TY - GEN
T1 - Heuristic methods for designing unimodular code sequences with performance guarantees
AU - Ragi, Shankarachary
AU - Chong, Edwin K.P.
AU - Mittelmann, Hans
N1 - Funding Information:
The work of S. Ragi and H. D. Mittelmann was supported in part by Air Force Office of Scientific Research under grant FA 9550-15-1 -0351. The work of E. K. P. Chong was supported in part by National Science Foundation under grant CCF-1422658.
Publisher Copyright:
© 2017 IEEE.
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 - Unimodular codes
KW - heuristic methods
KW - radar codes
KW - string submodularity
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
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
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.
T2 - 2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017
Y2 - 5 March 2017 through 9 March 2017
ER -