This paper presents cyclic shift phase rotation (CSPR), an innovative technique designed to mitigate the peak-to-average power ratio (PAPR) in coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems. CSPR demonstrates notable improvements when compared to traditional techniques, such as discrete Fourier transform spread (DFT-spread) and selective mapping (SLM). CSPR eliminates the need for side information, additional inverse fast Fourier transforms (IFFTs), and complex search processes that are needed by other techniques. Analytical evaluations confirm that CSPR requiresO(N log C0) operations, which is significantly lower than theO(M · N logN) complexity of SLM and theO(L · n log n) complexity of DFT-spread. The CSPR has been evaluated within the CO-OFDM transmission. At a distance of 800 km, CSPR facilitates a 3 dB reduction in the required optical signal-to-noise ratio (OSNR) necessary for achieving hard-decision forward error correction (H-FEC) when compared to DFT-spread utilizing 112 sub-bands, and it exceeds the performance of the SLM at low OSNR with the use of 64 candidates. Moreover, it exhibits an 8 dB enhancement in the Q-factor over transmission distances extending up to 2000 km under nonlinear conditions. These results position CSPR as an effective and efficient solution for PAPR mitigation, significantly improving system performance, and reducing hardware complexity.

In this contribution we present a novel method for constructing orthogonal pulses for UWB impulse radio transmission under the FCC spectral mask constraint. In contrast to previous work we combine a convex formulation of the spectral design with Lowdin's orthogonalization method [1], which delivers a shift--orthogonal basis optimally close (in energy) to the initial pulse, which generates (in a stable way) the shift--invariant space. The convex formulation of the spectral design is achieved by approximating the FCC mask with a finite--order filter matched to Gaussian monocycles as input. The output pulse then has high energy concentration in the passband (NESP value). Using Lowdin's orthogonalization we compute the corresponding shift--orthogonal pulse. We show that our approach is able to generate for finitely many shifts, orthogonal equal energy pulses with nearly the same NESP value. Furthermore, we show that the orthogonalization procedure can be well approximated using the Zak transform allowing for an efficient implementation with the discrete Fourier transform. Surprisingly, we could observe, that for certain parameters, this approximation yields almost the same performance as the exact Lowdin method.