Subband approach to system identification

System identification is a technique in which an adaptive model with free parameters is adapted to match an unknown system model based on the knowledge of its input and its noisy output. There is a main division in system identification between time-domain and frequency-domain methods. The subband identification method can be thought of as an intermediate stage between these two methods, or as a generalization of them, since they can be considered as particular cases of the subband method. The subband method was proposed to alleviate the computational complexity of the time-domain method (fullband method) in applications where the adaptive model is FIR with a large tap size (e.g., echo cancellation in speech signal processing). This thesis has two main purposes. The first one is to provide a theoretical probabilistic analysis of the subband identification method. In this analysis, the input-output signals involved are assumed to be random processes. The aim is to analyze the stochastic properties of the subband signals, to study whether or not the identification result depends on the particular realization (of the random process) used in identification, whether or not the identification result converges to its “best possible” and at which speed it approaches its limit. To do this analysis, we have generalized existing results for fullband identification. The second purpose is to analyze the subband method from a practical point of view. We provide a comprehensive design method for a subband identification system, in which all the design variables are optimized for minimizing the computational cost, while maintaining a given asymptotic residual error and the maximum asymptotic convergence rate. We also compare the performance of the subband method with that of the fullband method. This comparison shows that significant computational savings can be offered by the subband method. Finally, as an application of the subband approach, we propose two channel equalization methods for the modulation scheme known as orthogonal frequency-division multiplexing (OFDM). We find that the subband approach offers significant improvements over the traditional channel equalization methods.