608 research outputs found
Joint Beamforming and Power Control in Coordinated Multicell: Max-Min Duality, Effective Network and Large System Transition
This paper studies joint beamforming and power control in a coordinated
multicell downlink system that serves multiple users per cell to maximize the
minimum weighted signal-to-interference-plus-noise ratio. The optimal solution
and distributed algorithm with geometrically fast convergence rate are derived
by employing the nonlinear Perron-Frobenius theory and the multicell network
duality. The iterative algorithm, though operating in a distributed manner,
still requires instantaneous power update within the coordinated cluster
through the backhaul. The backhaul information exchange and message passing may
become prohibitive with increasing number of transmit antennas and increasing
number of users. In order to derive asymptotically optimal solution, random
matrix theory is leveraged to design a distributed algorithm that only requires
statistical information. The advantage of our approach is that there is no
instantaneous power update through backhaul. Moreover, by using nonlinear
Perron-Frobenius theory and random matrix theory, an effective primal network
and an effective dual network are proposed to characterize and interpret the
asymptotic solution.Comment: Some typos in the version publised in the IEEE Transactions on
Wireless Communications are correcte
Nonnegative Matrix Inequalities and their Application to Nonconvex Power Control Optimization
Maximizing the sum rates in a multiuser Gaussian channel by power control is a nonconvex NP-hard problem that finds engineering application in code division multiple access (CDMA) wireless communication network. In this paper, we extend and apply several fundamental nonnegative matrix inequalities initiated by Friedland and Karlin in a 1975 paper to solve this nonconvex power control optimization problem. Leveraging tools such as the Perron–Frobenius theorem in nonnegative matrix theory, we (1) show that this problem in the power domain can be reformulated as an equivalent convex maximization problem over a closed unbounded convex set in the logarithmic signal-to-interference-noise ratio domain, (2) propose two relaxation techniques that utilize the reformulation problem structure and convexification by Lagrange dual relaxation to compute progressively tight bounds, and (3) propose a global optimization algorithm with ϵ-suboptimality to compute the optimal power control allocation. A byproduct of our analysis is the application of Friedland–Karlin inequalities to inverse problems in nonnegative matrix theory
The role of asymptotic functions in network optimization and feasibility studies
Solutions to network optimization problems have greatly benefited from
developments in nonlinear analysis, and, in particular, from developments in
convex optimization. A key concept that has made convex and nonconvex analysis
an important tool in science and engineering is the notion of asymptotic
function, which is often hidden in many influential studies on nonlinear
analysis and related fields. Therefore, we can also expect that asymptotic
functions are deeply connected to many results in the wireless domain, even
though they are rarely mentioned in the wireless literature. In this study, we
show connections of this type. By doing so, we explain many properties of
centralized and distributed solutions to wireless resource allocation problems
within a unified framework, and we also generalize and unify existing
approaches to feasibility analysis of network designs. In particular, we show
sufficient and necessary conditions for mappings widely used in wireless
communication problems (more precisely, the class of standard interference
mappings) to have a fixed point. Furthermore, we derive fundamental bounds on
the utility and the energy efficiency that can be achieved by solving a large
family of max-min utility optimization problems in wireless networks.Comment: GlobalSIP 2017 (to appear
A combinatorial approximation algorithm for CDMA downlink rate allocation
This paper presents a combinatorial algorithm for downlink rate allocation in Code Division Multiple Access (CDMA) mobile networks. By discretizing the coverage area into small segments, the transmit power requirements are characterized via a matrix representation that separates user and system characteristics. We obtain a closed-form analytical expression for the so-called Perron-Frobenius eigenvalue of that matrix, which provides a quick assessment of the feasibility of the power assignment for a given downlink rate allocation. Based on the Perron-Frobenius eigenvalue, we reduce the downlink rate allocation problem to a set of multiple-choice knapsack problems. The solution of these problems provides an approximation of the optimal downlink rate allocation and cell borders for which the system throughput, expressed in terms of utility functions of the users, is maximized
