DocumentCode :
1425692
Title :
Time-Delay Estimation From Low-Rate Samples: A Union of Subspaces Approach
Author :
Gedalyahu, Kfir ; Eldar, Yonina C.
Author_Institution :
Dept. of Electr. Eng., Technion - Israel Inst. of Technol., Haifa, Israel
Volume :
58
Issue :
6
fYear :
2010
fDate :
6/1/2010 12:00:00 AM
Firstpage :
3017
Lastpage :
3031
Abstract :
Time-delay estimation arises in many applications in which a multipath medium has to be identified from pulses transmitted through the channel. Previous methods for time delay recovery either operate on the analog received signal, or require sampling at the Nyquist rate of the transmitted pulse. In this paper, we develop a unified approach to time delay estimation from low-rate samples. This problem can be formulated in the broader context of sampling over an infinite union of subspaces. Although sampling over unions of subspaces has been receiving growing interest, previous results either focus on unions of finite-dimensional subspaces, or finite unions. The framework we develop here leads to perfect recovery of the multipath delays from samples of the channel output at the lowest possible rate, even in the presence of overlapping transmitted pulses, and allows for a variety of different sampling methods. The sampling rate depends only on the number of multipath components and the transmission rate, but not on the bandwidth of the probing signal. This result can be viewed as a sampling theorem over an infinite union of infinite dimensional subspaces. By properly manipulating the low-rate samples, we show that the time delays can be recovered using the well-known ESPRIT algorithm. Combining results from sampling theory with those obtained in the context of direction of arrival estimation, we develop sufficient conditions on the transmitted pulse and the sampling functions in order to ensure perfect recovery of the channel parameters at the minimal possible rate.
Keywords :
direction-of-arrival estimation; signal sampling; ESPRIT algorithm; Nyquist rate; analog received signal; direction of arrival estimation; finite-dimensional subspaces; low-rate samples; multipath delays; sampling methods; sampling theory; time delay recovery; time-delay estimation; Sub-Nyquist sampling; time-delay estimation; union of subspaces;
fLanguage :
English
Journal_Title :
Signal Processing, IEEE Transactions on
Publisher :
ieee
ISSN :
1053-587X
Type :
jour
DOI :
10.1109/TSP.2010.2044253
Filename :
5419949
Link To Document :
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