OFDM channel estimation in the presence of NBI and the effect of misspecified NBI model

The presence of narrowband interference (NBI) and thermal noise leads to a contaminated Gaussian (CG) noise probability density function (pdf) at the OFDM receiver. The Cramer-Rao lower bound for channel estimation in the presence of CG noise is analyzed for two NBI pdfs, namely, the Gaussian and the Cauchy pdfs. We then derive the mean square error (MSE) when the actual NBI pdf differs from the NBI pdf for which the estimator is designed, i.e., when the NBI pdf is misspecified. Based on this theoretical MSE analysis, we show that: (i) Even if the maximum likelihood estimator (MLE) designed for the CG noise pdf assuming Cauchy NBI is used when the actual CG pdf has Gaussian NBI, the degradation in MSE performance is negligible; (ii) However, if the MLE for CG pdf designed assuming Gaussian NBI is used for channel estimation in CG noise where the NBI is actually Cauchy, a very poor MSE performance is obtained. This analysis suggests that it is pragmatic to use the MLE designed assuming Cauchy NBI, as it is robust to misspecification of the NBI pdf. Further, an iteratively reweighted least squares algorithm is proposed for implementing the MLE for the CG model with either Gaussian or Cauchy NBI.