Multi-Way Array Fitting Algorithm And Its Application On Wireless Communications

In the area of wireless communications,the output signals of receiver often include different dimension resources such as space,time,frequency and so on.Hence,the output signals of the receiver can be naturally formulated into a multi-way array(also known as tensor)model.While the uniqueness of decomposition condition is satisfied,a fitting algorithm can be adopted to compute the tensor decomposition for the semi-blind or blind identification of wireless signal parameters.Meanwhile,the tensor-based approach also yields a better performance than the traditional two-dimensional matrix signal processing methods.This thesis mainly focuses on the multi-way array fitting algorithm and its applications on different wireless communication systems.Based on the idea of low rank decomposition of tensors,different tensor models are deeply investigated under various wireless communication scenarios,such as multiple-input multiple-output(MIMO)relays,uniform linear arrays.Besides,corresponding fitting algorithms are designed to estimate the wireless signal parameters.Therefore,the main work and contributions in this thesis are listed as follows:(1)A channel estimation approach for multi-user uplink amplify-and-forward(AF)relay systems via parallel factor(PARAFAC)analysis is presented in this thesis.Firstly,the users transmit a training sequence to the relay nodes for one time.Then the relays amplify the received data with different amplifying matrices and forward these amplified data to the base station.Finally,the received data at the station can be constructed as a PARAFAC model with a three-dimensional space.While the uniqueness of decomposition condition is satisfied,a Levenberg-Marquardt(LM)fitting algorithm is proposed to estimate the channel parameters of both user-relay and relay-base station links.Since the training sequence is transmitted by the users only once,the proposed method has a higher spectral efficiency.When the factor matrix of the tensor model is a highly collinear one,the LM method yields much faster convergence speed than the bilinear alternating least-squares(BALS)approach.(2)In MIMO relay systems,the channel state information(CSI)is usually acquired by using training-based channel estimation techniques.Unfortunately,the frequent use of the training sequences will occupy much more bandwidth.For this issue,a Nested PARAFAC-based joint channel estimation and symbol detection method in MIMO relay systems is proposed in this thesis.The encoding scheme at the source node introduces the time-domain spreading with a linear constellation precoding.Then,a set of amplifying matrices are utilized by the relays to amplify and forward the received data to the destination.The received signal at the destination can be formulated as a fourth-order tensor model,which is referred to as the Nested PARAFAC model.Based on this tensor model,a semi-blind detection algorithm is presented to jointly recover the channels and information symbols.Theory analysis and numerical examples show that the proposed approach not only outperforms existing methods,but also performs well in both correlated channels scenario.(3)By combining the noncircular(NC)property and structure property of the signals with the low rank decomposition of tensor analysis,a complete study on direction-of-arrival(DOA)estimation of NC signals for uniform linear array(ULA)via Vandermonde constrained PARAFAC decomposition is provided in this thesis.The proposed method can be seen as a generalization of ESPRIT method from matrix to the tensor case.The identifiablility and computational complexity of the proposed method are also analyzed.Compared with the conventional PARAFAC method,the proposed method has a more relaxed uniqueness condition,which enables the proposed method to identify more sources.Moreover,the proposed method consistently has a higher estimation accuracy and a much lower computational complexity than the PARAFAC method.The simulation results show that the proposed method has a better DOA estimation performance than the NC-ESPRIT and NC-RI-PM methods.