Block Diagonalization Algorithm Research Articles

Block Diagonal Representation Learning for Hyperspectral Band Selection

Hyperspectral band selection is viewed as an effective dimension reduction method. Recently, researchers present graph-based clustering for hyperspectral image (HSI) processing. However, most of them conduct clustering on a fixed data matrix so that it is sensitive to the quality of initial matrix. Moreover, these algorithms apply spectral clustering to obtain the final clustering result in increasing the time consumption. Based on these facts, we propose a block diagonal representation learning algorithm (BDRLA) in this paper. BDRLA generates a high-quality similarity matrix by approximating the initial affinity matrix. Meanwhile, motivated to the spectral bands distance similarity matrix has a clear diagonal structure, a block diagonal similarity matrix with ordered partition points based upon the ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -norm is constructed. By doing so, the obtained similarity matrix is directly applied to subsequent processing without extracting the clustering indicators. Additionally, in order to estimate the importance of bands, dictionary learning is adopted to select the representative band in each cluster. Extensive experiment results on three public datasets indicate that the bands selected by the proposed method achieve satisfactory performance.

Mixed Precision Recursive Block Diagonalization for Bivariate Functions of Matrices

Various numerical linear algebra problems can be formulated as evaluating bivariate function of matrices. The most notable examples are the Fréchet derivative along a direction, the evaluation of (univariate) functions of Kronecker-sum-structured matrices, and the solution of, Sylvester matrix equations. In this work, we propose a recursive block diagonalization algorithm for computing bivariate functions of matrices of small to medium size, for which dense linear algebra is appropriate. The algorithm combines a blocking strategy, as in the Schur--Parlett scheme, and an evaluation procedure for the diagonal blocks. We discuss two implementations of the latter. The first is a natural choice based on Taylor expansions, whereas the second is derivative-free and relies on a multiprecision perturb-and-diagonalize approach. In particular, the appropriate use of multiprecision guarantees backward stability without affecting the efficiency in the generic case. This makes the second approach more robust. The whole method has cubic complexity, and it is closely related to the well-known Bartels--Stewart algorithm for Sylvester matrix equations when applied to $f(x,y)=\frac{1}{x+y}$. We validate the performances of the proposed numerical method on several problems with different conditioning properties.

Hybrid Beamforming and Data Stream Allocation Algorithms for Power Minimization in Multi-User Massive MIMO-OFDM Systems

A hybrid beamforming structure is suggested as one of the solutions to reduce implementation costs and energy consumption in millimeter-wave massive multiple-input, multiple-output (MIMO) systems. In this study, an optimization problem of resource allocation was formulated to minimize the total system transmission power on downlink under a certain quality-of-service (QoS), such as bit/block error rates and data rates for each user, and the solution was proposed therein. Our proposed stream incremental algorithm can dynamically adjust the number of data streams for each user according to the channel state information. Precoding and combining schemes need to be developed to solve the formulated problem and also are proposed in this paper to be paired up with the stream incremental algorithm. Our proposed algorithms consider the practical modulation and coding scheme for transmission in various data stream allocation and beamforming designs. The proposed algorithms provide beamforming solutions for millimeter-wave massive MIMO systems, which achieve comparable performance to that of a fully digital block-diagonalization (BD) algorithm with a lower implementation cost and outperform those of modified existing hybrid beamforming algorithms. Simulation results demonstrate the efficacy of the proposed schemes by allocating the different numbers of data streams for each user according to the channel state information. The simulation results verified that the proposed method can achieve a good trade-off between complexity and performance on comparison with the modified existing schemes and the full digital solutions.

