A Low Computational Complexity Algorithm for PTS based PAPR Reduction Scheme in OFDM Systems

A Low Computational Complexity Algorithm for PTS based PAPR Reduction Scheme in OFDM Systems

T. Chalapathi, M. Tech Student, and M. Madhu Babu, Faculty

Department of Electronics & Communication Engineering Jawaharlal Nehru Technological University

Anantapur, India

Abstract

Peak-to-Average Power Ratio (PAPR) is the major drawback in Orthogonal Frequency Division Multiplexing (OFDM) systems, which may result in signal distortion, loss of orthogonality in OFDM signals etc. Hence it is the most concerned problem in OFDM systems, which has to be reduced. Of all the available PAPR reduction techniques, Partial Transmit Sequence (PTS) scheme is the most efficient and attractive one. But, the original PTS scheme requires large computations in order to transmit the optimum signal with low PAPR from all available combinations of candidate signals. This paper proposes a new efficient PTS scheme which utilizes the correlation property among all available candidate signals to reduce the computational complexity.

1. Introduction

   Orthogonal Frequency Division Multiplexing (OFDM) is a parallel multicarrier transmission scheme, where a high-rate serial data stream is split up into a set of low-rate sub streams, each of which is modulated on a separate subcarrier. The basic principle of OFDM is to split a high-rate data stream into a number of lower rate streams that are transmitted simultaneously over a number of subcarriers. Because the symbol duration increases for lower rate parallel subcarriers, the relative amount of dispersion in time caused by multipath delay spread is decreased. Intersymbol interference is eliminated almost completely by introducing a guard time in every OFDM symbol. In the guard time, the symbol is cyclically extended to avoid intercarrier interference.

   OFDM is a multicarrier technique which is used commonly all over the world. It is widely adopted & standardized in the world. A number of applications [4],

   [5] and standards which use OFDM include Digital Audio Broadcasting (DAB), Digital Video Broadcasting (DVB), WiFi (IEEE 802.11a/g/j/n), World Wide Interoperability for Microwave Access (WiMAX-IEEE 802.16), Ultra Wide Band Wireless Personal Area Network (UWB Wireless PAN-IEEE 802.15.3a) and Mobile Broadband Wireless Access (MBWA-IEEE802.20). One of the main reason to use OFDM is to increase the Robustness against frequency-selective fading or narrowband interference. Inverse Fast Fourier Transform (IFFT) and FFT are used in OFDM to multiplex the signals together at the

   transmitter, and demultiplex the signals in the receiver, respectively.

   OFDM has many advantages like, it is an efficient way to deal with multipath fading, it is robust against narrowband interference and etc. Beside all these advantages, the major disadvantage and exclusive drawback of the OFDM is the PAPR which increases the complexity of A/D & D/A converters [7] and also reduces the efficiency of the RF power amplifiers. Hence this problem of high PAPR has become a major concerned problem in the OFDM systems. Thus several PAPR reduction techniques [13] have been implemented which are categorized as the Signal Distortion techniques (like Clipping), Coding techniques and Scrambling Sequence techniques (like PTS scheme). Of all the PAPR techniques, PTS scheme has been found to an efficient and attractive method that has several advantages over others. In PTS, an input data sequence is divided into a number of disjoint subblocks, which are then weighted by a set of phase factors to create a set of candidate signals. Finally, the candidate with the lowest PAPR is chosen for transmission. This PTS scheme has a major drawback that it requires a very large number of computations to identify and select the optimum candidate signal that has a low PAPR from all the available combinations of candidate signals. This computational complexity has been reduced by implementing several modified techniques like iterative flipping, but all these techniques are implemented by reducing & eliminating the some of the candidate signals which has caused in the information loss.

   This paper proposes a new PTS scheme to reduce the PAPR in OFDM systems with low & much reduced computational complexity. In this paper, we reduce the Computational Complexity in PTS scheme, by using the correlation property between the available candidate signals, instead of reducing the number of candidate signals and thus no information is being lost. This scheme achieves the PAPR reduction same as the conventional PTS scheme and reduces the computational complexity to a large extent. In section II, we introduce the concept of OFDM signal and overview of the PAPR problem. The conventional PTS scheme has been explained in the section III. The new PTS scheme to reduce the computational complexity has been implemented in section IV. Section V gives the computational analysis and focuses on the simulation results. The last section i.e. section VI concludes our paper.

