High-convergence-speed low-computation-complexity SVD algorithm for MIMO-OFDM systems

This paper presents a low complexity hardware design for computing Singular Value Decomposition (SVD) of the radio communication channel characteristic matrix. The hardware developed is suitable for computing the SVD of a sequence of 3 ×3 complex-value matrices used in MIMO-OFDM standards, such as the IEEE 802.11n. The information of the right singular-vector matrix can be fed back to the transmitter for linear precoding to improve the error performance when facing the channel matrix with rank deficiency problem. The time for the SVD of one complex matrix is limited to about 400 ns. When the channels have short coherent time, the information derived by SVD should be sent from the receiver to the transmitter as soon as possible to keep the precoding performance. The algorithms to decompose the channel matrix were implemented using the Virtex-II xq2v1000-4bg575 FPGA from Xilinx as the target device with Maximum combinational path delay: 109.338ns. The implementation concentrates on utilizing the features of the FPGA to speed up operations and reduce the area required.

The previously proposed first-order perturbation-based algorithm and linear constrained least mean square (LMS) based algorithm for channel matrix singular value decomposition (SVD) in multiple - input multiple - output (MIMO) orthogonal frequency division multiplexing (OFDM) systems are evaluated and compared in this paper from orthogonality, signal to noise plus interference ratio (SINR) and bit error rate (BER) view points. Due to approximations made in the perturbation-based algorithm to reduce its complexity, studies show that the estimates of the right and left singular matrices do not become unitary in this algorithm. This phenomenon causes more spatial interference and therefore the perturbation-based algorithm has less performance in comparison with the LMS-based algorithm at high SNRs.

In this paper, a unified algebraic transformation approach is presented for designing parallel recursive and adaptive digital filters and singular value decomposition (SVD) algorithms. The approach is based on the explorations of some algebraic properties of the target algorithms' representations. Several typical modern digital signal processing examples are presented to illustrate the applications of the technique. They include the cascaded orthogonal recursive digital filter, the Givens rotation-based adaptive inverse QR algorithm for channel equalization, and the QR decomposition-based SVD algorithms. All three examples exhibit similar throughput constraints. There exist long feedback loops in the algorithms' signal flow graph representation, and the critical path is proportional to the size of the problem. Applying the proposed algebraic transformation techniques, parallel architectures are obtained for all three examples. For cascade orthogonal recursive filter, retiming transformation and orthogonal matrix decompositions (or pseudo-commutativity) are applied to obtain parallel filter architectures with critical path of five Givens rotations. For adaptive inverse QR algorithm, the commutativity and associativity of the matrix multiplications are applied to obtain parallel architectures with critical path of either four Givens rotations or three Givens rotations plus two multiply-add operations, whichever turns out to be larger. For SVD algorithms, retiming and associativity of the matrix multiplications are applied to derive parallel architectures with critical path of eight Givens rotations. The critical paths of all parallel architectures are independent of the problem size as compared with being proportional to the problem size in the original sequential algorithms. Parallelism is achieved at the expense of slight increase (or the same for the SVD case) in the algorithms' computational complexity.

Rapidly growing demand for high data rates in wireless communication systems is the cause of the merging of Multiple Input Multiple Output (MIMO) and Orthogonal Frequency Division Multiplexing (OFDM) techniques. MIMO-OFDM technique needs Radio Frequency (RF) front end in each antenna, which is not effective for large dimensional antenna size. Therefore, RF front end on the receiver side will be simplified using a single RF technique based on the Electrically Steerable Parasitic Array Radiator (ESPAR) antenna. In real life, a channel cannot be ideal. Therefore, before the signal is transmitted, that signal must be coded to minimized errors when the data transmission process. Convolutional code is a coding technique that can detect and correct error bit (error control coding) and that it is expected to reduce the quantity of Bit Error Rate (BER). In this research, a simulation is designed to analyze single RF performance on the MIMO-OFDM system using Vertical Bell Laboratories Space-Time (VBLAST) detection for convolutional code encoder and Viterbi decoder. The result simulation shows that the channel estimation technique works well on the MIMO-OFDM system using single RF, which is shown in the magnitude and phase curves against the subcarrier index between the theory channel and the estimated channel are at almost the same points. VBLAST-ZF detector performance is shown in the BER curve against SNR, where the difference BER value for SNR value 10 dB between the theory channel and the estimated channel is 0.001499. Channel coding technique using convolutional code encoder and Viterbi decoder with a rate of ½ works well on the MIMO-OFDM system using single RF which is shown in the BER curve against SNR, where BER value with coding technique is smaller than BER value without coding technique.

