Introduction

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