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Being capable of enhancing the spectral efficiency (SE), faster-than-Nyquist (FTN) signaling is a promising approach for wireless communication systems. This paper investigates the doubly-selective (i.e., time- and frequency-selective) channel estimation and data detection of FTN signaling. We consider the intersymbol interference (ISI) resulting from both the FTN signaling and the frequency-selective channel and adopt an efficient frame structure with reduced overhead. We propose a novel channel estimation technique of FTN signaling based on the least sum of squared errors (LSSE) approach to estimate the complex channel coefficients at the pilot locations within the frame. In particular, we find the optimal pilot sequence that minimizes the mean square error (MSE) of the channel estimation. To address the time-selective nature of the channel, we use a low-complexity linear interpolation to track the complex channel coefficients at the data symbols locations within the frame. To detect the data symbols of FTN signaling, we adopt a turbo equalization technique based on a linear soft-input soft-output (SISO) minimum mean square error (MMSE) equalizer. Simulation results show that the MSE of the proposed FTN signaling channel estimation employing the designed optimal pilot sequence is lower than its counterpart designed for conventional Nyquist transmission. The bit error rate (BER) of the FTN signaling employing the proposed optimal pilot sequence shows improvement compared to the FTN signaling employing the conventional Nyquist pilot sequence. Additionally, for the same SE, the proposed FTN signaling channel estimation employing the designed optimal pilot sequence shows better performance when compared to competing techniques from the literature.

Motivated by Fredholm theory, we develop a framework to establish the convergence of spectral methods for operator equations $\mathcal L u = f$. The framework posits the existence of a left-Fredholm regulator for $\mathcal L$ and the existence of a sufficiently good approximation of this regulator. Importantly, the numerical method itself need not make use of this extra approximant. We apply the framework to finite-section and collocation-based numerical methods for solving differential equations with periodic boundary conditions and to solving Riemann--Hilbert problems on the unit circle. We also obtain improved results concerning the approximation of eigenvalues of differential operators with periodic coefficients.

This article develops a random effects quantile regression model for panel data that allows for increased distributional flexibility, multivariate heterogeneity, and time-invariant covariates in situations where mean regression may be unsuitable. Our approach is Bayesian and builds upon the generalized asymmetric Laplace distribution to decouple the modeling of skewness from the quantile parameter. We derive an efficient simulation-based estimation algorithm, demonstrate its properties and performance in targeted simulation studies, and employ it in the computation of marginal likelihoods to enable formal Bayesian model comparisons. The methodology is applied in a study of U.S. residential rental rates following the Global Financial Crisis. Our empirical results provide interesting insights on the interaction between rents and economic, demographic and policy variables, weigh in on key modeling features, and overwhelmingly support the additional flexibility at nearly all quantiles and across several sub-samples. The practical differences that arise as a result of allowing for flexible modeling can be nontrivial, especially for quantiles away from the median.

Providing ultra-reliable and low-latency transmission is a current issue in wireless communications (URLLC). While it is commonly known that channel coding with large codewords improves reliability, this usually necessitates using interleavers, which incur undesired latency. Using short codewords is a necessary adjustment that will eliminate the requirement for interleaving and reduce decoding latency. This paper suggests a coding and decoding system that, combined with the high spectral efficiency of spatial multiplexing, can provide URLLC over a fading wireless channel. Random linear codes (RLCs) are used over a block-fading massive multiple input-multiple-output (mMIMO) channel followed by zero-forcing (ZF) detection and guessing random additive noise decoding (GRAND). A variation of GRAND, called symbol-level GRAND, originally proposed for single-antenna systems, is generalized to spatial multiplexing. Symbol-level GRAND is much more computationally effective than bit-level GRAND as it takes advantage of the structure of the constellation of the modulation. The paper analyses the performance of symbol-level GRAND depending on the orthogonality defect (OD) of the underlying lattice. Symbol-level GRAND takes advantage of the a priori probability of each error pattern given a received symbol, and specifies the order in which error patterns are tested. The paper further proposes to make use of further side-information that comes from the mMIMO channel-state information (CSI) and its impacts on the reliability of each antenna. This induces an antenna sorting order that further reduces the decoding complexity by over 80 percent when comparing with bit-level GRAND.

This paper tackles the problem of missing data imputation for noisy and non-Gaussian data. A classical imputation method, the Expectation Maximization (EM) algorithm for Gaussian mixture models, has shown interesting properties when compared to other popular approaches such as those based on k-nearest neighbors or on multiple imputations by chained equations. However, Gaussian mixture models are known to be non-robust to heterogeneous data, which can lead to poor estimation performance when the data is contaminated by outliers or follows non-Gaussian distributions. To overcome this issue, a new EM algorithm is investigated for mixtures of elliptical distributions with the property of handling potential missing data. This paper shows that this problem reduces to the estimation of a mixture of Angular Gaussian distributions under generic assumptions (i.e., each sample is drawn from a mixture of elliptical distributions, which is possibly different for one sample to another). In that case, the complete-data likelihood associated with mixtures of elliptical distributions is well adapted to the EM framework with missing data thanks to its conditional distribution, which is shown to be a multivariate $t$-distribution. Experimental results on synthetic data demonstrate that the proposed algorithm is robust to outliers and can be used with non-Gaussian data. Furthermore, experiments conducted on real-world datasets show that this algorithm is very competitive when compared to other classical imputation methods.

