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A fundamental algorithm for data analytics at the edge of wireless networks is distributed principal component analysis (DPCA), which finds the most important information embedded in a distributed high-dimensional dataset by distributed computation of a reduced-dimension data subspace, called principal components (PCs). In this paper, to support one-shot DPCA in wireless systems, we propose a framework of analog MIMO transmission featuring the uncoded analog transmission of local PCs for estimating the global PCs. To cope with channel distortion and noise, two maximum-likelihood (global) PC estimators are presented corresponding to the cases with and without receive channel state information (CSI). The first design, termed coherent PC estimator, is derived by solving a Procrustes problem and reveals the form of regularized channel inversion where the regulation attempts to alleviate the effects of both receiver noise and data noise. The second one, termed blind PC estimator, is designed based on the subspace channel-rotation-invariance property and computes a centroid of received local PCs on a Grassmann manifold. Using the manifold-perturbation theory, tight bounds on the mean square subspace distance (MSSD) of both estimators are derived for performance evaluation. The results reveal simple scaling laws of MSSD concerning device population, data and channel signal-to-noise ratios (SNRs), and array sizes. More importantly, both estimators are found to have identical scaling laws, suggesting the dispensability of CSI to accelerate DPCA. Simulation results validate the derived results and demonstrate the promising latency performance of the proposed analog MIMO. Funding Agencies|ELLIIT; KAW Foundation; Research Grants Council of the Hong Kong Special Administrative Region, China [HKU RFS2122-7S04]; RGC [17208319, 17209917]; Key R&D Program of Shaanxi [2021KWZ-05]

Orthogonal signal-division multiplexing (OSDM) is a generalized modulation scheme to bridge the gap between orthogonal frequency-division multiplexing (OFDM) and single-carrier frequency-domain equalization. It allows significantly more flexibility in system design; however, over doubly-selective channels, it suffers from a special signal distortion structure, namely inter-vector interference, which is analogous to inter-carrier interference in conventional OFDM. To analyze its effect, in this paper, the complex exponential basis expansion model (CE-BEM) is used to approximate the doubly-selective channel. We show that the composite channel matrix of OSDM systems is cyclically block banded in this case, and the blocks in its main band can be further diagonalized. By exploiting this unique matrix structure, low-complexity block and serial OSDM equalization algorithms are then proposed. These two equalization algorithms are based on block LDLH factorization and block iterative matrix inversion, respectively, both of which are implemented in a transformed domain to avoid direct inversion of large matrices. In addition, a CE-BEM channel estimation method is designed for OSDM systems, which uses frequency-shifted Chu sequences as pilots to ease the computation. Numerical simulations are finally provided to justify the validity of our channel equalization and estimation algorithms.

We consider the channel estimation of a time-slotted wireless communication system with a mobile user and a base station, where the base station employs an M-element (M >; 1) antenna array. The uplink single-input multiple-output (SIMO) channel is usually estimated by training sequence within each time slot. To improve the estimation performance, the channel estimate is often refined by projecting it to the corresponding spatial signal subspace. However, this projection will not work when the number of resolvable multipath rays is larger than that of the antenna array elements, which makes the channel matrix full row rank. In this paper, we formulate the channel estimation under the space-time signal model for this full-row-rank case, and propose a new method by space-time signal subspace projection using both training and unknown data sequences. To further improve the accuracy of the channel estimate, the soft information fed back from the decoder can be used. By involving this soft information, we propose another new channel estimation method. This method approximately follows the maximum likelihood (ML) criterion and is therefore referred to as the approximated ML channel estimation. Numerical results show that these methods can be performed separately or jointly to improve the performance of channel estimation by training sequences.

International audience; In this paper, the problem of joint carrier frequency offset (CFO) and channel estimation for OFDM systems over the fast time-varying frequency-selective channel is explored within the framework of the expectation-maximization (EM) algorithm and parametric channel model. Assuming that the path delays are known, a novel iterative pilot-aided algorithm for joint estimation of the multipath Rayleigh channel complex gains (CG) and the carrier frequency offset (CFO) is introduced. Each CG time-variation, within one OFDM symbol, is approximated by a basis expansion model (BEM) representation. An autoregressive (AR) model is built to statistically characterize the variations of the BEM coefficients across the OFDM blocks. In addition to the algorithm, the derivation of the hybrid Cramér-Rao bound (HCRB) for CFO and CGs estimation in our context of very high mobility is provided. We show that the proposed EM has a lower computational complexity than the optimum maximum a posteriori estimator and yet incurs only an insignificant loss in performance.

