Multiple-input Multiple-output Channel Matrix Research Articles

Over-the-Air Split Machine Learning in Wireless MIMO Networks

In split machine learning (ML), different partitions of a neural network (NN) are executed by different computing nodes, requiring a large amount of communication cost. As over-the-air computation (OAC) can efficiently implement all or part of the computation at the same time of communication, thus by substituting the wireless transmission in the traditional split ML framework with OAC, the communication load can be eased. In this paper, we propose to deploy split ML in a wireless multiple-input multiple-output (MIMO) communication network utilizing the intricate interplay between MIMO-based OAC and NN. The basic procedure of the OAC split ML system is first provided, and we show that the inter-layer connection in a NN of any size can be mathematically decomposed into a set of linear precoding and combining transformations over a MIMO channel carrying out multi-stream analog communication. The precoding and combining matrices which are regarded as trainable parameters, and the MIMO channel matrix, which are regarded as unknown (implicit) parameters, jointly serve as a fully connected layer of the NN. Most interestingly, the channel estimation procedure can be eliminated by exploiting the MIMO channel reciprocity of the forward and backward propagation, thus greatly saving the system costs and/or further improving its overall efficiency. The generalization of the proposed scheme to the conventional NNs is also introduced, i.e., the widely used convolutional NNs. We demonstrate its effectiveness under both the static and quasi-static memory channel conditions with comprehensive simulations.

Lattice Reduction Aided Probability Data Association Detector for MIMO Systems

The performance of symbol detection in multiple-input multiple-output (MIMO) systems is largely determined by the achievable diversity order. The inter antenna interference (IAI), however, can limit detectors’ ability to take full advantage of diversity. This occurs because off-diagonal channel coefficients of the MIMO channel matrix are not mutually orthogonal. Nevertheless, this can be mitigated with the aid of lattice reduction (LR), which aims to increase the orthogonality among these coefficients. We propose a LR aided probability data association (PDA) detector that achieves a similar diversity order to that of the optimum detector but with significant less computational complexity.

Distributed Multiuser MIMO for LiFi: Experiments in an Operating Room

Networked optical wireless communication, also denoted as LiFi, is expected to play an important role in so-called smart hospitals. In this paper, we present the first experimental study of LiFi in an operating room at Motol University Hospital in Prague, Czech Republic. First, we perform one-to-one measurements using an optical transmitter (Tx) and receiver (Rx) and observe that channels with a free LOS provide sufficient signal strength for mobile communication inside the operating room. Then we combine the individual LOS links into a multiple-input multiple-output (MIMO) link using four distributed transmitters representing a wireless infrastructure, and six distributed receivers representing medical devices. In this configuration, at least two strong singular values of the MIMO channel matrix are observed which allow spatial multiplexing. By appropriately clustering the transmitters and selecting the users, mobile devices can be served in parallel. For data transmission, several multiplexing schemes such as time-division multiple access (TDMA) with one and two best links, TDMA with spatial reuse, space-division multiple access (SDMA) with two best links with and without zero forcing (ZF) are considered. Results show that SDMA with ZF increases the data rate by 2.7 times compared to baseline TDMA, resulting in a total data rate of 600 Mbit/s.

Toeplitz structured subspace for multi-channel blind identification methods

This paper addresses the problem of blind identification of multichannel systems. It proposes three different novel algorithms by exploiting the inherent Toeplitz /Sylvester structures impeded in the system model. The first algorithm is the structured signal subspace (SSS) method, which involves direct estimation of the signal from a multiple-input multiple-output (MIMO) system. The second algorithm is the structured channel subspace (SCS) method, whereby the MIMO channel matrix is estimated by employing its embedded Toeplitz structure. The last algorithm deals with the bilinear blind identification by utilizing the information (embedded structure) of both row and column subspaces of the received signals. The proposed methods exploit the block Sylvester structure of the signal and the channel matrix to formulate a quadratic cost function whose minimization enables us to estimate the desired system parameters. The simulation results of the proposed structured subspace methods are appealing in different scenarios.

