MIMO Channel Estimation Using the Variational Expectation-Maximization Method

It is now widely accepted that knowledge can be acquired from networks by clustering their vertices according to the connection profiles. Many methods have been proposed and in this paper we concentrate on the Stochastic Block Model (SBM). The clustering of vertices and the estimation of SBM model parameters have been subject to previous work, and numerous inference strategies such as variational expectation maximization (EM) and classification EM have been proposed. However, SBM still suffers from a lack of criteria to estimate the number of components in the mixture. To our knowledge, only one model-based criterion, Integrated Complete-data Likelihood (ICL), has been derived for SBM in the literature. It relies on an asymptotic approximation of the integrated complete-data likelihood and recent studies have shown that it tends to be too conservative in the case of small networks. To tackle this issue, we propose a new criterion that we call Integrated Likelihood Variational Bayes (ILvb), based on a non-asymptotic approximation of the marginal likelihood. We describe how the criterion can be computed through a variational Bayes EM algorithm.

In this paper, performance of the Alamouti space- time code (STC) [1] and performance of the concatenation between the convolutional code and the Alamouti STC are derived. In order to describe realistic performance issues, we assume that the channel estimates are calculated from linear filters using noisy pilot symbols. We also assume non-quasi- static channels, spatially correlated transmit antennas and finite- depth interleaving. Two types of receivers are investigated for the Alamouti STC, namely, the linear-combining space-time decoder (LC-STD) and the maximum-likelihood space-time decoder (ML- STD). Two types of receivers are investigated for the concatenated system, namely, the LC-STD with the ML convolutional decoder and the joint Alamouti and convolutional ML decoder. The results have shown that the LC-STD is more sensitive to the Doppler spread than the ML-STD. However, since the ML- STD is very sensitive to the channel estimation error, the gains provided by the decoder in fast fading channels will be offset unless an optimized channel estimator is employed. Performance comparisons between the Alamouti systems and the SISO systems indicate that, when the system environment is not ideal, the SISO systems may outperform the Alamouti systems. Lastly, analytical results are compared with simulation results to illustrate the accuracy of the analysis.

In this paper, a new joint symbol detection and channel estimation algorithm is proposed for MIMO-OFDM systems over frequency-selective fading channels using the variational Bayesian expectation-maximization (VBEM) algorithm. Since the VBEM algorithm can provide distribution-estimates of the parameters, the statistical information about the channel uncertainty is exploited to improve the evaluation of the extrinsic information in the soft-input soft-output detector which identifies the significant symbol combinations via list sphere decoder. In addition, two channel estimators are derived based on the posterior distributions of the transmitted symbols which are obtained from the space-time detection. The VBEM iterations are embedded in the turbo-processing of the receiver. Simulation results demonstrate that the proposed VBEM algorithm has more robust performance over the conventional EM techniques.

After a few decades’ evolution of wireless communication systems, to ensure reliable highspeed communication over unreliable wireless channels is still one of the major challenges facing researchers and engineers. The use of multiple antennas at transmitter and receiver, known as multiple-input multiple-output (MIMO) communications, is one promising technology delivering desired wireless services. The main goal of this thesis is to study two important issues in wireless MIMO communication systems: receiver design for coded MIMO systems, and diversity-multiplexing tradeoff analysis in general fading channels. In the first part of this thesis, we decompose the receiver design problem into two subproblems: MIMO channel estimation and MIMO detection. For the MIMO channel estimation, we develop an expectation-maximization (EM) based semi-blind channel and noise covariance matrix estimation algorithm for space-time coding systems under spatially correlated noise. By incorporating the proposed channel estimator into the iterative receiver structure, both the channel estimation and the error-control decoding are improved significantly. We also derive the modified Cramer-Rao bounds (MCRB) for the unknown parameters as the channel estimation performance metric, and demonstrate that the proposed channel estimation algorithm can achieve the MCRB after several iterations. For the MIMO detection, we propose a novel lowcomplexity MIMO detection algorithm, which has only cubic order computational complexity, but with near-optimal performance. For a 4×4 turbo-coded system, we show that the proposed detector had the same performance as the maximum a posteriori (MAP) detector for BPSK modulation, and 0.1 dB advantage over the approximated MAP detector (list sphere decoding algorithm) for 16-QAM modulation at BER = 10−4. In the second part of this thesis, we derive the optimal diversity-multiplexing tradeoff for

Space time codes (STC) have been shown to be used well with the Multiple Input Multiple Output (MIMO) channel. The Orthogonal STC (OSTC) family of codes is known to achieve full diversity as well as very simple implementation of the Maximum Likelihood (ML) decoder. However, it was proven that with a complex symbol constellation one cannot achieve a full rate code when the number of transmitting antennas is larger than two. Quasi-OSTC can have full rate even for more than two transmitting antennas but with the penalty of decoding complexity which becomes severe if the constellation size is high. In order to tackle these inherent drawbacks of the OSTC/QSTC we propose a new STC code that, when used with a new transmission and decoding methods, achieves full rate while maintaining linear complexity decoding for any number of transmit antennas. Also if the transmitter knows the strongest channel (through minimal feedback) the code also achieves full diversity along with better error rate than the OSTC and the QSTC.

