Training-based Estimation Research Articles

Distributed Blind Estimation Over Sensor Networks

Distributed estimation, where a set of nodes collaboratively estimate some parameters of interest from noisy measurements, has received much attention in both science and engineering. Recent studies mainly focus on distributed non-blind or training-based estimation, that is, a training signal and its desired output are both known to the distributed receivers. However, in some applications, it is physically difficult, if not impossible, to get a training signal in prior. Besides, the use of training signals consumes much channel bandwidth. So, it is more preferable for the receivers to perform distributed estimation without the assistance and expense of training sequences, i.e., distributed blind estimation . In this paper, the problem of distributed blind estimation over sensor networks is considered, and a kind of distributed diffusion generalized Sato algorithm is proposed to design a blind equalizer for channel equalization and source signal estimation. The stability of the proposed method in mean and mean-square senses is analyzed theoretically, and its performance is verified numerically by a series of simulations.

No Downlink Pilots Are Needed in TDD Massive MIMO

We consider the Massive Multiple-Input Multiple-Output downlink with maximum-ratio and zero-forcing processing and time-division duplex operation. To decode, the users must know their instantaneous effective channel gain. Conventionally, it is assumed that by virtue of channel hardening, this instantaneous gain is close to its average and hence that users can rely on knowledge of that average (also known as statistical channel information). However, in some propagation environments, such as keyhole channels, channel hardening does not hold. We propose a blind algorithm to estimate the effective channel gain at each user, that does not require any downlink pilots. We derive a capacity lower bound of each user for our proposed scheme, applicable to any propagation channel. Compared with the case of no downlink pilots (relying on channel hardening), and compared with training-based estimation using downlink pilots, our blind algorithm performs significantly better. The difference is especially pronounced in environments that do not offer channel hardening.

Channel estimation for full-duplex relay transmission in cloud radio access networks

Relay in full-duplex (FD) mode can achieve higher spectrum efficiency than that in half-duplex mode, while it is crucial to suppress relay self-interference to ensure transmission quality which requires instantaneous channel state information (CSI). In this paper, the channel estimation issue in FD amplify-andforward relay networks is considered, where the training-based estimation technique is adopted. Firstly, the least square (LS) estimation is implemented to obtain composite channel coefficients of source-relay-destination (SRD) channel and relay loop-interference (LI) channel in order to assist destination in performing data detection. Secondly, both LS and maximum likelihood estimation methods are utilized to perform individual channel estimation aiming at supporting successive interference cancelation at destination. Finally, simulation results demonstrate the effectiveness of both composite and individual channel estimation, and the presented ML method can achieve lower MSEs than LS solution.

Adaptive Joint Semi-blind Estimation of CFO and Channel for OFDM Systems

The large number of subcarriers, used in OFDM systems, increases the sensivity to frequency offset which results from a Doppler shift, due to mobile movement, as well as from a mismatch between the carrier frequencies at the transmitter and receiver. The problem of channel estimation in a practical OFDM receiver that suffers from CFO has been addressed in this paper. We first derived the modified MUSIC based blind CFO estimator. Next, we propose new joint training-based and joint semi-blind CFO and channel estimation for OFDM systems. Whereas the training-based estimator only assumes knowledge of pilot tones, the semi-blind estimator assumes knowledge of the virtual subcarriers (VSCs). For both estimators we derive a maximum likelihood (ML) algorithm for block processing and LMS algorithm for adaptive processing. It is demonstrated that the CFO estimators are able to perform well with a very small number of OFDM blocks. The performance of our estimators was investigated by simulations.