Singular Value Decomposition (SVD) algorithm is a good method in Collaborative Filtering (CF) algorithm. But the traditional SVD method faces the matrix sparse problem, people solve this problem by Latent Factor Model (LMF). The data imbalances problem also troubles us. The algorithm of this paper combines Slope One and SVD algorithm to solve the data imbalances problem. First, we use Slope One algorithm to deal with the users who have few rating records. Then this kind of user will have more rating records. And we can use new data set to train the SVD model to predict the final results. The experiment results show that our algorithm is better than the traditional Slope One and SVD algorithm.

The combination of multiple-input multiple-output (MIMO) and orthogonal frequency division multiplexing (OFDM) technologies gives wireless communications systems the advantages of lower bit error rate (BER) and higher data rate in frequency-selective fading environments. However, the main drawback of the MIMO-OFDM systems is the increase of complexity, and thus cost. In this paper, we propose an antenna selection method for a MIMO-OFDM receiver. The proposed method selects a proper combination of polarization antenna elements at receive antenna branches to achieve lower BER performance. Using the channel impulse responses measured in an indoor environment, numerical results show that the proposed selection method works effectively for the realistic channel and promises a great deal of decrease in computational complexity

Independent component analysis for multiple-input multiple-output wireless communication systems

A wireless multiple-input multiple-output (MIMO) communications transceiver is a promising candidate for next generation wireless systems. It can enhance the capacity and reliability of the communication link. MIMO is enabled by the presence of multiple transmitting antennas and multiple receiving antennas in the communication link. The benefits of MIMO communication are obtained through a combination of antenna arrays, signal processing, and coding algorithms, which adapt the link to the changing channel. In this critical review paper, a propagation-oriented viewpoint is adopted to discuss wireless MIMO. We give an overview of current research areas and discuss some open problems.

Singular value decomposition (SVD) is a useful technique to mitigate co-space interference (CSI) in multiple input multiple output (MIMO) systems employing orthogonal frequency division multiplexing (OFDM) scheme. The SVD based frequency-domain broadband beamforming (FBBF) approach uses the beamforming matrices in both transmitter and receiver sides for each subchannel matrix. However, when the MIMO- OFDM system has a large number of subchannels, the FBBF technique is very complex due to computing the SVD of each subchannel separately. In this paper, we propose a new approach to eliminate CSI and intersymbol interference (ISI) in time- domain and frequency-domain, respectively. By the use of polynomial matrix SVD based on SBR2 algorithm, the MIMO- OFDM system is decomposed to the parallel decoupled single input single output (SISO) OFDM systems. In this way, the CSI is eliminated by time-domain broadband beamforming (TBBF) in both transmitter and receiver sides and ISI is mitigated in each SISO-OFDM system by frequency-domain equalization. The performance of the proposed method is evaluated by computer simulations for fixed broadband wireless communication system developed based on the WiMax. Simulation results show that the proposed method achieves good performance in concerned SNR interval.

Wireless network is one of the most important things in the development of telecommunication. However, the existing wireless technology has not been able to efficiently create a very high data rate because it was very sensitive to fading. Therefore, Orthogonal Frequency Division Multiplexing (OFDM) technology combined with MIMO (Multiple Input Multiple Output) transceiver system was used to gain more diversity and bandwidth efficiency. The propagation performed on the OFDM MIMO system was multipath propagation. To reduce Intersymbol Interference (ISI) was used Zero Forcing (ZF) equalizer which works by combining channel response and equalizer response itself to eliminate ISI. This study aims to determine the effect of Zero Forcing Equalizer on OFDM MIMO system using rayleigh fading channel and compared the result with OFDM MIMO STBC system. The research method used was simulation using MatLab R2015a. The simulation results showed that the performance of OFDM MIMO ZF system was worse than OFDM MIMO STBC system i.e BER vs EbNo simulation, eye diagram simulation, and constellation diagram simulation. The OFDM MIMO ZF system was required an Eb / No value more than 25 dB to achieve BER 10-4 while the OFDM MIMO STBC system only required an Eb / No value of 10.5 dB to achieve BER 10-4. The eye pattern generated by the OFDM MIMO ZF system was more closed and the dispersion of constellation signals away from the ideal point while OFDM MIMO STBC system displayed a more open eye pattern and the dispersion of its constellation signal closer to the ideal point. It indicated more ISI occurs in the OFDM MIMO ZF system than that in OFDM MIMO STBC system.

