## 1 Introduction  
The development of the sixth generation (6G) wireless communication system has been accompanied by the introduction of new technologies, among which terahertz (THz) technology, also referred to as one of the ten technologies that will innovate the future world, is a breakthrough spectrum technology [1; 2]. It offers a wide transmission bandwidth to cater to the increasing demand for higher transmission rates, and thus it has emerged as a crucial component in 6G communication. Terahertz communication typically involves the utilization of the electromagnetic waves within a frequency range spanning from 0.1 THz to 10 THz and a wavelength range from 3 mm to 30 \(\mu\)m. Its wavelength lies between the microwave and the far-infrared regions, providing an abundance of spectrum resources that remain unexplored [3]. One of the characteristics of the THz communication is ultra-wide bandwidth. Due to the abundant spectrum of resources brought by the very high frequency, the expected bandwidth of THz communication ranges from several GHz to tens of GHz, surpassing that of the current 5G bandwidth. Therefore, it can achieve an ultra-high rate of up to 1 Tbps, which is 10 to 100 times of the current 5G peak rate [4]. The other characteristics encompass remarkable penetrability [5], the capacity to traverse non-metallic materials without inflicting any damage, and the low energy levels that minimize harm to living organisms, thereby facilitating non-destructive testing. Furthermore, it provides finer time resolution for capturing subtle momentary forms and ensures utmost confidentiality. In THz communication, achieving an ultra-wide bandwidth involves the following challenges. Hardware cost and implementation complexity set limitations for the maximum subcarrier spacing and the size of the fast Fourier transform (FFT) of orthogonal frequency division multiplexing (OFDM), which may hinder the utilization of the ultra-wide bandwidth in THz scenarios. Currently, the maximum subcarrier spacing is limited to 960 kHz and the maximum FFT size is restricted to 4096 points, resulting in a bandwidth limitation of around 4 GHz when considering oversampling and guard intervals. To support a larger bandwidth in OFDM baseband processing, there are typically two solutions, i.e., increasing the subcarrier spacing or the FFT size. However, increasing the subcarrier spacing leads to a shorter symbol duration, while a sufficiently long cyclic prefix is still required to combat multipath delay. This solution results in a higher proportion of cyclic prefix overhead and reduces the spectral efficiency. Typically, the complexity of \(N\)-point IFFT is \(N\)log\(N\)[6]. The current hardware faces challenges in regard to accommodating the large size of the FFT. Therefore, it prompts us to propose a new waveform that enables the realization of ultra-wideband THz communication. The waveforms predominantly employed in the current fifth generation (5G) standards encompass cyclic prefix-orthogonal frequency division multiplexing (CP-OFDM) and discrete Fourier transform spread orthogonal frequency division multiplexing (DFT-s-OFDM). In recent years, a plethora of investigations have been conducted on waveforms [7], including some new waveforms based on OFDM: (1) Filter-bank multi-carrier (FBMC) [8] is a form of real number modulation that separates the real and imaginary components of the modulated symbols, utilizing filters to achieve real orthogonality. (2) Generalized frequency division multiplexing (GFDM) [9; 10] adopts a cyclic filter for each OFDM subcarrier and introduces block modulation technology; however, there is interference between subcarriers. (3) Filter bank orthogonal frequency division multiplexing (FB-OFDM) [11; 12; 13] utilizes polyphase filters for each subcarrier, with the subcarriers being approximately orthogonal. (4) Universal filtered multi-carrier (UFMC) [14] performs filtering on a set of consecutive subcarriers. Due to the long time-domain filter function, there is inter-symbol interference in the time domain.