Reduction of Peak-to-Average Power Ratio in Orthogonal Frequency Division Multiplexing System Using Haar Wavelet Approach

In Orthogonal Frequency Division Multiplexing (OFDM) based systems, with the increasing demand for data rate and reliability in Wireless communications and devices, several issues become very important like bandwidth efficiency, quality of service and radio coverage. However, OFDM is very sensitive to nonlinear effects due to the high peak-to-average power ratio (PAPR) owned by the transmitted signals and does not show robustness to spectral null channels. This paper proposes a novel BPSK OFDM system based on Haar wavelet transformation. The PAPR reduced by 10 log10 2 ≈ 3 dB at most, compared with the conventional OFDM system and shows robustness to spectral null channels, improving BER performance 3 dB at most. Finally, theoretical and simulated results of the Cumulative Distribution Functions (CDFs) of both Conventional and Proposed OFDM are compared to show that the Proposed OFDM has better performance than the Conventional OFDM.

New Distance Concept and Graph Theory Approach for Certain Coding Techniques Design and Analysis

A New graph distance concept introduced for certain coding techniques helped in their design and analysis as in the case of distance-preserving mappings and spectral shaping codes. A graph theoretic construction, mapping binary sequences to permutation sequences and inspired from the k-cube graph has reached the upper bound on the sum of the distances for certain values of the length of the permutation sequence. The new introduced distance concept in the k-cube graph helped better understanding and analyzing for the first time the concept of distance-reducing mappings. A combination of distance and the index-permutation graph concepts helped uncover and verify certain properties of spectral null codes, which were previously difficult to analyze.