A Construction of Pairwise Co-prime Integer Matrices of Any Dimension and Their Least Common Right Multiple

Compared with co-prime integers, co-prime integer matrices are more challenging due to the non-commutativity. In this paper, we present a new family of pairwise co-prime integer matrices of any dimension and large size. These matrices are non-commutative and have low spread, i.e., their ratios of peak absolute values to mean absolute values (or the smallest non-zero absolute values) of their components are low. When matrix dimension is larger than $2$, this family of matrices differs from the existing families, such as circulant, Toeplitz matrices, or triangular matrices, and therefore, offers more varieties in applications. In this paper, we first prove the pairwise coprimality of the constructed matrices, then determine their determinant absolute values, and their least common right multiple (lcrm) with a closed and simple form. We also analyze their sampling rates when these matrices are used as sampling matrices for a multi-dimensional signal. The proposed family of pairwise co-prime integer matrices may have applications in multi-dimensional Chinese remainder theorem (MD-CRT) that can be used to determine integer vectors from their integer vector remainders modulo a set of integer matrix moduli, and also in multi-dimensional sparse sensing and multirate systems.

Maximum Likelihood Estimation Based Complex-Valued Robust Chinese Remainder Theorem and Its Fast Algorithm

Recently, a multi-channel self-reset analog-to-digital converter (ADC) system with complex-valued moduli has been proposed. This system enables the recovery of high dynamic range complex-valued bandlimited signals at low sampling rates via the Chinese remainder theorem (CRT). In this paper, we investigate complex-valued CRT (C-CRT) with erroneous remainders, where the errors follow wrapped complex Gaussian distributions. Based on the existing real-valued CRT utilizing maximum likelihood estimation (MLE), we propose a fast MLE-based C-CRT (MLE C-CRT). The proposed algorithm requires only $2L$ searches to obtain the optimal estimate of the common remainder, where $L$ is the number of moduli. Once the common remainder is estimated, the complex number can be determined using the C-CRT. Furthermore, we obtain a necessary and sufficient condition for the fast MLE C-CRT to achieve robust estimation. Finally, we apply the proposed algorithm to ADCs. The results demonstrate that the proposed algorithm outperforms the existing methods.

Learnable Residual-based Latent Denoising in Semantic Communication

A latent denoising semantic communication (SemCom) framework is proposed for robust image transmission over noisy channels. By incorporating a learnable latent denoiser into the receiver, the received signals are preprocessed to effectively remove the channel noise and recover the semantic information, thereby enhancing the quality of the decoded images. Specifically, a latent denoising mapping is established by an iterative residual learning approach to improve the denoising efficiency while ensuring stable performance. Moreover, channel signal-to-noise ratio (SNR) is utilized to estimate and predict the latent similarity score (SS) for conditional denoising, where the number of denoising steps is adapted based on the predicted SS sequence, further reducing the communication latency. Finally, simulations demonstrate that the proposed framework can effectively and efficiently remove the channel noise at various levels and reconstruct visual-appealing images.

Beam Structured Turbo Receiver for HF Skywave Massive MIMO

In this paper, we investigate receiver design for high frequency (HF) skywave massive multiple-input multiple-output (MIMO) communications. We first establish a modified beam based channel model (BBCM) by performing uniform sampling for directional cosine with deterministic sampling interval, where the beam matrix is constructed using a phase-shifted discrete Fourier transform (DFT) matrix. Based on the modified BBCM, we propose a beam structured turbo receiver (BSTR) involving low-dimensional beam domain signal detection for grouped user terminals (UTs), which is proved to be asymptotically optimal in terms of minimizing mean-squared error (MSE). Moreover, we extend it to windowed BSTR by introducing a windowing approach for interference suppression and complexity reduction, and propose a well-designed energy-focusing window. We also present an efficient implementation of the windowed BSTR by exploiting the structure properties of the beam matrix and the beam domain channel sparsity. Simulation results validate the superior performance of the proposed receivers but with remarkably low complexity.

