221 research outputs found
Convolution operations arising from Vandermonde matrices
Different types of convolution operations involving large Vandermonde
matrices are considered. The convolutions parallel those of large Gaussian
matrices and additive and multiplicative free convolution. First additive and
multiplicative convolution of Vandermonde matrices and deterministic diagonal
matrices are considered. After this, several cases of additive and
multiplicative convolution of two independent Vandermonde matrices are
considered. It is also shown that the convergence of any combination of
Vandermonde matrices is almost sure. We will divide the considered convolutions
into two types: those which depend on the phase distribution of the Vandermonde
matrices, and those which depend only on the spectra of the matrices. A general
criterion is presented to find which type applies for any given convolution. A
simulation is presented, verifying the results. Implementations of all
considered convolutions are provided and discussed, together with the
challenges in making these implementations efficient. The implementation is
based on the technique of Fourier-Motzkin elimination, and is quite general as
it can be applied to virtually any combination of Vandermonde matrices.
Generalizations to related random matrices, such as Toeplitz and Hankel
matrices, are also discussed.Comment: Submitted to IEEE Transactions on Information Theory. 16 pages, 1
figur
On the Nash Equilibria in Decentralized Parallel Interference Channels
In this paper, the 2-dimensional decentralized parallel interference channel
(IC) with 2 transmitter-receiver pairs is modelled as a non-cooperative static
game. Each transmitter is assumed to be a fully rational entity with complete
information on the game, aiming to maximize its own individual spectral
efficiency by tuning its own power allocation (PA) vector. Two scenarios are
analysed. First, we consider that transmitters can split their transmit power
between both dimensions (PA game). Second, we consider that each transmitter is
limited to use only one dimension (channel selection CS game). In the first
scenario, the game might have either one or three NE in pure strategies (PS).
However, two or infinitely many NE in PS might also be observed with zero
probability. In the second scenario, there always exists either one or two NE
in PS. We show that in both games there always exists a non-zero probability of
observing more than one NE. More interestingly, using Monte-Carlo simulations,
we show that the highest and lowest network spectral efficiency at any of the
NE in the CS game are always higher than the ones in the PA.Comment: 6 pages, 4 figures, presented in ICCC Kyoto 201
From Spectrum Pooling to Space Pooling: Opportunistic Interference Alignment in MIMO Cognitive Networks
We describe a non-cooperative interference alignment (IA) technique which
allows an opportunistic multiple input multiple output (MIMO) link (secondary)
to harmlessly coexist with another MIMO link (primary) in the same frequency
band. Assuming perfect channel knowledge at the primary receiver and
transmitter, capacity is achieved by transmiting along the spatial directions
(SD) associated with the singular values of its channel matrix using a
water-filling power allocation (PA) scheme. Often, power limitations lead the
primary transmitter to leave some of its SD unused. Here, it is shown that the
opportunistic link can transmit its own data if it is possible to align the
interference produced on the primary link with such unused SDs. We provide both
a processing scheme to perform IA and a PA scheme which maximizes the
transmission rate of the opportunistic link. The asymptotes of the achievable
transmission rates of the opportunistic link are obtained in the regime of
large numbers of antennas. Using this result, it is shown that depending on the
signal-to-noise ratio and the number of transmit and receive antennas of the
primary and opportunistic links, both systems can achieve transmission rates of
the same order.Comment: Submitted to IEEE Trans. in Signal Processing. Revised on 23-11-0
Finite Dimensional Statistical Inference
In this paper, we derive the explicit series expansion of the eigenvalue
distribution of various models, namely the case of non-central Wishart
distributions, as well as correlated zero mean Wishart distributions. The tools
used extend those of the free probability framework, which have been quite
successful for high dimensional statistical inference (when the size of the
matrices tends to infinity), also known as free deconvolution. This
contribution focuses on the finite Gaussian case and proposes algorithmic
methods to compute the moments. Cases where asymptotic results fail to apply
are also discussed.Comment: 14 pages, 13 figures. Submitted to IEEE Transactions on Information
Theor
Introducing Hierarchy in Energy Games
In this work we introduce hierarchy in wireless networks that can be modeled
by a decentralized multiple access channel and for which energy-efficiency is
the main performance index. In these networks users are free to choose their
power control strategy to selfishly maximize their energy-efficiency.
