The impulse response of wireless channels between the N t transmit and N r receive antennas of a MIMO-OFDM system are group approximately sparse (ga-sparse), i.e., the N t N r channels have a small number of significant paths relative to the channel delay spread and the time-lags of the significant paths between transmit and receive antenna pairs coincide. Often, wireless channels are also group approximately cluster sparse (gac-sparse), i.e., every ga-sparse channel consists of clusters, where a few clusters have all strong components while most clusters have all weak components. In this work, we cast the problem of estimating the ga-sparse and gac-sparse block-fading and time-varying channels in the Sparse Bayesian Learning (SBL) framework, and propose a bouquet of novel algorithms for pilotbased channel estimation and joint channel estimation and data detection in MIMO-OFDM systems. The proposed joint channel estimation and data detection schemes are capable of recovering ga-sparse and gac-sparse channels even when the measurement matrix is only partially known. Further, we employ a first order autoregressive modeling of the temporal variation of the wireless ga-sparse and gac-sparse channels and propose a recursive Kalman filtering and smoothing (KFS) technique for joint channel estimation, tracking and data detection. The KFS framework exploits the correlation structure in the time-varying , IEEE Transactions on Signal Processing 2 channel. We also propose novel, parallel-implementation based, low complexity techniques for estimating gac-sparse channels. Monte Carlo simulations illustrate the efficacy of proposed techniques in terms of mean square error (MSE) and coded bit error rate (BER) performance. In particular, we demonstrate the performance benefits offered by algorithms that exploit the gac-sparse structure in the wireless channel.
Abstract-In this paper, we derive Hybrid, Bayesian and Marginalized Cramér-Rao lower bounds (HCRB, BCRB and MCRB) for the single and multiple measurement vector Sparse Bayesian Learning (SBL) problem of estimating compressible vectors and their prior distribution parameters. We assume the unknown vector to be drawn from a compressible Student-t prior distribution. We derive CRBs that encompass the deterministic or random nature of the unknown parameters of the prior distribution and the regression noise variance. We extend the MCRB to the case where the compressible vector is distributed according to a general compressible prior distribution, of which the generalized Pareto distribution is a special case. We use the derived bounds to uncover the relationship between the compressibility and Mean Square Error (MSE) in the estimates. Further, we illustrate the tightness and utility of the bounds through simulations, by comparing them with the MSE performance of two popular SBL-based estimators. It is found that the MCRB is generally the tightest among the bounds derived and that the MSE performance of the Expectation-Maximization (EM) algorithm coincides with the MCRB for the compressible vector.Through simulations, we demonstrate the dependence of the MSE performance of SBL based estimators on the compressibility of the vector for several values of the number of observations and at different signal powers.Index Terms-Sparse Bayesian learning, mean square error, Cramér-Rao lower bounds, expectation maximization.
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