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

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.

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.

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.

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.

Killing Operator for the Kerr Metric

When D: E →F is a linear differential operator of order q between the sections of vector bundles over a manifold X of dimension n, it is defined by a bundle map Φ: Jq(E) →F=F0 that may depend, explicitly or implicitly, on constant parameters a, b, c, ... . A “direct problem” is to find the generating compatibility conditions (CC) in the form of an operator D1: F0 →F1. When D is involutive, that is when the corresponding system Rq = ker (Φ) is involutive, this procedure provides successive first order involutive operators D1, ..., Dn. Though D1 οD = 0 implies ad (D) οad(D1) = 0 by taking the respective adjoint operators, then ad (D) may not generate the CC of ad (D1) and measuring such “gaps” led to introduce extension modules in differential homological algebra. They may also depend on the parameters and such a situation is well known in ordinary or partial control theory. When Rq is not involutive, a standard prolongation/projection (PP) procedure allows in general to find integers r, s such that the image of the projection at order q+r of the prolongation is involutive but it may highly depend on the parameters. However, sometimes the resulting system no longer depends on the parameters and the extension modules do not depend on the parameters because it is known that they do not depend on the differential sequence used for their definition. The purpose of this paper is to study the above problems for the Kerr (m, a), Schwarzschild (m, 0) and Minkowski (0, 0) parameters while computing the dimensions of the inclusions for the respective Killing operators. Other striking motivating examples are also presented.

Adaptive Secure Transmission for Wireless Powered Communication Networks

This paper investigates secure transmission in a wireless powered communication network(WPCN)with an energy harvesting(EH)source configured with multiple antennas.In the WPCN,the EH source harvests energy from the radio frequency(RF)signals broadcasted by a power beacon(PB),and purely relies on the harvested energy to communicate with the destination in the presence of passive eavesdroppers.It is noteworthy that the RF-EH source is equipped with a finite energy storage to accumulate the harvested energy for the future usage.Moreover,due to energy-constraint and complexitylimitation,the multi-antenna source is only configured with a single RF-chain.To enhance the security for the WPCN,we propose two adaptive transmission schemes,i.e.,energy-aware transmit antenna selection(EATAS)and energy-aware differential spatial modulation(EADSM).According to the energy status and the channel quality,the source adaptively decides whether to transmit confidential information or harvest RF energy.To evaluate the secrecy performance of the proposed schemes,we first study the evolution of the energy storage,and then derive the analytical expressions of connection outage probability(COP),secrecy outage probability(SOP)and efficient secrecy throughput(EST).Numerical results demonstrate that our proposed schemes outperform the existing schemes,i.e.,time-switching based TAS(TS-TAS)Received:May 19,2020 Revised:Sep.13,2020 Editor:Deli Qiao and accumulate-then-transmit(ATT).And,increasing the transmit power of the PB or the capacity of the source’s energy storage is helpful to improve the secrecy performance.Moreover,there exists an optimal transmission rate for each proposed scheme to achieve best secrecy performance.

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.

THE EFFECT OF HOT DRAWN ON THE PHYSICAL AGING OF ATACTIC POLYSTYRENE

The physical aging behavior of atactic polystyrene (aPS) films achieved under different drawing conditions has been studied by optical birefringence and modulate differential scanning: calorimeter (m.d.s.c.). The results show that on annealing at specific temperature below glass transition temperatue (T-g), the enthalpy relaxation (Delta H) and T-g decrease with increasing of birefringence (Delta n). On the other baud, the effect of molecular draw ratio (MDR) is confusing: Delta H and T-g decrease with increasing of MDR in the early stage of aging, but the MDR's effect become unobvious with the development of aging. It may be concluded that the ordered domain generated by the drawing below or above glass transition temperature will affect the development of physical aging behavior. The viewpoint of cohesional entanglement is used to account for the above observations.

Canonical Form Associated with an r-Jacobi Algebra

In this paper, we denote by A a commutative and unitary algebra over a commutative field K of characteristic 0 and r an integer ≥1. We define the notion of r-Jacobi algebra A and we construct the canonical form associated with the r-Jacobi algebra A.

Differential space-time block-diagonal codes

A new differential space-time code, called differential space-time block-diagonal code （DSTBDC）, is proposed for multiple-input multiple-output （MIMO） wireless communication systems. By exploiting the block-diagonal construction of DSTBDC, we can design a variety of high-performance DSTBDC, especially for the cases of large numbers of transmit antennas and high date rates. In flat fading channels, DSTBDC outperforms traditional differential space-time codes if the data rate is higher than 1 bps/Hz, especially when the number of transmit antennas is large. In frequency-selective fading channels, multiple-input multiple-output orthogonal frequency-division multiplexing （MIMO-OFDM） systems using DSTBDC have the powerful ability to achieve very high diversity gain in space, time, and frequency simultaneously. Due to the special orthogonal construction, DSTBDC has a simple decoding algorithm. In addition, DSTBDC can significantly save the cost of radio frequency circuits.

Medical image lossless compression based on combining an integer wavelet transform with DPCM

To improve the classical lossless compression of low efficiency,a method of image lossless compression with high efficiency is presented.Its theory and the algorithm implementation are introduced.The basic approach of medical image lossless compression is then briefly described.After analyzing and implementing differential plus code modulation(DPCM)in lossless compression,a new method of combining an integer wavelet transform with DPCM to compress medical images is discussed.The analysis and simulation results show that this new method is simpler and useful.Moreover,it has high compression ratio in medical image lossless compression.