To suppress the interference to Licensed Users (LUs) in orthogonal frequency division multiplexing (OFDM)-based Cognitive Radios (CR) systems, a novel spectral precoding scheme is proposed. The precoder matrix is obtained by the singular value decomposition (SVD) algorithm. Analysis and simulations show that the proposed scheme can significantly suppress the power interference by tens of decibels in contrast to the uncoded schemes at a little cost of precoding efficiency. Meanwhile, the peak-to-average-power-ratio (PAPR) is expected to be unaffected and the bit-error-rate (BER) performance over multipath fading channel is improved.

Change point detection is essential to understand the time-evolving structure of dynamic networks. Recent research shows that a latent semantic indexing (LSI)-based algorithm effectively detects the change points of a dynamic network. The LSI-based method involves a singular value decomposition (SVD) on the data matrix. In a dynamic scenario, recomputing the SVD of a large matrix each time new data arrives is prohibitively expensive and impractical. A more efficient approach is to incrementally update the decomposition. However, in the classical incremental SVD (incSVD) algorithm, the information of the newly added columns is not fully considered in updating the right singular space, resulting in an approximation error which cannot be ignored. This paper proposes an enhanced incSVD (EincSVD) algorithm, in which the right singular matrix is calculated in an alternative way. An adaptive EincSVD (AEincSVD) algorithm is also proposed to further reduce the computational complexity. Theoretical analysis proves that the approximation error of the EincSVD is smaller than that of the incSVD. Simulation results demonstrate that the EincSVD and the AEincSVD perform much better than the incSVD on change point detection, and the performance of the EincSVD is comparable to the batch SVD algorithm.

Estimates of the past thermal state of the land surface are crucial to assess the magnitude of current anthropogenic climate change, as well as to assess the ability of Earth System Models to forecast the evolution of the climate near the ground, not included in standard meteorological records. Subsurface temperature data are able to retrieve long-term changes in surface energy balance –from decadal to millennial time scales, thus constituting an important record of the dynamics of the climate system that contributes low-frequency information to proxy-based paleoclimatic reconstructions. A broadly used technique to retrieve past temperature and heat flux histories from subsurface temperature profiles based on a Singular Value Decomposition (SVD) algorithm was able to take into account a limited number of sources of uncertainty, with recent works attempting to increase the number of factors considered in uncertainty estimates. Nevertheless, the SVD methodology did not define a statistical framework for aggregating inversions of individual profiles to derive global results, which lead to estimates of global and regional uncertainties that are difficult to interpret. To alleviate the lack of a conceptual framework for estimating uncertainties in past temperature and heat flux histories at regional and global scales, we combine a new bootstrapping sampling strategy with the broadly used SVD algorithm, and assess its performance against the original SVD technique and another technique based on generating perturbed parameter ensembles of inversions. The new bootstrap approach is able to reproduce the prescribed surface temperature series used to derive an artificial profile. Bootstrap results are also in agreement with the global mean surface temperature history and the global mean heat flux history retrieved in previous studies. Furthermore, the new bootstrap technique provides with a meaningful uncertainty range for the inversion of large sets of subsurface temperature profiles. We suggest the use of this new approach particularly for aggregating results from a number of individual profiles, and to this end, we release the programs used to derive all inversions in this study as a suite of codes labelled CIBOR 1.0: Codes for Inverting BORholes, version 1.0.

The electrical wireless network build 4G TD-LTE network in 1.8GHz band, orthogonal frequency division multiplexing (OFDM) and multiple input multiple output (MIMO) are the key technologies. The OFDM system is sensitive to carrier frequency offset (CFO) and hence accurate CFO estimates for the OFDM system are essential. In this paper, we study the problem of carrier frequency offset (CFO) in multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems, and then a multi-invariance PM algorithm is proposed to estimate CFO in MIMO-OFDM system. The proposed algorithm employs the property of multi-invariance. Simulations show that the proposed algorithm has a better CFO estimation performance than PM.

We propose a new algorithm for the computation of a singular value decomposition (SVD) low-rank approximation of a matrix in the matrix product operator (MPO) format, also called the tensor train matrix format. Our tensor network randomized SVD (TNrSVD) algorithm is an MPO implementation of the randomized SVD algorithm that is able to compute dominant singular values and their corresponding singular vectors. In contrast to the state-of-the-art tensor-based alternating least squares SVD (ALS-SVD) and modified alternating least squares SVD (MALS-SVD) matrix approximation methods, TNrSVD can be up to 13 times faster while achieving better accuracy. In addition, our TNrSVD algorithm also produces accurate approximations in particular cases where both ALS-SVD and MALS-SVD fail to converge. We also propose a new algorithm for the fast conversion of a sparse matrix into its corresponding MPO form, which is up to 509 times faster than the standard tensor train SVD method while achieving machine precision accuracy. The efficiency and accuracy of both algorithms are demonstrated in numerical experiments.