PAPR Reduction in MIMO-OFDM via Power Efficient Transmit Waveform Shaping

In this paper we revisit the long standing problem of peak-to-average power ratio minimization in MIMO-OFDM systems, with a new angle of approach on a well-known scheme. Utilizing the principles of tone reservation, we place dummy symbols, i.e., complex coefficients, on unused space-frequency resources with the aim to jointly minimize the transmit signal PAPR and the self-power consumption of the dummy symbols. This joint minimization is solved using three different proposed algorithms exhibiting varying degrees of computational complexity and PAPR reduction performance. Our proposed framework utilizes the strict PAPR expression, i.e., we take into account the average transmit power of the antenna, to simultaneously reduce the PAPR on all antennas while keeping the self-power consumption of the scheme minimal. Our simulation results show that this optimization objective provides better worst-case PAPR reduction and dummy symbol power consumption performance compared to the peak power minimization objective widely utilized in the tone reservation literature. Finally, we propose a novel take on a well-known block-diagonalization algorithm by exploiting knowledge on dummy symbol allocations, resulting in high-gain data streams in downlink transmission.

Research on 5G‐Oriented Wireless Sensor Array of Millimeter Hybrid Beam Sensing Terminal

With the rapid development of information technology, facing the problems and new challenges brought by mobile Internet and Internet of things technology, as one of the key technologies of 5G, millimeter‐wave mobile communication (28/38/60/70 GHz) which can realize gigabit (GB/s, or even higher) data transmission rate has also attracted extensive attention of wireless researchers all over the world, it has quickly become a research hotspot in the field of wireless communication. In the millimeter‐wave massive MIMO downlink wireless sensor system, a block diagonal beamforming algorithm based on the approximate inverse of Neumann series is improved to obtain complete digital beamforming. Then, when designing hybrid beamforming, channel estimation and high‐dimensional singular value decomposition are required for traditional analog and digital hybrid beamforming. A low complexity hybrid beamforming scheme is designed. An improved gradient projection algorithm is proposed in the design of analog beamforming, which can solve the problem of high computational complexity and less damage to guarantee and rate. Simulation results show that the hybrid beam terminal of the sensor reduces the number of RF links required for full digital beamforming and is as close to the spectral efficiency performance of full digital beamforming as possible. The results show that the performance of the designed hybrid beamforming scheme can still be close to that of the pure digital beamforming scheme without involving channel estimation and SVD decomposition.

Analysis of spatial correlation of precoding indoor MIMO visible light communication system

In order to solve the problem of multi-user interference and the subchannel strength generated by the block diagonalization (BD) algorithm in multi-user MIMO (MU-MIMO) indoor visible light communication, the bit error rate of the indoor MU-MIMO visible light communication system is optimized by using the substream selected BD algorithm. This paper establishes the channel model for MU-MIMO indoor visible light communication and compares the channel spatial correlation between the 4×4 MIMO and 8×8 MIMO in different indoor system layout modes by using the control variable method and taking different parameters of LED and PD distance, the system capacity and bit error rate performance of substream selected BD algorithm and BD algorithm are compared and analyzed. The results show that with the continuous enhancement of spatial correlation, the bit error rate performance decreases, and the substream selected BD algorithm can bring a gain of more than 4 dB compared with BD algorithm.

Blind separation of complex-valued satellite-AIS data for marine surveillance: a spatial quadratic time-frequency domain approach

&lt;p&gt;In this paper, the problem of the blind separation of complex-valued Satellite-AIS data for marine surveillance is addressed. Due to the specific properties of the sources under consideration: they are cyclo-stationary signals with two close cyclic frequencies, we opt for spatial quadratic time-frequency domain methods. The use of an additional diversity, the time delay, is aimed at making it possible to undo the mixing of signals at the multi-sensor receiver. The suggested method involves three main stages. First, the spatial generalized mean Ambiguity function of the observations across the array is constructed. Second, in the Ambiguity plane, Delay-Doppler regions of high magnitude are determined and Delay-Doppler points of peaky values are selected. Third, the mixing matrix is estimated from these Delay-Doppler regions using our proposed non-unitary joint zero-(block) diagonalization algorithms as to perform separation.&lt;/p&gt;

