Modulation Spaces Research Articles

Модель керування рухом космічних розподілених енергетичних систем

The goal of this article is to develop a generalized mathematical model for controlling the motion of the spacecraft of a space industrial platform’s distributed power system. Space industrialization is one of the promising lines of industrial development in the world. The development of space industrial technologies will allow one to solve a number of problems in the production of unique products unavailable under terrestrial conditions. The main types of these products include semiconductor materials, materials made by 3D printing in microgravity, space modules of sunshade systems, space metallurgy products, space debris processing products, and high-purity space biology substances. Taking this into account, a certain amount of electricity is required for the manufacture of one or another product. Given that some space industrial processes can consume a significant amount of electricity, a space industrial platform's own power generation may not be sufficient. Because of this, it was proposed to use additional energy resources through the development of a distributed power supply system for a space industrial platform. A group of power spacecraft is envisaged to collect and accumulate electric energy and transmit it in a contactless way to the receivers of the space industrial platform. The article presents mathematical models for the analysis of the orbital, angular, and relative motion of power spacecraft and receiver spacecraft. Algorithms are proposed for calculating the parameters of the power spacecraft orientation and stabilization system. A generalized model is constructed for determining the maximum distance and time interval of power spacecraft to platform electric power transmission using microwave radiation. The model developed allows one to choose the power spacecraft design parameters at the stage of conceptual design of space industrial platform power systems.

Pseudo-differential operators on Orlicz modulation spaces

We deduce continuity properties for pseudo-differential operators with symbols in quasi-Banach Orlicz modulation spaces when rely on other quasi-Banach Orlicz modulation spaces. In particular we extend some earlier results.

A Note on the Invertibility of the Gabor Frame Operator on Certain Modulation Spaces

We consider Gabor frames generated by a general lattice and a window function that belongs to one of the following spaces: the Sobolev space V_1 = H^1(mathbb {R}^d), the weighted L^2-space V_2 = L_{1 + |x|}^2(mathbb {R}^d), and the space V_3 = mathbb {H}^1(mathbb {R}^d) = V_1 cap V_2 consisting of all functions with finite uncertainty product; all these spaces can be described as modulation spaces with respect to suitable weighted L^2 spaces. In all cases, we prove that the space of Bessel vectors in V_j is mapped bijectively onto itself by the Gabor frame operator. As a consequence, if the window function belongs to one of the three spaces, then the canonical dual window also belongs to the same space. In fact, the result not only applies to frames, but also to frame sequences.

Chern numbers of topological phonon band crossing determined with inelastic neutron scattering

Topological invariants in the band structure, such as Chern numbers, are crucial for the classification of topological matters and dictate the occurrence of exotic properties, yet their direct spectroscopic determination has been largely limited to electronic bands. Here, we use inelastic neutron scattering in conjunction with ab initio calculations to identify a variety of topological phonon band crossings in MnSi and CoSi single crystals. We find a distinct relation between the Chern numbers of a band-crossing node and the scattering intensity modulation in momentum space around the node. Given sufficiently high resolution, our method can be used to determine arbitrarily large Chern numbers of topological phonon band-crossing nodes.

Receiver Designs for Variant Precoded Signed Space Modulation Techniques

Emerging wireless applications are increasingly seeking systems that can provide desirable performance properties with scale. Properties include better power consumption, cost, and error performance. As a result, advances in space modulation hardware thus far have introduced a variety of models attaining these various desirable properties. While many techniques focus on transmitter hardware, approaches involving precoding have emerged to simplify receiver hardware. As such, an existing family of hardware implementation models, referred to as receive space modulation techniques (RSMTs), exists offering different realization options. RSMTs essentially eliminate the need for a full RF receive chain for each antenna at the receiver. It follows that all RSMTs introduced to date achieve realizations through a single spatial dimension. However, a recently introduced transmitter-based technique called signed space modulation (SSM) adds a second spatial dimension that increases the spectral efficiency without the need for nonspatial symbols. In this article, novel hardware design models based on SSM are applied at the receiver by introducing precoding, adding more techniques to the family of RSMTs. The introduced models are compared in terms of cost, power, and computational complexity against receive quadrature space shift keying (RQSSK) that has shown the most favorable traits in past comparisons against other RSMTs.

