Factor graph based linear minimum mean square error equalization for wireless communications /

Thesis Type: Postgraduate

Institution Of The Thesis: Orta Doğu Teknik Üniversitesi, Faculty of Engineering, Department of Electrical and Electronics Engineering, Turkey

Approval Date: 2014

Student: PINAR ŞEN



In this work, we have studied on a reduced complexity factor graph based linear minimum mean square error (LMMSE) filter as an equalizer for different wireless communication problems. First, we introduce an efficient way of computing extrinsic bit log-likelihood ratio (LLR) values for the LMMSE estimation through the previously presented graph structure in the literature compatible with higher order alphabets. In addition, we propose to adapt this graph structure so that it has the ability of including the non-white statistics of a random process. Our new structure, which corresponds to block LMMSE filtering under a Gaussian autoregressive (AR) process, has the advantage of complexity linearly increasing with the block length and the ease of incorporating the a priori information of the input signals whenever possible. Extensive simulations and comparisons to the theoretical calculations show that our method performs identical with the optimal block LMMSE filtering for Gaussian input signals. Moreover, the proposed method can be used for any random process with a known (or estimated) autocorrelation function by use of an approximation to an AR process as detailed in this study. To support this idea, we present an application for which the proposed graph structure can be used as an equalizer through the mentioned approximation. Both the intersymbol interference (ISI) and the effect of non-white noise inherent in Faster-than-Nyquist (FTN) signaling are shown to be handled by our method. In order to incorporate the statistics of noise signal into the factor graph over which the LMMSE algorithm is implemented, we suggest using a known method in the literature for modelling the noise signal as an autoregressive (AR) process. Based on these improvements, we show that the proposed low complexity receiver structure performs close to the optimal decoder operating in ISI-free ideal scenario without FTN signaling through simulations. In the last part of our work, we propose to enlarge the state space model of the previous graph structure in order to remove inter-symbol and inter-stream interference in multiple input multiple output (MIMO) communication. The resultant representation inflicted on the graph provides a time domain equalizer having computational complexity linearly increasing with block length. Also, owing to the Gaussian assumption used in the presented cycle free factor graph, the complexity of the suggested method is not affected by the size of the signalling space. The extrinsic bit LLR transition algorithm that we introduce can be applied for this scenario straightforwardly. Overall, we provide an efficient receiver structure reaching high data rates in frequency selective MIMO systems whose performance is shown to be very close to a genie-aided matched filter bound through extensive simulations.