Blind Equalization for Tomlinson-Harashima Precoded Systems
Thesis DisciplineElectrical Engineering
Degree GrantorUniversity of Canterbury
Degree NameMaster of Engineering
At a communications receiver the observed signal is a corrupted version of the transmitted signal. This distortion in the received signal is due to the physical characteristics of the channel, including multipath propagation, the non-idealities of copper wires and impulse noise. Equalization is a process to combat these distortions in order to recover the original transmitted signal. Roughly stated, the equalizer tries to implement the inverse transfer function of the channel while taking into account the channel noise. The equalizer parameters can be tuned to this inverse transfer function using an adaptive algorithm. In many cases, the algorithm uses a training sequence to drive the equalizer parameters to the optimum solution. But, for time-varying channels or multiuser channels the use of a training sequence is inefficient in terms of bandwidth, as bandwidth is wasted due to the periodic re-transmission of the training sequence. A blind equalization algorithm is a practical method to eliminate this training sequence. An equalizer adapted using a blind algorithm is a key component of a bandwidth efficient receiver for broadcast and point-to-multipoint communications. The initial convergence performance of a blind adaptive equalizer depends on the higher-order statistics of the transmitted signal. In modern digital systems, Tomlinson-Harashima precoding (THP) is often used for signal shaping and to mitigate the error propagation problem of a decision feedback equalizer (DFE). The concept of THP comes from pre-equalization. In fact, it is a nonlinear form of pre-equalization, which bounds the higher-order statistics of the transmitted signal. But, THP and blind equalization are often viewed as incompatible equalization techniques. In this research, we give multiple scenarios where blind equalization of a THP-encoded signal might arise. With this motivation we set out to answer the question, can a blind equalizer successfully acquire a THP-encoded signal? We investigate the combination of a Tomlinson-Harashima precoder on the transmitter side and a blind equalizer on the receiver side. By bounding the kurtosis of the THP-encoded signal, we show that THP actually aids the initial convergence of blind equalization. We find that, as the symbol constellation size increases, the THP-encoded signal kurtosis approaches that of a uniform distribution, not a Gaussian. We investigate the compatibility of blind equalization with THP-encoded signals for both SISO and MIMO systems. In a SISO system, conventional blind algorithms can be used to counter the distortions introduced in the received signal. However, in a MIMO system with multiple users, the other users act as interferers on the desired user's signal. Hence, modified blind algorithms need to be applied to mitigate these interferers. For both SISO and MIMO systems, we show that the THP encoder ensures that the signal distribution approaches a non-Gaussian distribution. Using Monte Carlo simulations, we study the effects of Tomlinson-Harashima precoding on the performance of Bussgang-type blind algorithms and verify our theoretical analysis. The major contributions of this thesis are: • A demonstration that a blind equalizer can successfully acquire a THP-encoded signal for both SISO and MIMO systems. We show that THP actually aids blind equalization, as it ensures that the transmitted signal is non-Gaussian. • An analytical quantification of the effects of THP on the transmitted signal statistics. We derive a novel bound on the kurtosis of the THP-encoded signal. • An extension of the results from a single-user SISO scenario to multiple users and a MIMO scenario. We demonstrate that our bound and simulated results hold for these more general cases. Through our work, we have opened the way for a novel application of training sequence-less equalization: to acquire and equalize THP-encoded signals. Using our proposed system, periodic training sequences for a broadcast or point-to-multipoint system can be avoided, improving the bandwidth efficiency of the transceiver. Future modem designs with THP encoding can make use of our advances for bandwidth efficient communication systems.