Novel time-frequency differential space-time modulation for multi-antenna OFDM systems

Differential space-time （DST） modulation has been proposed recently for multiple-antenna systems over Rayleigh fading channels, where neither the transmitter nor the receiver knows the fading coefficients. Among existing schemes, differential modulation is always performed in the time domain and suffers performance degradations in frequency-selective fading channels. In order to combat the fast time and frequency-selective fading, a novel time-frequency differential space-time （TF-DST） modulation scheme, which adopts differential modulation in both time and frequency domains, is proposed for multi-antenna orthogonal frequency division multiplexing （OFDM） system. A corresponding suboptimal yet low-complexity non-coherent detection approach is also proposed. Simulation results demonstrate that the proposed system is robust for time and frequency-selective Rayleigh fading channels.

A NOVEL LINEAR DIFFERENTIAL SPACE-TIME MODULATION

Based on the Complex Orthogonal Linear Dispersion (COLD) code,a novel linear Differ- ential Space-Time Modulation (DSTM) design is proposed in this paper.Compared with the existing nonlinear DSTM schemes based on group codes,the proposed linear DSTM scheme is easier to design, enjoys full diversity and allows for a simplified differential receiver,which can detect the transmitted symbols separately.Furthermore,compared with the existing linear DSTM based on orthogonal design, our new construction can be applied to any number of transmit antennas.Similar to other algorithms, the proposed scheme also can be demodulated with or without channel estimates at the receiver,but the performance degrades approximately by 3dB when estimates are not available.

Differential space-time modulation based on orthogonal design for cooperative network

Differential modulation was widely used for wireless networks in which channel estimation was diffi-cult.Based on orthogonal design,a novel distributed differential space-time coding/decoding scheme forM-PSK modulations was proposed,which had a high code rate of 2/3 and second-order diversity for thetwo-user cooperative networks.The performance of decode-and-forward (DF) protocols was evaluated.Simulations show that the differential space-time modulation scheme in this paper has better bit error rate(BER) performance or higher code rate than the schemes proposed by Tarasak and Wang when interuserchannel states are good enough.The impacts of transmission error between two users for the whole systemBER performance were also investigated.

A New High Rate Differential Space-Time-Frequency Modulation for MIMO-OFDM

In this paper, we propose a new differential space-time-frequency （DSTF） modulation for MIMOOFDM system with four transmit-antennas and arbitrary receive-antennas, which can improve the transmission rate since it can adopt high order quadrature amplitude modulation （QAM） modulation. Our proposed DSTF scheme embeds some full diversity full rate （FDFR） quasi-orthogonal space-time codes （QOSTBC） with QAM modulation into the frequency intervals and adopts the differential modulation in both time and frequency domains. The simulation results demonstrate that the proposed DSTF scheme can improve transmission rate greatly. Compared with the conventional differential unitary space-time modulation （DUSTM）, it can get better transmission performance in high transmission rate for MIMO-OFDM system.

Differential modulation based on space-time block codes

A differential modulation scheme using space-time block codes is put forward. Compared with other schemes, our scheme has lower computational complexity and has a simpler decoder. In the case of three or four transmitter antennas, our scheme has a higher rate a higher coding gain and a lower bit error rate for a given rate. Then we made simulations for space-time block codes as well as group codes in the case of two, three, four and five transmit antennas. The simulations prove that using two transmit antennas, one receive antenna and code rate of 4 bits/s/Hz, the differential STBC method outperform the differential group codes method by 4 dB. Useing three, four and five transmit antennas, one receive antenna, and code rate of 3 bits/s/Hz are adopted, the differential STBC method outperform the differential group codes method by 5 dB, 6. 5 dB and 7 dB, respectively. In other words, the differential modulation scheme based on space-time block code is better than the corresponding differential modulation scheme

Differential Scheme for Reconfigurable Intelligent Surface-Based Spatial Modulation System

In this paper,a differential scheme is proposed for reconfigurable intelligent surface(RIS)assisted spatial modulation,which is referred to as RISDSM,to eliminate the need for channel state information(CSI)at the receiver.The proposed scheme is an improvement over the current differential modulation scheme used in RIS-based systems,as it avoids the high-order matrix calculation and improves the spectral efficiency.A mathematical framework is developed to determine the theoretical average bit error probability(ABEP)of the system using RIS-DSM.The detection complexity of the proposed RIS-DSM scheme is extremely low through the simplification.Finally,simulations results demonstrate that the proposed RIS-DSM scheme can deliver satisfactory error performance even in low signal-to-noise ratio environments.

