PAPR Reduction in OFDM using Reduced Complexity Selective Mapping Technique

PAPR Reduction in OFDM using Reduced Complexity Selective Mapping Technique

Gagandeep Singh

PG Student,ECE Department Punjabi University

Patiala, Punjab,INDIA

Dr. Ranjit Kaur

Associate Professor,ECE Department Punjabi University

Patiala, Punjab,INDIA

Abstract Orthogonal Frequency Division Multiplexing (OFDM) is the most promising technique available and is most commonly used due to its advantages like very high data rate, noise immunity and efficient bandwidth utilization. One of the major drawback of OFDM is its high Peak to Average Power Ratio (PAPR). In this paper Selective mapping is used to perform PAPR reduction and same time reducing its complexity so that its implementation uses less floor area and on chip requirements. Results shows that PAPR reduction is similar to Conventional SLM but new technique is less complex than original one in terms of IFFT blocks used and Multipliers used in the process.

This paper is organized as follows: Section I describes OFDM system. Section II describes PAPR in OFDM system. Section III describes Improved SLM as PAPR reduction techniques. Section IV describes simulation results and Section V describes conclusion.

II. PAPR IN OFDM SIGNAL

Let the input data block of length N be represented by block X S [ X1 , X 2, X 3 …X N 1 ] , Thus OFDM symbol can be written as:

e

N 1

Keywords – Orthogonal frequency division multiplexing (OFDM), Peak to average power ratio (PAPR), Selective Mapping (SLM), Bit Error Rate (BER), Digital Subscriber Line

(DSL), Partial Transmit Sequence (PTS).

Z (s) = X

k 1

j 2kf0t

S

(1)

Where Z(s) is the OFDM symbol,

X S is the input data

1. INTRODUCTION

Orthogonal Frequency Division Multiplexing (OFDM) is a digital transmission Technique developed to meet the increasing demand of higher data rates in wireless and

block and N is the number of symbols in input data block.

PAPR is defined as the ratio of Peak to Average Power. Mathematically PAPR can be defined as following:

wired communications. Due to its high data rate handling capacity, it is most often used in high speed networks like Digital Video Broadcasting (DVB), Digital Subscriber Line

(DSL) and in wireless communication[3][12]. The main

PAPR Z

s

maxZ s 2

EZ s2

(2)

disadvantage in using OFDM is its high Peak to Average Power Ratio (PAPR). Such a high PAPR causes the linear amplifier to have large dynamic range which is difficult to accommodate[8].

Where Z (s) is the OFDM signal,

signal power, E Z s2 power[3].

maxZ s2 is the peak is the average signal

Thus it becomes necessary to reduce the PAPR to keep the High Power Amplifier (HPA) in linear range. There are numerous techniques available for PAPR reduction. These are categorized as Signal Distortion Techniques and Signal Scrambling Techniques. Distortion Techniques causes signal distortion and Bit Error Rate (BER) to grow after certain point, whereas Signal Scrambling techniques causes no harm to the OFDM signal. The only disadvantage in using signal scrambling techniques is their increased system complexity[3][6].

1. SELECTIVE MAPPING

   Selective Mapping is a Signal Scrambling technique to reduce PAPR in OFDM system. The advantage in using this technique is that it does not effects the system performance in terms of Bit Error Rate. The only disadvantage in using this technique is its high complexity. The basic concept behind this technique is the phase rotation of the modulated data before performing IFFT operation. After performing phase rotations, the signal with lowest PAPR is selected [2][8][4].

   Fig. 1. Block diagram of SLM technique[2]

   Let the input data block be represented as

   Where is the oversampling factor, N is no. of sub-carrier, U is total no. of independent phase sequences.

   A. IMPROVED SELECTIVE MAPPING

   The drawback in using Conventional Selective Mapping is its high Implementation complexity. The complexity of this technique increases exponentially upon increasing the number of phase sequence and number of subcarriers in OFDM system.

   So, here a new and improved SLM technique is presented which is less complex than conventional SLM but the original concept remains intact and PAPR reduction is similar to Conventional SLM. This technique is modified

   X S [ X 0

   , X1,

   X 2 …X

   T

   ]

   N 1

   (3)

   to incorporate only one IFFT block and multiplier in place

   And independent phase sequences are given by

   of multiple ones and replace the parallel processing with serial processing. Figure below illustrates the Single IFFT

   BU [BU , BU …..BU

   ]T ,U (1,2….U )

   (4)

   block SLM.

