Multiple-output Case Research Articles

MSTGAN: A Multi-Slot Conditional Generative Adversarial Network Based on Swin Transformer for Channel Estimation

Accurate channel estimation is the key to enhance the transmission performance of communication systems. In this letter, we propose a multi-slot conditional generative adversarial network (cGAN) based on Swin Transformer called MSTGAN for channel estimation in a single-input single-output (SISO) scenario. Specifically, the proposed MSTGAN could learn the temporal correlation feature from continuous channel slots by the 3D convolution and extract the deep feature well by the Swin Transformer to improve the accuracy of channel estimation. The model is trained with data augmentation to reduce the computational cost for offline training. The simulation results demonstrate that the proposed method outperforms the linear minimum mean square error (LMMSE) method and other deep learning methods. Furthermore, extension schemes of the MSTGAN to the multiple-input multiple-output (MIMO) case are also provided.

Range-Division Multiplexing for MIMO OFDM Joint Radar and Communications

An orthogonal frequency-division multiplexing (OFDM) waveform enables simultaneous radar sensing and communications. In the multiple-input multiple-output (MIMO) case with several transmit (Tx) antennas, multiplexing the transmit signals is usually implemented using equidistant subcarrier interleaving (ESI), thus allowing the separation of the transmit signals in frequency domain. In this work, a multiplexing technique denoted as range-division multiplexing (RDMult) is analyzed, which allows separating signals radiated by different Tx antennas along the range axis of a range-Doppler map. This work also investigates the effects of RDMult on the communication task. It turns out that RDMult heavily distorts the channel statistics by introducing a repetitive pattern of deep fading holes, which severely distort the transmission of data. To combat this issue, this work proposes a communication system especially designed for RDMult, including methods for data estimation, channel estimation and synchronization. Simulations confirm the effectiveness of these concepts in terms of bit error ratio (BER) performance.

Performance analysis and precoder design for IRS-assisted MIMO system with non-linear power amplifiers

In this work, a point-to-point intelligent-reflecting-surface (IRS) assisted single input single output (SISO) model is first developed and later modified to the multiple-input multiple-output (MIMO) case. For the SISO case, the transmitter or the access point (AP) is assumed to be equipped with a non-linear memory-less power amplifier (PA). A PA is assumed to be present for each data stream at the AP or base station (BS) side for the MIMO case. For both cases, three different types of PAs (A) Soft envelope limiter (SEL), (B) Solid-state power amplifier (SSPA), and (C) Travelling wave tube amplifier (TWTA) are considered. A Bussgang decomposition of the transmitted signal is then utilized for further analysis. A modified channel model is conceived for the AP-IRS-User equipment (UE) link based on the reflecting IRS elements’ radar cross-section (RCS). For the SISO system, both perfect and imperfect geometries of IRS elements with uniformly distributed element size errors are considered. An approximate closed-form expression for the upper bound on the above system’s spectral efficiency (SE) with ideal IRS elements is derived. The expression of the SE for two special cases of (A) Infinitely large IRS and (B) Ideal PA is deduced. Approximate closed-form expressions of various quality parameters for the IRS-assisted MIMO system with ideal and non-ideal PAs are also derived and verified numerically. Maximum ratio transmission (MRT) based precoder for this system is designed assuming that the information about the BS-UE link, BS-IRS-UE link, and the non-linear PA statistics is available at the BS. A closed-form expression for the SE of this system with this precoder is then derived and verified for various parametric situations.

An Efficient MMW 3-D Imaging Algorithm for Near-Field MIMO-SAR With Nonuniform Transmitting Array

In this letter, an efficient millimeter-wave (MMW) frequency-domain imaging algorithm is presented for 3-D object reconstruction of the near-field multiple-input–multiple-output synthetic aperture radar (MIMO-SAR) with nonuniform transmitting array. For each single-input–multiple-output (SIMO) case of the MIMO-SAR setup, the precise spectral echo expression is derived by spherical-wave decomposition and fast Fourier transform (FFT) operations. To obtain the linear phase in range direction, the multiorder approximation theory is employed to expand the coupling phases, and thus the target subimage can be reconstructed by utilizing phase compensation, central wavenumber approximation, and inverse FFT. Finally, the fully focused 3-D image for MIMO setup will be realized through accumulating all the SIMO subimages. Compared with the existing representative algorithms, our method avoids complicated interpolation and achieves high-quality fast imaging with only matrix multiplication and a small amount of iteration operations. The experimental results validate the effectiveness of the proposed algorithm.

