Study On Characteristic Factorization Of Blind Equalizable Channel Matrix For FIR-MIMO Systems

The objective of communications is to transfer the messages. For a wireless communicationsystem, the existence of the multiple access interference and the presence of inter-symbolinterference affects the transformation of the messages, detection and recovery of signals. Insome content, multiple access interference can be decreased by multi-user detection, whileequalization can used to eliminate the inter-symbol interference caused by the non-idealcharacteristics of channels. Apparently, the balance capability of the wireless channel willdirectly affect and determine the transmission of wireless channel capacity and utilization. Inorder to improve the channel bandwidth utilization, "blind equalization" method came into being,the method using only the received sequence itself and the priori information to balance thechannel.The conditions guarantee the FIR-MIMO wireless channel to be blindly equalizable is oneof the important hot topics investigated by researchers in the literature. The concrete conditionsare continuously extended by the research scholars, from the initially extremely harsh conditionsto the reversible conditions, and later to the semi-reversible condition. In this thesis, based on theprevious research, we investigate the channel matrix. Using the polynomial matrix theory, wegive the universal factorization H(z) =H₁(z)D(z)Q for the channel matrix under differentequalizable conditions. In addition, analysis on the channel matrix characteristic factorizationalso prove in theory that: the irreducible condition is a special case of reversible conditions,while the former two ones are included in the third one, semi-reversible conditions, which is ablandly equalizable condition and can be applied to the most widest range. It can be seen fromthe characteristics of the channel matrix that the irreducible channel matrix is just a basis, theextension of the conditions to be blindly equalizable is mathematically equivalent to be cascadeda special system. Different properties of the cascaded systems correspond to a system which canbe applied to a different equalizable range area.As an application of the former theory, based on the blind equalizable theory under thesemi-reversible conditions, to detect the QPSK complex signal efficiently for the FIR-MIMOsystems, this thesis transform the problems of the blind multiuser detection into a quadraticprogramming optimization problem subjecting to some relatively simple binary constraints usingthe matrix transformation. The complexity of solving the approximation algorithms is onlypolynomial. Simulation results indicate that: in the case of the FIR-MIMO channels withcommon zeros, comparing with the subspace method, the algorithm in this thesis is suitable for awider range with better performance. This thesis consists of five chapters, the first introduces the research background andsignificance of this topic; the second chapter provides an overview of the blind equalization ofcommunication systems; the third chapter describes in detail the FIR-MIMO system model andpresents universal factorization of the channel matrix under three blindly equalizable conditions.Moreover, using the above-mentioned models and it's theories, under the conditions that thetransmission signal belongs to a finite alphabet set and the channel having common zeros, wegive the method of directly signal detection of the system. The fourth chapter gives the specificsimulation of the directly blindly detection of the complex transmission signal. The fifth chapteris a summary of the full text of the work and discussion of the future work.