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We investigate the problem of message transmission over time-varying single-user multiple-input multiple-output (MIMO) Rayleigh fading channels with average power constraint and with complete channel state information available at the receiver side (CSIR). To describe the channel variations over the time, we consider a first-order Gauss-Markov model. We completely solve the problem by giving a single-letter characterization of the channel capacity in closed form and by providing a rigorous proof of it.

Let $W$ be a binary-input memoryless symmetric (BMS) channel with Shannon capacity $I(W)$ and fix any $\alpha > 0$. We construct, for any sufficiently small $\delta > 0$, binary linear codes of block length $O(1/\delta^{2+\alpha})$ and rate $I(W)-\delta$ that enable reliable communication on $W$ with quasi-linear time encoding and decoding. Shannon's noisy coding theorem established the \emph{existence} of such codes (without efficient constructions or decoding) with block length $O(1/\delta^2)$. This quadratic dependence on the gap $\delta$ to capacity is known to be best possible. Our result thus yields a constructive version of Shannon's theorem with near-optimal convergence to capacity as a function of the block length. This resolves a central theoretical challenge associated with the attainment of Shannon capacity. Previously such a result was only known for the erasure channel. Our codes are a variant of Ar{\i}kan's polar codes based on multiple carefully constructed local kernels, one for each intermediate channel that arises in the decoding. A crucial ingredient in the analysis is a strong converse of the noisy coding theorem when communicating using random linear codes on arbitrary BMS channels. Our converse theorem shows extreme unpredictability of even a single message bit for random coding at rates slightly above capacity.

Modern wireless cellular networks use massive multiple-input multiple-output (MIMO) technology. This technology involves operations with an antenna array at a base station that simultaneously serves multiple mobile devices which also use multiple antennas on their side. For this, various precoding and detection techniques are used, allowing each user to receive the signal intended for him from the base station. There is an important class of linear precoding called Regularized Zero-Forcing (RZF). In this work, we propose Adaptive RZF (ARZF) with a special kind of regularization matrix with different coefficients for each layer of multi-antenna users. These regularization coefficients are defined by explicit formulas based on SVD decompositions of user channel matrices. We study the optimization problem, which is solved by the proposed algorithm, with the connection to other possible problem statements. We also compare the proposed algorithm with state-of-the-art linear precoding algorithms on simulations with the Quadriga channel model. The proposed approach provides a significant increase in quality with the same computation time as in the reference methods.

The paper studies the multi-user precoding problem as a non-convex optimization problem for wireless multiple input and multiple output (MIMO) systems. In our work, we approximate the target Spectral Efficiency function with a novel computationally simpler function. Then, we reduce the precoding problem to an unconstrained optimization task using a special differential projection method and solve it by the Quasi-Newton L-BFGS iterative procedure to achieve gains in capacity. We are testing the proposed approach in several scenarios generated using Quadriga~-- open-source software for generating realistic radio channel impulse response. Our method shows monotonic improvement over heuristic methods with reasonable computation time. The proposed L-BFGS optimization scheme is novel in this area and shows a significant advantage over the standard approaches. The proposed method has a simple implementation and can be a good reference for other heuristic algorithms in this field.

This paper provides a comprehensive framework to analyze the performance of non-orthogonal multiple access (NOMA) in the downlink transmission of a single-carrier and multi-carrier terahertz (THz) network. Specifically, we first develop a novel user pairing scheme for the THz-NOMA network which ensures the performance gains of NOMA over orthogonal multiple access (OMA) for each individual user in the NOMA pair and adapts according to the molecular absorption. Then, we characterize novel outage probability expressions considering a single-carrier and multi-carrier THz-NOMA network in the presence of various user pairing schemes, Nakagami-m channel fading, and molecular absorption noise. We propose a moment-generating-function (MGF) based approach to analyze the outage probability of users in a multi-carrier THz network. Furthermore, for negligible thermal noise, we provide simplified single-integral expressions to compute the outage probability in a multi-carrier network. Numerical results demonstrate the performance of the proposed user-pairing scheme and validate the accuracy of the derived expressions.

