Name
Abstract | ||
|---|---|---|
In this paper, we study a simple correlation-based strategy for estimating the unknown delay and amplitude of a signal based on a small number of noisy, randomly chosen frequency-domain samples. We model the output of this “compressive matched filter” as a random process whose mean equals the scaled, shifted autocorrelation function of the template signal. Using tools from the theory of empirical processes, we prove that the expected maximum deviation of this process from its mean decreases sharply as the number of measurements increases, and we also derive a probabilistic tail bound on the maximum deviation. Putting all of this together, we bound the minimum number of measurements required to guarantee that the empirical maximum of this random process occurs sufficiently close to the true peak of its mean function. We conclude that for broad classes of signals, this compressive matched filter will successfully estimate the unknown delay (with high probability and within a prescribed tolerance) using a number of random frequency-domain samples that scales inversely with the signal-to-noise ratio and only logarithmically in the observation bandwidth and the possible range of delays. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1109/TIT.2013.2243495 | IEEE Transactions on Information Theory |
Keywords | DocType | Volume |
delay estimation,filtering theory,compressive matched filter,correlation-based strategy,limited frequency samples,matched filtering,noisy frequency-domain samples,probabilistic tail,random frequency-domain samples,randomly chosen frequency-domain samples,shifted autocorrelation function,signal amplitude,template signal,unknown delay estimation,compressive sensing (cs),random processes,tone estimation,empirical process,autocorrelation function,frequency domain,signal to noise ratio,information theory,matched filter,random process | Journal | 59 |
Issue | ISSN | Citations |
6 | 0018-9448 | 10 |
PageRank | References | Authors |
0.69 | 17 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Armin Eftekhari | 1 | 129 | 12.42 |
| Justin K. Romberg | 2 | 5856 | 514.08 |
| Michael B. Wakin | 3 | 4299 | 271.57 |