DOA Estimation Based On PARAFAC Technology

With the development of wireless communication recently years, Lots of arithmetic is referred in the signal measurement and parameter estimation fields. The analytical tools changed from earlier two order statistics to the high order statistics, to the line and non-line transformation of the time-frequency distribute and wavelet transformation. The objects changed from simple stationary and Gauss signal system to non-stationary and non-Gauss complicated system. Those make the theories applying to physical systems better. but in the existing methods there are several disadvantages, for example in the problem of direction-of-arrive, the main issue of this paper, the classical arithmetic are always referred based on the statistic characteristic, and the sensor array signal processing always concern to the eigenvalu decomposition of large size matrix etc. so the complexity of calculation is a matter that make lots of scholar cannot resolve, and it induce that the theoretic of DOA cannot be used in the practice system perfectly. We refer to a new solution- parallel factor technique in this text, for the method doesn't concern with the statistics, it provide a idea that can reduce the amount of calculation via lots of research, on the other hand, it provide a new mean to resolve other subject about sensor array signal processing.The parallel factor technic has been applied in the chemistry realm at the earlier stage, which is used to decompose or identifies the three way data mainly. Because the direction of arrive, blind signal separation etc. problem could be converted to a issue of multi-way matrix decomposition, more and more scholar begin research it in signal processing and wireless communication fields recently, and the related theory have got the booming development. contrast to which, the research of three way matrix is little internal, a few application of parallel-factor analysis can be found in chemistry filed. The paper about three way matrix related theory and arithmetic haven't been found at present.The theses mainly discuss the three way matrix and related theory after study the classical arithmetic of DOA estimation.(1) Unfolding of three way matrix, the research of the theory of three way matrix doesn't profound enough at present, so the classical analysis method of three way matrix is based on the two way matrix, which need to build the connect between the three way matrix and two way matrix . This is the main idea of three way matrix analysis, the model of PARAFAC and TUCKER3 in the theses are all build on the unfolding of three way matrix, we can use the complexity operation of matrix easier by the unfolding of matrix .(2) The PARAFAC model of three way matrix, the model is the most classical method to analysis the three way matrix, it build the connect between the slice of three matrix in three differ direction and the two way matrix, through which we can identity the three way matrix by the two way matrix error theory, in all of this, the most classical arithmetic is alter least square, which is referred based on the least square error. We present the math model of PARAFAC and the theory of identifiability about it, lastly, we provide the process of the alter least square arithmetic.(3) TUCKER3 model of three way matrix, the classical arithmetic of sensor array signal processing are all based on the statistics characteristic, so it always need lots of sampling, that lead to the data numbers in one way is far larger than the other two way in three way matrix, related theorem proved that in the process of three way matrix identification lots of data are redundancy, so we refer to the TUCKER3 model in the text, the model is used to compress the data without information loss, we present the math model of TUCKER3 and the theory of identifiability about it, lastly, we provide the arithmetic procession.(4) The COMFAC arithmetic of three way matrix, in sensor array signal processing, the data numbers in one way are always far larger than the other two way, which lead us to compress the data by TUCKER3 model naturally, then we can identify the compressed matrix by PARAFAC model, this is the main idea of COMFAC arithmetic, we provide the arithmetic procession in the text.(5) The DOA estimate based on the decomposition of three way matrix, the main idea of this method is origin from the ESPRIT arithmetic, differently, wedivide the sensor array into several subarray and build the three way matrix by the output of subarray, then we can resolve the DOA estimation by the theory of three way matrix decomposition, we provide the detailed process of arithmetic theory. (6) The verification of COMFAC arithmetic and the DOA estimation based onPARAFAC were proved by the MATLAB simulation, at last, we analysis the simulation result.The simulation proved the availability of the arithmetic; however the amount of calculation is still larger, the signification of the thesis is:(1) Refer to a new method of the three way matrix decomposition in signal processing fields, provide the basic notion and basic theory of it, and produce a new mean to resolve the other subject in signal processing.(2) In the subject of DOA estimation, provide a new arithmetic based on three way metrix decomposition, the arithmetic in the thesis doesn't concern with the static characteristic, so it build a new method from the root, with the continually research of multi- way matrix, the little amount calculation arithmetic based on multi- way matrix decomposition to estimate DOA is a valuable direction to research.