Abstract
We develop polynomial-time heuristic methods to solve unimodular quadratic programming (UQP) approximately, which is known to be NP-hard. In the UQP framework, we maximize a quadratic function of a vector of complex variables with unit modulus. Several problems in active sensing and wireless communication applications boil down to UQP. With this motivation, we present two new heuristic methods with polynomial complexity to solve the UQP approximately. The first method is called dominant-eigenvector-matching; here the solution is picked that matches the complex arguments of the dominant eigenvector of the Hermitian matrix in the UQP formulation. We also provide a performance guarantee for this method. The second heuristic method, a greedy strategy, is shown to provide a performance guarantee of (1 - 1/e) with respect to the optimal objective value given that the objective function possesses a property called string submodularity. We also present results from simulations to demonstrate the performance of these heuristic methods.
| Original language | English (US) |
|---|---|
| Title of host publication | 2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - Proceedings |
| Publisher | Institute of Electrical and Electronics Engineers Inc. |
| Pages | 3221-3225 |
| Number of pages | 5 |
| ISBN (Electronic) | 9781509041176 |
| DOIs | |
| State | Published - Jun 16 2017 |
| Event | 2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - New Orleans, United States Duration: Mar 5 2017 → Mar 9 2017 |
Other
| Other | 2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 |
|---|---|
| Country | United States |
| City | New Orleans |
| Period | 3/5/17 → 3/9/17 |
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Keywords
- heuristic methods
- radar codes
- string submodularity
- Unimodular codes
- unimodular quadratic programming
ASJC Scopus subject areas
- Software
- Signal Processing
- Electrical and Electronic Engineering
Cite this
Heuristic methods for designing unimodular code sequences with performance guarantees. / Ragi, Shankarachary; Chong, Edwin K.P.; Mittelmann, Hans.
2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2017. p. 3221-3225 7952751.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - Heuristic methods for designing unimodular code sequences with performance guarantees
AU - Ragi, Shankarachary
AU - Chong, Edwin K.P.
AU - Mittelmann, Hans
PY - 2017/6/16
Y1 - 2017/6/16
N2 - We develop polynomial-time heuristic methods to solve unimodular quadratic programming (UQP) approximately, which is known to be NP-hard. In the UQP framework, we maximize a quadratic function of a vector of complex variables with unit modulus. Several problems in active sensing and wireless communication applications boil down to UQP. With this motivation, we present two new heuristic methods with polynomial complexity to solve the UQP approximately. The first method is called dominant-eigenvector-matching; here the solution is picked that matches the complex arguments of the dominant eigenvector of the Hermitian matrix in the UQP formulation. We also provide a performance guarantee for this method. The second heuristic method, a greedy strategy, is shown to provide a performance guarantee of (1 - 1/e) with respect to the optimal objective value given that the objective function possesses a property called string submodularity. We also present results from simulations to demonstrate the performance of these heuristic methods.
AB - We develop polynomial-time heuristic methods to solve unimodular quadratic programming (UQP) approximately, which is known to be NP-hard. In the UQP framework, we maximize a quadratic function of a vector of complex variables with unit modulus. Several problems in active sensing and wireless communication applications boil down to UQP. With this motivation, we present two new heuristic methods with polynomial complexity to solve the UQP approximately. The first method is called dominant-eigenvector-matching; here the solution is picked that matches the complex arguments of the dominant eigenvector of the Hermitian matrix in the UQP formulation. We also provide a performance guarantee for this method. The second heuristic method, a greedy strategy, is shown to provide a performance guarantee of (1 - 1/e) with respect to the optimal objective value given that the objective function possesses a property called string submodularity. We also present results from simulations to demonstrate the performance of these heuristic methods.
KW - heuristic methods
KW - radar codes
KW - string submodularity
KW - Unimodular codes
KW - unimodular quadratic programming
UR - http://www.scopus.com/inward/record.url?scp=85023743515&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85023743515&partnerID=8YFLogxK
U2 - 10.1109/ICASSP.2017.7952751
DO - 10.1109/ICASSP.2017.7952751
M3 - Conference contribution
AN - SCOPUS:85023743515
SP - 3221
EP - 3225
BT - 2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
ER -