Bayesian Neural Network Detector for an Orthogonal Time Frequency Space Modulation

The orthogonal time frequency space (OTFS) modulation is proposed for beyond 5G wireless systems to deal with high mobility communications. The existing low complexity OTFS detectors’ performance is suboptimal in rich scattering environments where there are a large number of moving reflectors that reflect the transmitted signal towards the receiver. In this letter, we propose an OTFS detector, referred to as the BPICNet OTFS detector that integrates NN, Bayesian inference, and parallel interference cancellation concepts. Simulation results show that the proposed detector outperforms the state-of-the-art.

Spectral Efficiency of OTFS Based Orthogonal Multiple Access With Rectangular Pulses

In this paper, we consider Orthogonal Time Frequency Space (OTFS) modulation based multiple-access (MA). We specifically consider Orthogonal MA methods (OMA) where the user terminals (UTs) are allocated non-overlapping physical resource in the delay-Doppler (DD) and/or time-frequency (TF) domain. Well known OMA methods include, i) Guard Band (GB) based MA (GBMA), ii) Interleaved Delay Doppler MA (IDDMA), iii) Interleaved Time Frequency MA (ITFMA). The spectral efficiency (SE) performance of these OMA methods has <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">only</i> been studied for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ideal</i> transmit and receive pulses. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">With ideal pulses</i> , IDDMA and ITFMA are free from multi-user interference (MUI) and unlike GBMA they <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">do not</i> use guard bands in the DD/TF domain. Since ideal pulses are not realizable, in this paper we study the SE performance of these OMA methods with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">practical rectangular pulses</i> . For these OMA methods, we derive the expression for the received DD/TF domain symbols at the base station (BS) receiver and the effective DD domain channel matrix when rectangular pulses are used. Study of these expressions reveals the presence of MUI when rectangular pulses are used, although the amount of MUI in IDDMA is observed to be significantly smaller than that in ITFMA. We also derive the expression for the achievable sum SE. Through simulations, for practical values of the received signal-to-noise ratio, we observe that with rectangular pulses the sum SE achieved by the IDDMA method is significantly higher than that achieved by the ITFMA and GBMA methods.

Error Performance of Rectangular Pulse-Shaped OTFS With Practical Receivers

In this letter, we investigate error performance of rectangular pulse-shaped orthogonal time frequency space (OTFS) modulation with a practical receiver. Specifically, we consider an essential bandpass filter at receiver RF front-end, which has been ignored in existing works. We analyse the effect of rectangular pulses on practical OTFS receiver performance, and derive the exact forms of interference in delay-Doppler (DD) domain. We demonstrate that the transmitted information symbols in certain regions of the DD domain are severely contaminated. As a result, there is an error floor in the receiver error performance, which needs to be addressed for such OTFS waveform in practical systems.

Gaussian AMP Aided Model-Driven Learning for OTFS System

Orthogonal time frequency space (OTFS) modulation, which converts the fast time-varying channel in the time-frequency domain into a time-invariant channel in the delay-Doppler(DD) domain, can mitigate the fading caused by the dynamic change of the channel. Nevertheless, due to the influence of the Doppler effect, it is challenging for traditional algorithms to acquire the desired detection results. To this end, this letter proposes a Gaussian approximate message passing (GAMP) aided model-driven signal detection algorithm. It first expands the existing GAMP algorithm into a corresponding deep neural network. Then, a unique set of trainable parameters, including one damping factor and two stepping factors, are constructed to improve the algorithm’s convergence. Simulation results demonstrate that the designed model-driven signal detection algorithm outperforms the original GAMP by about 2 dB at the bit error ratio (BER) of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1\times 10^{-4}$ </tex-math></inline-formula> .

