Toeplitz Compressed Sensing Matrices With Applications to Sparse Channel Estimation

Compressed sensing (CS) has recently emerged as a powerful signal acquisition paradigm. In essence, CS enables the recovery of high-dimensional sparse signals from relatively few linear observations in the form of projections onto a collection of test vectors. Existing results show that if the entries of the test vectors are independent realizations of certain zero-mean random variables, then with high probability the unknown signals can be recovered by solving a tractable convex optimization. This work extends CS theory to settings where the entries of the test vectors exhibit structured statistical dependencies. It follows that CS can be effectively utilized in linear, time-invariant system identification problems provided the impulse response of the system is (approximately or exactly) sparse. An immediate application is in wireless multipath channel estimation. It is shown here that time-domain probing of a multipath channel with a random binary sequence, along with utilization of...

• Type: Journal
• Year: 2010
• Where: TIT
• Authors: Jarvis Haupt, Waheed Uz Zaman Bajwa, Gil M. Raz, Robert Nowak
• Keywords: Education, Multipath Channel, Statistical Dependencies, Test Vectors, TIT 2010