In this paper, we consider the narrowband interference problem for orthogonal frequency division multiplexing (OFDM)based cognitive radio (CR) systems, in which parts of the OFDM subcarriers and parts of the data frame can be seriously interfered, resulting in significant performance degradation. We propose a scheme of iterative noise plus interference estimation and decoding (IED) to mitigate the performance degradation caused by the narrowband interference, which is based on expectation maximization (EM) algorithm. To reduce the number of OFDM symbols for time domain averaging required in the proposed scheme, and adapt the proposed scheme to rapid changing narrowband interference conditions, we also propose an IED scheme with frequency domain partial averaging (IED-FPA). Moreover, we derive the Cramér-Rao lower bounds for unbiased noise plus interference variance estimations, and they can be achieved via the proposed IED schemes. Simulation results show that the proposed IED-FPA scheme can effectively achieve the same performance as that of the optimal maximum likelihood decoder with full knowledge of the power plus interference variances, and the proposed IED-FPA scheme is very robust with respect to the number of the interfered subcarriers and positive errors of the knowledge of the interfered subcarriers' number. Recently, many research efforts have been devoted to the study in the literature. With the assumption that the noise variance at each subcarrier is independent of each other, expectation maximization (EM) and decision directed algorithms were proposed for noise variances estimation in Reference [3]. However, the proposed algorithm in Reference [3] requires a large amount of data to be processed for an accurate estimate. Based on the rough estimate of the transmitted data symbols, authors in References [4] and [5] considered the estimation of the interference from Bluetooth to IEEE 802.11g WLAN. However, they did not consider the correlation of the interference variances