The impact of quasi-equally spaced sensor topologies on signal reconstruction

A wireless sensor network with randomly deployed nodes can be used to provide an irregular sampling of a physical field of interest. We assume that a sink node collects the data gathered by the sensors and uses a linear filter for the reconstruction of a bandlimited scalar field defined over a d-dimensional domain. Sensors' locations are assumed to be known at the sink node, up to a certain position error. We then take the mean square error (MSE) of the reconstructed field as performance metric, and evaluate the effect of both uniform and quasi-equally spaced sensor layouts on the quality of the reconstructed field. We define a parameter that provides a measure of the regularity of the sensors deployment, and, through asymptotic analysis, we derive the MSE in the case of different sensor spatial distributions. For two of them, an approximate closed form expression is obtained. We validate our analysis through numerical results, and we show that an excellent match exists between analysis and simulation even for a small number of sensors.

[1]  Peter G. Casazza,et al.  Perturbation of Regular Sampling in Shift-Invariant Spaces for Frames , 2006, IEEE Transactions on Information Theory.

[2]  Martin Vetterli,et al.  Reconstruction of irregularly sampled discrete-time bandlimited signals with unknown sampling locations , 2000, IEEE Trans. Signal Process..

[3]  Özgür B. Akan,et al.  Spatio-temporal correlation: theory and applications for wireless sensor networks , 2004, Comput. Networks.

[4]  A. Rahimi,et al.  Simultaneous localization, calibration, and tracking in an ad hoc sensor network , 2006, 2006 5th International Conference on Information Processing in Sensor Networks.

[5]  Martin Vetterli,et al.  On the optimal density for real-time data gathering of spatio-temporal processes in sensor networks , 2005, IPSN 2005. Fourth International Symposium on Information Processing in Sensor Networks, 2005..

[6]  Emanuele Viterbo,et al.  Performance of Linear Field Reconstruction Techniques With Noise and Uncertain Sensor Locations , 2007, IEEE Transactions on Signal Processing.

[7]  B. Liu,et al.  Error bounds for jittered sampling , 1965 .

[8]  Benhong Zhang,et al.  Parametric Signal Estimation Using Sensor Networks in the Presence of Node Localization Errors , 2005, Conference Record of the Thirty-Ninth Asilomar Conference onSignals, Systems and Computers, 2005..

[9]  B. Hofmann-Wellenhof,et al.  Introduction to spectral analysis , 1986 .

[10]  H. Vincent Poor,et al.  Sensor configuration and activation for field detection in large sensor arrays , 2005, IPSN 2005. Fourth International Symposium on Information Processing in Sensor Networks, 2005..

[11]  Antonia Maria Tulino,et al.  Random Matrix Theory and Wireless Communications , 2004, Found. Trends Commun. Inf. Theory.

[12]  Ian F. Akyildiz,et al.  Wireless sensor networks: a survey , 2002, Comput. Networks.

[13]  Lang Tong,et al.  Impact of Data Retrieval Pattern on Homogeneous Signal Field Reconstruction in Dense Sensor Networks , 2006, IEEE Transactions on Signal Processing.

[14]  Deborah Estrin,et al.  Coping with irregular spatio-temporal sampling in sensor networks , 2004, CCRV.

[15]  R. Daley Atmospheric Data Analysis , 1991 .

[16]  F. Marvasti Nonuniform sampling : theory and practice , 2001 .

[17]  S. Kay Fundamentals of statistical signal processing: estimation theory , 1993 .

[18]  T. Strohmer,et al.  Efficient numerical methods in non-uniform sampling theory , 1995 .

[19]  S. Smale,et al.  Shannon sampling and function reconstruction from point values , 2004 .

[20]  Emanuele Viterbo,et al.  Bandlimited Field Reconstruction for Wireless Sensor Networks , 2007, ArXiv.

[21]  H. Rauhut Random Sampling of Sparse Trigonometric Polynomials , 2005, math/0512642.

[22]  Pradeep K. Khosla,et al.  Sensing capacity for discrete sensor network applications , 2005, IPSN 2005. Fourth International Symposium on Information Processing in Sensor Networks, 2005..

[23]  Giuseppe Caire,et al.  Successive interference cancellation with SISO decoding and EM channel estimation , 2001, IEEE Journal on Selected Areas in Communications.

[24]  Thomas Strohmer,et al.  How to recover smooth object boundaries in noisy medical images , 1996, Proceedings of 3rd IEEE International Conference on Image Processing.

[25]  Petre Stoica,et al.  Introduction to spectral analysis , 1997 .

[26]  Ying Zhang,et al.  Robust distributed node localization with error management , 2006, MobiHoc '06.

[27]  H. Feichtinger,et al.  Error analysis in regular and irregular sampling theory , 1993 .

[28]  David G. Long,et al.  Image reconstruction and enhanced resolution imaging from irregular samples , 2001, IEEE Trans. Geosci. Remote. Sens..

[29]  David C. Moore,et al.  Robust distributed network localization with noisy range measurements , 2004, SenSys '04.