The Research Of Blind Equalization Algorithm Based On The High-order Cyclic Cumulants

As a new adaptive equalization algorithm, blind equalization technique can effectively eliminate inter-symbol interference and improve communication quality, so it is one of the key technologies of the digital communications. Blind equalization techniques developed nearly forty years, a lot of algorithms have been proposed by scholars from various countries. But most of the blind equalization algorithms are based on the assumption that is the transmitted signal is stationary signal. In fact, the communication signal has periodic stationarity. Therefore the use of cyclostationary properties of signals to blind equalization can be true and accurate.The following works have been done in this paper.(1) The cyclostationary theory is analysed, the relationship and transformation methods of time-varying cumulant, time-varying moment, cyclic cumulants and cyclic moment are introduced in this paper. According to second order cyclic cumulant are sensitive to noise and channel order estimated, a blind equalization using fourth-order cyclic cumulants is proposed in the paper. Then the singular value decomposition is used to solve the channel coefficients. So the equalizer can be constructed and transmitted sequence can be recovered.(2) The forth-order and second-order cyclic cumulants of the signal input and output is studied in this paper. The SW criterion and Gadzow criterion are introduced. Then the blind equalization techniques based on the forth-second order normalized cycle cumulation is proposed. By defining the four-second order normalized cumulant of the output signal as the cost function, the blind equalization algorithm based on the high order cyclic cumulant proposed in the paper is attributed to the unconstrained condition extreme value problem solving, thereby reducing the complexity of the algorithm.(3) The reason why the third-order cyclic cumulant can't be used directly in the blind equalization is analysed, then the symmetric-to-antisymmetric transformation method is proposed to solve this problem. At the input, the send signal is transformed into an asymmetric signal, and at the output, the receive signal is transformed into a symmetric signal. Third-order cycle cumulant is simpler than the fourth-order cyclic cumulant, so according to characteristics of the normalization algorithm, the the blind equalization technique based on the third-second order normalized cyclic cumulant is proposed. The third-second order normalized cumulant of the output signal is defined as the cost function. By maximizing the cost function to recover transmitted sequence, effectively improves the practicability of the algorithm.