A construction of authentication codes with arbitration based on orthogonal spaces

In this paper we give a new construction of authentication codes with arbitration using orthogonal spaces. Some parameters and the probabilities of successful attacks are computed.

Rank-generating functions and Poincaré polynomials of lattices in finite orthogonal space of even characteristic

The geometry of classical groups over finite fields is widely used in many fields.In this paper,we study the rank-generating function,the characteristic polynomial,and the Poincarépolynomial of lattices generated by the orbits of subspaces under finite orthogonal groups of even characteristic.We also determine their expressions.

Performance Analysis for Orthogonal Time Frequency Space Modulation Systems with Generalized Waveform

Orthogonal time-frequency space(OTFS),which exhibits beneficial advantages in high-mobility scenarios,has been considered as a promising technology in future wireless communication systems.In this paper,a universal model for OTFS systems with generalized waveform has been developed.Furthermore,the average bit error probability(ABEP)upper bounds of the optimal maximum likelihood(ML)detector are first derived for OTFS systems with generalized waveforms.Specifically,for OTFS systems with the ideal waveform,we elicit the ABEP bound by recombining the transmitted signal and the received signal.For OTFS systems with practical waveforms,a universal ABEP upper bound expression is derived using moment-generating function(MGF),which is further extended to MIMO-OTFS systems.Numerical results validate that our theoretical ABEP upper bounds are concur with the simulation performance achieved by ML detectors.

Design and Analysis of Spatial Modulation Based Orthogonal Time Frequency Space System

In this paper,we design a spatial modulation based orthogonal time frequency space(SMOTFS)system to achieve improved transmission reliability and meet the high transmission rate and highspeed demands of future mobile communications,which fully utilizes the characteristics of spatial modulation(SM)and orthogonal time frequency space(OTFS)transmission.The detailed system design and signal processing of the SM-OTFS system have been presented.The closed-form expressions of the average symbol error rate(ASER)and average bit error rate(ABER)of the SM-OTFS system have been derived over the delay-Doppler channel with the help of the union bounding technique and moment-generating function(MGF).Meanwhile,the system complexity has been evaluated.Numerical results verify the correctness of the theoretical ASER and ABER analysis of the SM-OTFS system in the high signal-to-noise ratio(SNR)regions and also show that the SM-OTFS system outperforms the traditional SM based orthogonal frequency division multiplexing(SM-OFDM)system with limited complexity increase under mobile conditions,especially in high mobility scenarios.

Schedule algorithm for mitigating inter-cell interference based on orthogonal complement space

In order to avoid severe performance degradation led by the inter-cell interference (ICI) in orthogonal frequency division multiple access (OFDMA) systems with a frequency reused factor (FRF) of 1,distributed schedule algorithm (DS-OCS) and distributed proportional fairness schedule algorithm (DPFS-OCS) based on orthogonal complement space (OCS) were proposed. The first right and left singular vectors of the channel that the user experienced were selected as the transmitting and receiving beamforming vectors. An interference space was spanned by the left singular vectors of the entire interference users in the same channel. The most suitable user lay in the OCS of the interference space was scheduled to avoid suffering interference from neighboring cells based on the criterion of system capacity maximizing and proportional fairness. The simulation results show that the average system capacity can be improved by 2%-4% compared with the DS-OCS algorithm with the Max C/I algorithm,by 6%-10% compared with the DPFS-OCS algorithm with the PF algorithm.

CANONICAL REPRESENTATIONS AND DEGREE OF FREEDOM FORMULAE OF ORTHOGONAL TENSORS IN N-DIMENSIONAL EUCLIDEAN SPACE

In this paper, with the help of the eigenvalue properties of orthogonal tensors in n-dimensional Euclidean space and the representations of the orthogonal tensors in 2-dimensional space, the canonical representations of orthogonal tensors in n-dimensional Euclidean space are easily gotten. The paper also gives all the constraint relationships among the principal invariants of arbitrarily given orthogonal tensor by use of Cayley-Hamilton theorem; these results make it possible to solve all the eigenvalues of any orthogonal tensor based on a quite reduced equation of m-th order, where m is the integer part ofn \2. Finally, the formulae of the degree of freedom of orthogonal tensors are given.