Distributed Algorithms for Spectral and Energy-Efficiency Maximization of K-User Interference Channels

In this paper, we propose a cooperative distributed framework to optimize a variety of rate and energy-efficiency (EE) utility functions, such as the minimum-weighted rate or the global EE, for the K-user interference channel. We focus on the single-input multiple-output (SIMO) case, where each user, based solely on local channel state information (CSI) and limited exchange information from other users, optimizes its transmit power and receive beamformer, although the framework can also be extended to the multiple-output multiple-input (MIMO) case. The distributed framework combines an alternating optimization approach with majorization-minimization (MM) techniques, thus ensuring convergence to a stationary point of the centralized cost function. Closed-form power update rules are obtained for some utility functions, thus obtaining very fast convergence algorithms. The receivers treat interference as noise (TIN) and apply the beamformers that maximize the signal-to-interference-plus-noise (SINR). The proposed cooperative distributed algorithms are robust against channel variations and network topology changes and, as our simulation results suggest, they perform close to the centralized solution that requires global CSI. As a benchmark, we also study a non-cooperative distributed framework based on the so-called “signal-to-leakage-plus-noise ratio” (SNLR) that further reduces the overhead of the cooperative version.

Exponential convergence of recursive least squares with forgetting factor for multiple-output systems

We extend results of the recursive-least-squares-with-forgetting-factor identifier for single-input-single-output systems to the multiple-output case by, under the assumption of persistence of excitation, deriving the corresponding minimized objective function and by showing exponential convergence of the estimation error.

Element-wise Bayesian regularization for fast and adaptive force reconstruction

In time domain force reconstruction problems, regularization techniques are widely adopted to solve the intrinsic ill-posedness or ill-conditioning. Different techniques are selected for forces with different temporal profiles, such as Tikhonov regularization for smooth forces and ℓ1 regularization for sparse forces. However, in lack of prior information on force temporal distribution, choosing the appropriate regularization technique is troublesome. In this paper, we propose a novel regularization technique that can reconstruct forces with different types of temporal profiles at known locations. The proposed method, named Element-wise Bayesian regularization, is formulated under the hierarchical Bayesian framework, with an individual prior distribution assumed for each element in the unknown force history. An appropriate regularization level is automatically and adaptively set for each individual element through conditional maximization of the posterior probability of force history. The proposed method is validated by a cantilever plate simulation, an engineering-scale tank simulation, and a laboratory tank experiment under different noise levels and force types. The results conclude that the proposed method accurately reconstruct force histories without any prior information at a fast computation speed under various conditions. The presented work primarily focuses on the single input multiple output case, but the presented methodology can be easily extended towards the multiple input multiple output case.

GBDT-MO: Gradient-Boosted Decision Trees for Multiple Outputs

Gradient-boosted decision trees (GBDTs) are widely used in machine learning, and the output of current GBDT implementations is a single variable. When there are multiple outputs, GBDT constructs multiple trees corresponding to the output variables. The correlations between variables are ignored by such a strategy causing redundancy of the learned tree structures. In this article, we propose a general method to learn GBDT for multiple outputs, called GBDT-MO. Each leaf of GBDT-MO constructs predictions of all variables or a subset of automatically selected variables. This is achieved by considering the summation of objective gains over all output variables. Moreover, we extend histogram approximation into the multiple-output case to speed up training. Various experiments on synthetic and real data sets verify that GBDT-MO achieves outstanding performance in terms of accuracy, training speed, and inference speed.

Robustness Analysis of MIMO Mechatronic Systems in the Frequency Domain

A new and general method of robustness analysis for linear dynamic systems containing both electrical and mechanical components is proposed in this paper. The method is based on the convex optimization theory and, therefore, it is accurate, efficient, and scales well with the number of unknown variables. The method is applied to two examples: a piezoelectric harvester (single-input single-output case) and a double mass–spring–damper system (multiple-input multiple-output (MIMO) case). In both cases, upper and lower bounds of the magnitude response are computed and compared to the Monte Carlo method. The results show that parametric variation affect strongly the performance output, uncertainty must be taken into account for a robust design, and that the proposed method is a great improvement to the existing method in the literature.

Steady-State Performance of an Adaptive Combined MISO Filter Using the Multichannel Affine Projection Algorithm

The combination of adaptive filters is an effective approach to improve filtering performance. In this paper, we investigate the performance of an adaptive combined scheme between two adaptive multiple-input single-output (MISO) filters, which can be easily extended to the case of multiple outputs. In order to generalize the analysis, we consider the multichannel affine projection algorithm (APA) to update the coefficients of the MISO filters, which increases the possibility of exploiting the capabilities of the filtering scheme. Using energy conservation relations, we derive a theoretical behavior of the proposed adaptive combination scheme at steady state. Such analysis entails some further theoretical insights with respect to the single channel combination scheme. Simulation results prove both the validity of the theoretical steady-state analysis and the effectiveness of the proposed combined scheme.

