Research On Signal Processing Technology Based On Low Rank Decomposition Of Multi-way Arrays

Low rank decomposition of multi-way arrays is a method of multi-way data analysis, which is a novel approach in signal processing. In wireless communication, some signal processing problems can be analyzed using multi-way array low rank decomposition. With communication signals formulated into the multi-way array model, signal processing algorithms can be designed based on the uniqueness property of decomposition of the multi-way model for signal detection and parameter estimation. These types of algorithm are usually blind methods since no extra pilots are needed.This thesis presents an innovative study of signal processing based on the low rank decomposition of multi-way array. By exploiting the signal property in the low rank decomposition of multi-way array , novel signal processing algorithms are proposed. The algorithm performance is analyzed theoretically and then quantitatively with their application on many types of communication systems. The main contents of this thesis are as follows:1) The structure property of communication signal is involved in low rank decomposition of multi-way array analysis. Structure constrained PARAFAC models, which are more suitable to model communication signals, and the related signal processing algorithms are proposed. Firstly, based on the orthogonality of spreading codes in DS-CDMA signals, we proposed a new orthogonal constrained PARAFAC receiver (OC-PARAFAC) for DS-CDMA system. This receiver can implement multi-user detection without any knowledge of channel fading or spreading codes. Comparing to the traditional PARAFAC receiver, OC-PARAFAC receiver has lower BER and faster convergence speed. Secondly, we propose a structure constrained PARAFAC model based on the structure property of communication signal. Two algorithms, TALSP and TALSSIC, are also proposed to fit this model. Received signals of many communication systems can be modeled and analyzed by this constrained model. According to the structure constrained PARAFAC model and the specific system, new signal processing algorithms are proposed. Thanks to the structural constraints, the proposed model can describe the structure property of communication signals more suitable than normal PARAFAC model, and the uniqueness condition of the model is also improved. Signal processing algorithms based on the proposed model usually have better BER, parameters estimation and convergence performance than related PARAFAC-based algorithms. 2) The theoretical performance of structure constrained PARAFAC-based signal processing algorithms is studied. Theoretical performance of the PARAFAC-based algorithm can be evaluated by Cramer-Rao Bound (CRB) of trilinear decomposition. As the CRB of normal trilinear decomposition was given, this thesis propose the constrained Cramer-Rao bound (CCRB) of constrained trilinear decomposition based on the CCRB theory. We find that the CCRB of constrained trilinear decomposition is lower than CRB of normal trilinear decomposition, which theoretically shows that if some structures are involved in transmitted signals, the proposed structure constrained PARAFAC based algorithm have lower performance bound than traditional PARAFAC-based algorithm in signal processing. This thesis also analyzes the CCRB of trilinear decomposition under different constraints, which can show the performance of algorithms affected by different constraints. Simulation results show that the performances of the proposed TALSP algorithm and TALSSIC algorithm are close to their performance bound as the SNR increased. Therefore, these two algorithms are both asymptotically effective.3) Several new parameter estimation algorithms are proposed based on low rank decomposition of multi-way arrays and the structure of array signals,. Firstly, parameter identifiability of uniform linear array in different scenario is analyzed based on matrix decomposition. The related parameter identifiability results are demonstrated, which provide an algebraic foundation of the effectiveness of parameter estimation algorithms proposed later. Secondly, a PARAFAC-based direction of arrival (DOA) estimation algorithm, named PARAFAC-DEA, is proposed. This algorithm can not only achieve DOA estimation and signal detection, but also pair the estimated angles with waves of users, simultaneously. The DOA estimation performance of PARAFAC-DEA is better than traditional ESPRIT algorithm. Thirdly, based on the parallel profiles with linear dependencies (PARALIND) model, we propose a new joint angle/delay estimation algorithm, named PARALIND-JADE. The proposed algorithm outperforms traditional joint angle/delay estimation algorithm. It also can distinguish the parameters of different users naturally and achieve parameters pairing.4) Multiuser detection and parameter estimation in CDMA system are studied based on PARALIND decomposition. Firstly, a joint multiuser detection and DOA estimation algorithm, which can be used in multipath asynchronous CDMA system, is proposed. This algorithm, named PARALIND-MDAE, can recovery signals and estimate DOA information of all multipath of users simultaneously. The performance of DOA estimation is better than ESPRIT algorithm. Secondly, a new blind multiuser detection algorithm for MIMO-CDMA system, named PARALIND-CM, is proposed based on PARALIND analysis. This algorithm can recovery signals of all users without any knowledge of channel fading and user spreading codes of each user. It can automatically identify the transmitting signals from antennae array of each user.5) Two new blind algorithms, named KRP-ILSP and KRP-SIC, are proposed based on low rank decomposition of two-way array and the structure property of received signals of DS-CDMA system and oversampling system. These two algorithms exploit Khatri-Rao product structure of the space-time channel matrix of received signals and rank-1 projection strategy to achieve uniqueness of two-way array decomposition. According to the property of KRP-ILSP and KRP-SIC, a combined blind signal detection algorithm, name KRPBSD, is also proposed for DS-CDMA system and oversampling system. KRPBSD can recovery signals without any knowledge of channel fading and user spreading codes (or time manifold). KRPBSD is monotonically convergent and has good BER performance and fast convergence speed. It is still valid in processing small data block.