Second-Order Statistics-Based Semi-Blind Techniques for Channel Estimation in Millimeter-Wave MIMO Analog and Hybrid Beamforming

Semi-blind (SB) channel estimation is conceived for millimeter wave (mmWave) analog-beamforming (AB) and hybrid-beamforming (HB)-based multiple-input multiple-output (MIMO) systems, which also exploits the data symbols for improving the estimation accuracy. A novel aspect of the proposed framework is that it directly estimates the analog beamformer/ combiner weights without necessitating the estimation of the entire mmWave MIMO channel matrix. By involving powerful matrix perturbation theoretic techniques, a closed-form expression is derived for the mean-squared-error (MSE) of the mmWave-AB-SB algorithm. As a further novelty, our mmWave-HB-SB technique relies on the decomposition of the channel matrix as the product of a decorrelating and a unitary matrix. Subsequently, the former is estimated purely relying on the unknown data symbols, whereas the latter is estimated exclusively from the training vectors. A lower bound on the MSE of the proposed mmWave-HB-SB technique is derived using the constrained Cramer-Rao lower bound (CRLB) framework. Furthermore, the performance gain of our mmWave-HB-SB technique over the conventional purely training-based scheme is also quantified analytically. Our simulation results demonstrate the superiority of the techniques advocated over the existing solutions and also verify the accuracy of our analytical findings.

Low-complexity MIMO demultiplexing scheme based on geometric vector extraction in visible light communication system

As one of the main optical wireless communication technologies, visible light communication (VLC) is considered a promising supplement in 5G/6G and the internet of things (IoT) networks. The multiple-input–multiple-output (MIMO) multiplexing scheme can significantly enhance a VLC system’s performance. To handle the blind MIMO demultiplexing, geometric vector extraction (GVE) algorithms are used in a mixture space (MS), which has not been presented in the extant literature. In a 2 × 2 VLC MIMO scenario, the singular value decomposition of an arbitrary MIMO channel matrix is introduced to discuss the one-to-one relationship between channel-matrix elements and the outline-shape conversion starting from the transmitted rectangular-shaped points in the MS. By extracting the vector features of the adjacent sides of the received parallelogram-shaped constellation points, we can obtain the elements of an unknown channel matrix and recover the superposed signals transmitted by two light-emitting diodes (LED). To obtain a vector from these constellation points, clustering is required to obtain the scattered points’ centroids in advance. To avoid falling into a local minimum, we present a clustering algorithm with an initial-position-expansion pre-processing stage to place the initial centroids with the greatest accumulated distance. To enhance the computational efficiency, we enhance the clustering algorithm via a single iteration to obtain the centroids, which we named the GVE-for-iteration-once (GVE–IO) algorithm. The enhanced algorithm has an equivalent or better MIMO demultiplexing performance and quick convergence performance compared to the fast independent component analysis (FastICA) algorithm. Moreover, the GVE–IO algorithm’s computational complexity and measured running time is reduced to 29% and 23%, respectively, of the FastICA algorithm’ time costs. Finally, the experimental investigation shows that the proposed scheme exhibits a significantly reduced computational complexity in all discussed voltage peak-to-peak (Vpp) cases of LED and a Q-value enhancement in two-thirds of the Vpp combination regions for 50 input points.

Semi-blind joint channel estimation and data detection on sphere manifold for MIMO with high-order QAM signaling

A low-complexity semi-blind scheme is proposed for joint channel estimation and data detection on sphere manifold for multiple-input multiple-output (MIMO) systems with high-order quadrature amplitude modulation signaling. Specifically, the optimal channel estimator is expressed in the least squares form in terms of the received signals and unknown transmitted data, and by splitting the channel and transmitted data into their real parts and imaginary parts, the data detection becomes a problem defined on a scaled sphere manifold in the real domain. Our semi-blind algorithm consists of three stages: (i) a few training symbols are employed to provide a rough initial MIMO channel estimate which in turn yields the initial zero-forcing (ZF) estimate of data samples; (ii) the Riemannian conjugate gradient algorithm is used to estimate the data samples in real domain, and the detected data samples are used to estimate the final MIMO channel matrix; and (iii) the final ZF data detection is carried out based on the final MIMO channel estimate. In particular, we present the first order Riemannian geometry of the sphere manifold which is utilized in the Riemannian conjugate gradient algorithm for solving (ii). Simulation results are employed to demonstrate the effectiveness of the proposed approach.