Specifically, we introduce hierarchy in two different ways: 1. Assuming
single-user decoding at the receiver, we investigate a Stackelberg formulation
of the game where one user is the leader whereas the other users are assumed to
be able to react to the leader's decisions; 2. Assuming neither leader nor
followers among the users, we introduce hierarchy by assuming successive
interference cancellation at the receiver. It is shown that introducing a
certain degree of hierarchy in non-cooperative power control games not only
improves the individual energy efficiency of all the users but can also be a
way of insuring the existence of a non-saturated equilibrium and reaching a
desired trade-off between the global network performance at the equilibrium and
the requested amount of signaling. In this respect, the way of measuring the
global performance of an energy-efficient network is shown to be a critical
issue.Comment: Accepted for publication in IEEE Trans. on Wireless Communication
Cooperative Spectrum Sensing Using Random Matrix Theory
In this paper, using tools from asymptotic random matrix theory, a new
cooperative scheme for frequency band sensing is introduced for both AWGN and
fading channels. Unlike previous works in the field, the new scheme does not
require the knowledge of the noise statistics or its variance and is related to
the behavior of the largest and smallest eigenvalue of random matrices.
Remarkably, simulations show that the asymptotic claims hold even for a small
number of observations (which makes it convenient for time-varying topologies),
outperforming classical energy detection techniques.Comment: Submitted to International Symposium on Wireless Pervasive Computing
200
Power Allocation Games in Wireless Networks of Multi-antenna Terminals
We consider wireless networks that can be modeled by multiple access channels
in which all the terminals are equipped with multiple antennas. The propagation
model used to account for the effects of transmit and receive antenna
correlations is the unitary-invariant-unitary model, which is one of the most
general models available in the literature. In this context, we introduce and
analyze two resource allocation games. In both games, the mobile stations
selfishly choose their power allocation policies in order to maximize their
individual uplink transmission rates; in particular they can ignore some
specified centralized policies. In the first game considered, the base station
implements successive interference cancellation (SIC) and each mobile station
chooses his best space-time power allocation scheme; here, a coordination
mechanism is used to indicate to the users the order in which the receiver
applies SIC. In the second framework, the base station is assumed to implement
single-user decoding. For these two games a thorough analysis of the Nash
equilibrium is provided: the existence and uniqueness issues are addressed; the
corresponding power allocation policies are determined by exploiting random
matrix theory; the sum-rate efficiency of the equilibrium is studied
analytically in the low and high signal-to-noise ratio regimes and by
simulations in more typical scenarios. Simulations show that, in particular,
the sum-rate efficiency is high for the type of systems investigated and the
performance loss due to the use of the proposed suboptimum coordination
mechanism is very small
Quality-Of-Service Provisioning in Decentralized Networks: A Satisfaction Equilibrium Approach
This paper introduces a particular game formulation and its corresponding
notion of equilibrium, namely the satisfaction form (SF) and the satisfaction
equilibrium (SE). A game in SF models the case where players are uniquely
interested in the satisfaction of some individual performance constraints,
instead of individual performance optimization. Under this formulation, the
notion of equilibrium corresponds to the situation where all players can
simultaneously satisfy their individual constraints. The notion of SE, models
the problem of QoS provisioning in decentralized self-configuring networks.
Here, radio devices are satisfied if they are able to provide the requested
QoS. Within this framework, the concept of SE is formalized for both pure and
mixed strategies considering finite sets of players and actions. In both cases,
sufficient conditions for the existence and uniqueness of the SE are presented.
When multiple SE exist, we introduce the idea of effort or cost of satisfaction
and we propose a refinement of the SE, namely the efficient SE (ESE). At the
ESE, all players adopt the action which requires the lowest effort for
satisfaction. A learning method that allows radio devices to achieve a SE in
pure strategies in finite time and requiring only one-bit feedback is also
presented. Finally, a power control game in the interference channel is used to
highlight the advantages of modeling QoS problems following the notion of SE
rather than other equilibrium concepts, e.g., generalized Nash equilibrium.Comment: Article accepted for publication in IEEE Journal on Selected Topics
in Signal Processing, special issue in Game Theory in Signal Processing. 16
pages, 6 figure
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