A Fast Decoding Algorithm for Non-orthogonal Frequency Division Multiplexing Signals

A fast decoding algorithm based on Semidefinite relaxation combined with cutting plane is proposed for the detection of Non-orthogonal frequency division multiplexing (NFDM) signals. It shows that maximum likelihood (ML) detection of NFDM signals can be transformed into a semidefinite programming problem by relaxing rank one constraint. In order to tighten the performance gap between the relaxed combinatorial optimization problem and the optimum ML detection one, adding cutting planes are necessary. Simulations show that the optimum ML performance can be approached by the proposed algorithm. The loss in signal-to-noise ratio (SNR) compared with the ML detector is within ldB for the worst case. Moreover, the proposed algorithm's computational complexity is only proportional to a polynomial of the number of subcarriers rather than an exponential one of the optimum ML algorithm.