Robust Multipath Channel Identification with Partial Filter Information

1. IEEE North Jersey Advanced Communications Symposium, 2014 Robust Multipath Channel Identification with Partial Filter Information Kuang Cai﹡, Hongbin Li﹡, Joseph Mitola III † ﹡Department of Electrical and Computer Engineering, Stevens Institute of Technology, Hoboken, NJ 07030, USA †Mitola's STATISfaction, 4985 Atlantic View, St. Augustine, FL 32080, USA Introduction • Cramér–Rao bound (CRB) • To benchmark performances of proposed estimators • The filter response becomes a random parameter with existence of the perturbation • Bayesian CRB • Write all data blocks in one equation • Compute Fisher information matrix (FIM) • Constraint is applied in blind estimation to eliminate ambiguity • Compute constrained CRB based on FIM • Expansion for slowly time-varying channels • Channel response does not have significant change over one data block duration • Compute an initial sample covariance matrix and update it when a new output data block is available • Applied estimation algorithms based on the time-varying sample covariance matrix • The second-order statistics of the channel output contain sufficient information for blind channel estimation due to the cyclostationarity of the channel output induced by a fractionally spaced sampling • A subspace-based multipath channel identification based on exploiting knowledge of the transmit/receive filter was presented and popular • Simplicity and good performance • Requires full knowledge of the filter • Transmit/receive filter response is often partially known due to perturbations • I/Q imbalance at the transmit/receive side • Physical distortions due to environmental factors (i.e., temperature, humidity) • To improve the estimation performance, two algorithms are proposed • Subspace method based Iterative channel identification (conventional estimation) when accuracy of the prior knowledge is unknown • Robust channel identification when accuracy of the prior knowledge is partially known (the statistical knowledge of the perturbation is available) : Forgetting factor, Numerical Results System Model • System model • Composite channel • Discrete time model • Filter perturbation model : Input information sequence :Channel noise (AWGN) : Transmit/receive filter : Multipath channel : th data block : Block Toeplitz channel matrix Fig.1 Fig.2 : Nominal filter response : Unknown perturbation error modeled as a random variable with zero mean and variance Channel Identification • Subspace decomposition of the sample covariance of channel output • According to the orthogonality between channel and noise, given the filter response, the channel estimate can be achieved by minimizing • Iterative channel identification • Accuracy of prior knowledge unknown • Given the channel response, the filter estimate can be achieved by minimizing • Use nominal filter response as an initial estimate of filter to initialize an iterative procedure that estimates the channel and filter response in a sequential fashion • Robust channel identification • Accuracy of prior knowledge partially known (statistical knowledge of perturbation) • Develop a knowledge-aided robust estimation algorithm • Define an ellipsoidal uncertainty bound for the difference between the filter response and its estimate • Estimate the filter within this bound • The estimation problem can be solved by the Lagrange multiplier methodology • Apply the iterative channel identification • Estimate the filter with the robust estimation • Estimate the channel with the subspace method : Eigenvectors span on the signal subspace : Eigenvectors span on the noise subspace : Sample covariance matrix Fig. 3 Fig.4 • Simulation settings • BPSK input • Raised-cosine pulse shaping filter with roll-off factor 0.1 • Multipathchannel • Four ray (time-invariant channel) • Two ray (time-varying channel) : th Eigenvector belongs to the noise subspace : Block Toeplitz matrix formed by : Convolutional matrix formed by filter response • Results • Fig. 1 and 2 show the results for time-invariant channels • Fig. 3, 4 and 5 show the results for time-varying channels Fig.5 Conclusions : Convolutional matrix formed by channel response • We examine two cases, in which the transmit/receive filter is affected by unknown perturbation, and propose the corresponding estimators • With the statistical knowledge of the perturbation, the robust estimation achieved better performance than the conventional estimation • Robust estimation algorithm also works for the slowly time-varying channels Future Work • Explore the application of robust channel identification in OFDM systems