**- DSP log - http://www.dsplog.com -**

Trying out PAPR reduction for OFDM by multiplication with j

Posted By __Krishna Sankar__ On July 2, 2008 @ 6:08 am In __OFDM__ | __47 Comments__

In this post, we will explore a probable way of **reducing PAPR (peak to average power ratio) in OFDM** by changing the phase of some of the subcarriers. This is in response to the comment to post on Peak to Average power ratio for OFDM ^{[1]}, where Mr. Elibom suggested to reduce the PAPR by cyclically rotate some of the subcarriers and using.

Further, the presentation in the IEEE TGN, PAPR in HT-LTF (11-06/1595r1) ^{[2]}, mentions that in 40MHz mode where a 128pt FFT is used, PAPR of HT-LTF (High Throughput Long Training Field) can be reduced by multiplying the upper 20MHz subcarriers by j. Using quick Matlab simulations, we will try to validate that claim for HT-LTF and further check the PAPR for a general random BPSK and QPSK modulation.

The peak to average power ratio for a signal is defined as

, where

corresponds to the conjugate operator.

Expressing in deciBels,

.

**Matlab/Octave script for computing PAPR in HT-LTF**

close all; clear all;

nFFT = 128; nDSC = 114;

% The 128pt HT-LTF sequence for 40MHz as defined in 11-06/1595r4

htLTF = [ zeros(1,6) 1 1 -1 -1 1 1 -1 1 -1 1 1 1 1 1 1 -1 -1 1 1 -1 1 -1 1 1 1 1 1 ...

1 -1 -1 1 1 -1 1 -1 1 -1 -1 -1 -1 -1 1 1 -1 -1 1 -1 1 -1 1 1 1 1 -1 -1 -1 1 0 ...

0 0 -1 1 1 -1 1 1 -1 -1 1 1 -1 1 -1 1 1 1 1 1 1 -1 -1 1 1 -1 1 -1 1 1 1 1 1 ...

1 -1 -1 1 1 -1 1 -1 1 -1 -1 -1 -1 -1 1 1 -1 -1 1 -1 1 -1 1 1 1 1 zeros(1,5)];

x1F = htLTF; % no rotation

x2F = [htLTF(1:64) j*htLTF(65:128)]; % with 90degree rotation

% Taking iFFT, time domain

x1t = (nFFT/sqrt(nDSC))*ifft(fftshift(x1F.')).'; % no rotation

x2t = (nFFT/sqrt(nDSC))*ifft(fftshift(x2F.')).'; % with rotation

% computing the peak to average power ratio for symbol without rotation

meanSquareValue1 = sum(x1t.*conj(x1t),2)/nFFT;

peakValue1 = max(x1t.*conj(x1t),[],2);

paprSymbol1 = peakValue1./meanSquareValue1;

paprSymbol1dB = 10*log10(paprSymbol1)

% computing the peak to average power ratio for symbol with 90 degree rotation

meanSquareValue2 = sum(x2t.*conj(x2t),2)/nFFT;

peakValue2 = max(x2t.*conj(x2t),[],2);

paprSymbol2 = peakValue2./meanSquareValue2;

paprSymbol2dB = 10*log10(paprSymbol2)

As claimed in slide7 of power point presentation PAPR In HT-LTF (11-06/1595r1) ^{[2]}, the PAPR with

(a) No rotation is 5.6317dB and

(b) With 90 degree rotation is 3.4066dB.

So, around **2.2dB reduction in PAPR **is achieved.

Armed with the above result, I tried to simulate the PAPR for with random BPSK (and QPSK) modulation on a 128pt FFT with and without rotating the upper 20MHz subcarriers by j.

Click here to download the Matlab/Octave script for simulating PAPR for BPSK/QPSK modulation OFDM with j rotation ^{[4]}

The results from the simulations is shown below.

**Figure: OFDM PAPR for BPSK/QPSK with j rotation**

**Observations**

1. For random BPSK sequence, the multiplication by j resulted in increase of PAPR by around 0.5dB.

2. For random QPSK sequence, the PAPR with and without multiplication by j is almost the same.

Based on the above simulation results, may I conclude that there is **no noticable reduction in PAPR by multiplying upper 20MHz subcarriers by j**. There might be some special cases (like HT-LTF sequence), where the multiplication by j reduces PAPR. However for **random BPSK/QPSK sequence**, there is **no improvement**.

Article printed from DSP log: **http://www.dsplog.com**

URL to article: **http://www.dsplog.com/2008/07/02/ofdm-papr-reduction-multiplication-by-j/**

URLs in this post:

[1] comment to post on Peak to Average power ratio for OFDM: **http://www.dsplog.com/2008/02/24/peak-to-average-power-ratio-for-ofdm/#comment-591**

[2] PAPR in HT-LTF (11-06/1595r1): **https://mentor.ieee.org/802.11/file/06/11-06-1595-01-000n-papr-in-ht-ltf.ppt**

[3] Joint Proposal PHY specification document (11-05/1102r4): **https://mentor.ieee.org/802.11/file/05/11-05-1102-04-000n-joint-proposal-phy-specification.doc**

[4] Matlab/Octave script for simulating PAPR for BPSK/QPSK modulation OFDM with j rotation: **http://www.dsplog.com/db-install/wp-content/uploads/2008/07/script_papr_ofdm_tgn_j_rotation.m**

[5] Image: **http://www.dsplog.com/db-install/wp-content/uploads/2008/07/papr_ofdm_tgn_j_rotation_bpsk_qpsk.png**

[6] click here to SUBSCRIBE : **http://www.feedburner.com/fb/a/emailverifySubmit?feedId=1348583&loc=en_US**

Click here to print.

Copyright © 2007-2012 dspLog.com. All rights reserved. This article may not be reused in any fashion without written permission from http://www.dspLog.com.