   0 1 N 1

   Where BU

   is the phase sequence, U is the total no. of

   If the number of sub-blocks is M, then the data block can

   Phase sequences and T is the length of input data block.

   After applying Phase rotation, IFFT is applied to obtain data block with different PAPR value and phase

   be expressed as:

   (7)

   sequences[2].

   After serial to parallel conversion one data block can be

   represented as:

   X U [ X U , X U ,…..X U ]T

   (5)

   0 1 N 1

   (8)

   Where X U is the OFDM symbol generated after IFFT

   operation. After this the stream with lowest PAPR is selected for transmission. CCDF is used for PAPR representation. CCDF of PAPR in SLM can be represented as

   Each of the sub-blocks is then multiplied with independent phase sequences and passed through an N-point IFFT block to obtain the corresponding SLM. Which is given by:

   P(PAPR PAPR0) (1 (1 e PAPR 0 ).N )U

   (6)

   Fig. 2. Block diagram of proposed SLM

   Let the Phase Sequences is represented by:

   Where M is the total no of input data blocks and u is the no. of phase sequences of length equal to n. Considering

   Pu [ pu , pu …. pu ]

   (9)

   the number of phase sequences in SLM be 4 and input data

   0 1 n1

   Where u is the no. of total phase sequences each of lenth n.The above Phase sequence is multiplied with data block to perform phase rotation.

   block be 64, then quantitative analysis can be summarized as in following table:

   Table II. Shows quantative analysis with example

   u

   Zn Xn * P

   (10)

   Process	Original SLM	Single IFFT Block SLM
   N- point IFFT blocks required	256	64
   Phase Multipliers required	256	64
   PAPR calculations performed	256	256

   SLM output for first block in first phase sequence will be:

   Yn IFFT [Zn ]

   (11)

2. SIMULATION RESULTS

It is observed that the results obtained from both the

PAPR of this SLM rotated OFDM symbol can be calculated as:

techniques are similar in PAPR reduction values but variation in time consumption of the two algorithms.

2

2

PAPR [Yn ] =

max[Yn ]

(12)

CCDF Plot for PAPR using SLM with 64 subcarriers

0

10

E[Yn ]

Pr(PAPR>PAPR0)

10

Similarly, the input data block is rotated U number of times -1

and is stored in Memory Buffer temporarily. The PAPR is calculated for each sequence and lowest one is selected for transmission. Similarly next data block enters the system and same steps are repeated for total number of data

-2

blocks. 10

Simple mathematical calculations have been done for both the techniques to find out the number of times these operations have to be performed. The values are enlisted in the following Table:

Table I. Shows quantative analysis

-3

10

2 4 6 8 10 12 14

PAPR0/dB

Fig 3. CCDF Plot of PAPR using proposed SLM for 64 sub-carriers

with U=2,4.

In the above graph of proposed SLM for 64 sub-carriers , PAPR levels are reduced with the increase phase sequences(U).

CCDF Plot for PAPR using SLM with 64 subcarriers

0

10

primary OFDM

SLM U=8

SLM U=16

SLM U=32

-1

Pr(PAPR>PAPR0)

10

-2

10

-3

10

2 4 6 8 10 12 14

PAPR0/dB

Fig. 4. CCDF Plot of PAPR using proposed SLM for 64 sub-carriers with U=8,16,32.

From the above graph of proposed SLM it is observed that PAPR levels keep on decreasing as Phase sequences are increased. but the margin of decrease in value of PAPR keeps on decreasing with the increase in value of U.

IV. CONCLUSION

In this paper, OFDM is studied and new SLM technique is implemented. This technique performs PAPR reduction similar to original SLM technique as shown in the graphs but implementation complexity is reduced to great extent. This technique does not cause out of band radiations or degrades BER performance. As in this technique hardware is reduced to great extent in terms of IFFT blocks and Phase multipliers used. But this technique reduces throughput of data as it takes large time for processing of data. So we can use this technique for less no. of phase sequences.

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