ROTATION CONSTELLATION FOR DIFFERENTIAL UNITARY SPACE-TIME MODULATION

A new constellation which is the multiplication of the rotation matrix and the diagonal matrix ac- cording to the number of transmitters is proposed to increase the diversity product, the key property to the performance of the differential unitary space-time modulation. Analyses and the simulation results show that the proposed constellation performs better and 2dB or more coding gain can be achieved over the traditional cyclic constellation.

Multi-Branch Fractional Multi-Bit Differential Detection of Continuous Phase Modulation with Decision Feedback

Differential detection of continuous phase modulation suffers from significant intersymbol interference. To reduce bit error rate, multi-branch fractional multi-bit differential detection (MFMDD) with decision feed-back is proposed. By introducing decision feedback in multi-bit differential detected signals, severe inter-symbol interference can be removed. Simulation results show that the proposed structure can greatly im-proves the performance compared with MFMDD without decision feedback, and the performance of 9 FMDD is very near to the performance of the coherent detection.

AN INTEGRATION METHOD WITH FITTING CUBIC SPLINE FUNCTIONS TO A NUMERICAL MODEL OF 2ND-ORDER SPACE-TIME DIFFERENTIAL REMAINDER——FOR AN IDEAL GLOBAL SIMULATION CASE WITH PRIMITIVE ATMOSPHERIC EQUATIONS

In this paper,the forecasting equations of a 2nd-order space-time differential remainder are deduced from the Navier-Stokes primitive equations and Eulerian operator by Taylor-series expansion.Here we introduce a cubic spline numerical model(Spline Model for short),which is with a quasi-Lagrangian time-split integration scheme of fitting cubic spline/bicubic surface to all physical variable fields in the atmospheric equations on spherical discrete latitude-longitude mesh.A new algorithm of"fitting cubic spline—time step integration—fitting cubic spline—……"is developed to determine their first-and2nd-order derivatives and their upstream points for time discrete integral to the governing equations in Spline Model.And the cubic spline function and its mathematical polarities are also discussed to understand the Spline Model’s mathematical foundation of numerical analysis.It is pointed out that the Spline Model has mathematical laws of"convergence"of the cubic spline functions contracting to the original functions as well as its 1st-order and 2nd-order derivatives.The"optimality"of the 2nd-order derivative of the cubic spline functions is optimal approximation to that of the original functions.In addition,a Hermite bicubic patch is equivalent to operate on a grid for a 2nd-order derivative variable field.Besides,the slopes and curvatures of a central difference are identified respectively,with a smoothing coefficient of 1/3,three-point smoothing of that of a cubic spline.Then the slopes and curvatures of a central difference are calculated from the smoothing coefficient 1/3 and three-point smoothing of that of a cubic spline,respectively.Furthermore,a global simulation case of adiabatic,non-frictional and"incompressible"model atmosphere is shown with the quasi-Lagrangian time integration by using a global Spline Model,whose initial condition comes from the NCEP reanalysis data,along with quasi-uniform latitude-longitude grids and the so-called"shallow atmosphere"Navier-Stokes primitive equations in the spherical coordinates.The Spline Model,which adopted the Navier-Stokes primitive equations and quasi-Lagrangian time-split integration scheme,provides an initial ideal case of global atmospheric circulation.In addition,considering the essentially non-linear atmospheric motions,the Spline Model could judge reasonably well simple points of any smoothed variable field according to its fitting spline curvatures that must conform to its physical interpretation.

