Tensor Decomposition-Based Channel Estimation and Sensing for Millimeter Wave MIMO-OFDM V2I Systems

An integrated sensing and communication(ISAC)scheme for a millimeter wave(mmWave)multiple-input multiple-output orthogonal frequency division multiplexing(MIMO-OFDM)Vehicle-to-Infrastructure(V2I)system is presented,in which both the access point(AP)and the vehicle are equipped with large antenna arrays and employ hybrid analog and digital beamforming structures to compensate the path loss,meanwhile compromise between hardware complexity and system performance.Based on the sparse scattering nature of the mmWave channel,the received signal at the AP is organized to a four-order tensor by the introduced novel frame structure.A CANDECOMP/PARAFAC(CP)decomposition-based method is proposed for time-varying channel parameter extraction,including angles of departure/arrival(AoDs/AoAs),Doppler shift,time delay and path gain.Then leveraging the estimates of channel parameters,a nonlinear weighted least-square problem is proposed to recover the location accurately,heading and velocity of vehicles.Simulation results show that the proposed methods are effective and efficient in time-varying channel estimation and vehicle sensing in mmWave MIMOOFDM V2I systems.

Gradient Descent for Symmetric Tensor Decomposition

Symmetric tensor decomposition is of great importance in applications.Several studies have employed a greedy approach,where the main idea is to first find a best rank-one approximation of a given tensor,and then repeat the process to the residual tensor by subtracting the rank-one component.In this paper,we focus on finding a best rank-one approximation of a given orthogonally order-3 symmetric tensor.We give a geometric landscape analysis of a nonconvex optimization for the best rank-one approximation of orthogonally symmetric tensors.We show that any local minimizer must be a factor in this orthogonally symmetric tensor decomposition,and any other critical points are linear combinations of the factors.Then,we propose a gradient descent algorithm with a carefully designed initialization to solve this nonconvex optimization problem,and we prove that the algorithm converges to the global minimum with high probability for orthogonal decomposable tensors.This result,combined with the landscape analysis,reveals that the greedy algorithm will get the tensor CP low-rank decomposition.Numerical results are provided to verify our theoretical results.

An Innovative Approach for the Short-term Traffic Flow Prediction

Traffic flow prediction plays an important role in intelligent transportation applications,such as traffic control,navigation,path planning,etc.,which are closely related to people's daily life.In the last twenty years,many traffic flow prediction approaches have been proposed.However,some of these approaches use the regression based mechanisms,which cannot achieve accurate short-term traffic flow predication.While,other approaches use the neural network based mechanisms,which cannot work well with limited amount of training data.To this end,a light weight tensor-based traffic flow prediction approach is proposed,which can achieve efficient and accurate short-term traffic flow prediction with continuous traffic flow data in a limited period of time.In the proposed approach,first,a tensor-based traffic flow model is proposed to establish the multi-dimensional relationships for traffic flow values in continuous time intervals.Then,a CANDECOMP/PARAFAC decomposition based algorithm is employed to complete the missing values in the constructed tensor.Finally,the completed tensor can be directly used to achieve efficient and accurate traffic flow prediction.The experiments on the real dataset indicate that the proposed approach outperforms many current approaches on traffic flow prediction with limited amount of traffic flow data.

Fourier matrices and Fourier tensors

The Fourier matrix is fundamental in discrete Fourier transforms and fast Fourier transforms.We generalize the Fourier matrix,extend the concept of Fourier matrix to higher order Fourier tensor,present the spectrum of the Fourier tensors,and use the Fourier tensor to simplify the high order Fourier analysis.