3,928 research outputs found
Exact distributions of finite random matrices and their applications to spectrum sensing
The exact and simple distributions of finite random matrix theory (FRMT) are critically important for cognitive radio networks (CRNs). In this paper, we unify some existing distributions of the FRMT with the proposed coefficient matrices (vectors) and represent the distributions with the coefficient-based formulations. A coefficient reuse mechanism is studied, i.e., the same coefficient matrices (vectors) can be exploited to formulate different distributions. For instance, the same coefficient matrices can be used by the largest eigenvalue (LE) and the scaled largest eigenvalue (SLE); the same coefficient vectors can be used by the smallest eigenvalue (SE) and the Demmel condition number (DCN). A new and simple cumulative distribution function (CDF) of the DCN is also deduced. In particular, the dimension boundary between the infinite random matrix theory (IRMT) and the FRMT is initially defined. The dimension boundary provides a theoretical way to divide random matrices into infinite random matrices and finite random matrices. The FRMT-based spectrum sensing (SS) schemes are studied for CRNs. The SLE-based scheme can be considered as an asymptotically-optimal SS scheme when the dimension K is larger than two. Moreover, the standard condition number (SCN)-based scheme achieves the same sensing performance as the SLE-based scheme for dual covariance matrix [Formula: see text]. The simulation results verify that the coefficient-based distributions can fit the empirical results very well, and the FRMT-based schemes outperform the IRMT-based schemes and the conventional SS schemes
Exploiting Channel Memory for Multi-User Wireless Scheduling without Channel Measurement: Capacity Regions and Algorithms
We study the fundamental network capacity of a multi-user wireless downlink
under two assumptions: (1) Channels are not explicitly measured and thus
instantaneous states are unknown, (2) Channels are modeled as ON/OFF Markov
chains. This is an important network model to explore because channel probing
may be costly or infeasible in some contexts. In this case, we can use channel
memory with ACK/NACK feedback from previous transmissions to improve network
throughput. Computing in closed form the capacity region of this network is
difficult because it involves solving a high dimension partially observed
Markov decision problem. Instead, in this paper we construct an inner and outer
bound on the capacity region, showing that the bound is tight when the number
of users is large and the traffic is symmetric. For the case of heterogeneous
traffic and any number of users, we propose a simple queue-dependent policy
that can stabilize the network with any data rates strictly within the inner
capacity bound. The stability analysis uses a novel frame-based Lyapunov drift
argument. The outer-bound analysis uses stochastic coupling and state
aggregation to bound the performance of a restless bandit problem using a
related multi-armed bandit system. Our results are useful in cognitive radio
networks, opportunistic scheduling with delayed/uncertain channel state
information, and restless bandit problems.Comment: 17 pages, 8 figures. Submitted to IEEE Transactions on Information
Theory. The whole paper is revised and the title is changed for better
clarification
Energy-aware Sparse Sensing of Spatial-temporally Correlated Random Fields
This dissertation focuses on the development of theories and practices of energy aware sparse sensing schemes of random fields that are correlated in the space and/or time domains. The objective of sparse sensing is to reduce the number of sensing samples in the space and/or time domains, thus reduce the energy consumption and complexity of the sensing system. Both centralized and decentralized sensing schemes are considered in this dissertation.
Firstly we study the problem of energy efficient Level set estimation (LSE) of random fields correlated in time and/or space under a total power constraint. We consider uniform sampling schemes of a sensing system with a single sensor and a linear sensor network with sensors distributed uniformly on a line where sensors employ a fixed sampling rate to minimize the LSE error probability in the long term. The exact analytical cost functions and their respective upper bounds of these sampling schemes are developed by using an optimum thresholding-based LSE algorithm. The design parameters of these sampling schemes are optimized by minimizing their
respective cost functions. With the analytical results, we can identify the optimum sampling period and/or node distance that can minimize the LSE error probability.
Secondly we propose active sparse sensing schemes with LSE of a spatial-temporally correlated random field by using a limited number of spatially distributed sensors. In these schemes a central controller is designed to dynamically select a limited number of sensing locations according to the information revealed from past measurements,and the objective is to minimize the expected level set estimation error.The expected estimation error probability is explicitly expressed as a function of the selected sensing locations, and the results are used to formulate the optimal sensing location selection problem as a combinatorial problem. Two low complexity greedy algorithms are developed by using analytical upper bounds of the expected estimation error probability.