Downlink Multiuser Hybrid Beamforming for MmWave Massive MIMO-NOMA System with Imperfect CSI

This paper aims to provide a comprehensive scheme with limited feedback for downlink millimeter wave (mmWave) multiuser multiple-input multiple-output (MIMO) nonorthogonal multiple access (NOMA) system. Based on the feedback of the best beam and the channel quality information (CQI) on this beam, the users are grouped into a cluster having the same or coherent best beam and the maximal CQI-difference. To further reduce the intercluster interference, only the candidate cluster can join the cluster set whose intercluster correlation with the existing clusters is lower than threshold. Based on the results of clustering, mmWave hybrid beamforming is designed. To improve the user experience, each cluster selects the best beam of the user with the higher guaranteed rate requirement as the analog beamforming vector. For digital beamforming, the weak user applies the block diagonalization algorithm based on the strong user’s effective channel to reduce its intracluster interference. Finally, an intracluster power allocation algorithm is developed to maximize the power difference in each cluster which is beneficial to improve the successive interference cancelation (SIC) performance of the strong user. Finally, simulation results show that the proposed MIMO-NOMA scheme offers a higher sum rate than the traditional orthogonal multiple access (OMA) scheme under practical conditions.

Bidiagonalization of (k, k + 1)-tridiagonal matrices

Abstract In this paper,we present the bidiagonalization of n-by-n (k, k+1)-tridiagonal matriceswhen n &lt; 2k. Moreover,we show that the determinant of an n-by-n (k, k+1)-tridiagonal matrix is the product of the diagonal elements and the eigenvalues of the matrix are the diagonal elements. This paper is related to the fast block diagonalization algorithm using the permutation matrix from [T. Sogabe and M. El-Mikkawy, Appl. Math. Comput., 218, (2011), 2740-2743] and [A. Ohashi, T. Sogabe, and T. S. Usuda, Int. J. Pure and App. Math., 106, (2016), 513-523].

A Fuzzy Co-Clustering Algorithm via Modularity Maximization

In this paper we propose a fuzzy co-clustering algorithm via modularity maximization, named MMFCC. In its objective function, we use the modularity measure as the criterion for co-clustering object-feature matrices. After converting into a constrained optimization problem, it is solved by an iterative alternative optimization procedure via modularity maximization. This algorithm offers some advantages such as directly producing a block diagonal matrix and interpretable description of resulting co-clusters, automatically determining the appropriate number of final co-clusters. The experimental studies on several benchmark datasets demonstrate that this algorithm can yield higher quality co-clusters than such competitors as some fuzzy co-clustering algorithms and crisp block-diagonal co-clustering algorithms, in terms of accuracy.

Leakage-based precoding algorithms for multiple streams per terminal MU-MIMO systems

Mobile networks rely extensively on multi-input multi-output (MIMO) communications to increase the data rate and improve signal quality. In multi-user MIMO (MU-MIMO) the signals are steered at the base station, forming multiple beams to the several user terminals (UTs). This is achieved by precoding the signals to be sent to the UTs. In leakage-based precoding, the precoding vectors are selected so that the signal to leakage plus noise ratio is maximized, where leakage is the amount of signal that is meant for a given UT but is received by the other UTs. This technique gives better results than techniques that completely eliminate the interference without regard to the signal or noise level (zero forcing solutions) like the block diagonal (BD) algorithm. However, current leakage-based algorithms are only optimal in the case of single-antenna UTs. In this paper, we propose simplified versions of these algorithms suitable for multiple streams per UTs, and compare its performance with existing solutions. Simulation results show an increase in performance. One of the versions does not require any Singular Value Decomposition (SVD) while the other does SVD of a much smaller matrix. Both still achieve better performance than the competition.