The average bit error rate (ABER) performance of an orbital angular momentum (OAM) multiplexing-based free-space optical (FSO) system with multiple-input multiple-output (MIMO) architecture has been investigated over atmospheric turbulence considering channel estimation and space-time coding. The impact of different types of space-time coding, modulation orders, turbulence strengths, receive antenna numbers on the transmission performance of this OAM-FSO system is also taken into account. On the basis of the proposed system model, the analytical expressions of the received signals carried by the k-th OAM mode of the n-th receive antenna for the vertical bell labs layered space-time (V-Blast) and space-time block codes (STBC) are derived, respectively. With the help of channel estimator carrying out with least square (LS) algorithm, the zero-forcing criterion with ordered successive interference cancellation criterion (ZF-OSIC) equalizer of V-Blast scheme and Alamouti decoder of STBC scheme are adopted to mitigate the performance degradation induced by the atmospheric turbulence. The results show that the ABERs obtained by channel estimation have excellent agreement with those of turbulence phase screen simulations. The ABERs of this OAM multiplexing-based MIMO system deteriorate with the increase of turbulence strengths. And both V-Blast and STBC schemes can significantly improve the system performance by mitigating the distortions of atmospheric turbulence as well as additive white Gaussian noise (AWGN). In addition, the ABER performances of both space-time coding schemes can be further enhanced by increasing the number of receive antennas for the diversity gain and STBC outperforms V-Blast in this system for data recovery. This work is beneficial to the OAM FSO system design.

In a recent contribution, assuming pilot-only based channel estimation, we proposed an improved receiver which reduces the impact of channel uncertainty on the decoder performance. Here, we focus on semi-blind channel estimation based on expectation-maximization (EM) algorithm and propose an improved receiver design by an appropriate use of the channel estimation error statistics. This is done by means of an equivalent formulation of the EM algorithm from which we extract the statistics of the estimation errors. This additional soft information is used at each iteration of the receiver in a Bayesian framework to improve the performance of iterative detection. Our approach is compared to the conventional EM algorithm where the channel estimation error statistics are not available and where the receiver uses the channel estimate as if it was the perfect channel (also known as mismatched detection). Numerical results in the context of orthogonal frequency-division multiplexing show that the proposed approach outperforms the classically-used EM algorithm in terms of bit error rates.

Multipath fading is one of the primary factors for degrading the performance in a wireless network. Information theoretic and past research suggest the use various diversity techniques to combat fading in wireless networks. Antenna diversity, a form of diversity technique, when incorporated in a wireless transceiver increases the system capacity and is one of the effective methods to combat fading in wireless systems. Also, recent research by Laneman et.al., Sendonaris et.al. suggests that cooperation among users in a wireless networks is an effective approach for a better signal reception in multipath fading environments. The diversity gains obtained by cooperation among the users of a wireless network is termed as cooperative diversity . Although, prior research in cooperative diversity considers users equipped with single antenna, in practical scenarios users may be able to accommodate multiple antennas due to the recent advanced research in semiconductor industry. Hence, the primary purpose of this thesis is to design, simulate and analyze an end-end performance of multi-antenna wireless systems employing cooperative multi antenna relay nodes so as to exploit the cooperative diversity and antenna diversity simultaneously in a wireless networks. Three main contributions to the area of cooperative multiple-input multiple-output (MIMO) wireless systems is presented in this thesis. First, we perform information theoretic analysis to study the impact of antenna arrays on cooperative wireless networks and propose the best possible distribution of antenna arrays among the three terminals of a simple three terminal cooperative relay network. Second, we design, simulate, and analyze a cooperative multiple-input multiple-output (MIMO) wireless systems employing orthogonal space-time block codes as proposed by Alamouti in 1998 with a decode-and-forward (DF) relay terminal. We implement a maximal ratio combining receiver that provides almost twice the diversity gain with respect to point-point multiple input multiple output link. Finally, we implement a practical receiver for cooperative reception using multiple antennas at all nodes based on Bell-Labs Layered Space Time architecture (BLAST). We incorporate a practical adaptive decode-and-forward (DF) relaying technique for reliable signal retransmission for both Alamouti space-time coding and the BLAST schemes. Results presented in terms of bit error rates and throughput show that remarkable performance gains are achievable by combining the concepts drawn from space-time coding, cooperative relaying and array processing.

We recently introduced the high-resolution nonnegative matrix factorization (HR-NMF) model for analyzing mixtures of nonstationary signals in the time-frequency domain, and highlighted its capability to both reach high spectral resolution and reconstruct high quality audio signals. In order to estimate the model parameters and the latent components, we proposed to resort to an expectation-maximization (EM) algorithm based on a Kalman filter/smoother. The approach proved to be appropriate for modeling audio signals in applications such as source separation and audio inpainting. However, its computational cost is high, dominated by the Kalman filter/smoother, and may be prohibitive when dealing with high-dimensional signals. In this paper, we consider two different alternatives, using the variational Bayesian EM algorithm and two mean-field approximations. We show that, while significantly reducing the complexity of the estimation, these novel approaches do not alter its quality.

