Stability Proof of Iterative Interference Cancellation for OFDM Signals With Blanking Nonlinearity in Impulsive Noise Channels

Blanking nonlinearity is a widely applied technique for suppressing impulsive noise. However, for orthogonal frequency-division multiplexing signals, the blanking nonlinearity induces intercarrier interference, which must be removed in order to fully exploit the advantage of the blanking nonlinearity and to avoid performance degradation. For this purpose, interference cancellation techniques are attracting a considerable attention. Particularly, the nonlinear iterative ones show a good complexity-performance behavior. Nevertheless, one of the most important features of nonlinear iterative methods in the context of interference cancellation often remains disregarded: The stability. In this correspondence, we prove the asymptotical stability in the sense of Lyapunov of a nonlinear iterative interference cancellation technique for OFDM signals with blanking nonlinearity in impulsive noise channels. This is achieved by reformulating the considered technique as a multithreshold recurrent neural network and by taking advantage of the extensive research on the Lyapunov stability of recurrent neural networks. We show that the considered nonlinear iterative interference cancellation technique either reaches a fixed point or a limit cycle of length two. The obtained results can be utilized to find an upper bound on the required number of iterations to settle on a fixed point.