## Peak to Average Power Ratio - PAPR basics

This article describes about **Peak to Average Power Ratio** or **PAPR basics**,
its importance in wireless system and PAPR reduction techniques.

### Description

In Modulation schemes such as OFDM transmitter time domain signal will have higher PAPR, which leads to various distortions in the transmitter chain and degradation of system performance i.e. BER/PER. Also requires highly linear power amplifier which increases cost of the system. PAPR is ratio of peak power to average power of time domain complex baseband signal which is to be transmitted. We will discuss PAPR reduction techniques below.

### PAPR Reduction Techniques

Following section describes on **PAPR reduction techniques** viz. Clipping, Peak Windowing, Scrambling, Block Coding, Selected Mapping (SLM) and Partial Transmit Sequences (PTS).

**Clipping:**

The simple method is to clip the transmitted signal, which is modeled as multiplication or convolution of signal having high PAPR with window function. Undesired widening of the signal due to clipping is limited using filter technique. Various window functions such as cosine, Kaiser and Hamming are available.

Pros:Simple

Cons:Causes interference/distortion/out band emission which degrades the system performance. Filtering after clipping can reduce the distortion/emission but may also cause some peak re-growth.

**Peak Windowing**

Here large signal peak of the signal is multiplied with a Gaussian shaped window. Suitable window function is selected for multiplication from Cosine, Kaiser and Hamming windows.

Pros: Simple

Cons:Both BER and out of band radiation is increased.

**Scrambling**

This technique utilize scrambling technique to polarities of the subcarriers which removes the correlation among the subcarriers irrespective of the user codes used. PAPR will be greatly reduced as it will spread the information over larger band.

Pros:About 5 dB of PAPR is achieved using this technique in certain cases.

Cons:Gives poor performance when number of subcarriers increase.

**Block Coding**

Find out the code words with minimum PAPR from a given set of code words. Map the input data blocks to these selected code words.

All block codes provide a low PAPR which is typically below 3 dB for small number of carriers.

Pros: Lowest PAPR

Cons: Low data rate and Significant overhead

Block Coding Sequences, most commonly used are Walsh, Gold, Orthogonal Gold, and Zadoff-Chu sequences. Zadoff Chu is used in LTE.

**Selected Mapping (SLM) **

The concept here is any one single data vector of the transmitter signal can have multiple representations. Out of these lowest PAPR time domain vector is selected for transmission.

Pros:Lowest PAPR

Cons: Complexity issue as SLM scheme needs multiple IFFT operation.

**Partial Transmit Sequence (PTS) **

This method is similar to SLM, but divides the frequency vector into smaller blocks before applying the phase transformations.

Pros: Lowest PAPR
and Little redundancy.

Cons: Increased system complexity.

### PAPR MATLAB Source code

Refer PTS Algorithm for PAPR reduction implemented in MATLAB.