PAPR Reduction with PTS Algorithm in MATLAB

This section covers the PTS (Partial Transmit Sequence) Algorithm for LTE IQ packet PAPR reduction using MATLAB.

Why Reduce PAPR?

PAPR stands for Peak-to-Average Power Ratio of a time-domain signal, $x(t)$. It’s the ratio between the maximum instantaneous power and the average power.

$PAPR = \frac{max(|x(t)|^2)}{mean(|x(t)|^2)}$

Lower PAPR leads to higher power efficiency, extending battery life. This page focuses on the PTS algorithm for PAPR reduction.

PTS Algorithm Explained

Here’s how the PTS algorithm works:

PTS algorithm

STEP 1: Partition the data symbols ($X$) into M disjoint sub-blocks, $X^{(i)}$, where $1 \le i \le M$, such that:

$X = \sum\_{i=1}^{M} X^{(i)}$

STEP 2: Transform the sub-blocks, $X^{(i)}$, into M time-domain partial transmit sequences, $x^{(i)}$:

$x^{(i)} = IFFT(X^{(i)}) ; \quad 1 \le i \le M$

STEP 3: Independently rotate these sequences by phase factors, $b_i$, where:

$b_i = exp(j \phi_i) ; \quad 1 \le i \le M$

STEP 4: Combine the rotated sequences to produce the time-domain OFDM signal packet, $x$:

x = \sum_{i=1}^{M} b_i * x^{(i)}

The PTS algorithm selects a vector $b$ such that the PAPR of the resulting transmit sequence, $x(t)$, is minimized.

IQ vectors from different wireless standards exhibit varying PAPR time-domain patterns depending on the complex modulation schemes used and the OFDM/OFDMA structure. Thorough simulations are necessary to account for these variations.

Implementing PTS in MATLAB

Downloading and Loading the Input Vector

First, download and load the provided IQ vector into your MATLAB workspace:

[Download LTE IQ vector](link to LTE IQ vector - not provided in original text, needs adding )

MATLAB Code for PAPR Reduction

Load the baseband IQ vector and apply the following algorithm. Plot the CCDF (Complementary Cumulative Distribution Function) curve for both the input IQ packet and the output (after the PTS algorithm is applied) IQ packet.

The provided IQ vector is for an LTE signal with 1.4MHz bandwidth and an FFT size of 128.

%%% removing CP
A=tx_data_frame(1,:)
B1=A(:,11:1:138)'
B2=A(:,148:1:275)'
B3=A(:,285:1:412)'
B4=A(:,422:1:549)'
B5=A(:,559:1:686)'
B6=A(:,696:1:823)'
B7=A(:,833:1:960)'
B8=A(:,971:1:1098)'
B9=A(:,1108:1:1235)'
B10=A(:,1245:1:1372)'
B11=A(:,1382:1:1509)'
B12=A(:,1519:1:1646)'
B13=A(:,1656:1:1783)'
B14=A(:,1793:1:1920)'
CZ= [B1' B2' B3' B4' B5' B6' B7' B8' B9' B10' B11' B12' B13' B14']

%%%%implementing pts algorithm
B11=exp(i*(2*pi/1))*B1
B21=exp(i*(2*pi/2))*B2
B31=exp(i*(2*pi/3))*B3
B41=exp(i*(2*pi/4))*B4
B51=exp(i*(2*pi/5))*B5
B61=exp(i*(2*pi/6))*B6
B71=exp(i*(2*pi/7))*B7
B81=exp(i*(2*pi/8))*B8
B91=exp(i*(2*pi/9))*B9
B101=exp(i*(2*pi/10))*B10
B111=exp(i*(2*pi/11))*B11
B121=exp(i*(2*pi/12))*B12
B131=exp(i*(2*pi/13))*B13
B141=exp(i*(2*pi/14))*B14
B1Z= [B11' B21' B31' B41' B51' B61' B71' B81' B91' B101' B111' B121' B131' B141']

%%% creating input vector to provide as input for PTS algorithm
%%%This is impaired packet
ts=(256/4e6);
doppler=0.1;
tau=[0.0 0.4 0.9];
pdb=[0 -15 -20];
chan = rayleighchan(ts,doppler,tau,pdb); %TS is the sample time of the input
%0.1e-3; %signal, in seconds. FD is the maximum Doppler shift, in Hertz.
%100 Hz
map_out_chl=filter(chan,CZ(1,1:end));
figure(1);
[N,Z3] = hist(abs(B1Z), 1792);
semilogy(Z3,1-cumsum(N)/max(cumsum(N)),'blue')
hold on
title ('CCDF')
xlabel ('dB')
ylabel ('BER')
grid off;
figure(1);
[N,Z3] = hist(abs(map_out_chl), 1792);
semilogy(Z3,1-cumsum(N)/max(cumsum(N)),'red')

% Example of plotting CCDF in MATLAB (more general)
data = randn(1,100000); % Replace with your actual data
papr = 10*log10(abs(data).^2./mean(abs(data).^2));

% Calculate CCDF
[counts, centers] = hist(papr, 100);
cdf = cumsum(counts) / sum(counts);
ccdf = 1 - cdf;

% Plotting the CCDF on a semilogy scale
figure;
semilogy(centers, ccdf, 'LineWidth', 2);
grid on;
xlabel('PAPR (dB)');
ylabel('Probability (CCDF)');
title('CCDF of PAPR');

PTS algorithm for PAPR reduction