GENERALIZED WEIGHTED SOBOLEV SPACES AND APPLICATIONS TO SOBOLEV ORTHOGONAL POLYNOMIALS Ⅱ

We present a definition of general Sobolev spaces with respect to arbitrary measures, Wk,p(Ω,μ) for 1 .≤p≤∞.In [RARP] we proved that these spaces are complete under very light conditions. Now we prove that if we consider certain general types of measures, then Cτ∞(R) is dense in these spaces. As an application to Sobolev orthogonal polynomials, toe study the boundedness of the multiplication operator. This gives an estimation of the zeroes of Sobolev orthogonal polynomials.

High-Precision Doppler Frequency Estimation Based Positioning Using OTFS Modulations by Red and Blue Frequency Shift Discriminator

Orthogonal Time Frequency and Space(OTFS) modulation is expected to provide high-speed and ultra-reliable communications for emerging mobile applications, including low-orbit satellite communications. Using the Doppler frequency for positioning is a promising research direction on communication and navigation integration. To tackle the high Doppler frequency and low signal-to-noise ratio(SNR) in satellite communication, this paper proposes a Red and Blue Frequency Shift Discriminator(RBFSD) based on the pseudo-noise(PN) sequence.The paper derives that the cross-correlation function on the Doppler domain exhibits the characteristic of a Sinc function. Therefore, it applies modulation onto the Delay-Doppler domain using PN sequence and adjusts Doppler frequency estimation by red-shifting or blue-shifting. Simulation results show that the performance of Doppler frequency estimation is close to the Cramér-Rao Lower Bound when the SNR is greater than -15dB. The proposed algorithm is about 1/D times less complex than the existing PN pilot sequence algorithm, where D is the resolution of the fractional Doppler.

Performance of MIMO Systems Using Space Time Block Codes (STBC)

Digital Communications, in relation to wireless networks, have taken off in recent years due to the expanding need to communicate faster and more efficiently. A popular way to achieve this is by using wireless Multiple Input Multiple Output (MIMO) communication systems. MIMO systems utilize Space Time Block Codes (STBC) as one of the leading ways to obtain higher data rates with limited bandwidth and power. With several STBC methods currently available, this paper analyzes simulations using Orthogonal Space Time Block Codes (OSTBC) in Rayleigh fading channels to evaluate the performance of MIMO systems. The selection to use a Rayleigh fading channel as a model for a non-line-of-sight (nLOS) environment is selected to mimic installations where a large number of signal paths and reflections are expected. All simulations are coded, generated and plotted using MATLAB resulting in graphical data representing the bit-error rate (BER) to signal-to-noise ratio (Eb/N0) or SNR. Each simulation captures how different configurations of key variables including code rate, diversity and antenna count can impact system performance. Four modulation schemes (BPSK, QPSK, 16-QAM and 64-QAM) are included in each simulation. Conclusive evidence based upon these simulations suggests higher diversity gains were achieved with a greater number of antennas. The most significant factor for increasing system performance was using a lower count of transmit antennas with a higher count of receive antennas.

Trajectory Planning for OTFS-Based UAV Communications

Unmanned aerial vehicles(UAVs)have attracted growing research interests in recent years,which can be used as cost-effective aerial platforms to transmit collected data packets to ground access points(APs).Thus,it is crucial to investigate robust airto-ground(A2G)wireless links for high-speed UAVs.However,the A2G wireless link is unstable as it suffers from large path-loss and severe Doppler effect due to the high mobility of UAVs.In order to meet these challenges,we propose an orthogonal time frequency space(OTFS)-based UAV communication system to relief the Doppler effect.Besides,considering that the energy of UAV is limited,we optimize the trajectory planning of UAV to minimize the energy consumption under the constraints of bit error rate(BER)and transmission rate,where the Doppler compensation is taken into account.Simulation results show that the performance of OTFS-based UAV system is superior to orthogonal frequency division multiplexing(OFDM)-based UAV systems,which can accomplish transmission tasks over shorter distances with lower energy consumption.