SIGNAL CONSTELLATIONS DESIGN FOR DIFFERENTIAL UNITARY SPACE-TIME IN MIMO-OFDM SYSTEM OVER FREQUENCY-SELECTIVE FADING CHANNELS

In this paper, the design of signal constellations parameters is studied for Differential Unitary Space-Time Modulation (DUSTM) based on the design criterion of maximizing the diversity product. Further, noninteger searching method for the signal constellation parameters design is proposed in order to get better codes. Experimental results show that under the different Doppler spread and data transmission rate, the proposed design performs better than the previous design using integer parameters in Multiple Input Multiple Output Orthogonal Frequency Division Multiplexing (MIMO-OFDM) system over frequency-selective fading channels.

SR-DCSK Cooperative Communication System with Code Index Modulation:A New Design for 6G New Radios

This paper proposes a high-throughput short reference differential chaos shift keying cooperative communication system with the aid of code index modulation,referred to as CIM-SR-DCSK-CC system.In the proposed CIM-SR-DCSK-CC system,the source transmits information bits to both the relay and destination in the first time slot,while the relay not only forwards the source information bits but also sends new information bits to the destination in the second time slot.To be specific,the relay employs an N-order Walsh code to carry additional log_(2)N information bits,which are superimposed onto the SRDCSK signal carrying the decoded source information bits.Subsequently,the superimposed signal carrying both the source and relay information bits is transmitted to the destination.Moreover,the theoretical bit error rate(BER)expressions of the proposed CIMSR-DCSK-CC system are derived over additive white Gaussian noise(AWGN)and multipath Rayleigh fading channels.Compared with the conventional DCSKCC system and SR-DCSK-CC system,the proposed CIM-SR-DCSK-CC system can significantly improve the throughput without deteriorating any BER performance.As a consequence,the proposed system is very promising for the applications of the 6G-enabled lowpower and high-rate communication.

Minimum Resolution of the Minkowski, Schwarzschild and Kerr Differential Modules

Our recent arXiv preprints and published papers on the solution of the Riemann-Lanczos and Weyl-Lanczos problems have brought our attention on the importance of revisiting the algebraic structure of the Bianchi identities in Riemannian geometry. We also discovered in the meantime that, in our first GB book of 1978, we had already used a new way for studying the compatibility conditions (CC) of an operator that may not be necessarily formally integrable (FI) in order to construct canonical formally exact differential sequences on the jet level. The purpose of this paper is to prove that the combination of these two facts clearly shows the specific importance of the Spencer operator and the Spencer δ-cohomology, totally absent from mathematical physics today. The results obtained are unavoidable because they only depend on elementary combinatorics and diagram chasing. They also provide for the first time the purely intrinsic interpretation of the respective numbers of successive first, second, third and higher order generating CC. However, if they of course agree with the linearized Killing operator over the Minkowski metric, they largely disagree with recent publications on the respective numbers of generating CC for the linearized Killing operator over the Schwarzschild and Kerr metrics. Many similar examples are illustrating these new techniques, providing in particular a few resolutions in which the orders of the successive operators may go “up and down” surprisingly, like in the conformal situation for various dimensions.

Multiple symbol differential detection based on sphere decoding for unitary space-time modulation

Recently, a multiple symbol differential （MSD） sphere decoding （SD） algorithm for unitary spacetime modulation over quasi-static channel has been proved to achieve the performance of maximumlikelihood （ML） detection with relatively low complexity. However, an error floor occurs if the algorithm is applied over rapid-fading channels. Based on the assumption of continuous fading, a multiple symbol differential automatic sphere decoding （MSDASD） algorithm is developed by incorporating a recursive form of an ML metric into automatic SD （ASD） algorithm. Furthermore, two algorithms, termed as MSD approximate ASD （MSDAASD） and MSD pruning ASD （MSDPASD）, are proposed to reduce computational complexity and the number of comparisons, respectively. Compared with the existing typical algorithms, i.e., multiple symbol differential feedback detection （MS-DFD） and noncoherent sequence detection （NSD）, the performance of the proposed algorithms is much superior to that of MS-DFD and a little inferior to that of NSD, while the complexity is lower than that of MS-DFD in most cases and significantly lower than that of NSD.

