Anti-sparse representation for continuous function by dual atomic norm with application in OFDM

Anti-sparse representation for continuous functions is a concerning problem in wireless communication and control systems. In this paper, a dual atomic norm minimization problem with bounded deviation constraints is setup to achieve such anti-sparse representation. The solution to such convex optimization problem is studied, and its dual problem is unveiled. By the choice of the atom set, the above general formulation finds application in the pre-sampled OFDM signal PAPR reduction both with and without tone reservation. In such case, the dual problem can be solved by semi-definite programming, and the solution directly gives the complex amplitude on every sub-channel of the transmission signal with reduced PAPR. In the numerical experiments, the performance of the proposed method is demonstrated for the 16 QaM OFDM signal PAPR reduction problem, and compared with the vector ℓ∞ norm minimization, the proposed method shows advantages in both PAPR and error rate.