An approach to multidimensional Fornasini–Marchesini state-space model realization w.r.t. columns of transfer matrices

This paper proposes a new approach that can generate a low-order Fornasini–Marchesini (F–M) model realization for a given n-D system by taking into account the column structural properties of its transfer matrix. Specifically, a new necessary and sufficient realization condition is developed for the F–M model realization based on a resolvent invariant space associated with the Gleason’s problem specified by the given n-D transfer matrix. Then, a new constructive procedure with respect to the columns of a given transfer matrix is proposed for constructing a low-order F–M model realization. In order to apply this procedure to the multiple-input multiple-output case more effectively, an improved realization procedure based on a polynomial description is also proposed. It will be shown, by both algorithmic analysis and illustrative examples, that for a transfer matrix having more rows than columns the proposed realization approach may generate a much lower realization order than the existing one with respect to the rows of a given n-D transfer matrix recently developed by Cheng et al. Particularly, for a given scalar transfer function, our new approach always generates an F–M model realization with lower order than the existing methods.

LED Selection and MAP Detection for Generalized LED Index Modulation

In this paper, we propose light-emitting diode (LED) selection that can be applied not only to the conventional Multiple-Input Multiple-Output (MIMO) case, but also to a larger MIMO configuration of generalized LED index modulation (GLIM) system with optical orthogonal frequency division multiplexing (OFDM) in visible light communication (VLC). Moreover, we derive a simplified implementation of the maximum a posteriori (MAP) detector when the number of LEDs is an even number larger than four. Simulation results show that the performance of MAP and LED selection is better than other detection algorithms for larger even numbers of LEDs and conventional GLIM for $4\times4$ transmission, respectively.

Interference Management in Ultradense Networks: A User-Centric Coalition Formation Game Approach

Ultradense networks have been identified as a promising technology to accomplish objectives of the fifth-generation wireless networks. However, the severe mutual interference generated by the densely deployed femtocells constitutes a great challenge. Different from the most prior studies that center on femtocell access points (FAPs) and neglect the influence of users’ location when allocating subchannels, a centralized user-centric merge-and-split rule based coalition formation game, which can be well supported in the framework of the cloud/centralized radio access network, is proposed. This user-centric game makes it possible to utilize user information (e.g., distance) in estimating interuser interference so that the interference mitigation can be more accurate and effective. Besides, a novel resource allocation algorithm based on graph theory is presented. It can eliminate intratier interference efficiently by allocating users who may severely interfere each other in the conflict-graph with orthogonal subchannels as far as possible in a distance-aware sequence, and allocating subchannels in a profit-calculating method if idle subchannels are unavailable. Furthermore, in order to overcome the limitation that “only one subchannel can be allocated to each user” in previous coalitional games, a supplementary allocation algorithm is put forward to allocate remainder subchannels such that the system spectral efficiency can be improved. Simulation results show that the proposed algorithms improve the aggregate throughput up to 51.04%, 62.70%, 157.46%, and 482.42% comparing with the coalition formation game transmitted in a time-division multiple access (TDMA) manner within each coalition with virtual multiple-input multiple-output (MIMO) case, the reuse 1 case, the FAP-centric coalition formation game with modified recursive core case, and the coalition formation game transmitted in a TDMA manner among users with virtual MIMO case, respectively. The coalitional game proposed in this paper converges to a final stable partition in finite iterations.

Comparison between Commensurate and Non-commensurate Fractional Systems

This article deals with fractional systems that rep-resent better physical process and guarantee a very small number of parameters that can reduces the computation time. It focuses in particular on the state-space representation which highlights the state variables and allows to study the internal behavior of the system taking into account the initial state. Moreover, this representation adapts better to the multiple input multiple-output case. It also discusses the discretization of fractional system to finally adapt the Model Predictive Control to apply it and shows its efficiency and performance in these systems. The main objective of this article is to compare the commensurate and non-commensurate fractional models performance, calculation time and ease of use.