Lastly we study the distributed estimations of a spatially correlated random field with decentralized wireless sensor networks (WSNs).
We propose a distributed iterative estimation algorithm that defines the procedures for both information propagation and local estimation in each iteration. The key parameters of the algorithm, including an edge weight matrix and a sample weight matrix, are designed by following the asymptotically optimum criteria. It is shown that the asymptotically optimum performance can be achieved by distributively projecting the measurement samples into a subspace related to the covariance matrices of data and noise samples
Cellular Interference Alignment
Interference alignment promises that, in Gaussian interference channels, each
link can support half of a degree of freedom (DoF) per pair of transmit-receive
antennas. However, in general, this result requires to precode the data bearing
signals over a signal space of asymptotically large diversity, e.g., over an
infinite number of dimensions for time-frequency varying fading channels, or
over an infinite number of rationally independent signal levels, in the case of
time-frequency invariant channels. In this work we consider a wireless cellular
system scenario where the promised optimal DoFs are achieved with linear
precoding in one-shot (i.e., over a single time-frequency slot). We focus on
the uplink of a symmetric cellular system, where each cell is split into three
sectors with orthogonal intra-sector multiple access. In our model,
interference is "local", i.e., it is due to transmitters in neighboring cells
only. We consider a message-passing backhaul network architecture, in which
nearby sectors can exchange already decoded messages and propose an alignment
solution that can achieve the optimal DoFs. To avoid signaling schemes relying
on the strength of interference, we further introduce the notion of
\emph{topologically robust} schemes, which are able to guarantee a minimum rate
(or DoFs) irrespectively of the strength of the interfering links. Towards this
end, we design an alignment scheme which is topologically robust and still
achieves the same optimum DoFs
Temporal connectivity in finite networks with non-uniform measures
Soft Random Geometric Graphs (SRGGs) have been widely applied to various
models including those of wireless sensor, communication, social and neural
networks. SRGGs are constructed by randomly placing nodes in some space and
making pairwise links probabilistically using a connection function that is
system specific and usually decays with distance. In this paper we focus on the
application of SRGGs to wireless communication networks where information is
relayed in a multi hop fashion, although the analysis is more general and can
be applied elsewhere by using different distributions of nodes and/or
connection functions. We adopt a general non-uniform density which can model
the stationary distribution of different mobility models, with the interesting
case being when the density goes to zero along the boundaries. The global
connectivity properties of these non-uniform networks are likely to be
determined by highly isolated nodes, where isolation can be caused by the
spatial distribution or the local geometry (boundaries). We extend the analysis
to temporal-spatial networks where we fix the underlying non-uniform
distribution of points and the dynamics are caused by the temporal variations
in the link set, and explore the probability a node near the corner is isolated
at time . This work allows for insight into how non-uniformity (caused by
mobility) and boundaries impact the connectivity features of temporal-spatial
networks. We provide a simple method for approximating these probabilities for
a range of different connection functions and verify them against simulations.
Boundary nodes are numerically shown to dominate the connectivity properties of
these finite networks with non-uniform measure.Comment: 13 Pages - 4 figure
Percolation and Connectivity in the Intrinsically Secure Communications Graph
The ability to exchange secret information is critical to many commercial,
governmental, and military networks. The intrinsically secure communications
graph (iS-graph) is a random graph which describes the connections that can be
securely established over a large-scale network, by exploiting the physical
properties of the wireless medium. This paper aims to characterize the global
properties of the iS-graph in terms of: (i) percolation on the infinite plane,
and (ii) full connectivity on a finite region. First, for the Poisson iS-graph
defined on the infinite plane, the existence of a phase transition is proven,
whereby an unbounded component of connected nodes suddenly arises as the
density of legitimate nodes is increased. This shows that long-range secure
communication is still possible in the presence of eavesdroppers. Second, full
connectivity on a finite region of the Poisson iS-graph is considered. The
exact asymptotic behavior of full connectivity in the limit of a large density
of legitimate nodes is characterized. Then, simple, explicit expressions are
derived in order to closely approximate the probability of full connectivity
for a finite density of legitimate nodes. The results help clarify how the
presence of eavesdroppers can compromise long-range secure communication.Comment: Submitted for journal publicatio
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