81,491 research outputs found
Near-Optimal Source Placement for Linear Physical Fields
In real-word applications, signal processing is often used to measure and control a physical field by means of sensors and sources, respectively. An aspect that has been often neglected is the optimization of the sources' locations. In this work, we discuss the source placement problem as the dual of the sensor placement problem and propose two polynomial-time algorithms, for scenarios with or without noise. Both algorithms are near-optimal and indicate the possibility to make the control of such physical fields easier, more efficient and stabler to noise
Judiciously distributing laser emitters to shape the desired far field patterns
The far-field pattern of a simple one-dimensional laser array of emitters
radiating into free space is considered. In the path of investigating the
inverse problem for their near fields leading to a target beam form,
surprisingly we found that the result is successful when the matrix of the
corresponding linear system is not well-scaled. The essence of our numerical
observations is captured by an elegant inequality defining the functional range
of the optical distance between two neighboring emitters. Our finding can
restrict substantially the parametric space of integrated photonic systems and
simplify significantly the subsequent optimizations
Deploy-As-You-Go Wireless Relay Placement: An Optimal Sequential Decision Approach using the Multi-Relay Channel Model
We use information theoretic achievable rate formulas for the multi-relay
channel to study the problem of as-you-go deployment of relay nodes. The
achievable rate formulas are for full-duplex radios at the relays and for
decode-and-forward relaying. Deployment is done along the straight line joining
a source node and a sink node at an unknown distance from the source. The
problem is for a deployment agent to walk from the source to the sink,
deploying relays as he walks, given that the distance to the sink is
exponentially distributed with known mean. As a precursor, we apply the
multi-relay channel achievable rate formula to obtain the optimal power
allocation to relays placed along a line, at fixed locations. This permits us
to obtain the optimal placement of a given number of nodes when the distance
between the source and sink is given. Numerical work suggests that, at low
attenuation, the relays are mostly clustered near the source in order to be
able to cooperate, whereas at high attenuation they are uniformly placed and
work as repeaters. We also prove that the effect of path-loss can be entirely
mitigated if a large enough number of relays are placed uniformly between the
source and the sink. The structure of the optimal power allocation for a given
placement of the nodes, then motivates us to formulate the problem of as-you-go
placement of relays along a line of exponentially distributed length, and with
the exponential path-loss model, so as to minimize a cost function that is
additive over hops. The hop cost trades off a capacity limiting term, motivated
from the optimal power allocation solution, against the cost of adding a relay
node. We formulate the problem as a total cost Markov decision process,
establish results for the value function, and provide insights into the
placement policy and the performance of the deployed network via numerical
exploration.Comment: 21 pages. arXiv admin note: substantial text overlap with
arXiv:1204.432
One-bit Distributed Sensing and Coding for Field Estimation in Sensor Networks
This paper formulates and studies a general distributed field reconstruction
problem using a dense network of noisy one-bit randomized scalar quantizers in
the presence of additive observation noise of unknown distribution. A
constructive quantization, coding, and field reconstruction scheme is developed
and an upper-bound to the associated mean squared error (MSE) at any point and
any snapshot is derived in terms of the local spatio-temporal smoothness
properties of the underlying field. It is shown that when the noise, sensor
placement pattern, and the sensor schedule satisfy certain weak technical
requirements, it is possible to drive the MSE to zero with increasing sensor
density at points of field continuity while ensuring that the per-sensor
bitrate and sensing-related network overhead rate simultaneously go to zero.
The proposed scheme achieves the order-optimal MSE versus sensor density
scaling behavior for the class of spatially constant spatio-temporal fields.Comment: Fixed typos, otherwise same as V2. 27 pages (in one column review
format), 4 figures. Submitted to IEEE Transactions on Signal Processing.
Current version is updated for journal submission: revised author list,
modified formulation and framework. Previous version appeared in Proceedings
of Allerton Conference On Communication, Control, and Computing 200
- …