Orthogonal Delay-Doppler Division Multiplexing Modulation

Inspired by the orthogonal time frequency space (OTFS) modulation, in this paper, we consider designing a multicarrier (MC) modulation on delay-Doppler (DD) plane, to couple the modulated signal with a doubly-selective channel having DD resolutions. A key challenge for the design of DD plane MC modulation is to investigate whether a realizable pulse orthogonal with respect to the DD plane’s fine resolutions exists or not. To this end, we first indicate that a feasible DD plane MC modulation is essentially a type of staggered multitone modulation. Then, analogous to orthogonal frequency division multiplexing, we propose an orthogonal delay-Doppler division multiplexing (ODDM) modulation, and design the corresponding transmit pulse. Furthermore, we prove that the proposed transmit pulse is orthogonal with respect to the DD plane’s resolutions and therefore a realizable DD plane orthogonal pulse does exist. The orthogonality of this particular pulse significantly eases the derivation of the ODDM’s DD domain channel input-output relation, and yields a channel matrix with an elegant block-circulant-like structure. We demonstrate that the ODDM outperforms the OTFS in terms of out-of-band emission and bit error rate, by achieving perfect coupling between the modulated signal and the DD channel.

Low-Complexity LMMSE Receiver Design for Practical-Pulse-Shaped MIMO-OTFS Systems

Orthogonal time frequency space modulation (OTFS) scheme establishes reliable communication in a rapidly time-varying wireless channel with a high Doppler spread. We design a low-complexity linear minimum mean squared error (LMMSE) receiver for practical-pulse-shaped multiple-input multiple-output (MIMO)-OTFS systems. The proposed receiver exploits the inherent channel sparsity and the channel-agnostic structure of matrices involved in the LMMSE receiver, and has only a log-linear complexity. It provides exactly the same solution, and hence the same bit error rate (BER), as that of the conventional LMMSE receiver with a cubic order of complexity. We also derive, by using the Taylor series expansion and the results from random matrix theory, a tight closed-form approximation for the post-processing signal-to-noise-plus-interference ratio (SINR) expression of the proposed receiver. This expression is derived by assuming imperfect receive channel state information. We show using extensive numerical investigations that the derived SINR expression, when averaged over multiple channel realizations, accurately characterizes the BER of a MIMO-OTFS system.

Time and Frequency Synchronization for OTFS

In this letter, we propose timing offset (TO) and carrier frequency offset (CFO) estimators for orthogonal time frequency space modulation (OTFS). The proposed estimators do not require any additional training overheads as they deploy the same pilot signal that is used for channel estimation. Hence, no additional training overhead is required for synchronization, thanks to the periodic properties of the pilot signal in the delay-time domain. Our proposed TO estimator finds the start of each OTFS block by searching for a periodic sequence in delay and time dimensions. The CFO is then estimated by finding the mean of the angles of a two-dimensional correlation function at the best timing instant. As a novel aspect of these estimators, the multipath diversity of the channel is exploited to achieve a high estimation accuracy. Finally, we show the efficacy of our proposed synchronization techniques through extensive simulations.

Flexible Quadrature Spatial Pulse Amplitude Modulation for VLC Systems

Quadrature-spatial modulation (QSM) offers high spectral efficiency (SE) without interchannel interference for both radio frequency and visible light communication (VLC) systems. In this article, a new QSM scheme called flexible quadrature spatial pulse amplitude modulation (FQSPAM) is proposed for VLC systems. In space modulation techniques (SMTs), the data bit stream is divided into two groups as the index bits and the signal bits. These grouped bits are mapped independently to modulation symbols and indices of light-emitting diodes (LEDs). However, this mapping strategy puts a constraint on the number of LEDs and the size of the signal constellation. FQSPAM jointly designs the signal and spatial components of the constellation to overcome these limitations. This approach removes the constraint on the number of LEDs and the size of the signal constellation. The constellation design problem is formulated as a convex optimization problem to identify power-efficient constellations with different <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$M$</tex-math></inline-formula> values. A dimming-controlled optimization algorithm has also been proposed to take into account both illumination and communication at the same time. Analytical and numerical results show the improved bit error rate performance of the proposed FQSPAM compared to spatial pulse amplitude modulation and channel adaptive bit mapping.

