Research On Channel Equalization Based On Factor Graphs

Communication technology is a kind of information service, and the development of this technology is for transmitting and exchanging all forms of information more efficiently and more reliably. In any communication system, channel characteristics are very important to the performance of the whole system, especially for high speed or wireless communication. The non-ideal channel characteristics can distort the signal and cause serious inter-symbol interference. However, equalization can compensate for the fading channel and reduce or eliminate inter-symbol interference.The maximum a posteriori(MAP) algorithm is optimal in the sense of minimizing the probability of bit error, but the high computation complexity makes it impractical. At present, research on equalization mainly focuses on either reducing the complexity of MAP or searching for approximations to MAP, while this paper is based on the latter. Factor graph is a relatively new modeling framework that has proven useful in a wide variety of applications. By depicting the factorization of a global function of several variables as the product of several functions, each of a subset of the original set of variables, factor graph can provide a divide-and-conquer strategy to the problem and reduce the complexity.Based on the existing research, this paper focuses on channel equalization based on factor graphs and introduces the sum-product algorithm with message passing rules in detail. Simulation and analysis on algorithm performance compared to the traditional LMS algorithm are also included. The contents are as follows:1) Specify communication system model with ISI, with focus on the cause of ISI, the condition of no ISI and two traditional equalization algorithms based on filters which are LMS and DFE with performance simulation appended.2) Introduce factor graphs and the sum-product algorithm. How to solve marginal problems using factor graphs and message passing rules are described in detail, and the merits of factor graphs are indicated.3) Realize three equalization algorithms based on factor graphs, which are unconstrained linear equalization, constrained linear equalization and decision feedback equalization. Describe how to use the sum-product algorithm to fit the equalization into marginal problems and how to produce the estimates using message passing rules. All of the three algorithms are based on the criterion of LMMSE, which restricts the estimates to be linear functions of the received data to simplify the solution. The estimates of the transmitted data formed by the unconstrained equalizer are linear functions of the entire received sequence, while the constrained equalizer only considers a particular subset of observations. Due to the poor MSE performance of the above algorithms at low SNR, a method to resist the interference of noise on the estimates is proposed in this paper, and simulation results prove that. At last, factor graph is used to realize DFE algorithm which makes use of the decisions to eliminate the inter-symbol interference caused by former symbols. The simulation result shows its performance excels that of the constrained linear equalizer.