A joint precoding scheme for indoor downlink multi-user MIMO VLC systems

In this study, we aim to improve the system performance and reduce the implementation complexity of precoding scheme for visible light communication (VLC) systems. By incorporating the power-method algorithm and the block diagonalization (BD) algorithm, we propose a joint precoding scheme for indoor downlink multi-user multi-input-multi-output (MU-MIMO) VLC systems. In this scheme, we apply the BD algorithm to eliminate the co-channel interference (CCI) among users firstly. Secondly, the power-method algorithm is used to search the precoding weight for each user based on the optimal criterion of signal to interference plus noise ratio (SINR) maximization. Finally, the optical power restrictions of VLC systems are taken into account to constrain the precoding weight matrix. Comprehensive computer simulations in two scenarios indicate that the proposed scheme always has better bit error rate (BER) performance and lower computation complexity than that of the traditional scheme.

Model-based co-clustering for the effective handling of sparse data

With the exponential growth of text documents on the web, there is a genuine need for techniques that organize terms and documents, simultaneously, into meaningful clusters, thereby making large datasets easier to handle and interpret. Several block diagonal clustering algorithms have proven successful in identifying co-clusters of documents and words. However, despite their effectiveness, most of the existing methods do not provide a parameterizable model for tackling the problem of block diagonal identification. In this paper, we rely on mixture models, which offer strong theoretical foundations and considerable flexibility. More precisely, we propose a parsimonious latent block model based on the mixture of Poisson distributions and tailored for sparse high dimensional data such as document-term matrices. In order to efficiently estimate the model parameters, we derive two scalable co-clustering algorithms based on variational inference. Empirical results obtained on several real-world text datasets highlight the advantages of the proposed model and the corresponding co-clustering algorithms.

Minimum Sum-Mean-Square-Error Frequency-Domain Pre-Coding for Downlink Multi-User MIMO System in the Frequency-Selective Fading Channel

This paper proposes a new frequency-domain pre-coding algorithm for the downlink multi-user MIMO system in a frequency-selective fading channel, where each user is equipped with multiple antennas. The proposed algorithm is based on the minimum sum-mean-square-error (Min-SMSE) criterion, which is able to eliminate both the multi-user and multi-antenna interferences, resulting in an improved bit error rate (BER) performance. Compared with the traditional optimal Min-SMSE algorithm, the proposed algorithm can reduce the computational complexity through simplifying the iterative and power allocation processes. Furthermore, the theoretical BER and ergodic sum-rate are derived in detail. In addition, we define and analyze the complexity of the pre-coding algorithms. Simulation results show that the proposed algorithm compares favorably with the optimal Min-SMSE and traditional block diagonalization (BD) algorithms in the sense of the ergodic sum-rate due to the approximately equal power allocation. The BER performance of the proposed algorithm is close to that of the optimal one and much better than that of the BD algorithm in both the uncorrelated and correlated channels. Moreover, the computational complexity of the sub-optimal Min-SMSE algorithm is significantly less than that of its optimal counterpart, especially in the low SNR region.

A Nonorthogonal Joint Block Diagonalization Algorithm Avoiding Degenerate Solutions

The joint block diagonalization algorithm is instrumental to the convolution blind signal separation. However, the nonorthogonal joint block diagonalization algorithm based on a Weighted least-squares (WLS) criterion sometimes converges to the degenerate or trivial solution. It is simple to avoid the trivial solution by adding some constraint on the de-mixing matrix. But the degenerate solution is hard to be excluded. This paper probes the phenomenon of the degenerate solution. By adding a new penalty function to the WLS criterion, an efficient algorithm which can avoid the degenerate solution is developed. Through the theoretical derivation and numerical simulation, we can make the conclusion that the proposed algorithm is more robust and not sensitive to the square or non-square mixing matrix.

