Iterative Inversion of (ELAA-)MIMO Channels Using Symmetric Rank-$1$ Regularization

While iterative matrix inversion methods excel in computational efficiency, memory optimization, and support for parallel and distributed computing when managing large matrices, their limitations are also evident in multiple-input multiple-output (MIMO) fading channels. These methods encounter challenges related to slow convergence and diminished accuracy, especially in ill-conditioned scenarios, hindering their application in future MIMO networks such as extra-large aperture array (ELAA). To address these challenges, this paper proposes a novel matrix regularization method termed symmetric rank-$1$ regularization (SR-$1$R). The proposed method functions by augmenting the channel matrix with a symmetric rank-$1$ matrix, with the primary goal of minimizing the condition number of the resultant regularized matrix. This significantly improves the matrix condition, enabling fast and accurate iterative inversion of the regularized matrix. Then, the inverse of the original channel matrix is obtained by applying the Sherman-Morrison transform on the outcome of iterative inversions. Our eigenvalue analysis unveils the best channel condition that can be achieved by an optimized SR-$1$R matrix. Moreover, a power iteration-assisted (PIA) approach is proposed to find the optimum SR-$1$R matrix without need of eigenvalue decomposition. The proposed approach exhibits logarithmic algorithm-depth in parallel computing for MIMO precoding. Finally, computer simulations demonstrate that SR-$1$R has the potential to reduce iterative iterations by up to $33\%$, while also significantly improve symbol error probability by approximately an order of magnitude.

Near-Field Fading Channel Modeling for ELAAs: From Communication to ISAC

Extremely large aperture array (ELAA) is anticipated to serve as a pivotal feature of future multiple-input multiple-output (MIMO) systems in 6G. Near-field (NF) fading channel models are essential for reliable link-level simulation and ELAA system design. In this article, we propose a framework designed to generate NF fading channels for both communication and integrated sensing and communication (ISAC) applications. The framework allows a mixed of line of sight (LoS) and non-LoS (NLoS) links. It also considers spherical wave model and spatially non-stationary shadow fading. Based on this framework, we propose a three-dimensional (3D) fading channel model for ELAA systems deployed with a uniform rectangular array (URA). It can capture the impact of sensing object for ISAC applications. Moreover, all parameters involved in the framework are based on specifications or measurements from the 3rd Generation Partnership Project (3GPP) documents. Therefore, the proposed framework and channel model have the potential to contribute to the standard in various aspects, including ISAC, extra-large (XL-) MIMO, and reconfigurable intelligent surface (RIS) aided MIMO systems. Finally, future directions for ELAA are presented, including not only NF channel modeling but also the design of next-generation transceivers.

On Chernoff Lower-Bound of Outage Threshold for Non-Central $χ^2$-Distributed Beamforming Gain in URLLC Systems

The cumulative distribution function (CDF) of a non-central $\chi^2$-distributed random variable (RV) is often used when measuring the outage probability of communication systems. For ultra-reliable low-latency communication (URLLC), it is important but mathematically challenging to determine the outage threshold for an extremely small outage target. This motivates us to investigate lower bounds of the outage threshold, and it is found that the one derived from the Chernoff inequality (named Cher-LB) is the most effective lower bound. This finding is associated with three rigorously established properties of the Cher-LB with respect to the mean, variance, reliability requirement, and degrees of freedom of the non-central $\chi^2$-distributed RV. The Cher-LB is then employed to predict the beamforming gain in URLLC for both conventional multi-antenna systems (i.e., MIMO) under first-order Markov time-varying channel and reconfigurable intellgent surface (RIS) systems. It is exhibited that, with the proposed Cher-LB, the pessimistic prediction of the beamforming gain is made sufficiently accurate for guaranteed reliability as well as the transmit-energy efficiency.

Near and Far Field Model Mismatch: Implications on 6G Communications, Localization, and Sensing

The upcoming 6G technology is expected to operate in near-field (NF) radiating conditions thanks to high-frequency and electrically large antenna arrays. While several studies have already addressed this possibility, it is worth noting that NF models introduce heightened complexity, the justification for which is not always evident in terms of performance improvements. Therefore, this paper delves into the implications of the disparity between NF and far-field (FF) models concerning communication, localization, and sensing systems. Such disparity might lead to a degradation of performance metrics like localization accuracy, sensing reliability, and communication efficiency. Through an exploration of the effects arising from the mismatches between NF and FF models, this study seeks to illuminate the challenges confronting system designers and offer valuable insights into the balance between model accuracy, which typically requires a high complexity and achievable performance. To substantiate our perspective, we also incorporate a numerical performance assessment confirming the repercussions of the mismatch between NF and FF models.

On Chernoff Lower-Bound of Outage Threshold for Non-Central $χ^2$-Distributed MIMO Beamforming Gain

The cumulative distribution function (CDF) of a non-central $\chi^2$-distributed random variable (RV) is often used when measuring the outage probability of communication systems. For adaptive transmitters, it is important but mathematically challenging to determine the outage threshold for an extreme target outage probability (e.g., $10^{-5}$ or less). This motivates us to investigate lower bounds of the outage threshold, and it is found that the one derived from the Chernoff inequality (named Cher-LB) is the most {effective} lower bound. The Cher-LB is then employed to predict the multi-antenna transmitter beamforming-gain in ultra-reliable and low-latency communication, concerning the first-order Markov time-varying channel. It is exhibited that, with the proposed Cher-LB, pessimistic prediction of the beamforming gain is made sufficiently accurate for guaranteed reliability as well as the transmit-energy efficiency.