A multiple-choice knapsack based algorithm for CDMA downlink rate differentiation under uplink coverage restrictions
This paper presents an analytical model for downlink rate allocation in Code Division Multiple Access (CDMA) mobile networks. By discretizing the coverage area into small segments, the transmit power requirements are characterized via a matrix representation that separates user and system characteristics. We obtain a closed-form analytical expression for the so-called Perron-Frobenius eigenvalue of that matrix, which provides a quick assessment of the feasibility of the power assignment for a given downlink rate allocation. Based on the Perron-Frobenius eigenvalue, we reduce the downlink rate allocation problem to a set of multiple-choice knapsack problems. The solution of these problems provides an approximation of the optimal downlink rate allocation and cell borders for which the system throughput, expressed in terms of downlink rates, is maximized. \u
Maximizing sum rate and minimizing MSE on multiuser downlink: Optimality, fast algorithms and equivalence via max-min SIR
Maximizing the minimum weighted SIR, minimizing the weighted sum MSE and maximizing the weighted sum rate in a multiuser downlink system are three important performance objectives in joint transceiver and power optimization, where all the users have a total power constraint. We show that, through connections with the nonlinear Perron-Frobenius theory, jointly optimizing power and beamformers in the max-min weighted SIR problem can be solved optimally in a distributed fashion. Then, connecting these three performance objectives through the arithmetic-geometric mean inequality and nonnegative matrix theory, we solve the weighted sum MSE minimization and weighted sum rate maximization in the low to moderate interference regimes using fast algorithms
Generalized Perron--Frobenius Theorem for Nonsquare Matrices
The celebrated Perron--Frobenius (PF) theorem is stated for irreducible
nonnegative square matrices, and provides a simple characterization of their
eigenvectors and eigenvalues. The importance of this theorem stems from the
fact that eigenvalue problems on such matrices arise in many fields of science
and engineering, including dynamical systems theory, economics, statistics and
optimization. However, many real-life scenarios give rise to nonsquare
matrices. A natural question is whether the PF Theorem (along with its
applications) can be generalized to a nonsquare setting. Our paper provides a
generalization of the PF Theorem to nonsquare matrices. The extension can be
interpreted as representing client-server systems with additional degrees of
freedom, where each client may choose between multiple servers that can
cooperate in serving it (while potentially interfering with other clients).
This formulation is motivated by applications to power control in wireless
networks, economics and others, all of which extend known examples for the use
of the original PF Theorem.
We show that the option of cooperation between servers does not improve the
situation, in the sense that in the optimal solution no cooperation is needed,
and only one server needs to serve each client. Hence, the additional power of
having several potential servers per client translates into \emph{choosing} the
best single server and not into \emph{sharing} the load between the servers in
some way, as one might have expected.
The two main contributions of the paper are (i) a generalized PF Theorem that
characterizes the optimal solution for a non-convex nonsquare problem, and (ii)
an algorithm for finding the optimal solution in polynomial time
Asynchronous Gossip for Averaging and Spectral Ranking
We consider two variants of the classical gossip algorithm. The first variant
is a version of asynchronous stochastic approximation. We highlight a
fundamental difficulty associated with the classical asynchronous gossip
scheme, viz., that it may not converge to a desired average, and suggest an
alternative scheme based on reinforcement learning that has guaranteed
convergence to the desired average. We then discuss a potential application to
a wireless network setting with simultaneous link activation constraints. The
second variant is a gossip algorithm for distributed computation of the
Perron-Frobenius eigenvector of a nonnegative matrix. While the first variant
draws upon a reinforcement learning algorithm for an average cost controlled
Markov decision problem, the second variant draws upon a reinforcement learning
algorithm for risk-sensitive control. We then discuss potential applications of
the second variant to ranking schemes, reputation networks, and principal
component analysis.Comment: 14 pages, 7 figures. Minor revisio
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