LCMV Beamforming for a Novel Wireless Local Positioning System: Nonstationarity and Cyclostationarity Analysis
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Research Article LCMV Beamforming for a Novel Wireless Local Positioning System: Nonstationarity and Cyclostationarity Analysis Hui Tong, Jafar Pourrostam, and Seyed A. Zekavat Department of Electrical and Computer Engineering, Michigan Technological University, 1400 Townsend Drive, Houghton, MI 49931, USA Received 24 June 2006; Revised 29 January 2007; Accepted 21 May 2007 Recommended by Kostas Berberidis This paper investigates the implementation of a novel wireless local positioning system (WLPS). WLPS main components are: (a) a dynamic base station (DBS) and (b) a transponder, both mounted on mobiles. The DBS periodically transmits ID request signals. As soon as the transponder detects the ID request signal, it sends its ID (a signal with a limited duration) back to the DBS. Hence, the DBS receives noncontinuous signals periodically transmitted by the transponder. The noncontinuous nature of the WLPS leads to nonstationary received signals at the DBS receiver, while the periodic signal structure leads to the fact that the DBS received signal is also cyclostationary. This work discusses the implementation of linear constrained minimum variance (LCMV) beamforming at the DBS receiver. We demonstrate that the nonstationarity of the received signal causes the sample covariance to be an inaccurate estimate of the true signal covariance. The errors in this covariance estimate limit the applicability of LCMV beamforming. A modified covariance matrix estimator, which exploits the cyclostationarity property of WLPS system is introduced to solve the nonstationarity problem. The cyclostationarity property is discussed in detail theoretically and via simulations. It is shown that the modified covariance matrix estimator significantly improves the DBS performance. The proposed technique can be applied to periodic-sense signaling structures such as the WLPS, RFID, and reactive sensor networks. Copyright © 2007 Hui Tong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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INTRODUCTION
This paper investigates how to implement optimal beamforming for a novel wireless local positioning system (WLPS). We focus on how to estimate covariance matrix for optimal beamforming, because the specific signaling scheme in this WLPS, that is, cyclostationarity, enables a novel covariance matrix estimator. The WLPS consists of two main components [1]: a dynamic base station (DBS) and a transponder (or possibly a number of transponders), all mounted on mobiles. The DBS periodically transmits ID request signals (a short burst of energy). Each time a transponder detects the ID request signal, it sends its unique ID (a signal with a limited duration) back to the DBS. In the WLPS, the DBS detects and tracks the positions and IDs of the transponders in its coverage area. The position of a transponder is determined by the combination of time-of-arrival (TOA) and direction-of-arr
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