In most of the existing work on the equalizer design problem, it was assumed that the models of the communication channels are precisely known. However, this is not the case in the real world. The parameters of the channels are always subject to uncertainties or even time-varying variations. Without considering the uncertainties or variations during the design procedure, the indeed existing uncertainties and variations would degrade or even deteriorate the performance of the designed equalizers. Therefore, it is practically demanding to investigate the deconvolution problem for channels subject to uncertainties or time-varying variations.
So ZHANG Hui and SHI Yang of University of Victoria, Aryan Saadat Mehr of University of Saskatchewan and HUANG Haining of Institute of Acoustics, Chinese Academy of Sciences carried out a series of studies and considered the worst case in the study: arbitrarily time-varying channels which are more general and can cover the parameter uncertainties and variations.
In the research, the scientists investigate the optimal design of finite impulse response (FIR) filters for equalization/deconvolution and tackle with the problem of designing an optimal FIR equalizer for communication channels in the presence of time-varying parameters and when observations are intermittent. They incorporate two practical yet challenging constraints into the modeling of the equalization system: (1) the parameters of the communication channel model are arbitrarily time-varying within a polytope with finite known vertices; (2) at the received end, the received signal is usually intermittent due to network-induced packet dropouts which are modeled by a stochastic Bernoulli distribution. Under the stochastic theory framework, a robust design method for the FIR equalizer is proposed such that the equalization system can achieve the prescribed energy-to-peak performance even it is subject to uncertainties, external noise, and data missing. Sufficient conditions for the existence of the equalizer are derived by a set of linear matrix inequalities (LMIs). An illustrative design example demonstrates the design procedure and the effectiveness of the proposed method. In addition, the relationship between the minimal energy-to-peak performance index and the value for the available measurements, and the relationship between the minimal energy-to-peak performance index and the order of the equalizer were investigated via the numerical example.
This research result was published on the recently issued journal of Signal Processing (2011, 91(7): 1651-1658).