Multiuser Detection for Nonlinear MIMO Uplink

For the multiple-input multiple-output (MIMO) uplink employing high-order quadrature amplitude modulation (QAM) signaling and with nonlinear high power amplifiers (HPAs) at mobile users’ transmitters, the existing multiuser detection methods can no longer be applied. We propose a novel nonlinear multiuser detection scheme for the nonlinear MIMO uplink. Specifically, we adopt an effective B-spline parameterization of the nonlinear transmit HPAs and derive an efficient and accurate algorithm to identify the nonlinear MIMO uplink channel, including the nonlinear B-spline model of the nonlinear transmit HPAs and the estimate of the linear MIMO channel matrix. Moreover, as the direct result of this nonlinear MIMO channel identification, the B-spline inverse model of nonlinear transmit HPAs can readily be identified. The nonlinear multiuser detection can be effectively implemented by the zero-forcing linear detection based on the estimated linear MIMO channel and followed by compensating the nonlinear distortion of the nonlinear transmit HPAs based on the estimated B-spline inverse model. An extensive simulation investigation is performed to demonstrate the effectiveness of our proposed nonlinear multiuser detection scheme for nonlinear MIMO uplink with high-order QAM signaling.

Accurate Channel Estimation for Millimeter-Wave MIMO Systems

Channel estimation is of great challenge for millimeter-wave (mmWave) multiple-input multiple-output (MIMO) systems. The underlying reason can be attributed to two facts. One is the huge dimension of MIMO channel matrix, since mmWave systems typically employ large antenna arrays at both the transmitter and receiver to realize sufficient link margin. The other fact is the limited number of radio-frequency chains available for transmitter/receiver array, due to the power and cost limitations. This paper proposes a two-stage accurate channel estimation scheme for mmWave MIMO. Initially, we utilize sparse Bayesian learning to obtain a coarse channel estimate. Then we refine the channel estimate by iteratively maximizing the likelihood function of channel parameters. It is shown through simulations that the proposed scheme significantly outperforms the counterparts, and can achieve accurate channel estimation performance.

Experimental Evaluation of the Tri-Polarized MIMO Channel Properties Based on a Compact Multimode Antenna

Based on a planar and compact antenna, extensive measurements are conducted to investigate the behavior of the colocated tri-polarized multiple-input multiple-output (MIMO) system working at 3.5 GHz. Several scenarios with different multipath distributions have been considered, including a reverberation chamber (RC) and also some line-of-sight (LOS) and obstructed LOS (OLOS) real-world indoor environments. Many channel parameters of the MIMO system are analyzed based on the measured data, including cross-polarization discrimination (XPD), Ricean K-factor, correlation coefficient (CC), MIMO channel capacity gain (CG), channel eigenvalues, and ellipticity statistic (ES). The results show that for a multi-polarized MIMO system, the effects of polarization coupling and transition depend strongly on the polarimetric scattering characteristic of the environments. Furthermore, in all the scenarios tested, three non-zero eigenvalues of the MIMO channel matrix are obtained, which indicates that three independent subchannels can be supported by the tri-polarized MIMO system.

PAPR-Aware Massive MIMO-OFDM Downlink

We investigate the peak-to-average power ratio (PAPR) reduction problem in orthogonal frequency-division multiplexing-based massive multi-user (MU) multiple-input multiple-output (MIMO) downlink systems. In this paper, we develop a downlink transmission scheme that performs jointly MU precoding and PAPR reduction (PP) by exploiting the excess degrees of freedom offered by equipping the BS by a large number of antennas. Specifically, the joint MU precoding and PAPR reduction scheme is formulated as a simple convex optimization problem solved via steepest gradient descent (GD) approach. Then, we develop a novel algorithm, referred to as MU-PP-GDm, to reduce the PAPR of the transmitted signals by exploiting the high-dimensional null space of the MIMO channel matrix while maintaining an excellent transmission quality. The simulation results show that the proposed MU-PP-GDm has low computational complexity and can achieve substantial PAPR performance with a fast convergence rate.

