Analysis of Weighted Fractional Fourier Transform Based Hybrid Carrier Signal Characteristics

Recently, a weighted fractional Fourier transform (WFRFT) based hybrid carrier (HC) system has been proposed, which can converge single-carrier (SC) and multi-carrier (MC) systems. The cost and power dissipation of analog components often dominate in practical HC systems. Therefore, in this paper, we analyze the baseband HC signal characteristics, including average signal power, power spectral density (PSD), probability density function (PDF), peak-to-average power ratio (PAPR), and complementary cumulative distribution function (CCDF), using a continuous-time HC signal approximation method. Through theoretical analysis and simulation validation, it is proved that the approximation method does not change the average signal power, bandwidth and out-of-band emission (OOBE). The theoretical PDF expression of HC signal with the approximation method is then proposed. Furthermore, the PDF can also explain why the PAPR of baseband continuous-time HC signal is higher than that of discrete-time HC signal. The PAPR performance and the power amplifier (PA) efficiency of HC systems in different conditions are analyzed. Through the PDF analysis of HC signal envelope and the numerical computations of PAPR, it is shown that the approximation method can offer a precise characteristic description for HC signal, which can help to improve the system PAPR performance and the PA efficiency.