Abstract
We study the problem of recovering an n-dimensional BPSK signal from m linear noise-corrupted measurements using the box relaxation method which relaxes the discrete set {±1}n to the convex set [-1,1]n to obtain a convex optimization algorithm followed by hard thresholding. When the noise and measurement matrix have iid standard normal entries, we obtain an exact expression for the bit-wise probability of error Pe in the limit of n and m growing and m/n fixed. At high SNR our result shows that the Pe of box relaxation is within 3dB of the matched filter bound (MFB) for square systems, and that it approaches the (MFB) as m grows large compared to n. Our results also indicate that as m, n → ∞, for any fixed set of size k, the error events of the corresponding k bits in the box relaxation method are independent.
| Original language | English (US) |
|---|---|
| Title of host publication | 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) |
| Publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| Pages | 3776-3780 |
| Number of pages | 5 |
| ISBN (Print) | 9781479999880 |
| DOIs | |
| State | Published - Jun 24 2016 |
| Externally published | Yes |
Bibliographical note
KAUST Repository Item: Exported on 2020-10-01Acknowledgements: This work was supported in part by the National Science Foundation under grants CNS-0932428, CCF-1018927, CCF-1423663 and CCF-1409204, by a grant from Qualcomm Inc., by NASAs Jet Propulsion Laboratory through the President and Directors Fund, by King Abdulaziz University, and by King Abdullah University of Science and Technology. Xu’s work is supported by Simons Foundation, Iowa Energy Center, KAUST, and NIH 1R01EB020665-01.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.