OUP accepted manuscript

We propose a scalable algorithmic framework for exact Bayesian variable selection and model averaging in linear models under the assumption that the Gram matrix is block-diagonal, and as a heuristic for exploring the model space for general designs. In block-diagonal designs our approach returns the most probable model of any given size without resorting to numerical integration. The algorithm also provides a novel and efficient solution to the frequentist best subset selection problem for block-diagonal designs. Posterior probabilities for any number of models are obtained by evaluating a single one-dimensional integral, and other quantities of interest such as variable inclusion probabilities and model-averaged regression estimates are obtained by an adaptive, deterministic one-dimensional numerical integration. The overall computational cost scales linearly with the number of blocks, which can be processed in parallel, and exponentially with the block size, rendering it most adequate in situations where predictors are organized in many moderately-sized blocks. For general designs, we approximate the Gram matrix by a block-diagonal matrix using spectral clustering and propose an iterative algorithm that capitalizes on the block-diagonal algorithms to explore efficiently the model space. All methods proposed in this paper are implemented in the R library mombf.

A Linear Recoding and Power Allocation Scheme with Complex Parameters Based on Block Diagonalization Algorithm

MIMO system performance mainly by correlation of spatial interference presence and space, In order to overcome these effects, it is necessary by pre-coding technology to achieve, Here we mainly use block diagonalization algorithm both linear pre-coding for analysis and further integration of the average power allocation algorithm and power allocation algorithm MATLAB simulation. Through research and data analysis, system performance block diagonalization algorithm is better than under zero forcing algorithms. When the same number of transmit antennas, the number of receive antennas are the same, the average power and power calculation algorithm with SNR increases, can effectively channel capacity to achieve the desired optimum value.

FAST BLOCK DIAGONALIZATION OF $(k,k')$-PENTADIAGONAL MATRICES

In this paper, we provide a block diagonalization algorithm of (k,k ' )-pentadiagonal matrices. The algorithm is a structure-preserving algorithm in that the small diagonal blocks essentially have the same nonzero structure as the original one, and it can be regarded as an extension of the block diagonalization algorithm of k-tridiagonal matrices in (T. Sogabe, M.E.A. El-Mikkawy, Appl. Math. Compute., 218 (2011), 2740-2743).

A Low-Complexity Block Diagonalization Algorithm for MU-MIMO Two-Way Relay Systems with Complex Lattice Reduction

We design a scheme of precoding matrices for two-way multiuser relay systems, where a multiantenna relay station (RS) operating in an amplify-and-forward model simultaneously receives information from all multiple-antenna users. Considering the feasibility in mathematical analysis, users are distributed in two symmetrical groups. To reduce the complexity of proposed precoding scheme, we employ the QR decomposition and complex lattice reduction (CLR) transform to replace the two times singular value decomposition (SVD) of conventional BD-based precoding algorithm by introducing a combined channel inversion to eliminate the multiple users interference (MUI). Simulation and performance analysis demonstrate that the proposed LR-MMSE algorithm has not only a better bit error rate (BER) performance, a higher sum-rate, and simple architecture, but also 89.8% and 35.5% less complexity compared to BD- and MMSE-based scheme.

Computer Simulation and Field Experiment for Downlink Multiuser MIMO in Mobile WiMAX System.

The transmission performance for a downlink mobile WiMAX system with multiuser multiple-input multiple-output (MU-MIMO) systems in a computer simulation and field experiment is described. In computer simulation, a MU-MIMO transmission system can be realized by using the block diagonalization (BD) algorithm, and each user can receive signals without any signal interference from other users. The bit error rate (BER) performance and channel capacity in accordance with modulation schemes and the number of streams were simulated in a spatially correlated multipath fading environment. Furthermore, we propose a method for evaluating the transmission performance for this downlink mobile WiMAX system in this environment by using the computer simulation. In the field experiment, the received power and downlink throughput in the UDP layer were measured on an experimental mobile WiMAX system developed in Azumino City in Japan. In comparison with the simulated and experimented results, the measured maximum throughput performance in the downlink had almost the same performance as the simulated throughput. It was confirmed that the experimental mobile WiMAX system for MU-MIMO transmission successfully increased the total channel capacity of the system.