OTFS Modulation and PAPR Reduction for IoT-Railways

The internet of things(IoT)has been widely considered to be integrated with high-speed railways to improve safety and service.It is important to achieve reliable communication in IoT for railways(IoT-R)under high mobility scenarios and strict energy constraints.Orthogonal time frequency space(OTFS)modulation is a two-dimensional modulation technique that has the potential to overcome the challenges in high Doppler environments.In addition,OTFS can have lower peak-to-average power ratio(PAPR)compared to orthogonal frequency division multiplexing,which is especially important for the application of IoT-R.Therefore,OTFS modulation for IoT-R is investigated in this paper.In order to decrease PAPR of OTFS and promote the application of OTFS modulation in IoT-R,the peak windowing technique is used in this paper.This technique can reduce the PAPR of OTFS by reducing the peak power and does not require multiple iterations.The impacts of different window functions,window sizes and clipping levels on PAPR and bit error rate of OTFS are simulated and discussed.The simulation results show that the peak windowing technique can efficiently reduce the PAPR of OTFS for IoT-R.

Low-complexity iterative equalization for OTFS based on alternating minimization

To achieve robust communication in high mobility scenarios,an iterative equalization algorithm based on alternating minimization(AM)is proposed for the orthogonal time frequency space(OTFS)system.The algorithm approximates the equalization problem to a convex function optimization problem in the real-valued domain and solves the problem iteratively using the AM algorithm.In the iterative process,the complexity of the proposed algorithm is reduced further based on the study of the cyclic structure and sparse property of the OTFS channel matrix in the delay-Doppler(DD)domain.The new method for OTFS is simulated and verified in a high-speed mobile scenario and the results show that the proposed equalization algorithm has excellent bit error rate performance with low complexity.

UAMP-Based Delay-Doppler Channel Estimation for OTFS Systems

Orthogonal time frequency space(OTFS)technique,which modulates data symbols in the delay-Doppler(DD)domain,presents a potential solution for supporting reliable information transmission in highmobility vehicular networks.In this paper,we study the issues of DD channel estimation for OTFS in the presence of fractional Doppler.We first propose a channel estimation algorithm with both low complexity and high accuracy based on the unitary approximate message passing(UAMP),which exploits the structured sparsity of the effective DD domain channel using hidden Markov model(HMM).The empirical state evolution(SE)analysis is then leveraged to predict the performance of our proposed algorithm.To refine the hyperparameters in the proposed algorithm,we derive the update criterion for the hyperparameters through the expectation-maximization(EM)algorithm.Finally,Our simulation results demonstrate that our proposed algorithm can achieve a significant gain over various baseline schemes.

Orthogonal Discriminant Improved Local Tangent Space Alignment Based Feature Fusion for Face Recognition

Improved local tangent space alignment (ILTSA) is a recent nonlinear dimensionality reduction method which can efficiently recover the geometrical structure of sparse or non-uniformly distributed data manifold. In this paper, based on combination of modified maximum margin criterion and ILTSA, a novel feature extraction method named orthogonal discriminant improved local tangent space alignment (ODILTSA) is proposed. ODILTSA can preserve local geometry structure and maximize the margin between different classes simultaneously. Based on ODILTSA, a novel face recognition method which combines augmented complex wavelet features and original image features is developed. Experimental results on Yale, AR and PIE face databases demonstrate the effectiveness of ODILTSA and the feature fusion method.