Differential Correspondences and Control Theory

When a differential field K having n commuting derivations is given together with two finitely generated differential extensions L and M of K, an important problem in differential algebra is to exhibit a common differential extension N in order to define the new differential extensions L∩M and the smallest differential field (L,M ) ⊂ N containing both L and M. Such a result allows to generalize the use of complex numbers in classical algebra. Having now two finitely generated differential modules L and M over the non-commutative ring D = K [d1,...,dn] = K [d] of differential operators with coefficients in K, we may similarly look for a differential module N containing both L and M in order to define L∩M and L+M. This is exactly the situation met in linear or non-linear OD or PD control theory by selecting the inputs and the outputs among the control variables. However, in many recent books and papers, we have shown that controllability was a built-in property of a control system, not depending on the choice of inputs and outputs. The purpose of this paper is thus to revisit control theory by showing the specific importance of the two previous problems and the part plaid by N in both cases for the parametrization of the control system. An important tool will be the study of differential correspondences, a modern name for what was called Bäcklund problem during the last century, namely the elimination theory for groups of variables among systems of linear or nonlinear OD or PD equations. The main difficulty is to revisit differential homological algebra by using noncommutative localization as a way to generalize the symbolic calculus in the style of Heaviside and Mikusinski. Finally, when M is a D-module, this paper is using for the first time the fact that the system R = homK (M,K) is a D-module for the Spencer operator acting on sections, avoiding thus behaviours, trajectories and signal spaces in a purely formal way, contrary to a few recent works on this difficult subject.

Some Properties of First Order Differential Operators

We study some properties of first order differential operators from an algebraic viewpoint. We show this last can be decomposed in sum of an element of a module and a derivation. From a geometric viewpoint, we give some properties on the algebra of smooth functions. The Dirac mass at a point is the best example of first order differential operators at this point. This allows to construct a basis of this set and its dual basis.

Decision-feedback subset aided multiple-symbol differential detection

In view of the inaccuracy of the estimated symbols on the edge of the observation window, a decision-feedback subset aided multiple-symbol differential detection(MSDD) framework, dubbed DF-S-MSDD, is proposed in ultra-wideband impulse radio(UWB-IR) system with differential space-time block-code(DSTBC) modulation. Specifically, motivated by the decision-feedback aided MSDD(DF-MSDD), a subset of the decision-feedback symbols is selected, and the optimal symbols are preserved, and then all the remaining symbols are optimized. Furthermore, the simulations validate that the proposed DF-S-MSDD provides solid bit error-rate performance with a low complexity in UWB-IR system with DSTBC modulation.

The Exact Solution of the Space-Time Fractional Modified Kdv-Zakharov-Kuznetsov Equation

In this paper, we get many new analytical solutions of the space-time nonlinear fractional modified KDV-Zakharov Kuznetsov (mKDV-ZK) equation by means of a new approach namely method of undetermined coefficients based on a fractional complex transform. These solutions have physics meanings in natural sciences. This method can be used to other nonlinear fractional differential equations.

LDPC based differential unitary space-frequency coding for MIMO-OFDM systems

This paper proposes a novel LDPC based differential unitary space-frequency coding (DUSFC) scheme for MIMO-OFDM systems when neither the transmitter nor the receiver has access to the channel state information (CSI). The new DUSFC strategy basically consists of coding across transmit antennas and OFDM tones simultaneously as well as differential modulation in the time-domain. It can fully exploit the inherent advantages provided by the multipath fading channels, resulting in a high degree of diversity. The state-of-the-art low-density parity-check (LDPC) codes are concatenated with our DUSFC as channel coding to improve the bit error rate (BER) performance considerably. Owing to the maximum multipath diversity and large coding advantages, LDPC-DUSFC strongly outperforms the differential unitary space-time coded OFDM techniques re- cently proposed in literature. The corresponding iterative decoding algorithm without channel estimation is finally provided to offer significant performance gain. Simulation results illustrate the merits of the proposed scheme.