Tomlinson – Harashima precoder
Yu.B. Nechaev, A.A. Malyutin
The basic task of all methods of processing of a signal in HF modems of transfer of the data is the struggle with ISI, caused by multipath distribution of a signal in the channel of communication. It is carried out through alignment of the channel of communication by that or other method. Thus the complete alignment of the transfer characteristic of the channel is theoretically possible, but is inexpedient because of increase of noise on an output of the device its carrying out. It is known, that if there is an opportunity of entering predistortion in a transmitted signal on the party of transfer, the alignment of the channel can be made complete, without increase of capacity of noise, on reception.
Optimum the linear algorithm of precoder work, received on a basis SVD of a channel matrix is. However given algorithm is combined in the computing attitude and is strongly sensitive to mistakes of estimations of parameters of the channel of communication. Considerably more simple methods of struggle with ISI with the help predistortion of a signal can be algorithms using nonlinear operations above a signal subject to transfer. One of them is the method named Tomlinson-Harashima precoder.
The initially given method was designed with the purpose of complete elimination ISI on reception and, hence, it can not ensure the good characteristics of a noise stability in channels with large noise level for the same reasons, on which on it are not capable equalizer, designed on similar criterion.
That is why, the task of updating of the given algorithm with the purpose is of interest: 1) optimization of its parameters not by criterion of complete elimination ISI, and by criterion of minimization of an average square of a mistake on an output; 2) account of discrepancy of estimations of parameters of the channel of communication, inevitable as a result of a primary error of measurements on reception and obsolescense them to the moment of use on transfer.
The offered algorithm of work nonlinear precoder generalizes algorithm of work Tomlinson-Harashima precoder, by minimization of total distortions of a signal as a result of influence ISI and noise, and also account of discrepancies of an estimation of parameters of the channel of communication, both on the party of reception, and on the party of transfer. At exact estimation of parameters of the channel the offered algorithm coincides with known. And at absence of noise - with algorithm completely eliminating ISI, but taking into account discrepancy of an estimation of the channel.
At the precisely known characteristics of the channel of communication on both parties of transfer offered precoder provides considerably smaller BER not only, than DFE equalizer with a feedback under the decision, but also smaller, than optimum, from the point of view of minimization BER, algorithm BCJR-MAP, and also smaller, than, optimum at reception as a whole, algorithm Viterbi.
At identical accuracy of estimations of the impulse characteristic on transmitting and reception the parties precoder provides the best characteristics of a noise stability, than any of algorithms of alignment carrying out processing only on the reception party. The research of dependence of the characteristics of a noise stability from a difference of errors of estimations of their channel of communication on transmitting and reception the parties has allowed to estimate the requirements to throughput and noise stability of the channel of a feedback, proceeding from an allowable ratio of errors of estimations on both parties of reception, at which the entering predistortion has advantage in comparison with alignment only on the party of reception.