   Input Data Source

   Serial to Parallel

   Converter

   N-point IFFT

   Sub Block Partition

   N-point IFFT

   N-point IFFT

   Phase Factors Optimization

   Selection of Optimal Combination of Phase Factors with lowest PAPR

   Parallel to Serial Conversion

   Figure 1. Partial Transmit Sequence Scheme Block Diagram

2. Background

   1. OFDM Signal

      Let there be N different subcarriers used to transmit the parallel information and let Sn,k denote the kth complex modulated symbol, then the nth OFDM block [6] is given by

      where the kth subcarrier signal is given by

      where .

      Thus, the outputs sn [12], [14] of the N-point IDFT of Sk are given by

      where

   2. PAPR

      The Peak-to-Average Power Ratio (PAPR) of the OFDM signal is defined as the ratio of the Maximum

      where denotes the magnitude of and denotes the expectation operation. Here, the peak power occurs when the N modulated symbols are added with the same phase.

3. Conventional PTS Scheme

   Partial Transmit Sequence (PTS) scheme [11] is the PAPR reduction technique in which, only part of the data of varying sub-carrier with low PAPR is transmitted which covers all the information to be sent in the signal as a whole. The block diagram of the PTS scheme is as shown in the Figure 1, above.

   As shown in Figure 1, in the Partial Transmit Sequence technique, input data block S is partitioned into M disjoint sub-blocks such that each sub-block is given by

   such that . Now, these sub-blocks are combined to minimize the PAPR in the time domain. The L times oversampled time domain signal of , is obtained by taking the inverse discrete fourier transform of length NL on concatenated with (L-1)N zeroes. These are called the Partial Transmit Sequences.

   Here, the complex phase factors given by

   power delivered by the Average power of the OFDM

   are introduced to combine

   signal. It is expressed as given below

   In other words,

   the partial transmit sequences. The set of complex phase factors is denoted by .

   Now, the time domain signal after combining all the partial transmit sequences by the use of the complex phase factors is given by

   write the first candidate signal derived from first prototype vector as

   where,

   Now, we can derive the second candidate signal from first candidate signal by using the sign change property as

   .

   In other words, the time domain partial transmit sequence by using IDFT can be expressed as

   Now, the objective is to find the set of phase factors which minimizes the PAPR. This implicates that we need to find the set of optimum phase factors, which when used to combine the M disjoint blocks will yield a candidate signal with low PAPR. Now, if we assume that there are W phase factors, then it would require for the PTS to search combinations to get an optimal set of phase factors which yields low PAPR signal. This indicates that the number of search increases [8] exponentially with number of blocks M. Thus, this conventional PTS scheme requires a large computations to get an optimal candidate signal with low PAPR.

4. A New Reduced Complexity PTS Scheme

   Here, we propose a new PTS scheme which reduces the computational complexity without reducing the number of candidate signals. In all available combinations there may be certain pairs which may have the same relations. Thus, we use the correlation property among these phase factors in each subset, such that the computational complexity is reduced.

   To start with our proposed method, let us first define the phase factors in a phase set. Let us denote the number of phase factors as W. If we take W=2, then it

   Where represents the kth phase weighting vector based on the ith prototype vector and is applied to the mth subblock of the PTS OFDM transmitted signal and indicates the sign of A.

   Similarly, we can write the i+1th candidate signal derived from this first prototype vector as

   Now, we can derive the first candidate signal that of the 2nd prototype vector denoted by from as given by

   Where indicates the previous prototype vector, and is the value which denote the change of the real & imaginary phase factors in the various prototype vectors.

   So in general, we can write the i+1th candidate signal derived from the second prototype vector as

   Combining all the above equations from 9 to 13, we can summarize the general equations to get the candidate signals as given below

   And

   indicates that there are two phase factors, one is in-phase & other is out-of-phase factor with phase factor set as {1,-

   1}. In same way, if we take W=4, then the phase factors

   set consists of {1,-1,j,-j} which indicates real & imaginary, in-phase & out-of-phase factors.

   Now, knowing these phase factors, we can create a fundamental combination known as Prototype Vectors. We derive all the other vectors from this prototype vector. For example, if W=2 & M=2, then the prototype vectors are {1,1} & {1, j). Because of using the correlation property, all the vectors derived from same prototype vector differ each other by a sign change only.

   Based on these phase factor, number of subblocks of the PTS, by knowing all the vectors, we can write the candidate signals. Hence by using the correlation property and knowing all the vectors, we can

   With all the above equations, we get the all possible candidate signals with reduced computational complexity. From these candidate signals, we choose the one with minimum PAPR for transmission.