This paper studies an integrated sensing and communication (ISAC) system for single-target detection in a cloud radio access network architecture. The system considers downlink communication and multi-static sensing approach, where ISAC transmit access points (APs) jointly serve the user equipments (UEs) and optionally steer a beam toward the target. A centralized operation of cell-free massive MIMO (multiple-input multiple-output) is considered for communication and sensing purposes. A maximum a posteriori ratio test detector is developed to detect the target in the presence of clutter, so-called target-free signals. Moreover, a power allocation algorithm is proposed to maximize the sensing signal-to-interference-plus-noise ratio (SINR) while ensuring a minimum communication SINR value for each UE and meeting per-AP power constraints. Two ISAC setups are studied: i) using only existing communication beams for sensing and ii) using additional sensing beams. The proposed algorithm's efficiency is investigated in both realistic and idealistic scenarios, corresponding to the presence and absence of the target-free channels, respectively. Although detection probability degrades in the presence of target-free channels that act as interference, the proposed algorithm significantly outperforms the interference-unaware benchmark by exploiting the statistics of the clutter. It has also been shown that the proposed algorithm outperforms the fully communication-centric algorithm, both in the presence and absence of clutter. Moreover, using an additional sensing beam improves the detection performance for a target with lower radar cross-section variances compared to the case without sensing beams.

Massive MIMO antennas in cellular systems help support a large number of users in the same time-frequency resource and also provide significant array gain for uplink reception. However, channel estimation in such large antenna systems can be tricky, not only since pilot assignment for multiple users is challenging, but also because the pilot overhead especially for rapidly changing channels can diminish the system throughput quite significantly. A pilotless transceiver where the receiver can perform blind demodulation can solve these issues and boost system throughput by eliminating the need for pilots in channel estimation. In this paper, we propose an iterative matrix decomposition algorithm for the blind demodulation of massive MIMO OFDM signals. This new decomposition technique provides estimates of both the user symbols and the user channel in the frequency domain simultaneously (to a scaling factor) without any pilots. Simulation results demonstrate that the lack of pilots does not affect the error performance of the proposed algorithm when compared to maximal-ratio-combining (MRC) with pilot-based channel estimation across a wide range of signal strengths.

Generalized mutual information (GMI) is used to compute achievable rates for fading channels with various types of channel state information at the transmitter (CSIT) and receiver (CSIR). The GMI is based on variations of auxiliary channel models with additive white Gaussian noise (AWGN) and circularly-symmetric complex Gaussian inputs. One variation uses reverse channel models with minimum mean square error (MMSE) estimates that give the largest rates but are challenging to optimize. A second variation uses forward channel models with linear MMSE estimates that are easier to optimize. Both model classes are applied to channels where the receiver is unaware of the CSIT and for which adaptive codewords achieve capacity. The forward model inputs are chosen as linear functions of the adaptive codeword's entries to simplify the analysis. For scalar channels, the maximum GMI is then achieved by a conventional codebook, where the amplitude and phase of each channel symbol are modified based on the CSIT. The GMI increases by partitioning the channel output alphabet and using a different auxiliary model for each partition subset. The partitioning also helps to determine the capacity scaling at high and low signal-to-noise ratios. A class of power control policies is described for partial CSIR, including a MMSE policy for full CSIT. Several examples of fading channels with AWGN illustrate the theory, focusing on on-off fading and Rayleigh fading. The capacity results generalize to block fading channels with in-block feedback, including capacity expressions in terms of mutual and directed information.

Due to the power consumption and high circuit cost in antenna arrays, the practical application of massive multiple-input multiple-output (MIMO) in the sixth generation (6G) and future wireless networks is still challenging. Employing low-resolution analog-to-digital converters (ADCs) and hybrid analog and digital (HAD) structure is two low-cost choice with acceptable performance loss.In this paper, the combination of the mixed-ADC architecture and HAD structure employed at receiver is proposed for direction of arrival (DOA) estimation, which will be applied to the beamforming tracking and alignment in 6G. By adopting the additive quantization noise model, the exact closed-form expression of the Cram\'{e}r-Rao lower bound (CRLB) for the HAD architecture with mixed-ADCs is derived. Moreover, the closed-form expression of the performance loss factor is derived as a benchmark. In addition, to take power consumption into account, energy efficiency is also investigated in our paper. The numerical results reveal that the HAD structure with mixed-ADCs can significantly reduce the power consumption and hardware cost. Furthermore, that architecture is able to achieve a better trade-off between the performance loss and the power consumption. Finally, adopting 2-4 bits of resolution may be a good choice in practical massive MIMO systems.

The novel concept of near-field non-orthogonal multiple access (NF-NOMA) communications is proposed. The near-filed beamfocusing enables NOMA to be carried out in both angular and distance domains. Two novel frameworks are proposed, namely, single-location-beamfocusing NF-NOMA (SLB-NF-NOMA) and multiple-location-beamfocusing NF-NOMA (MLB-NF-NOMA). 1) For SLB-NF-NOMA, two NOMA users in the same angular direction with distinct quality of service (QoS) requirements can be grouped into one cluster. The hybrid beamformer design and power allocation problem is formulated to maximize the sum rate of the users with higher QoS (H-QoS) requirements. To solve this problem, the analog beamformer is first designed to focus the energy on the H-QoS users and the zero-forcing (ZF) digital beamformer is employed. Then, the optimal power allocation is obtained. 2) For MLB-NF-NOMA, the two NOMA users in the same cluster can have different angular directions. The analog beamformer is first designed to focus the energy on both two NOMA users. Then, a singular value decomposition (SVD) based ZF (SVD-ZF) digital beamformer is designed. Furthermore, a novel antenna allocation algorithm is proposed. Finally, a suboptimal power allocation algorithm is proposed. Numerical results demonstrate that the NF-NOMA can achieve a higher spectral efficiency and provide a higher flexibility than conventional far-field NOMA.