arXiv subjects

Danila Zaev

Publications and source records attributed to Danila Zaev.

7 recordsLinked to original sources

arXiv2024

Massive MIMO Adaptive Modulation and Coding Using Online Deep Learning Algorithm

The paper describes an online deep learning algorithm (ODL) for adaptive modulation and coding in massive MIMO. The algorithm is based on a fully connected neural network, which is initially trained on the output of the traditional algorithm and then incrementally retrained by the service feedback of its output. We show the advantage of our solution over the state-of-the-art Q-learning approach. We provide system-level simulation results to support this conclusion in various scenarios with different channel characteristics and different user speeds. Compared with traditional OLLA, the algorithm shows a 10\% to 20\% improvement in user throughput in the full-buffer case.

cs.NI↗

arXiv2023

Adaptive Regularized Zero-Forcing Beamforming in Massive MIMO with Multi-Antenna Users

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 Singular Value Decomposition (SVD) 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 prove theoretical estimates of the number of conditionality of the inverse covariance matrix of the ARZF method and the standard RZF method, which is important for systems with fixed computational accuracy. Finally, We 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.

cs.IT↗

arXiv2022

Study on Precoding Optimization Algorithms in Massive MIMO System with Multi-Antenna Users

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.

cs.IT↗

arXiv2016

On some topics of analysis on noncommutative spaces

We consider a conservative Markov semigroup on a semi-finite $W^*$-algebra. It is known that under some reasonable assumptions it is enough to determine a kind of differential structure on such a 'noncommutative space'. We construct an analogue of a Riemannian metric in this setting, formulate a Poincaré-type inequality, provide existence and uniqueness results for quasi-linear elliptic and parabolic PDEs defined in terms of the constructed noncommutative calculus.

math.OA↗

arXiv2015

Decomposition of the Kantorovich problem and Wasserstein distances on simplexes

Let $X$ be a Polish space, $\mathcal{P}(X)$ be the set of Borel probability measures on $X$, and $T\colon X\to X$ be a homeomorphism. We prove that for the simplex $\mathrm{Dom} \subseteq \mathcal{P}(X)$ of all $T$-invariant measures, the Kantorovich metric on $\mathrm{Dom}$ can be reconstructed from its values on the set of extreme points. This fact is closely related to the following result: the invariant optimal transportation plan is a mixture of invariant optimal transportation plans between extreme points of the simplex. The latter result can be generalized to the case of the Kantorovich problem with additional linear constraints and the class of ergodic decomposable simplexes.

math.PR↗

arXiv2015

$L^p$-Wasserstein distances on state and quasi-state spaces of $C^*$-algebras

We construct an analogue of the classical $L^p$-Wasserstein distance for the state space of a $C^*$-algebra. Given an abstract Lipschitz gauge on a $C^*$-algebra $\mathcal{A}$ in the sense of Rieffel, one can define the classical $L^p$-Wasserstein distance on the state space of each commutative $C^*$-subalgebra of $\mathcal{A}$. We consider a projective limit of these metric spaces, which appears to be the space of all quasi-linear states, equipped with a distance function. We call this distance the projective $L^p$-Wasserstein distance. It is easy to show, that the state space of a $C^*$-algebra is naturally embedded in the space of its quasi-linear states, hence, the introduced distance is defined on the state space as well. We show that this distance is reasonable and well-behaved. We also formulate a sufficient condition for a Lipschitz gauge, such that the corresponding projective $L^p$-Wasserstein distance metricizes the weak$^*$-topology on the state space.

math.OA↗

arXiv2014

On the Monge-Kantorovich problem with additional linear constraints

We consider the modified Monge-Kantorovich problem with additional restriction: admissible transport plans must vanish on some fixed functional subspace. Different choice of the subspace leads to different additional properties optimal plans need to satisfy. Our main results are quite general and include several important examples. In particular, they include Monge-Kantorovich problems in the classes of invariant measures and martingales. We formulate and prove a criterion for existence of a solution, a duality statement of the Kantorovich type, and a necessary geometric condition on a support of optimal measure, which is analogues to the usual $c$-monotonicity.

math.FA↗