Sparse Channel Estimation for Interference Limited OFDM Systems and Its Convergence Analysis

Wireless communication channels are highly prone to interference in addition to the presence of additive white Gaussian noise (AWGN). Stochastic gradient (SG)-based non-parametric maximum likelihood (NPML) estimator, gives better channel estimates in the presence of Gaussian mixture (AWGN plus interference) noise processes, for subsequent use by the channel equalizer. However, for sparse channels, the SG-NPML-based channel estimator requires large iterations to converge. In this paper, we propose a natural gradient (NG)-based channel estimator for sparse channel estimation in the presence of high interference. We propose a generalized pth order warping transformation on channel coefficients space and then calculate the Riemannian metric tensor, thereby resulting in faster convergence in interference limited channels. The proposed algorithm is applied for IEEE 802.22 (based on orthogonal frequency division multiplexing) channel estimation in the presence of interference. Extensive simulations and experimental results show that the proposed NG-based algorithm converges faster than SG-NPML for the same mean squared error (MSE) floor with similar computational complexity per iteration as an SG-NPML algorithm. We also present convergence analysis of proposed NG-NPML algorithm in the presence of Gaussian mixture noise and derive an analytical expression for the steady-state MSE.