3,625 research outputs found
Power-bandwidth-distortion scaling laws for sensor networks
The goal of a class of sensor networks is to monitor an underlying physical reality at the highest possible fidelity. Sensors acquire noisy measurements and have to communicate them over a power- and possibly bandwidth-constrained interference channel to a set of base stations. The goal of this paper is to analyze, as a function of the number of sensors, the trade-offs between the degrees of freedom of the underlying physical reality, the communication resources (power, temporal and spatial bandwidth), and the resulting distortion at which the physical reality can be estimated by the base stations. The distortion can be expressed as the sum of two fundamentally different terms. The first term reflects the fact that the measurements are noisy. It depends on the number of sensors and on their locations, but it cannot be influenced by the communication resources. The second contribution to the distortion can be controlled by the communication resources, and the key question becomes: What resources are necessary to make it decay at least as fast as the first distortion term, as a function of the number of sensors? This question is answered threefold: First, a lower bound to the power-bandwidth trade-o is derived, showing that at least a constant to linearly increasing total power is required for typical cases (as a function of M). But is this also sufficient? In the second answer, communication strategies are considered where each sensor applies the best possible distributed compression algorithm, followed by capacity-achieving channel codes. For such a separation strategy, it is shown for typical cases that the power must increase exponentially as a function of the number of sensors, suggesting that the lower bound derived in this paper is far too optimistic. However, in the third answer, it is shown that this is not the case: For some example scenarios, the power requirements of the lower bound are indeed achievable, but joint source-channel coding is required. Finally, the problem of sensor synchronization is considered, and it is shown that the scaling laws derived in this paper continue to hold under a Rician fading model
High-resolution distributed sampling of bandlimited fields with low-precision sensors
The problem of sampling a discrete-time sequence of spatially bandlimited
fields with a bounded dynamic range, in a distributed,
communication-constrained, processing environment is addressed. A central unit,
having access to the data gathered by a dense network of fixed-precision
sensors, operating under stringent inter-node communication constraints, is
required to reconstruct the field snapshots to maximum accuracy. Both
deterministic and stochastic field models are considered. For stochastic
fields, results are established in the almost-sure sense. The feasibility of
having a flexible tradeoff between the oversampling rate (sensor density) and
the analog-to-digital converter (ADC) precision, while achieving an exponential
accuracy in the number of bits per Nyquist-interval per snapshot is
demonstrated. This exposes an underlying ``conservation of bits'' principle:
the bit-budget per Nyquist-interval per snapshot (the rate) can be distributed
along the amplitude axis (sensor-precision) and space (sensor density) in an
almost arbitrary discrete-valued manner, while retaining the same (exponential)
distortion-rate characteristics. Achievable information scaling laws for field
reconstruction over a bounded region are also derived: With N one-bit sensors
per Nyquist-interval, Nyquist-intervals, and total network
bitrate (per-sensor bitrate ), the maximum pointwise distortion goes to zero as
or . This is shown to be possible
with only nearest-neighbor communication, distributed coding, and appropriate
interpolation algorithms. For a fixed, nonzero target distortion, the number of
fixed-precision sensors and the network rate needed is always finite.Comment: 17 pages, 6 figures; paper withdrawn from IEEE Transactions on Signal
Processing and re-submitted to the IEEE Transactions on Information Theor
Estimation in Phase-Shift and Forward Wireless Sensor Networks
We consider a network of single-antenna sensors that observe an unknown
deterministic parameter. Each sensor applies a phase shift to the observation
and the sensors simultaneously transmit the result to a multi-antenna fusion
center (FC). Based on its knowledge of the wireless channel to the sensors, the
FC calculates values for the phase factors that minimize the variance of the
parameter estimate, and feeds this information back to the sensors. The use of
a phase-shift-only transmission scheme provides a simplified analog
implementation at the sensor, and also leads to a simpler algorithm design and
performance analysis. We propose two algorithms for this problem, a numerical
solution based on a relaxed semidefinite programming problem, and a closed-form
solution based on the analytic constant modulus algorithm. Both approaches are
shown to provide performance close to the theoretical bound. We derive
asymptotic performance analyses for cases involving large numbers of sensors or
large numbers of FC antennas, and we also study the impact of phase errors at
the sensor transmitters. Finally, we consider the sensor selection problem, in
which only a subset of the sensors is chosen to send their observations to the
FC.Comment: 28 pages, 5 figures, accepted by IEEE Transactions on Signal
Processing, Apr. 201
Sensing Capacity for Markov Random Fields
This paper computes the sensing capacity of a sensor network, with sensors of
limited range, sensing a two-dimensional Markov random field, by modeling the
sensing operation as an encoder. Sensor observations are dependent across
sensors, and the sensor network output across different states of the
environment is neither identically nor independently distributed. Using a
random coding argument, based on the theory of types, we prove a lower bound on
the sensing capacity of the network, which characterizes the ability of the
sensor network to distinguish among environments with Markov structure, to
within a desired accuracy.Comment: To appear in the proceedings of the 2005 IEEE International Symposium
on Information Theory, Adelaide, Australia, September 4-9, 200
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