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.

Orthogonal time frequency space (OTFS) can provide better error performance than orthogonal frequency division modulation in the high-speed scenario. However, the two-dimensional convolution between the information-bearing symbols and the channel response in the delay-Doppler domain induces high-complexity detection, which hinders the implementation of the OTFS. In this paper, expectation propagation (EP) is introduced in the OTFS system to improve the reliability compared to the message passing approaches. The low-complexity EP detection with a log-linear order is proposed by observing the sparsity and the block quasi-banded matrix structure of the time-domain matrix. The exploitation of the lower-upper factorization for the banded matrix, the forward or the back substitution algorithm for the lower or the upper triangular matrices reduces the complexity of the large-scale matrix inversion involved in the EP detection from a cubic order to a linear order. The error performance of the proposed scheme is further analyzed by utilizing the state evolution and discussed under the different frame sizes. Moreover, the proposed low-complexity detector is then explored together with the likelihood decoder in an iterative manner to further improve the reliability of the proposed receiver. Finally, the better error performance and the lower computational complexity of the proposed receiver are validated by the numerical results.

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.

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.

The orthogonal time frequency space (OTFS) modulation is resilient to doubly-selective wireless channels and thus can be employed in high-mobility multipath communications. However, the typical embedded pilot pattern requires high-power pilots and plenty of guards to tolerate large spread in both the delay and the Doppler domains, especially when estimating the precise channel state information. The requirements incur high peak-to-average power ratio (PAPR) and low spectral efficiency. To address these limitations, we proposes a novel pilot pattern, in which a sequence of pilot symbols are placed in the zero- Doppler grids spacing equally in the delay- Doppler domain. By carefully designing the value of each pilot symbol, the pilot pattern exhibit a comb -type in the time-frequency (TF) domain enabling channel estimation by a frequency interpolation. The proposed pattern spreads the pilot power among the multiple pilots and requires no guards. Unfortunately, we notice that the comb fingers become sparser and the channel interpolation is less accurate when the pilot power is spread over more symbols to lower the PAPR. We accordingly extend the proposed pattern to multiple non-overlapping pilot sequences with alternative characteristics. In this extension, the comb -type pilot pattern then has denser fingers which captures the channel variance over a large range of frequency. For channel estimation, we first jointly estimate the delays and a composite matrix associated with the Doppler shifts and the path gains by leveraging the row sparsity of the composite matrix. With the delay estimates, the Doppler shifts are subsequently estimated using the Fitz estimator, and the path gains are determined via the least squares estimation. Theoretical analysis and numerical results show that our approach achieves dynamic channel resilience, better channel estimation and bit error performance, and improves the spectral efficiency while reducing the PAPR.