Efficient utilization of the spectrum, increased resilience to inter-symbol interference (ISI) and simpler channel equalization are becoming important considerations in the design of wireless communication systems including visible light communication (VLC) systems. In this regard, orthogonal frequency division multiplexing (OFDM) has become a preferred modulation technique in wireless communication systems design. However, one of its major challenges is the high peak-to-average power ratio that leads to major inefficiencies. Symbol position permutation (SPP) is a distortion-less technique that achieves substantial PAPR reduction without BER degradation. However, the existing works focus on PAPR reduction using SPP for the radio frequency (RF) OFDM and the use of this technique in optical OFDM is not properly investigated. Therefore, in this paper, we present a new PAPR reduction technique based on lexicographical permutations called lexicographical symbol position permutation (LSPP) for PAPR reduction in direct current optical OFDM (DCO-OFDM). The proposed scheme is less complex than the conventional selective mapping (CSLM) scheme since there is no multiplication of the phase sequences with the DCO OFDM symbol to generate the candidate signals. We further introduce a new way of reducing the complexity by introducing a threshold PAPR and demonstrate that the complexity in terms of inverse fast Fourier transform (IFFT) operations can be reduced substantially depending on the selected threshold and the number of candidate signals.

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In direct current optical orthogonal frequency division multiplexing (DCO-OFDM) systems, the high peak-to-average power ratio (PAPR) has been a significant challenge. Recently, lexicographical symbol position permutation (LSPP) using random permutations has been introduced as an efficient solution to reduce high PAPR. In this paper, we aim to evaluate the effectiveness of LSPP by comparing both adjacent and interleaved lexicographical permutation sequences with random lexicographical permutation sequences. Our findings demonstrate that random permutation yields superior PAPR reduction performance results when compared to adjacent and interleaved permutation. However, in scenarios with a limited number of sub-blocks, the use of adjacent and interleaved permutation becomes more favorable, as they can eliminate the possibility of generating identical permutation sequences, a drawback of random permutation. Additionally, we propose a novel algorithm to determine the optimal number of candidate permutation sequences that can achieve acceptable PAPR reduction performance while adhering to computational complexity constraints defined by the system requirements.