Study and Analysis of OTFS and OFDM

High mobility wireless communication systems have been proposed to be robust to channel-induced Doppler shift using Orthogonal Time Frequency Space (OTFS) modulation. The OTFS modulation technique is described in this paper. In addition to being in the delay-Doppler (DD) domain, OTFS has a unique and important feature. The OTFS modulation offers maximum diversity over frequency and time when coupled with an equalizer. This technique converts fading, time-varying wireless channels into time-independent, non-fading interactions that reveal their underlying geometry. Even in challenging 5G deployment settings, OTFS achieves Massive MIMO throughput gains by scaling throughput linearly with MIMO order. An analysis of peak to average power ratio (PAPR) of OFTS modulation wave forms is presented in this paper. OTFS with rectangular pulses is characterized analytically using the complementary cumulative distribution function (CCDF). The simulated CCDF for the PAPR of OTFS is compared with that for orthogonal frequency division multiplexing (OFDM) for different pulse shapes. The results show that OTFS has a better PAPR than OFDM.

Pose Estimation Method for Non-Cooperative Target Based on Deep Learning

The scientific research strength in the aerospace field has become an essential criterion for measuring a country’s scientific and technological level and comprehensive national power, but in the grand scheme, many factors are beyond human control. As is known, the difficulty with non-cooperative target intersection docking is its failure to provide attitude information autonomously. The existing non-cooperative target poses estimation methods with low accuracy and high resource consumption. This paper proposes a deep-learning-based pose estimation method for solving these problems. The proposed pose estimation method consists of two distinctly innovative works. You Only Look Once v5 (YOLOv5) is an innovative and lightweight network that is used to pre-recognize non-cooperative targets. Another part introduces concurrent space and channel compressor theory modules in a lightweight High-Resolution Network (HRNet) to extend its advantages in real-time, and hence proposes a spatial and channel Squeeze and Excitation—Lightweight High-Resolution Network (scSE-LHRNet) network for pose estimation. To verify the superiority of the proposed network, experiments were conducted on a publicly available dataset with multiple evaluation metrics to compare and analyze existing methods. The experimental results show that the proposed pose estimation method dramatically reduces the complexity of the model, effectively decreases the amount of computation, and achieves significant pose estimation results.

Research on uplink performance of MIMO terrestrial-satellite laser communication based on OSM-MBM joint modulation

This paper proposes a multiple-input multiple-output (MIMO) terrestrial-satellite laser communication uplink system based on optical spatial modulation with medium-based modulation (OSM-MBM) joint modulation. The Málaga(M) distribution is used to describe the combined effects of near-ground turbulent light intensity scintillation, beam wander and angle of arrival fluctuation. The closed expression of the bit error rate (BER) of the OSM-MBM joint modulation MIMO terrestrial-satellite laser communication uplink is derived. The simulation analyzes the influence of transmitting radius, receiving aperture, beam divergence, zenith angle and signal-to-noise ratio on the system error performance, and compares it with traditional modulation, media-based modulation and optical space modulation. Finally, the experiment is verified by Monte Carlo. This research provides a theoretical reference for the engineering realization of the modulation technology for the MIMO terrestrial-satellite laser communication uplink system.

Parallel minimum mean square error equalization for reduced‐zero‐padding orthogonal time frequency space with the aid of unitary precoding

AbstractThis work studies the equalization method for the reduced‐prefix version of the orthogonal time frequency space (OTFS) modulation in which one zero‐padding (ZP) is inserted in each frame. We focus on applications in low data rate scenarios such as the Internet of Things, and will consider the case where the number of subcarriers and time slots are small. The idea of this work is to retain the large singular values of the channel matrix through linear transformations, while discarding the remaining small singular values. This makes it possible to avoid performance degradation due to small singular values when inverting the matrix in the minimum mean square error (MMSE) equalization. Specifically, a joint unitary precoding and signal linear transformation method is proposed for the reduced‐ZP OTFS modulation which decomposes the whole system into parallel subsystems. Then, the receiver can perform parallel MMSE equalization, where the singular values of each branch are not small. Simulation results show that the proposed method can achieve better bit error rate performance than the state‐of‐the‐art methods like message passing, unitary approximate message passing, and variational unitary approximate message passing.