This paper considers the problem of the joint channel and carrier frequency offset (CFO) estimation for asynchronous amplify-and-forward (AF) two-way relay networks (TWRNs). This problem has not been solved to the best of our knowledge, and the presence of timing offsets between the two terminals, in addition to the frequency offsets, makes it necessary to develop signal sampling and joint estimation schemes that explicitly take into account both offsets. As potential solutions, we investigate two estimation strategies. The first strategy is pilot-based estimation, and in this context, we develop the maximum-likelihood joint CFO and channel estimator. Then, we consider the semi-blind estimation strategy, proposing a novel estimator based on expectation maximization (EM). As an alternative to the EM, we also investigate decision-directed (DD) semi-blind estimation. The semi-blind Cramer-Rao bound (CRB) is also obtained as a benchmark. Extensive experiments are used to compare the different estimation methods, showing that the proposed EM algorithm yields significantly lower mean-squared error than both the pilot-based estimator and the DD estimator and converges to the obtained CRB. It also yields much better symbol error rates. This is achieved at a reasonable computational complexity, and only a limited number of EM iterations are sufficient for convergence. The main contribution of our work is the development of the EM estimator, the corresponding CRB, and the use of simulations to demonstrate the superior performance of the proposed EM algorithm compared to other potential solutions.

The authors consider a space–time coded (STC) orthogonal frequency-division multiplexing (OFDM) system with multiple transmitter and receiver antennas over correlated frequency- and time-selective fading channels. They propose first a maximum-likelihood (ML) receiver for space–time block code OFDM systems based on the expectation–maximisation (EM) algorithm. They then propose a low-density parity-check (LDPC)-code-based STC-OFDM system to interface with the EM algorithm. When comparing the proposed scheme with the conventional space–time trellis code, the LDPC-based STC significantly improves the system performance by exploiting both spatial and selective-fading diversity in wireless channels. Compared with the recently proposed turbo-code-based STC scheme, LDPC-based STC exhibits a lower complexity and more flexible scalability.

Accurate channel estimates are needed in space-time coded OFDM systems for decoding purposes. In this paper, a novel channel tracking algorithm based on space-time coded training and information symbols is presented. The algorithm takes advantage of the orthogonality properties of the space-time block codes and it is therefore capable of providing channel estimates without performance degradation due to estimation errors from adjacent channels. The algorithm is tested via Monte Carlo computer simulations using both slowly Rayleigh fading channels and time-invariant frequency selective channels and Alamouti space-time block coding. Computer simulations also show that this simple algorithm outperforms LMS-based approach without additional complexity.

This paper applies the expectation-maximization (EM) algorithm to address the problem of joint channel estimation and channel decoding in Physical-layer Network Coding (PNC) systems. The use of PNC can significantly improve the throughput of a relay network. The throughput advantage, however, is predicated on the availability of accurate channel estimates. For channel-coded PNC systems, a major challenge is that the maximum a posteriori probability (MAP) channel estimation is nontrivial due to 1) the overlapping of signals from multiple users received at the relay; and 2) the correlations among data symbols introduced by channel coding. In this paper, we show that an EM algorithm implemented on a factor graph framework is well suited to tackle this problem. Through iterative message passing, the channel estimation component and the channel decoding component in the factor graph interact to improve each other's results progressively. Simulation results indicate that just one EM iteration of our algorithm can significantly improve the channel estimation accuracy as well as the BER performance of channel-coded PNC systems.

It has been proved that when the transmit power is sufficiently large distributed space time codes can achieve the maximal diversity order in a wireless relay network. In the previous works, space time codes used in a wireless relay network are limited on unitary space time codes or orthogonal (or quasi- orthogonal) space time codes. In this paper, we apply general multi-layer full-rate space time codes generated by algebraic extension into the wireless relay network. Moreover, the optimal power allocation and the Chernoff upper bound of the pair-wise error probability (PEP) based on the maximum-likelihood (ML) decoding are calculated. Based on this bound, two design criteria of the multi-layer full-rate space time codes are provided.

Channel estimation is very challenging for millimeter wave (mmWave) massive multiple input multiple output (MIMO) systems with low-resolution analog-to-digital converters (ADCs) owing to the severe nonlinear distortion introduced by quantization. In this paper, we develop an advanced channel estimation method based on generalized expectation consistent signal recovery (GEC-SR) algorithm, which can obtain accurate channel state information from quantized signal. Specifically, we consider Laplacian prior to model angular domain mmWave channel coefficients and embed the expectation-maximization (EM) principle into GEC-SR algorithm to learn the unknown prior parameters. Numerical results show that our method outperforms state-of-the-art generalized-approximate-message-passing-based channel estimator, and can reduce the required pilot overhead significantly by using orthogonal pilot. © 2019 IEEE.