In this paper, we investigate the secure rate-splitting for the two-user multiple-input multiple-output (MIMO) broadcast channel with imperfect channel state information at the transmitter (CSIT) and a multiple-antenna jammer, where each receiver has equal number of antennas and the jammer has perfect channel state information (CSI). Specifically, we design the secure rate-splitting multiple-access in this scenario, where the security of splitted private and common messages is ensured by precoder design with joint nulling and aligning the leakage information, regarding to different antenna configurations. As a result, we show that the sum-secure degrees-of-freedom (SDoF) achieved by secure rate-splitting outperforms that by conventional zero-forcing. Therefore, we validate the superiority of rate-splitting for the secure purpose in the two-user MIMO broadcast channel with imperfect CSIT and a jammer.

Wireless systems must be resilient to jamming attacks. Existing mitigation methods require knowledge of the jammer's transmit characteristics. However, this knowledge may be difficult to acquire, especially for smart jammers that attack only specific instants during transmission in order to evade mitigation. We propose a novel method that mitigates attacks by smart jammers on massive multi-user multiple-input multiple-output (MU-MIMO) basestations (BSs). Our approach builds on recent progress in joint channel estimation and data detection (JED) and exploits the fact that a jammer cannot change its subspace within a coherence interval. Our method, called MAED (short for MitigAtion, Estimation, and Detection), uses a novel problem formulation that combines jammer estimation and mitigation, channel estimation, and data detection, instead of separating these tasks. We solve the problem approximately with an efficient iterative algorithm. Our results show that MAED effectively mitigates a wide range of smart jamming attacks without having any a priori knowledge about the attack type.

We study the problem of estimating the fixed point of a contractive operator defined on a separable Banach space. Focusing on a stochastic query model that provides noisy evaluations of the operator, we analyze a variance-reduced stochastic approximation scheme, and establish non-asymptotic bounds for both the operator defect and the estimation error, measured in an arbitrary semi-norm. In contrast to worst-case guarantees, our bounds are instance-dependent, and achieve the local asymptotic minimax risk non-asymptotically. For linear operators, contractivity can be relaxed to multi-step contractivity, so that the theory can be applied to problems like average reward policy evaluation problem in reinforcement learning. We illustrate the theory via applications to stochastic shortest path problems, two-player zero-sum Markov games, as well as policy evaluation and $Q$-learning for tabular Markov decision processes.

As investigations on physical layer security evolve from point-to-point systems to multi-user scenarios, multi-user interference (MUI) is introduced and becomes an unavoidable issue. Different from treating MUI totally as noise in conventional secure communications, in this paper, we propose a rate-splitting multiple access (RSMA)-based secure beamforming design, where user messages are split and encoded into common and private streams. Each user not only decodes the common stream and the intended private stream, but also tries to eavesdrop the private streams of other users. We formulate a weighted sum-rate (WSR) maximization problem subject to the secrecy rate requirements of all users. To tackle the non-convexity of the formulated problem, a successive convex approximation (SCA)-based approach is adopted to convert the original non-convex and intractable problem into a low-complexity suboptimal iterative algorithm. Numerical results demonstrate that the proposed secure beamforming scheme outperforms the conventional multi-user linear precoding (MULP) technique in terms of the WSR performance while ensuring user secrecy rate requirements.

In 1954, Alston S. Householder published Principles of Numerical Analysis, one of the first modern treatments on matrix decomposition that favored a (block) LU decomposition-the factorization of a matrix into the product of lower and upper triangular matrices. And now, matrix decomposition has become a core technology in machine learning, largely due to the development of the back propagation algorithm in fitting a neural network. The sole aim of this survey is to give a self-contained introduction to concepts and mathematical tools in numerical linear algebra and matrix analysis in order to seamlessly introduce matrix decomposition techniques and their applications in subsequent sections. However, we clearly realize our inability to cover all the useful and interesting results concerning matrix decomposition and given the paucity of scope to present this discussion, e.g., the separated analysis of the Euclidean space, Hermitian space, Hilbert space, and things in the complex domain. We refer the reader to literature in the field of linear algebra for a more detailed introduction to the related fields.