Orthogonal Time Frequency Space Modulation Based on the Discrete Zak Transform.

In orthogonal time frequency space (OTFS) modulation, information-carrying symbols reside in the delay-Doppler (DD) domain. By operating in the DD domain, an appealing property for communication arises: time-frequency (TF) dispersive channels encountered in high-mobility environments become time-invariant. OTFS outperforms orthogonal frequency division multiplexing (OFDM) in high-mobility scenarios, making it an ideal waveform candidate for 6G. Generally, OTFS is considered a pre- and postprocessing step for OFDM. However, the so-called Zak transform provides the fundamental relation between the DD and time domain. In this work, we propose an OTFS system based on the discrete Zak transform (DZT). To this end, we discuss the DZT and establish the input-output relation for time-frequency (TF) dispersive channels solely by the properties of the DZT. The presented formulation simplifies the derivation and analysis of the input-output relation of the TF dispersive channel in the DD domain. Based on the presented formulation, we show that operating in the DD incurs no loss in capacity.

Safety warning for lithium-ion batteries by module-space air-pressure variation under thermal runaway conditions

Lithium-ion batteries are widely used in scalable electrochemical energy-storage stations because of their excellent characteristics. However, safety issues seriously hinder their further development and promotion. This paper proposes a safety warning method based on module-space air-pressure variation to provide warnings for battery thermal runaway (TR). TR is induced by different battery faults (overcharge, overheat), and the air pressure in the module space varies during the battery venting process. To verify the effectiveness of the TR warning by air-pressure variation signal, experiments were conducted in sealed and ventilated modules. The air pressures of the sealed and ventilated module spaces for batteries under 13 A (1C) overcharge-induced TR conditions were 19.3 hPa and 3.05 hPa higher, respectively, than the corresponding air pressures under normal conditions. Under 6.5 A (0.5C) overcharge-induced TR conditions, the air pressure of the sealed module space increased by 14.43 hPa. Under overheat-induced TR conditions, the sealed module space air pressure increased by 6.52 hPa. Upon detecting an air-pressure variation signal, immediate measures such as charge stoppage effectively prevent the occurrence of battery TR. The average time interval between the warning signal and battery TR was 473 s. This research provides a new way to enhance the safety of lithium-ion battery energy-storage stations.

On the existence of optimizers for time–frequency concentration problems

We consider the problem of the maximum concentration in a fixed measurable subset $$\Omega \subset {\mathbb {R}}^{2d}$$ of the time-frequency space for functions $$f\in L^2({\mathbb {R}}^{d})$$ . The notion of concentration can be made mathematically precise by considering the $$L^p$$ -norm on $$\Omega $$ of some time–frequency distribution of f such as the ambiguity function A(f). We provide a positive answer to an open maximization problem, by showing that for every subset $$\Omega \subset {\mathbb {R}}^{2d}$$ of finite measure and every $$1\le p<\infty $$ , there exists an optimizer for $$\begin{aligned} \sup \{\Vert A(f)\Vert _{L^p(\Omega )}:\ f\in L^2({\mathbb {R}}^{d}),\ \Vert f\Vert _{L^2}=1 \}. \end{aligned}$$ The lack of weak upper semicontinuity and the invariance under time-frequency shifts make the problem challenging. The proof is based on concentration compactness with time–frequency shifts as dislocations, and certain integral bounds and asymptotic decoupling estimates for the ambiguity function. We also discuss the case $$p=\infty $$ and related optimization problems for the time correlation function, the cross-ambiguity function with a fixed window, and for functions in the modulation spaces $$M^q({\mathbb {R}}^{d})$$ , $$0<q<2$$ , equipped with continuous or discrete-type (quasi-)norms.