24 research outputs found
Scaling Laws of Cognitive Networks
We consider a cognitive network consisting of n random pairs of cognitive
transmitters and receivers communicating simultaneously in the presence of
multiple primary users. Of interest is how the maximum throughput achieved by
the cognitive users scales with n. Furthermore, how far these users must be
from a primary user to guarantee a given primary outage. Two scenarios are
considered for the network scaling law: (i) when each cognitive transmitter
uses constant power to communicate with a cognitive receiver at a bounded
distance away, and (ii) when each cognitive transmitter scales its power
according to the distance to a considered primary user, allowing the cognitive
transmitter-receiver distances to grow. Using single-hop transmission, suitable
for cognitive devices of opportunistic nature, we show that, in both scenarios,
with path loss larger than 2, the cognitive network throughput scales linearly
with the number of cognitive users. We then explore the radius of a primary
exclusive region void of cognitive transmitters. We obtain bounds on this
radius for a given primary outage constraint. These bounds can help in the
design of a primary network with exclusive regions, outside of which cognitive
users may transmit freely. Our results show that opportunistic secondary
spectrum access using single-hop transmission is promising.Comment: significantly revised and extended, 30 pages, 13 figures, submitted
to IEEE Journal of Special Topics in Signal Processin
Information Theoretic Operating Regimes of Large Wireless Networks
In analyzing the point-to-point wireless channel, insights about two
qualitatively different operating regimes--bandwidth- and power-limited--have
proven indispensable in the design of good communication schemes. In this
paper, we propose a new scaling law formulation for wireless networks that
allows us to develop a theory that is analogous to the point-to-point case. We
identify fundamental operating regimes of wireless networks and derive
architectural guidelines for the design of optimal schemes.
Our analysis shows that in a given wireless network with arbitrary size,
area, power, bandwidth, etc., there are three parameters of importance: the
short-distance SNR, the long-distance SNR, and the power path loss exponent of
the environment. Depending on these parameters we identify four qualitatively
different regimes. One of these regimes is especially interesting since it is
fundamentally a consequence of the heterogeneous nature of links in a network
and does not occur in the point-to-point case; the network capacity is {\em
both} power and bandwidth limited. This regime has thus far remained hidden due
to the limitations of the existing formulation. Existing schemes, either
multihop transmission or hierarchical cooperation, fail to achieve capacity in
this regime; we propose a new hybrid scheme that achieves capacity.Comment: 12 pages, 5 figures, to appear in IEEE Transactions on Information
Theor
Exact Capacity Scaling of Extended Wireless Networks
n source and destination pairs randomly located in an area extending linearly with n want to communicate with each other. Signals transmitted from one user to another at distance r apart are subject to a power attenuation of r^{-alpha} and random phase changes. Classical multihop architectures that decode and forward packets can deliver a sqrt{n}-scaling of the aggregate throughput, while recently proposed hierarchical cooperation achieves n^{2-alpha/2}-scaling, which is superior to multi-hop for alpha4, while the moderate-attenuation regime (2 2. Our result shows that the mentioned schemes are scaling-optimal, namely that no other scheme can beat hierarchical cooperation when alpha 3. The key ingredient is a careful evaluation of the scaling of the cut-set bound
Throughput Scaling of Wireless Networks With Random Connections
This work studies the throughput scaling laws of ad hoc wireless networks in
the limit of a large number of nodes. A random connections model is assumed in
which the channel connections between the nodes are drawn independently from a
common distribution. Transmitting nodes are subject to an on-off strategy, and
receiving nodes employ conventional single-user decoding. The following results
are proven:
1) For a class of connection models with finite mean and variance, the
throughput scaling is upper-bounded by for single-hop schemes, and
for two-hop (and multihop) schemes.
2) The throughput scaling is achievable for a specific
connection model by a two-hop opportunistic relaying scheme, which employs
full, but only local channel state information (CSI) at the receivers, and
partial CSI at the transmitters.
3) By relaxing the constraints of finite mean and variance of the connection
model, linear throughput scaling is achievable with Pareto-type
fading models.Comment: 13 pages, 4 figures, To appear in IEEE Transactions on Information
Theor
Fundamentals of Large Sensor Networks: Connectivity, Capacity, Clocks and Computation
Sensor networks potentially feature large numbers of nodes that can sense
their environment over time, communicate with each other over a wireless
network, and process information. They differ from data networks in that the
network as a whole may be designed for a specific application. We study the
theoretical foundations of such large scale sensor networks, addressing four
fundamental issues- connectivity, capacity, clocks and function computation.
To begin with, a sensor network must be connected so that information can
indeed be exchanged between nodes. The connectivity graph of an ad-hoc network
is modeled as a random graph and the critical range for asymptotic connectivity
is determined, as well as the critical number of neighbors that a node needs to
connect to. Next, given connectivity, we address the issue of how much data can
be transported over the sensor network. We present fundamental bounds on
capacity under several models, as well as architectural implications for how
wireless communication should be organized.
Temporal information is important both for the applications of sensor
networks as well as their operation.We present fundamental bounds on the
synchronizability of clocks in networks, and also present and analyze
algorithms for clock synchronization. Finally we turn to the issue of gathering
relevant information, that sensor networks are designed to do. One needs to
study optimal strategies for in-network aggregation of data, in order to
reliably compute a composite function of sensor measurements, as well as the
complexity of doing so. We address the issue of how such computation can be
performed efficiently in a sensor network and the algorithms for doing so, for
some classes of functions.Comment: 10 pages, 3 figures, Submitted to the Proceedings of the IEE