Orthogonal time frequency space (OTFS) as a newly proposed two-dimensional modulation scheme outperforms the orthogonal frequency division multiplexing in high-speed scenarios. Most recent studies focus on off-grid channel estimation with the ideal pulse which needs to satisfy the bi-orthogonality robustness condition but does not exist. In this paper, we consider an OTFS system with rectangular pulses and propose a grid evolution based off-grid sparse Bayesian inference (GESBI) by updating the virtual delay-Doppler grid to improve the accuracy of the channel estimation. In particular, different from the recently proposed off-grid channel estimation algorithms in OTFS where the virtual grid is fixed and uniform, the proposed channel estimation method consists of an external and internal iteration, where the grid evolution method performs in the external iteration to update the virtual grid to be non-uniform by utilizing the estimated on-grid and the off-grid information in the internal iteration. In addition, the grid evolution-based efficient sparse Bayesian inference with the student’s T distribution prior (T-GEESBI) is proposed to reduce the channel estimation complexity while improving the channel estimation accuracy. Specifically, the matrix inversion is avoided by approximating the posterior distribution. Then the equal non-convex problem is handled by utilizing the block coordinate descent method in a majorization-minimization framework. Furthermore, the two types of genie bounds on the mean squared error of the estimated channel coefficients are derived. Finally, both theoretical and numerical analyses demonstrate low complexity, convergence, and the efficiency of the proposed channel estimation approach.

In this study, generalized filter bank orthogonal frequency division multiplexing (GFB-OFDM) is proposed for 6G. In order to meet the different requirements of various scenarios in 6G, a unified structure of GFB-OFDM is designed by adopting the flexible capabilities of suitable transmission modules. In the proposed GFB-OFDM system, the coexistence of different numerologies in different sub-bands and/or the coexistence of single-carrier and multi-carrier waveforms are achieved for adjusting different scenarios in 6G. Finally, simulation results are provided to validate the BER performance of GFB-OFDM, showing that it is capable of achieving a comparable BER performance and much more flexible transmissions compared with the classic OFDM systems.

Terahertz (THz) communication is a crucial technique in sixth generation (6G) mobile networks, which allow for ultra-wide bandwidths to enable ultra-high data rate wireless communication. However, the current subcarrier spacing and the size of fast Fourier transform (FFT) of the orthogonal frequency division multiplexing (OFDM) in 5G NR are insufficient regarding the bandwidth requirements of terahertz scenarios. In this paper, a novel waveform is proposed to address the ultra-wideband issue, namely the generalized filter bank orthogonal frequency division multiplexing (GFB-OFDM) waveform. The main advantages are summarized as follows: (1) The K-point IFFT is implemented by two levels of IFFTs in smaller sizes, i.e, performing M-point IFFT in N times and performing N-point IFFT in M times, where $K=N\times M$. (2) The proposed waveform can accommodate flexible subcarrier spacings and different numbers of the subbands to provide various services in a single GFB-OFDM symbol. (3) Different bandwidths can be supported using a fixed filter since the filtering is performed on each subband. In contrast, the cyclic prefix orthogonal frequency division multiplexing (CP-OFDM) in 4G/5G requires various filters. (4) The existing detection for CP-OFDM can be directly employed as the detector of the proposed waveform. Lastly, the comprehensive simulation results demonstrate that GFB-OFDM outperforms CP-OFDM in terms of the out-of-band leakage, complexity and error performance.

This paper presents a low peak-to-average power ratio (PAPR) modulation scheme and demodulation method for low-cost terminals in sixth-generation (6G), which is called one plus delay (1 + D) pi/2(N + 1) BPSK. Explicitly, the modulation scheme is first generated based on pi/2 BPSK, then proceeded by interpolation and (1 + D) transformation. Simulation results show that the proposed (1 + D) pi/2(N + 1) BPSK scheme has lower PAPR and smaller out-of-band leakage in discrete Fourier transform spread orthogonal frequency division multiplexing (DFT-s-OFDM). Moreover, better performance can be attained by increasing the value of N. Finally, similar block error ratio (BLER) performance can be obtained at the same spectral efficiency of the conventional pi/2 BPSK scheme.

The space-terrestrial integrated network (STIN), a fundamental component of the broader space-air-ground integrated network, plays a critical role in the future communication infrastructure by facilitating global connectivity, efficient resource allocation, and robust service delivery. The generalized filter bank orthogonal frequency division multiplexing (GFB-OFDM) has emerged as an innovative waveform in this network that enables flexible subband processing, achieves low out-of-band emissions, and seamlessly supports both terrestrial and satellite systems. To further investigate the GFB-OFDM detection, this paper first derives the input-output relation of the communication system using the GFB-OFDM in a matrix form, which is then used to formulate both the linear and the nonlinear detection. Considering the tradeoff between limited reliability and high computational complexity of the existing detection schemes, a low-complexity expectation propagation detector is proposed for the GFB-OFDM system to strike a better balance. By applying the second-order Richardson iteration, the posterior mean vector of the transmitted symbols is approximated to avoid the direct matrix inversion, thereby reducing the computational complexity. We then adopt an approach to approximate the eigenvalues in each iteration such that the computational complexity involved by the matrix decomposition is significantly reduced while maintaining a competitive error performance. Furthermore, the computational complexities of various detection schemes are precisely analyzed and evaluated focusing on the numbers of the complex multiplications. At last, the error performance, the power spectral density and the peak-to-average power ratio of the GFB-OFDM and other waveforms are evaluated in the space-terrestrial scenario. The extensive simulation results validate our conclusion making it a promising solution for practical deployment in STIN scenarios such as low earth orbit satellite broadband communication.

Recently, a two-dimension (2D) modulation waveform of orthogonal time-frequency-space (OTFS) has been a popular 6G candidate to replace existing orthogonal frequency division multiplexing (OFDM). The extensive OTFS researches help to make both the advantages and limitations of OTFS more and more clear. The limitations are not easy to overcome as they come from OTFS on-grid 2D convolution channel model. Instead of solving OTFS inborn challenges, this paper proposes a novel 2D modulation waveform named orthogonal time-frequency division multiplexing (OTFDM). OTFDM uses a 2D dot-product channel model to cope with doubly-selectivity. Compared with OTFS, OTFDM supports grid-free channel delay and Doppler and gains a simple and efficient 2D equalization. The concise dot-division equalization can be easily combined with MIMO. The simulation result shows that OTFDM is able to bear high mobility and greatly outperforms OFDM in doubly-selective channel.