Convolutive-Error-Measure Analysis for Inverse Filtering and Minimum Total-Model-Order Determination Subject to Positive-Definiteness

To the best of our knowledge, there exists no explicit formulation of the exact L ₂ convolutive error for any arbitrary filter (system) and the corresponding truncated inverse filter. In addition, the approach to determine the minimum total-model-order of the inverse filter subject to the maximum allowable L ₂ convolutive error is also in demand. In this paper, we first derive the general formula of the L ₂ convolutive error measure with respect to the filter coefficients. According to this new error measure function, we design an optimal inverse finite impulse response (FIR) filter given the fixed model orders to achieve the minimum convolutive error. Then, we propose a new algorithm to determine the minimum total-model-order of the appropriate truncated inverse filter to achieve a specified convolutive error based on the discrete filled function approach. The numerical evaluation is demonstrated for a tradeoff between the total-model-order and the system performance, e.g., the bit error rate (BER) for a communication receiver compensated by an FIR equalizer.