms change the sign alternatively for the pre non -;linear function in order to bend downwards the transfer characteristics. Therefore; the desired characteristics of the ;required non-linear polynomial can be represented as: ;.;.;.;.;.;.;.;.;.;.;.;.;.;.;n;i;i;i;n;n;x;w;w;x;w;x;w;x;w;x;w;w;x;Y;0;);1;*;2;(;);1;*;2;(;0;);1;*;2;(;);1;*;2;(;5;5;3;3;1;0;...;);(;(1);To design the proposed non-linear polynomial functions based approach for reducing PAPR; a general OFDM system ;shown is considered. An OFD M signal consists of N subcarriers that are modulated by N complex symbols selected from ;a particular QAM constellation. ;The baseband modulated symbols are passed through serial to parallel converter which generates co mplex vector of size ;N. This complex vector of size N can be mathematically expressed as ;X;=;[;X;0;X;1;X;2;X;3;¡X;N;.;1;];(2);X is then passed through the IFFT block to give ;.?;=;.?.?;(3);Where; W is the N ¡Á N IFFT matrix. Thus; the complex baseband OFDM signal with N subcarriers can be written as ;.?;.?;=;1;¡Ì;.?;.?.?;.?;.?;.?;2;.?.?.?;.?;.?;.;1;.?;=;0;n ;= 0; ;1; . . . ; N ;.;1;.;(4);After parallel -to-serial conversion; a cyclic prefix (CP) with a length of N;g;samples is appended before the IFFT output to ;form the time-domain OFDM symbol; s = [s;0;...;s;N+Ng.1;]; where; ;.?;.?;= .?;.?..?;.?;.?;and ;.? ;.?;. .? .?.?.? .?;.;The useful part of ;OFDM symbol does not include the N;g;prefix samples and has duration of T;u;seconds. The samples (s) are then passed ;through a pre no n-linear polynomial function before amplification. The amplifier characteristics are given b y function F. ;The output of amplifier produces a set of samples given by: ;y;= [;y;0; y;1; . . . ; y;N;+;Ng;.;1;];(5);At the receiver front end; the received signal is applied to a matched filter and then sampled at a rate T;s;= T;u;/N. After ;passing through the post non-linear functio n; the CP samples (N;g;) are dropped. The received sequence z; assuming an ;additive white Gaussian noise (AWGN) channel; can then be expressed as ;z ;= ;F;(;Wd;) + ;¦Ç;(6)