A Novel Geometrical Model for Non-Stationary MIMO Vehicle-to-Vehicle Channels

A novel geometry-based statistical model for non-stationary multiple-input multiple-output (MIMO) vehicle-to-vehicle (V2V) Rayleigh fading channels is presented in this paper. The proposed model seeks to provide new insights into the non-stationary characteristics of MIMO V2V channels stemming from the time-varying propagation delays of the received multipath signal. To achieve this goal, the temporal evolution of the propagation delays is characterized following a simple, although theoretically sound, plane-wave propagation approach. The modelling framework presented here allows obtaining generic expressions for the space-time-frequency cross-correlation function of the MIMO V2V channel, unveiling in the process important features of the channel's correlation and stationary properties. The obtained results show that as a consequence of the time-varying character of the propagation delays, the elements of the MIMO channel matrix are non-wide-sense stationary uncorrelated scattering (non-WSSUS) random processes, as well as pairwise jointly non-wide-sense stationary (non-WSS). The particular cases where the proposed MIMO V2V channel model can be considered quasi-WSS are also discussed for the sake of completeness.

A Weighted Combining Algorithm for Spatial Multiplexing MIMO DF Relaying Systems

Jointly detecting the signals from the source and relay in a spatial multiplexing (SM) multiple-input multiple-output (MIMO) relaying system improves the transmit reliability significantly. However, the existing joint detection schemes for SM MIMO relaying systems, which achieve full diversity, such as the near maximum likelihood (ML) decoder, suffer from high complexity. In this paper, we propose a weighted combining (WC) algorithm, which is applied before the detector in the SM MIMO decode-and-forward relaying system. The proposed algorithm merges the received signal vectors from the source and relay into a combined signal without expanding their dimension, and formulates an equivalent MIMO channel matrix for the combined signal, resulting in a lower complexity for the subsequent detection. We analyze the performance of the proposed WC algorithm with ML detection in terms of the diversity order and computational complexity. An approximate upper bound on the symbol error probability (SEP) for the proposed algorithm is also derived. Simulation results show that in symmetric networks, the proposed WC algorithm achieves substantially lower complexity, while maintaining an SEP performance similar to that of the benchmark NML decoder. The consistency of the derived upper bound on the SEP is also verified by simulations.

Experimental study on the statistic characteristics of a 3x3 RF MIMO channel over a single conventional multimode fiber.

Based on the observed random fluctuation phenomenon of speckle pattern across multimode fiber (MMF) facet and received optical power distribution across three output ports, we experimentally investigate the statistic characteristics of a 3×3 radio frequency multiple-input multiple-output (MIMO) channel enabled by mode division multiplexing in a conventional 50µm MMF using non-mode-selective three-dimensional waveguide photonic lanterns as mode multiplexer and demultiplexer. The impacts of mode coupling on the MIMO channel coefficients, channel matrix, and channel capacity have been analyzed over different fiber lengths. The results indicate that spatial multiplexing benefits from the greater fiber length with stronger mode coupling, despite a higher optical loss.

Spatially Sparse Beamforming Training for Millimeter Wave MIMO Systems

To realize high beamforming gain and thus sufficient link budget, millimeter wave (MMW) multiple-input multiple-output (MIMO) systems employ large antenna arrays at both the transmitter and receiver. However, due to the power and cost limitation, only a limited number of radio frequency (RF) chains are available for MMW antenna arrays. In other words, the number of RF chains is far smaller than that of antenna elements. This MMW MIMO setup poses a formidable challenge for channel estimation, which is conventionally required to realize the optimal singular value decomposition (SVD) beamforming. To circumvent the formidable channel estimation, this paper proposes two iterative antenna training schemes for the SVD beamforming in MMW MIMO systems. Relying on the channel reciprocity in time division duplex, the proposed schemes employ power iteration and Lanczos iteration, respectively, to gradually approach the SVD beamforming. During iterations, we only need to estimate several channel-related vectors instead of the MIMO channel matrix. Thanks to the spatial sparsity in MMW channels, the training overheads required by the proposed schemes are moderate. Simulations demonstrate that the proposed schemes outperform the counterpart in terms of performance and training overhead, and can achieve the performance very close to that of the perfect SVD beamforming.