Alternative Normalized-Preconditioning for Scalable Iterative Large-MIMO Detection

Signal detection in large multiple-input multiple-output (large-MIMO) systems presents greater challenges compared to conventional massive-MIMO for two primary reasons. First, large-MIMO systems lack favorable propagation conditions as they do not require a substantially greater number of service antennas relative to user antennas. Second, the wireless channel may exhibit spatial non-stationarity when an extremely large aperture array (ELAA) is deployed in a large-MIMO system. In this paper, we propose a scalable iterative large-MIMO detector named ANPID, which simultaneously delivers 1) close to maximum-likelihood detection performance, 2) low computational-complexity (i.e., square-order of transmit antennas), 3) fast convergence, and 4) robustness to the spatial non-stationarity in ELAA channels. ANPID incorporates a damping demodulation step into stationary iterative (SI) methods and alternates between two distinct demodulated SI methods. Simulation results demonstrate that ANPID fulfills all the four features concurrently and outperforms existing low-complexity MIMO detectors, especially in highly-loaded large MIMO systems.

Leveraging User-Wise SVD for Accelerated Convergence in Iterative ELAA-MIMO Detections

Numerous low-complexity iterative algorithms have been proposed to offer the performance of linear multiple-input multiple-output (MIMO) detectors bypassing the channel matrix inverse. These algorithms exhibit fast convergence in well-conditioned MIMO channels. However, in the emerging MIMO paradigm utilizing extremely large aperture arrays (ELAA), the wireless channel may become ill-conditioned because of spatial non-stationarity, which results in a considerably slower convergence rate for these algorithms. In this paper, we propose a novel ELAA-MIMO detection scheme that leverages user-wise singular value decomposition (UW-SVD) to accelerate the convergence of these iterative algorithms. By applying UW-SVD, the MIMO signal model can be converted into an equivalent form featuring a better-conditioned transfer function. Then, existing iterative algorithms can be utilized to recover the transmitted signal from the converted signal model with accelerated convergence towards zero-forcing performance. Our simulation results indicate that proposed UW-SVD scheme can significantly accelerate the convergence of the iterative algorithms in spatially non-stationary ELAA channels. Moreover, the computational complexity of the UW-SVD is comparatively minor in relation to the inherent complexity of the iterative algorithms.

Space MIMO: Direct Unmodified Handheld to Multi-Satellite Communication

This paper examines the uplink transmission of a single-antenna handsheld user to a cluster of satellites, with a focus on utilizing the inter-satellite links to enable cooperative signal detection. Two cases are studied: one with full CSI and the other with partial CSI between satellites. The two cases are compared in terms of capacity, overhead, and bit error rate. Additionally, the impact of channel estimation error is analyzed in both designs, and robust detection techniques are proposed to handle channel uncertainty up to a certain level. The performance of each case is demonstrated, and a comparison is made with conventional satellite communication schemes where only one satellite can connect to a user. The results of our study reveal that the proposed constellation with a total of 3168 satellites in orbit can enable a capacity of 800 Mbits/sec through cooperation of $12$ satellites with and occupied bandwidth of 500 MHz. In contrast, conventional satellite communication approaches with the same system parameters yield a significantly lower capacity of less than 150 Mbits/sec for the nearest satellite.

Outage Tradeoff Analysis in a Downlink Integrated Sensing and Communication Network

This paper aims to analyze the stochastic performance of a multiple input multiple output (MIMO) integrated sensing and communication (ISAC) system in a downlink scenario, where a base station (BS) transmits a dual-functional radar-communication (DFRC) signal matrix, serving the purpose of transmitting communication data to the user while simultaneously sensing the angular location of a target. The channel between the BS and the user is modeled as a random channel with Rayleigh fading distribution, and the azimuth angle of the target is assumed to follow a uniform distribution. We use a maximum ratio transmission (MRT) beamformer to share resource between sensing and communication (S \& C) and observe the trade-off between them. We derive the approximate probability density function (PDF) of the signal-to-noise ratio (SNR) for both the user and the target. Subsequently, leveraging the obtained PDF, we derive the expressions for the user's rate outage probability (OP), as well as the OP for the Cramer-Rao lower bound (CRLB) of the angle of arrival (AOA). In our numerical results, we demonstrate the trade-off between S \& C, confirmed with simulations.

Collaborative Learning with a Drone Orchestrator

In this paper, the problem of drone-assisted collaborative learning is considered. In this scenario, swarm of intelligent wireless devices train a shared neural network (NN) model with the help of a drone. Using its sensors, each device records samples from its environment to gather a local dataset for training. The training data is severely heterogeneous as various devices have different amount of data and sensor noise level. The intelligent devices iteratively train the NN on their local datasets and exchange the model parameters with the drone for aggregation. For this system, the convergence rate of collaborative learning is derived while considering data heterogeneity, sensor noise levels, and communication errors, then, the drone trajectory that maximizes the final accuracy of the trained NN is obtained. The proposed trajectory optimization approach is aware of both the devices data characteristics (i.e., local dataset size and noise level) and their wireless channel conditions, and significantly improves the convergence rate and final accuracy in comparison with baselines that only consider data characteristics or channel conditions. Compared to state-of-the-art baselines, the proposed approach achieves an average 3.85% and 3.54% improvement in the final accuracy of the trained NN on benchmark datasets for image recognition and semantic segmentation tasks, respectively. Moreover, the proposed framework achieves a significant speedup in training, leading to an average 24% and 87% saving in the drone hovering time, communication overhead, and battery usage, respectively for these tasks.