Monday, December 22, 2008

Peak to Average Power Ratio II: An Introduction

A Signal Processing Perspective

The statistic properties of the PAPR of multi-carrier signals can be described by CCDF (Complementary Cumulative Distribution Function). If we assume the frequency-domain symbol is complex Gaussian distributed. When the number of subcarriers, L, become large, the instantaneous power of each multi-carrier signal chip can be modeled by a Chi-distributed signal with two degree of freedom.
CCDF( γ ) = Pr( PAPR > γ ) = 1- Pr( PAPR <= γ ) = 1 – [ Pr( p <= γ ) ]L >~ 1 – ( 1 – e )L 
Figure 1.  A statistic modeling of PAPR

A Coding Perspective

Given a code of length n, coding rate R, what is the achievable region of triplets (R, d, PMEPR) ?  What is the relationship between PMEPR and the minimum Euclid distance (mED) d* ? All these questions belong to a Sphere Packing Problem. Given a codeset of q-ary code c with length n, what is the relationship between the size of the codeset and minimum Hamming distance (mHD) D ? This is a Sphere Packing Problem again.
Figure 2.  A geometric modeling of PAPR

An Implementation Perspective

Figure 3. Rapp’s SSPA model
Figure 4. AM/AM characteristics of the Rapp SSPA model, P = 2. 

Popular PAPR Reduction Approaches

Clipping: In-band distortion mostly is negligible. But out-of-band distortion is more serious.
Filtering and Signal Processing
  • time-invariant linear filter results in less peak regrowth and lower PAPR than DFT filter in general, if there is no spectral masking.
  • Partial Transmit Signaling (PTS): divide/Group into clusters and each of them is done with a smaller IFFT. [Muller and Huber, 97]
  • Tone Reservation (TR): inserting anti-peak signals in unused or reserved subcarriers. The objective is to find the time-domain signal to be added into the original time-domain signal such that PAPR is reduced. [Tellado, 00]
Coding: The idea is to select a codeword with less PAPR. it still is an open problem to construct codes with both low PAPR and short Hamming distance.
Selected Mapping (SLM): it is based on selecting one of the transformed blocks for each data block, which has the lowest PAPR. [Bauml, Fisher and Huber, 96]
Constellation Optimization
  • Tone Injection (TI): the basic idea is to increase the constellation size so that each of the points in the original basic constellation can be mapped into several equivalent points in the expanded constellation.
  • Active constellation extension (ACE): similar to TI. [Krongold and Jones, 03]

Monday, December 8, 2008

Peak to Average Power Ratio I: OFDM PAPR Reduction

With the upcoming deployment of wideband wireless network with throughput greater than 100Mbps over high frequency bands such as 5-GHz band and the adopting of multicarrier modulations, more and more challenges are brought to system and hardware design. OFDM, frequently referred as multi-carrier modulation, is becoming the de facto standard for next-generation wideband wireless networks. However, one of the critical issues of OFDM as well as other multicarrier modulation scheme is its high peak-to-average power ratio (PAPR), which usually requires large backoff and highly efficient high power amplifier (HPA), large dynamic range analog-to-digital converter (ADC), high linearity up-converter, etc. These requirements lead to expensive hardware systems that are difficult to design. Hence it becomes more and more important to alleviate the burden of hardware design with employing advanced PAPR reduction technologies.

In this tutorial contribution, OFDM RF design challenges and PAPR reduction technologies are presented. They are discussed in terms of both theory and implementation with many examples. Especially a patent search is given too. There are five major parts in this tutorial. In the first part, an introduction to OFDM, the RF design challenges and the PAPR issue is presented. We outline the challenges, which include high power peak, linearity limitation, image rejection, phase noise and distortion, etc., brought to each component of OFDM RF design. Here we focus on high peak power and try to solve the PAPR issue, which is defined from both signal processing and coding perspectives. The problem of PAPR issue is outlined from implementation perspective with the discussion of the effectiveness of signal clipping, which is known as one of the simplest PAPR reduction technique. In the second part, an overview of most popular PAPR reduction approaches is given. It includes coding, signal processing and filtering, selection mapping, signal constellation optimization, etc. The pros and cons of these approaches are compared in terms of performance and implementation complexity. In the third part, PAPR reduction techniques adopted in existing standards are presented and discussed. We cover some of the most important standards including GSM, WCDMA, LTE and UMB. In the fourth part, many PAPR reduction patent examples are presented, followed by a presentation of our recent contributions to PAPR reduction. Our approaches are simple and efficient, with low implementation complexity on the receiver. The conclusions and further works are outlined in the last part.

In summary, this tutorial is intended to provide a comprehensive overview of PAPR reduction form OFDM for a wide array of audiences. It includes not only the background theory, implementation considerations and related standards but also our recent contributions.