Rethink Delay Doppler Channels and Time-Frequency Coding

In this paper, we rethink delay Doppler channels (also called doubly selective channels). We prove that no modulation schemes can compensate a non-trivial Doppler spread well. This means that the current active OTFS (that is the same as VOFDM) cannot compensate a non-trivial Doppler spread. We then discuss some of the existing methods to deal with time-varying channels, in particular time-frequency (TF) coding in an OFDM system. TF coding is equivalent to space-time coding in the math part. We also summarize state of the art on space-time coding that was an active research topic over 10 years ago.

CF-CGN: Channel Fingerprints Extrapolation for Multi-band Massive MIMO Transmission based on Cycle-Consistent Generative Networks

Multi-band massive multiple-input multiple-output (MIMO) communication can promote the cooperation of licensed and unlicensed spectra, effectively enhancing spectrum efficiency for Wi-Fi and other wireless systems. As an enabler for multi-band transmission, channel fingerprints (CF), also known as the channel knowledge map or radio environment map, are used to assist channel state information (CSI) acquisition and reduce computational complexity. In this paper, we propose CF-CGN (Channel Fingerprints with Cycle-consistent Generative Networks) to extrapolate CF for multi-band massive MIMO transmission where licensed and unlicensed spectra cooperate to provide ubiquitous connectivity. Specifically, we first model CF as a multichannel image and transform the extrapolation problem into an image translation task, which converts CF from one frequency to another by exploring the shared characteristics of statistical CSI in the beam domain. Then, paired generative networks are designed and coupled by variable-weight cycle consistency losses to fit the reciprocal relationship at different bands. Matched with the coupled networks, a joint training strategy is developed accordingly, supporting synchronous optimization of all trainable parameters. During the inference process, we also introduce a refining scheme to improve the extrapolation accuracy based on the resolution of CF. Numerical results illustrate that our proposed CF-CGN can achieve bidirectional extrapolation with an error of 5-17 dB lower than the benchmarks in different communication scenarios, demonstrating its excellent generalization ability. We further show that the sum rate performance assisted by CF-CGN-based CF is close to that with perfect CSI for multi-band massive MIMO transmission.

GDM4MMIMO: Generative Diffusion Models for Massive MIMO Communications

Massive multiple-input multiple-output (MIMO) offers significant advantages in spectral and energy efficiencies, positioning it as a cornerstone technology of fifth-generation (5G) wireless communication systems and a promising solution for the burgeoning data demands anticipated in sixth-generation (6G) networks. In recent years, with the continuous advancement of artificial intelligence (AI), a multitude of task-oriented generative foundation models (GFMs) have emerged, achieving remarkable performance in various fields such as computer vision (CV), natural language processing (NLP), and autonomous driving. As a pioneering force, these models are driving the paradigm shift in AI towards generative AI (GenAI). Among them, the generative diffusion model (GDM), as one of state-of-the-art families of generative models, demonstrates an exceptional capability to learn implicit prior knowledge and robust generalization capabilities, thereby enhancing its versatility and effectiveness across diverse applications. In this paper, we delve into the potential applications of GDM in massive MIMO communications. Specifically, we first provide an overview of massive MIMO communication, the framework of GFMs, and the working mechanism of GDM. Following this, we discuss recent research advancements in the field and present a case study of near-field channel estimation based on GDM, demonstrating its promising potential for facilitating efficient ultra-dimensional channel statement information (CSI) acquisition in the context of massive MIMO communications. Finally, we highlight several pressing challenges in future mobile communications and identify promising research directions surrounding GDM.

