Novel Nyquist-I filter to reduce PAPR for SC-FDMA scheme

5 G systems address growing broadband demands with OFDM-based technologies like SC-FDMA and OFDMA in LTE. A novel pulse shape is proposed for the transmitter-side uplink scheme using single-carrier frequency division multiple access (SC-FDMA) to reduce the Peak to Average Power Ratio (PAPR). The pulse shape combines a finite impulse response (FIR) filter in the frequency domain with a Nyquist-I pulse in the time domain. The optimization of the impulse response of the new pulse shape is achieved by using an envelope-constrained (EC) filter design to suppress the amplitude of the side-lobe. A new family of Nyquist-I pulses is presented, termed exponential raised cosine (ERC), featuring a novel design parameter gamma\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma $$\end{document} that offers additional degrees of freedom to minimize PAPR for a given roll-off factor alpha\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}. The sub-optimum value of gamma\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma $$\end{document} is analyzed with a defined range of values; however, gamma=0.3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma = 0.3$$\end{document} shows an impressive reduction in PAPR and gamma=0.1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma = 0.1$$\end{document} verifies an improvement in SER over the other values of gamma\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma $$\end{document}. The simple expression of the ERC shows a less complex design with an average elapsed time of 47.41x10-6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$<^>{-6}$$\end{document} seconds. Computer-based simulations are performed to identify a sub-optimal value gamma\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma $$\end{document} compared to other existing pulses, showing a significant reduction in PAPR for the interleaved mode of SC-FDMA.