Orthogonal procrustes based semi-blind MIMO channel estimation under space-time block code transmissions

This work investigates a novel semi-blind channel estimation for multiple-input multiple-output (MIMO) space-time block coding (STBC) systems. Algorithms for channel estimation based on whitening-rotation (WR) decomposition that provides a combined quality and spatial scalability is utilized. Using a space-time code-constrained input design, our approach exploits the orthogonality of the signal and noise subspaces in conjunction with orthogonal procrustes (OP) technique to obtain an accurate estimate of the unitary rotation matrix and, consequently, of the channel parameters. Unitary rotation matrices are parameterized a much fewer number of parameters, and significant estimation gains can then be achieved by estimation of such orthogonal matrices. Furthermore, the proposed semi-blind MIMO channel estimation approach is conducted to reduce the complexity of system design when the number of the receive antennas is no less than the number of transmit antennas. Computer simulations are conducted to corroborate the effectiveness of the proposed channel estimation, and they demonstrate the improved performance compared to the existing training-based estimation.

A Framework for Training-Based Estimation in Arbitrarily Correlated Rician MIMO Channels With Rician Disturbance

In this paper, we create a framework for training-based channel estimation under different channel and interference statistics. The minimum mean square error (MMSE) estimator for channel matrix estimation in Rician fading multi-antenna systems is analyzed, and especially the design of mean square error (MSE) minimizing training sequences. By considering Kronecker-structured systems with a combination of noise and interference and arbitrary training sequence length, we collect and generalize several previous results in the framework. We clarify the conditions for achieving the optimal training sequence structure and show when the spatial training power allocation can be solved explicitly. We also prove that spatial correlation improves the estimation performance and establish how it determines the optimal training sequence length. The analytic results for Kronecker-structured systems are used to derive a heuristic training sequence under general unstructured statistics. The MMSE estimator of the squared Frobenius norm of the channel matrix is also derived and shown to provide far better gain estimates than other approaches. It is shown under which conditions training sequences that minimize the non-convex MSE can be derived explicitly or with low complexity. Numerical examples are used to evaluate the performance of the two estimators for different training sequences and system statistics. We also illustrate how the optimal length of the training sequence often can be shorter than the number of transmit antennas.

Estimation of Carrier Frequency Offset for Multicarrier CDMA Uplink

This paper presents a training-based estimation method of carrier frequency offset (CFO) for multicarrier code-division multiple-access (MC-CDMA) uplink. The basic assumption is the same as in Morellis' work (OFDMA), i.e., active users in the network are classified into two categories: reference (synchronized) users (RUs) and new (asynchronized) users (NUs). But, we consider the system that RUs use CDMA to share the wireless medium. NUs employ time-division multiple-access (TDMA) for the training purpose. Our major idea is to perform the CFO estimation in the desired signal subspace that is orthogonal to the RU subspace. The proposed approach is investigated both in the subband and interleaved MC-CDMA systems. It is shown that implementation of the CFO estimation together with the training-pattern design could be relatively simple when users do not experience the considerable frequency-selective fade. In the highly frequency-selective fading scenario, an adaptive training-scheme is proposed to make the CFO estimator robust. We also consider NUs operating in the frequency-division multiple-access (FDMA) training mode. Due to the presence of inter-NU-interference, the estimation performance may be not as good as in the TDMA training mode. The performance degradation may be severe when RUs operate in the interleaved MC-CDMA. In this case, we propose an inter-NU-interference self-canceling training-pattern and use simulations to demonstrate its impact on the estimation performance

Training-based estimation of correlated MIMO fading channels in the presence of colored interference

In this paper, training-based estimation of correlated block fading channels in a multiple-antenna, multi-user environment is considered. The linear minimum mean squared error (LMMSE) estimator is presented first. The problem of optimally designing the training data set, so as to minimize the mean squared channel estimation error subject to a total transmit power constraint, is then addressed. The design is based on the assumption of the availability of the channel and interference second-order statistics at the transmitter. It is shown that the optimal transmission directions are dictated jointly by the eigen-decompositions of the channel and interference covariance matrices. Their roles, in the channel estimation and interference suppression tasks, respectively, are revealed in the optimal transmit beamformer structure. The simulation results demonstrate that the gain in the estimation performance from using the optimal training sequence increases considerably with increasing spatial fading correlation, especially in strong interference environments.