Movable Antenna Aided NOMA: Joint Antenna Positioning, Precoding, and Decoding Design

This paper investigates movable antenna (MA) aided non-orthogonal multiple access (NOMA) for multi-user downlink communication, where the base station (BS) is equipped with a fixed-position antenna (FPA) array to serve multiple MA-enabled users. An optimization problem is formulated to maximize the minimum achievable rate among all the users by jointly optimizing the MA positioning of each user, the precoding matrix at the BS, and the successive interference cancellation (SIC) decoding indicator matrix at the users, subject to a set of constraints including the limited movement area of the MAs, the maximum transmit power of the BS, and the SIC decoding condition. To solve this non-convex problem, we propose a two-loop iterative optimization algorithm that combines the hippopotamus optimization (HO) method with the alternating optimization (AO) method to obtain a suboptimal solution efficiently. Specifically, in the inner loop, the complex-valued precoding matrix and the binary decoding indicator matrix are optimized alternatively by the successive convex approximation (SCA) technique with customized greedy search to maximize the minimum achievable rate for the given positions of the MAs. In the outer loop, each user's antenna position is updated using the HO algorithm, following a novel nature-inspired intelligent optimization framework. Simulation results show that the proposed algorithms can effectively avoid local optimum for highly coupled variables and significantly improve the rate performance of the NOMA system compared to the conventional FPA system as well as other benchmark schemes.

6D Movable Antenna Enhanced Multi-Access Point Coordination via Position and Orientation Optimization

The effective utilization of unlicensed spectrum is regarded as an important direction to enable the massive access and broad coverage for next-generation wireless local area network (WLAN). Due to the crowded spectrum occupancy and dense user terminals (UTs), the conventional fixed antenna (FA)-based access points (APs) face huge challenges in realizing massive access and interference cancellation. To address this issue, in this paper we develop a six-dimensional movable antenna (6DMA) enhanced multi-AP coordination system for coverage enhancement and interference mitigation. First, we model the wireless channels between the APs and UTs to characterize their variation with respect to 6DMA movement, in terms of both the three-dimensional (3D) position and 3D orientation of each distributed AP's antenna. Then, an optimization problem is formulated to maximize the weighted sum rate of multiple UTs for their uplink transmissions by jointly optimizing the antenna position vector (APV), the antenna orientation matrix (AOM), and the receive combining matrix over all coordinated APs, subject to the constraints on local antenna movement regions. To solve this challenging non-convex optimization problem, we first transform it into a more tractable Lagrangian dual problem. Then, an alternating optimization (AO)-based algorithm is developed by iteratively optimizing the APV and AOM, which are designed by applying the successive convex approximation (SCA) technique and Riemannian manifold optimization-based algorithm, respectively. Simulation results show that the proposed 6DMA-enhanced multi-AP coordination system can significantly enhance network capacity, and both of the online and offline 6DMA schemes can attain considerable performance improvement compared to the conventional FA-based schemes.

Channel Estimation for Movable Antenna Aided Wideband Communication Systems

Movable antenna (MA) is an emerging technology that can significantly improve communication performance via the continuous adjustment of the antenna positions. To unleash the potential of MAs in wideband communication systems, acquiring accurate channel state information (CSI), i.e., the channel frequency responses (CFRs) between any position pair within the transmit (Tx) region and the receive (Rx) region across all subcarriers, is a crucial issue. In this paper, we study the channel estimation problem for wideband MA systems. To start with, we express the CFRs as a combination of the field-response vectors (FRVs), delay-response vector (DRV), and path-response tensor (PRT), which exhibit sparse characteristics and can be recovered by using a limited number of channel measurements at selected position pairs of Tx and Rx MAs over a few subcarriers. Specifically, we first formulate the recovery of the FRVs and DRV as a problem with multiple measurement vectors in compressed sensing (MMV-CS), which can be solved via a simultaneous orthogonal matching pursuit (SOMP) algorithm. Next, we estimate the PRT using the least-square (LS) method. Moreover, we also devise an alternating refinement approach to further improve the accuracy of the estimated FRVs, DRV, and PRT. This is achieved by minimizing the discrepancy between the received pilots and those constructed by the estimated CSI, which can be efficiently carried out by using the gradient descent algorithm. Finally, simulation results demonstrate that both the SOMP-based channel estimation method and alternating refinement method can reconstruct the complete wideband CSI with high accuracy, where the alternating refinement method performs better despite a higher complexity.