Time-delay estimation from low-rate samples: a union of subspaces approach

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 tra...

• Type: Journal
• Year: 2010
• Where: TSP
• Authors: Kfir Gedalyahu, Yonina C. Eldar
• Keywords: Artificial Intelligence, Infinite Union, Low-rate Samples, Possible Rate, TSP 2010