   Now, let us see the above reduced computational complexity PTS algorithm considering an example. Let us do the partial transmission of sequences by taking 3 subblocks i.e. M=3 and let us consider 4 phase factors set

   i.e. W=4.

   Rewriting the equations 14 & 15 using M=3 & W=4 to get the candidate signals, we can write

   and similarly we can write the equations so on till we get the last candidate signal i.e. . So, by using the equations from 16 to 19, we can write the candidate signals as follows

   Here, note that, due to the correlation property the computational complexity has been reduced to a large extant. Now, from these available candidate signals, we transmit the one with minimum PAPR.

5. Analytical & Simulation Results

   1. Computational Complexity Analysis

      In the previous section, we have seen how we had reduced the computational complexity of the proposed system. Here in this section, we analyse the computational complexity reduction by defining the term Computational Complexity Reduction Ratio (CCRR) of the proposed PTS scheme comparing with that of the conventional PTS scheme. The CCRR is given by

      From equation 14 it is clear that the number of

      multiplications required by the proposed PTS is given by

      And the number of multiplications required by the conventional PTS is given by

      Similarly, From equation 15, we can say that the number of additions required by the proposed PTS scheme has reduced to N because it is only necessary to calculate the . Hence, the ratio of the addition complexity of proposed scheme to that of conventional

      PTS scheme is .

      Now, if we take, M=6, then we get Addition CCRR as 80% and Multiplication CCRR as 98% with the proposed PTS scheme compared to the conventional PTS scheme. With this, we can say that the proposed PTS scheme can reduce the computational complexity to a very extant when compared to the conventional PTS scheme.

   2. Simulation Results

      In this proposed PTS scheme, we have not reduced the number of candidate signals as in other cases, but we have used the correlation property in order to reduce the computational complexity. In this regard we can prove this by observing the Complementary Cumulative Distribution Function CCDF [10] which is given by

      Here, taking z as , the Complementary Cumulative Distribution Function CCDF is given as the

      Here, as we have used the correlation property instead of reducing the number of candidate signals, we achieve the PAPR reduction as same as in the case of conventional PTS scheme. This is illustrated in the Fig. 2 in which we can see the coincidence of the theoretical evaluation and computer simulation results. The results have been simulated in the MATLAB.

      0

      10

      OFDM(Original)

      PTS(Conventional) PTS(Proposed)

      -1

      <—– CCDF —-->

      10

      -2

      10

      -3

      10

      2 3 4 5 6 7 8 9 10 11

      <—– PAPR in db —-->

      Figure 2. CCDF

6. Conclusion

   Conventional PTS scheme employs large computations to reduce the PAPR which is a major drawback in the OFDM systems. As analysed in section V, our new proposed PTS scheme reduces the computational complexity of the conventional PTS scheme to a very large extant. Also, the simulation results show that the proposed system achieves same PAPR reduction as the conventional system. Hence our proposed PTS scheme not only reduces the computational complexity to a great extant but also achieves the same PAPR reduction as that of the conventional system.

7. Acknowledgment

   Chalapathi would like to thank Mr. M. Madhu Babu, who had been guiding through out to complete the work successfully, and would also like to thank the HOD, ECE Department and other Professors for extending their help & support in giving technical ideas about the paper and motivating to complete the work effectively & successfully.

8. References

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3. Chih-Peng Li, Sen-Hung Wang, and Chin-Liang Wang, Novel Low-Complexity SLM Schemes for PAPR Reduction in OFDM Systems, IEEE

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Authors Profile

T. Chalapathi received his B.Tech Degree in Electronics & Communication Engineering from St. Johns College of Engineering & Technology, Yemmiganur, Kurnool, India. Presently he is pursuing his M. Tech in Digital Electronics & Communication Systems specialization in

the Department of Electronics & Communication Engineering from Jawaharlal Nehru Technological University, Anantapur, India. His research interests include Signal Processing, Control Systems, Ananlog & Digital Electronics and Communications.

Mr. M. Madhu Babu received his B.Tech Degree in Electronics & Communication Engineering AITS, Rajampet, Kadapa India. And he received his MTech in VLSI specialization from VNR VJIET, Hyderabad. Presently he is with his Ph.D in "FPGA Implementation of Low Power

and High Data Rate OFDM Communication System" under VLSI in the Department of ECE, from JNTU Anantapur, India. He is presently working as a Lecturer in the Department of Electronics & Communication Engineering, JNTU University, Anantapur. His research interests include VLSI and Communications.