Abstract
Probability density function (pdf) of the received signal is necessary for the distributed detection fusion when the unreliable channels between the local sensors and the fusion center are considered. Hitherto study has never been made on the statistical distribution of the demodulated OFDM signal over multipath fading channel. Modeling the OFDM system over the multi-path channel, we derived the pdf of the channel frequency domain impulse response by introducing the characteristic function. And the pdf of the demodulated OFDM signal on the receiver side is deduced based on the theory of spherically symmetric random vectors. In addition, an example of OFDM-based distributed detection fusion is presented to illustrate the application of the derived pdf. Simulations show that the fusion with signal statistic information generally does better than fusion without any signal statistic information, and achieves the same performance as the fusion with perfect channel state information if the channel signal-to-noise ratio is above 7 dB.
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B. Chen, L. Tong, and P. Varshney, “Channel-aware distributed detection in wireless sensor networks,” IEEE Signal Processing Magazine, vol. 23, no. 4, pp. 16–26, Jul. 2006.
H. R. Ahmadi and A. Vosoughi, “Impact of wireless channel uncertainty upon distributed detection system,” IEEE Transactions on Wireless Communications, vol. 12, no. 6, pp. 2566–2577, Jun. 2013.
Y. Yilmaz, G. V. Moustakides, and X. Wang, “Channel-aware decentralized detection via level-triggered sampling,” IEEE Transactions on Signal Processing, vol. 61, no. 2, pp. 300–315, Jan. 2013.
D. Ciuonzo, P. S. Rossi, and S. Dey, “Massive mimo channel-aware decision fusion,” IEEE Transactions on Signal Processing, vol. 63, no. 3, pp. 604–619, Feb. 2015.
B. Chen, R. Jiang, T. Kasetkasem, and P. Varshney, “Channel aware decision fusion in wireless sensor networks,” IEEE Transactions on Signal Processing, vol. 52, no. 12, pp. 3454–3458, 2004.
H. Mahmoud, T. Yucek, and H. Arslan, “OFDM for cognitive radio: merits and challenges,” IEEE Wireless Communications, vol. 16, no. 2, pp. 6–14, 2009.
C. R. Berger, B. Demissie, J. Heckenbach, P. Willett, and S. Zhou, “Signal processing for passive radar using OFDM waveforms,” IEEE Journal of Selected Topics in Signal Processing, vol. 4, no. 1, pp. 226–238, Feb. 2010.
S. Sen and A. Nehorai, “Adaptive OFDM radar for target detection in multipath scenarios,” IEEE Transactions on Signal Processing, vol. 59, no. 1, pp. 78–90, Jan 2011.
C. Sturm and W. Wiesbeck, “Waveform design and signal processing aspects for fusion of wireless communications and radar sensing,” Proceedings of the IEEE, vol. 99, no. 7, pp. 1236–1259, Jul. 2011.
R. F. Tigrek, W. De Heij, and P. V. Genderen, “OFDM Signals as the Radar Waveform to Solve Doppler Ambiguity,” IEEE Transactions On Aerospace And Electronic Systems, vol. 48, no. 1, pp. 130–143, Jan. 2012.
N. Nguyen-Thanh and I. Koo, “Optimal truncated ordered sequential cooperative spectrum sensing in cognitive radio,” IEEE Sensors Journal, vol. 13, no. 11, pp. 4188–4195, Nov. 2013.
S. Bokharaiee, H. H. Nguyen, and E. Shwedyk, “Blind spectrum sensing for ofdm-based cognitive radio systems,” IEEE Transactions on Vehicular Technology, vol. 60, no. 3, pp. 858–871, March 2011.
T. Weiss, J. Hillenbrand, A. Krohn, and F. K. Jondral, “Efficient signaling of spectral resources in spectrum pooling systems,” in SCVT, 2003, pp. 1–6.
R. Xu, M. Chen, J. Zhang, H. Wang, and W. Yu, “Report the sensing results using ofdma in cooperative spectrum sensing,” in 2010 International Conference on Wireless Communications and Signal Processing. Suzhou, China: IEEE, Oct. 21–23 2010, pp. 1–5.
W. Zhang and K. B. Letaief, “Cooperative spectrum sensing with transmit and relay diversity in cognitive radio networks,” IEEE Transaction on Wireless Communications, vol. 12, no. 7, pp. 4761–4766, Jul 2008.
R. Niu, B. Chen, and P. Varshney, “Fusion of decisions transmitted over Rayleigh fading channels in wireless sensor networks,” IEEE Transactions on Signal Processing, vol. 54, no. 3, pp. 1018–1027, Mar. 2006.
M.-S. Alouini and A. J. Goldsmith, “A unified approach for calculating error rates of linearly modulated signals over generalized fading channels,” IEEE Transactions on Communications, vol. 47, no. 9, pp. 1324–1334, Sep. 1999.
M. K. Simon and M.-S. Alouini, “A unified approach to the performance analysis of digital communication over generalized fading channels,” Proceedings of the IEEE, vol. 86, no. 9, pp. 1860–1877, Sep. 1998.
Z. Du, J. Chen, and N. C. Beaulieu, “Error Rate of OFDM Signals on Frequency Selective Nakagami-m Fading Channels,” in IEEE Global Telecommunications Conference, GLOBECOM’04. Dallas, Texas: IEEE, 29 Nov.–3 Dec. 2004, pp. 3994–3998.
Y.-P. Lin and S.-M. Phoong, “Window designs for DFT-based multicarrier systems,” IEEE Transactions on Signal Processing, vol. 53, no. 3, pp. 1015–1024, Mar. 2005.
A. Papoulis, Probability, Random Variables, and Stochastic Processes, 3rd ed. New York: McGraw-Hill, 1991.
M. Abramowitz and I. A. Stegun, Eds., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th ed. New York: Dover, 1970.
J. Goldman, “Detection in the presence of spherically symmetric random vectors,” IEEE Transaction on Information Theory, vol. 22, no. 1, pp. 52–59, Jan. 1976.
Acknowledgments
This work is supported by National Nature Science Foundation of China (Nos. 61201217, 61371124), and China Postdoctoral Science Foundation Grant (Nos. 2012M512085, 2013T60911). This paper was presented in part at WCSP 2010 and WCSP 2011.
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Xu, R. Density Function of the Received Signal in OFDM-based Distributed Detection Fusion System. Int J Wireless Inf Networks 22, 357–368 (2015). https://doi.org/10.1007/s10776-015-0281-0
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DOI: https://doi.org/10.1007/s10776-015-0281-0