NP-Completeness of Multicast Beamforming in Wireless Communication
Sagar Shrestha
TL;DR
This paper proves that the decision problem for multicast beamforming with real channel matrices is NP-complete and demonstrates its computational complexity through simulations using SAT/SMT solvers.
Contribution
It establishes the NP-completeness of the multicast beamforming decision problem with real matrices, extending prior NP-hardness results.
Findings
The problem is NP-complete for real channel matrices.
Simulations show the computational difficulty of solving the problem.
SAT/SMT solvers face significant challenges with this problem.
Abstract
In this work, the classical problem of multi-cast beamforming in wireless communication is reconsidered. An existing work has shown that the multi-cast beamforming problem is NP-hard. In this project, we show that the corresponding decision problem for real channel matrices and beamformers is NP-complete. Finally, we carry out simulations to reveal the computational complexity of solving the NP-complete beamforming problem in various setting using SAT/SMT solvers.
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Taxonomy
TopicsAdvanced MIMO Systems Optimization · Wireless Communication Networks Research · Cooperative Communication and Network Coding