Decoupling of Broadband Optical MIMO Systems Using the Multiple Shift SBR2 Algorithm

Polynomial singular value decomposition (PSVD) plays a very important role in broadband multiple-input multiple-output (MIMO) systems. One of its applications lies in the decoupling of MIMO convolutive mixing channel matrixin order to recover the transmitted signals corrupted by the channel interference (CI) at the receiver. In this paper, a novel algorithm, known as multiple shift second order sequential best rotation (MS-SBR2), is proposed to compute the approximate PSVD of the broadband MIMO channel matrix. Experimental examples, including a measured (2 × 2) optical MIMO channel impulse response using the multi-mode fiber (MMF) testbed, are presented to examine the proposed algorithm. Bit error rate (BER) performances are evaluated among different transmission schemes. In addition, power allocation (PA) schemes are investigated to further optimize the BER performance.

Analysis of the Spatial Correlation of Indoor MIMO PLC Channels

In this letter, an analysis of the spatial correlation of multiple-input multiple-output (MIMO) power line communications (PLC) channels in the frequency range 1–80 MHz is provided, where the term spatial correlation refers to the relation between the paths that form the MIMO channel matrix. The study is based on a large set of $2\times 2$ MIMO channels measured in four different countries. The presented statistical analysis of the condition number reveals three important facts. First, the spatial correlation is almost independent of frequency, which has important implications in the development of top-down MIMO PLC channel models. Second, the use of an alternative injection method can notably reduce the spatial correlation and, consequently, increase the system bit-rate. Third, there exist countries whose channels have larger spatial correlation values than others. Since spatial correlation plays a key role in the performance of MIMO PLC systems, a hypothesis relating the type of wiring deployed in the indoor power grid to the spatial correlation is given and supported by simulations.

A Low-Complexity Rank Indicator Determination Method for the LTE System

In a long term evolution (LTE) system, channel state information can be acquired at the transmitter (Tx) from three feedback parameters: the rank indicator (RI), precoding matrix indicator, and channel quality indicator. These parameters can facilitate the dynamic adjustment of signals at the Tx, thereby enhancing its transmission performance. In this paper, we propose a RI determination method for LTE system; the method is based on the eigen-value ratio test for a multiple-input multiple-output channel matrix. It has almost the same selection ability as that of the exhaustive full search method and offers the advantage of lower computational complexity compared with that of methods reported in the literature.

MIMO Optical Wireless Communications Using ACO-OFDM and a Prism-Array Receiver

In this paper, we analyze the performance of a prism-array receiver in a multiple-input multiple-output (MIMO) intensity-modulated direct-detection optical wireless communication system. The elements of the MIMO channel matrix depend on the geometry of each prism and the orientation of the prism relative to the optical transmitter. An expression is derived for each channel gain as a function of the angle of the prism, the aspect ratio and area of the receiving surface of the prism, and the orientation and distance between the transmitter and receiver. Results are presented for the directionality and overall field of view (FOV) of a receiver comprising six prisms, showing that compact receivers can be designed, which combine well-conditioned channel matrices with wide FOVs. Simulation results are presented for a typical indoor visible light communication system where four light-emitting diode lights transmit information using asymmetrically clipped optical orthogonal frequency division multiplexing and linear equalizers are used in the receiver. It is shown that the overall bit error rate depends very strongly on the angle of the prisms and on the position of the receiver, but that a simple six-prism receiver can successfully decouple the four transmitted signals at typical receiver positions within the room.

QR decomposition aided belief propagation detector for MIMO systems

A QR decomposition aided belief propagation (QR-BP) detector for multiple-input multiple-output (MIMO) systems is proposed. Before the iterative message passing process, linear transformation is performed by using the unitary matrix obtained from the QR decomposition of the original MIMO channel matrix. Then, the original MIMO channel matrix is replaced by an upper triangular channel matrix after the linear transformation and the proposed QR-BP detector operates over the new bipartite graph from the upper triangular channel matrix. Therefore, the number of cycles in the new bipartite graph is significantly decreased when compared with the fully connected bipartite graph from the original MIMO channel matrix. In addition, since the unitary matrix is utilised for the linear transformation, there is no information loss on the likelihoods estimated from noisy observations. Simulation results verify that the proposed QR-BP detector outperforms existing BP detectors and achieves near-optimum performance close to the maximum-likelihood detector in terms of bit error ratio.