[Paper Review] Performance Analysis of Error Control Coding Techniques for Peak-to-Average Power Ratio Reduction of Multicarrier Signals

Sanjay Singh, M. Sathish Kumar+1 more|arXiv (Cornell University)|Sep 21, 2012

PAPR reduction in OFDM15 references3 citations

TL;DR

This paper investigates the impact of various error control coding techniques—Hamming, cyclic, convolutional, Golay, and Reed-Muller codes—on peak-to-average power ratio (PAPR) reduction in BPSK-modulated OFDM systems. It demonstrates that Reed-Muller codes with parameters r=1, m=4 achieve the highest PAPR reduction of 2.2362 dB, outperforming other codes, while convolutional codes offer a favorable trade-off between PAPR reduction and hardware complexity.

ABSTRACT

Increasing demands on high data rate mobile communications services will inevitably drive future broadband mobile communication systems toward achieving data transmission rates in excess of 100 Mbps. One of the promising technologies which can satisfy this demand on high data rate mobile communications services is the Orthogonal Frequency Division Multiplexing (OFDM) transmission technology which falls under the general category of multicarrier modulation systems. OFDM is a spectrally efficient modulation technique that can achieve high speed data transmission over multipath fading channels without the need for powerful equalization techniques. However the price paid for this high spectral efficiency and less intensive equalization is low power efficiency. OFDM signals are very sensitive to non-linear effects due to the high peak-to-average power ratio (PAPR), which leads to the power inefficiency in the RF section of the transmitter. This paper analyzes the relation between aperiodic autocorrelation of OFDM symbols and PAPR. The paper also gives a comparative study of PAPR reduction performance of various channel coding techniques for the OFDM signals. For our study we have considered Hamming codes, cyclic codes, convolution codes, Golay and Reed-Muller codes. The results show that each of the channel coding technique has a different PAPR reduction performance. Coding technique with the highest value of PAPR reduction has been identified along with an illustration on PAPR reduction performances with respect to each code.

Motivation & Objective

• To address the high PAPR in OFDM systems, which limits power efficiency and increases hardware cost.
• To investigate the relationship between aperiodic autocorrelation of OFDM symbols and PAPR.
• To conduct a comparative analysis of PAPR reduction performance across multiple channel coding techniques in OFDM.
• To identify the most effective coding technique for PAPR reduction while considering encoder/decoder complexity.
• To provide a benchmark for combining coding with other PAPR reduction techniques like SLM.

Proposed method

• Modeling the OFDM signal using baseband complex envelope representation with N subcarriers.
• Defining PAPR as the ratio of maximum instantaneous power to average power over the symbol duration.
• Analyzing the influence of aperiodic autocorrelation of subcarrier sequences on PAPR through theoretical derivation.
• Applying various linear block codes (Hamming, cyclic, Golay, Reed-Muller) and convolutional codes to OFDM symbols to modify their signal structure.
• Using Monte Carlo simulations to generate CCDF (Complementary Cumulative Distribution Function) curves for PAPR comparison across coding schemes.
• Evaluating performance using PAPR reduction in dB and code rate as metrics, with results tabulated and visualized.

Experimental results

Research questions

• RQ1 How does the aperiodic autocorrelation of OFDM symbols relate to their PAPR?
• RQ2 Which channel coding technique provides the highest PAPR reduction in BPSK-modulated OFDM systems?
• RQ3 How do different coding techniques compare in terms of PAPR reduction and hardware complexity?
• RQ4 Can error control coding be effectively combined with existing PAPR reduction techniques like SLM?
• RQ5 What is the maximum achievable PAPR reduction using Reed-Muller codes with varying parameters r and m?

Key findings

• Reed-Muller codes with parameters r=1 and m=4 achieve the highest PAPR reduction of 2.2362 dB, outperforming all other codes studied.
• Convolutional codes with rate 1/2 and constraint length K=6 provide the second-best PAPR reduction of 2.0000 dB, offering a good balance between performance and complexity.
• The [23,12,7] Golay code reduces PAPR by 1.9677 dB, ranking third among the evaluated codes.
• Hamming codes with m=6 and cyclic codes with m=4 show lower PAPR reduction, at 1.4194 dB and 1.5161 dB respectively.
• Convolutional codes with rate 1/3 and K=9 reduce PAPR by 1.8710 dB, ranking below the 1/2 rate counterpart.
• The PAPR reduction performance of all codes is directly linked to their ability to suppress aperiodic autocorrelation of OFDM symbols, as derived from equation (5).