Target parameter estimation for OTFS-integrated radar and communications based on sparse reconstruction preprocessing

Orthogonal time-frequency space(OTFS)is a new modulation technique proposed in recent years for high Doppler wireless scenes.To solve the parameter estimation problem of the OTFS-integrated radar and communications system,we propose a parameter estimation method based on sparse reconstruction preprocessing to reduce the computational effort of the traditional weighted subspace fitting(WSF)algorithm.First,an OTFS-integrated echo signal model is constructed.Then,the echo signal is transformed to the time domain to separate the target angle from the range,and the range and angle of the detected target are coarsely estimated by using the sparse reconstruction algorithm.Finally,the WSF algorithm is used to refine the search with the coarse estimate at the center to obtain an accurate estimate.The simulations demonstrate the effectiveness and superiority of the proposed parameterestimation algorithm.

UAMP-Based Delay-Doppler Channel Estimation for OTFS Systems

Orthogonal time frequency space(OTFS)technique, which modulates data symbols in the delayDoppler(DD) domain, presents a potential solution for supporting reliable information transmission in highmobility vehicular networks. In this paper, we study the issues of DD channel estimation for OTFS in the presence of fractional Doppler. We first propose a channel estimation algorithm with both low complexity and high accuracy based on the unitary approximate message passing(UAMP), which exploits the structured sparsity of the effective DD domain channel using hidden Markov model(HMM). The empirical state evolution(SE) analysis is then leveraged to predict the performance of our proposed algorithm. To refine the hyperparameters in the proposed algorithm,we derive the update criterion for the hyperparameters through the expectation-maximization(EM) algorithm. Finally, Our simulation results demonstrate that our proposed algorithm can achieve a significant gain over various baseline schemes.

Automorphism Groups of Some Finite p-Groups

The automorphism group of G is determined, where G is a nonabelian p-group given by a central extension as 1→Zpm→G→Zp×…×Zp→1 such that its derived subgroup has order p.

A New and Efficient Approach to Determining the Rate of the Second-Order Symmetric Tensor and Its Isotropic Function

When the rate of a symmetric second-order symmetric tensor is discussed,the spin of the principal axis is involved.This paper proposes a method to establish the basis-free expression of the spin in terms of tensor and its rate by making use of the tensor function representation theorem.The proposed method is simple and the expression of the spin established is compact.To obtain the rate of the isotropic function of a second-order symmetric tensor,the fourth-order tangent tensor needs to be derived,which is the derivative of the tensor function to the second-order tensor.By decomposing the second-order symmetric tensor space into two orthogonal subspaces,the closed-form fourth-order tangent tensor is decomposed into two parts,which are linear mappings in these two orthogonal subspaces,respectively.These two linear mappings are derived in an extremely simple way.Finally,the method proposed in this paper is applied to obtain the expression of the relationship between material logarithmic strain rate and deformation rate.The whole process is simple and avoids tedious operations.

OTFSmodulation performance in a satellite-to-ground channel at sub-6-GHz and millimeter-wave bands with high mobility

Orthogonal time frequency space(OTFS)modulation has been widely considered for high-mobility scenarios.Satellite-to-ground communications have recently received much attention as a typical high-mobility scenario and face great challenges due to the high Doppler shift.To enable reliable communications and high spectral efficiency in satellite mobile communications,we evaluate OTFS modulation performance for geostationary Earth orbit and low Earth orbit satellite-to-ground channels at sub-6-GHz and millimeter-wave bands in both lineof-sight and non-line-of-sight cases.The minimum mean squared error with successive detection(MMSE-SD)is used to improve the bit error rate performance.The adaptability of OTFS and the signal detection technologies in satellite-to-ground channels are analyzed.Simulation results confirm the feasibility of applying OTFS modulation to satellite-to-ground communications with high mobility.Because full diversity in the delay-Doppler domain can be explored,different terminal movement velocities do not have a significant impact on the performance of OTFS modulation,and OTFS modulation can achieve better performance compared with classical orthogonal frequency division multiplexing in satellite-to-ground channels.It is found that MMSE-SD can improve the performance of OTFS modulation compared with an MMSE equalizer.