Distributed Sampling for Dense Sensor Networks: A “Bit-Conservation Principle”
We address the problem of deterministic oversampling of bandlimited sensor fields in a distributed communication-constrained processing environment, where it is desired for a central intelligent unit to reconstruct the sensor field to maximum pointwise accuracy. We show, using a dither-based sampling scheme, that is is possible to accomplish this using minimal inter-sensor communication with the aid of a multitude of low-precision sensors. Furthermore, we show the feasibility of having a flexible tradeoff between the average oversampling rate and the Analog to Digital (A/D) quantization precision per sensor sample with respect to achieving exponential accuracy in the number of bits per Nyquist-period, thereby exposing a key underpinning “conservation of bits” principle. That is, we can distribute the bit budget per Nyquist-period along the amplitude-axis (precision of A/D converter) and space (or time or space-time) using oversampling in an almost arbitrary discrete-valued manner, while retaining the same reconstruction error decay profile. Interestingly this oversampling is possible in a highly localized communication setting, with only nearest-neighbor communication, making it very attractive for dense sensor networks operating under stringent inter-node communication constraints. Finally we show how our scheme incorporates security as a by-product due to the presence of an underlying dither signal which can be used as a natural encryption device for security. The choice of the dither function enhances the security of the network.
Unable to display preview. Download preview PDF.
- 1.R. J. Marks, II, Introduction to Shannon Sampling and Interpolation Theory. New York, USA: Springer-Verlag, 1990.Google Scholar
- 2.J. Chou, D. Petrovic, and K. Ramchandran, “Tracking and exploiting correlations in dense sensor networks,” in Asilomar Conference on Signals, Systems and Computers, (Pacific Grove, CA), Nov 2002.Google Scholar
- 3.Z. Cvetković and M. Vetterli, “Error-rate Characteristics of Oversampled Analog-to-Digital Conversion,” IEEE Trans. on Information Theory, vol. 44, pp. 1961–1964, Sep 1998.Google Scholar
- 5.Z. Cvetković and I. Daubechies, “Single Bit oversampled A/D conversion with exponential accuracy in bit rate,” Proceeding DCC, pp. 343–352, March 2000.Google Scholar
- 6.Z. Cvetković, I. Daubechies, and B. F. Logan, “Interpolation of Bandlimited functions from quantized Irregular Samples,” Proceeding DCC, pp. 412–421, April 2002.Google Scholar
- 8.G. H. Hardy, J. E. Littlewood, and G. Polya, Inequalities. London, UK: Cambridge University Press, 1959.Google Scholar
- 9.M. Vetterli, P. Marzilliano, and T. Blu, “Sampling Signals with Finite Rate of Innovation,” IEEE Trans. Signal Proc., pp. 1417–1428, June 2002.Google Scholar
- 10.P. Gupta and P. R. Kumar, “The Capacity of Wireless Networks,” IEEE Trans. on Information Theory, vol. IT-46, pp. 388–404, Mar. 2000.Google Scholar