The Degrees of Freedom of the Interference Channel With a Cognitive Relay Under Delayed Feedback

This paper studies the interference channel with a cognitive relay under delayed feedback. Three types of delayed feedback are studied: delayed channel state information at the transmitter, delayed output feedback, and delayed Shannon feedback. Outer bounds are derived for the degrees of freedom (DoF) region of the two-user multiple-input multiple-output interference channel with a cognitive relay with delayed feedback as well as without feedback. For the single-input single-output scenario, optimal schemes are proposed based on retrospective interference alignment. It is shown that while a cognitive relay without feedback cannot improve the sum-DoF in the two-user single-input single-output interference channel, delayed feedback in the same scenario can increase the sum-DoF to $4/3$ . For the multiple-input multiple-output case, achievable schemes are obtained via extensions of retrospective interference alignment, leading to the DoF regions that meet the respective upper bounds.

Estimating Cortical Feature Maps with Dependent Gaussian Processes.

A striking example of brain organisation is the stereotyped arrangement of cell preferences in the visual cortex for edges of particular orientations in the visual image. These "orientation preference maps" appear to have remarkably consistent statistical properties across many species. However fine scale analysis of these properties requires the accurate reconstruction of maps from imaging data which is highly noisy. A new approach for solving this reconstruction problem is to use Bayesian Gaussian process methods, which produce more accurate results than classical techniques. However, so far this work has not considered the fact that maps for several other features of visual input coexist with the orientation preference map and that these maps have mutually dependent spatial arrangements. Here we extend the Gaussian process framework to the multiple output case, so that we can consider multiple maps simultaneously. We demonstrate that this improves reconstruction of multiple maps compared to both classical techniques and the single output approach, can encode the empirically observed relationships, and is easily extendible. This provides the first principled approach for studying the spatial relationships between feature maps in visual cortex.

Node estimate for sparse random vector functional-link networks

A random vector functional-link (RVFL) network is a neural network composed of a randomised hidden layer and an adaptable output layer. Training such a network is reduced to a linear least-squares problem, which can be solved efficiently. Still, selecting a proper number of nodes in the hidden layer is a critical issue, since an improper choice can lead to either overfitting or underfitting for the problem at hand. Additionally, small sized RVFL networks are favoured in situations where computational considerations are important. In the case of RVFL networks with a single output, unnecessary neurons can be removed adaptively with the use of sparse training algorithms such as Lasso, which are suboptimal for the case of multiple outputs. In this paper, we extend some prior ideas in order to devise a group sparse training algorithm which avoids the shortcomings of previous approaches. We validate our proposal on a large set of experimental benchmarks, and we analyse several state-of-the-art optimisation techniques in order to solve the overall training problem. We show that the proposed approach can obtain an accuracy comparable to standard algorithms, while at the same time resulting in extremely sparse hidden layers.

Graph‐based stochastic model for high‐speed railway cutting scenarios

This study proposes a stochastic channel model based on the propagation graph theory for high-speed railway (HSR) cutting scenarios. Single-input single-output wideband measurements are conducted under a cutting for acquiring realistic channel data. The propagation graph covering line of sight, single bounced and double bounced conditions is used to describe the measured propagation scenario and generate the virtual channel impulse responses. The graph model is validated focusing on small-scale characteristics such as Ricean K-factor, delay and frequency dispersions, and a close agreement is achieved between model and measurement results. In particular, the verified model is extended to the multiple-input multiple-output case for simulation analysis of MIMO performance of the measured environment, concentrating on the spatial correlation and the ergodic capacity. The proposed model can facilitate the reliable simulation and evaluation of MIMO systems in the HSR cutting scenario.

Partial FFT Demodulation for MIMO-OFDM Over Time-Varying Underwater Acoustic Channels

Partial FFT demodulation is a newly-emerging technique to mitigate the inter-carrier interference (ICI) of orthogonal frequency division multiplexing (OFDM) systems over time-varying underwater acoustic channels. In this letter, we extend the partial FFT demodulation method for a single-input single-output (SISO) configuration to the multiple-input multiple-output (MIMO) case. By assuming no channel knowledge, we design an adaptive algorithm which performs sliding-window channel estimation, partial FFT combining and data detection across subcarriers iteratively. Furthermore, a new parameter “residual ICI span” is introduced to counteract the post-combining ICI and provide a better system performance.

-optimisation and fixed poles of multivariable sampled-data systems with delay

Using the parametric transfer matrix (PTM) of sampled-data (SD) systems with pure time delay, the paper generalises the polynomial method for solving the -optimisation problem to the multiple-input multiple-output (MIMO) case. The generalisation is not only a formal act, because in the MIMO case, the PTM method leads to a minimisation problem for a singular quadratic functional, which is connected with honest technical difficulties. Therefore, the paper introduces a special transformation to overcome these difficulties. Some general properties of -optimal SD systems with delay are investigated. Notice that there always exists a subset of so-called fixed poles, which is responsible for a principal performance restriction of the -optimal control loop.