In this paper, we deal with channel estimation for orthogonal frequency-division multiplexing (OFDM) systems. The channels are assumed to be time-varying (TV) and approximated by a basis expansion model (BEM). Due to the time-variation, the resulting channel matrix in the frequency domain is no longer diagonal, but approximately banded. Based on this observation, we propose novel channel estimators to combat both the noise and the out-of-band interference. In addition, the effect of a receiver window on channel estimation is also studied. Our claims are supported by simulation results, which are obtained considering Jakes' channels with fairly high Doppler spreads

We treat decision-directed channel tracking (DDCT) in mobile orthogonal frequency-division multiplexing (OFDM) systems as an outlier contaminated Gaussian regression problem, where the source of outliers are the incorrect symbol decisions. Existing decision-directed estimators such as the expectation-maximization (EM)-based estimators and the 2-D-MMSE estimator do not appropriately downweight incorrect/ poor decisions while defining the channel estimator, and hence suffer from error propagation at high fade rates. We propose to use generalized M estimators for decision-directed channel estimation and apply extreme value theory in conjunction with the Huber's cost function for outlier detection and downweighting. Significant reduction in error propagation is obtained by identifying and downweighting those symbol decisions that act as outliers before using them for channel estimation. The proposed estimators clearly outperform the 2-D-MMSE and the EM-based estimators in terms of simulated error rate performance at high fade rates. These estimators also have performance comparable to (or better than) pilot-assisted Kalman-filter-based channel tracking schemes with only modest increase in complexity. Thus, a 6% to 12% increase in data throughput is obtained without loss in performance when compared with the pilot-assisted schemes, even when DDCT is applied over frame durations experiencing two to three fade cycles. � 2007 IEEE.

In time-slotted mobile communication systems with antenna array at the receiver, the space-time channel matrix is conventionally estimated by transmitting pilot symbols within each data packet (or block). This work is focused on reduced rank (RR) estimation methods that exploit the low-rank property of the space-time channel matrix to estimate single or multiple user channels from the observation of single or multiple training blocks. The proposed RR methods allow to improve the estimate accuracy by reducing the set of unknown parameters (rank reduction) and extending the training set (multiblock processing). The maximum likelihood RR estimate is obtained as the projection of the prewhitened full-rank (FR) estimate onto the spatial or temporal signal subspace. The paper shows that, even for time varying channels, these subspaces can be considered to be slowly varying, and therefore, they can be estimated with increased accuracy by properly exploiting training signals from several blocks. The analytical and numerical performance in terms of mean square error for the RR estimate shows that the main advantage of the proposed method with respect to the conventional FR one can be ascribed to the reduced complexity of the channel parameterization.

This paper deals with the estimation of the channel impulse response (CIR) in orthogonal frequency division multiplexed (OFDM) systems. In particular, we focus on two pilot-aided schemes: the maximum likelihood estimator (MLE) and the Bayesian minimum mean square error estimator (MMSEE). The advantage of the former is that it is simpler to implement as it needs no information on the channel statistics. On the other hand, the MMSEE is expected to have better performance as it exploits prior information about the channel. Theoretical analysis and computer simulations are used in the comparisons. At SNR values of practical interest, the two schemes are found to exhibit nearly equal performance, provided that the number of pilot tones is sufficiently greater than the CIRs length. Otherwise, the MMSEE is superior. In any case, the MMSEE is more complex to implement.

For pt.I see ibid., vol.47, no.7, p.1988-2006 (1999). Transmitter redundancy introduced using finite impulse response (FIR) filterbank precoders offers a unifying framework for single- and multiuser transmissions. With minimal rate reduction, FIR filterbank transmitters with trailing zeros allow for perfect (in the absence of noise) equalization of FIR channels with FIR zero-forcing equalizer filterbanks, irrespective of the input color and the channel zero locations. Exploiting this simple form of redundancy, blind channel estimators, block synchronizers, and direct self-recovering equalizing filterbanks are derived in this paper. The resulting algorithms are computationally simple, require small data sizes, can be implemented online, and remain consistent (after appropriate modifications), even at low SNR colored noise. Simulations illustrate applications to blind equalization of downlink CDMA transmissions, multicarrier modulations through channels with deep fades, and superior performance relative to CMA and existing output diversity techniques relying on multiple antennas and fractional sampling.