Whitening-rotation-based semi-blind MIMO channel estimation

This paper proposes a whitening-rotation (WR)-based algorithm for semi-blind estimation of a complex flat-fading multi-input multi-output (MIMO) channel matrix H. The proposed algorithm is based on decomposition of H as the matrix product H=WQ/sup H/, where W is a whitening matrix and Q is unitary rotation matrix. The whitening matrix W can be estimated blind using only received data while Q is estimated exclusively from pilot symbols. Employing the results for the complex-constrained Cramer-Rao Bound (CC-CRB), it is shown that the lower bound on the mean-square error (MSE) in the estimate of H is directly proportional to its number of unconstrained parameters. Utilizing the bounds, the semi-blind scheme is shown to be very efficient when the number of receive antennas is greater than or equal to the number of transmit antennas. Closed-form expressions for the CRB of the semi-blind technique are presented. Algorithms for channel estimation based on the decomposition are also developed and analyzed. In particular, the properties of the constrained maximum-likelihood (ML) estimator of Q for an orthogonal pilot sequence is examined, and the constrained estimator for a general pilot sequence is derived. In addition, a Gaussian likelihood function is considered for the joint optimization of W and Q, and its performance is studied. Simulation results are presented to support the algorithms and analysis, and they demonstrate improved performance compared to exclusively training-based estimation.

Subspace system identification for training-based MIMO channel estimation

The application of state-space-based subspace system identification methods to training-based estimation for quasi-static multi-input–multi-output (MIMO) frequency-selective channels is explored with the motivation for better model approximation performance. A modification of the traditional subspace methods is derived to suit the non-contiguous nature of training data in mobile communication systems. To track the time variation of the channel, a new recursive subspace-based channel estimation is proposed and demonstrated in simulation with practical MIMO channel models. The comparison between the state-space-based channel estimation algorithm and the FIR-based Recursive Least Squares algorithm shows the former is a more robust modeling approach than the latter.

An Efficient Code-Timing Estimator for DS-CDMA Systems over Resolvable Multipath Channels

We consider the problem of training-based code-timing estimation for the asynchronous direct-sequence code-division multiple-access (DS-CDMA) system. We propose a modified large-sample maximum-likelihood (MLSML) estimator that can be used for the code-timing estimation for the DS-CDMA systems over the resolvable multipath channels in closed form. Simulation results show that MLSML can be used to provide a high correct acquisition probability and a high estimation accuracy. Simulation results also show that MLSML can have very good near-far resistant capability due to employing a data model similar to that for adaptive array processing where strong interferences can be suppressed.

Code acquisition in transmit diversity ds-cdma systems

In this paper, two code acquisition schemes are studied for use in conjunction with transmit diversity direct-sequence code-division multiple access (DS-CDMA). One is a training-based single-user maximum-likelihood (SUML) estimator, which can achieve code acquisition very fast at low computational complexity. The other is a blind estimator based on the multiple signal classification (MUSIC) algorithm. Two recently proposed transmit diversity schemes known as orthogonal transmit diversity simulcast (OTD-S) and space-time selective spreading transmit diversity (STSTD) are considered. While the advantages of transmit diversity from the detection standpoint are well known, less is known about how code acquisition performance is affected by the use of transmit diversity. Through the analysis in this paper, it is proven that the SUMI. estimator should give the same performance in both the OTD-S and STSTD schemes in a single-user environment. In a multiple-user environment, simulation results show that the STSTD system offers slightly better code acquisition performance. It is also seen that the SUML estimators provide significantly better code acquisition performance than the MUSIC estimators in either transmit diversity system. From the standpoint of robustness to carrier frequency offset, it Is found that the training-based SUML estimator is very sensitive to frequency offset, while the MUSIC estimator is quite robust. A simple frequency offset estimator to be used in conjunction with the SUML estimator is also proposed and is shown to make the timing estimator quite tolerant of substantial frequency offsets.