This paper introduces a single-input multiple-output (SIMO) feedforward approach to the single-channel loudspeaker equalization problem. Using a polynomial multivariable control framework, a spatially robust equalizer is derived based on a set of room transfer functions (RTFs) and a multipoint mean-square error (MSE) criterion. In contrast to earlier multipoint methods, the polynomial approach provides analytical expressions for the optimum filter, involving the RTF polynomials and certain spatial averages thereof. However, a direct use of the optimum solution is questionable from a perceptual point of view. Despite its multipoint MSE optimality, the filter exhibits similar, albeit less severe, problems as those encountered in nonrobust single-point designs. First, in the case of mixed phase design it is shown to cause residual "pre-ringings" and undesirable magnitude distortion in the equalized system. Second, due to insufficient spatial averaging when using a limited number of RTFs in the design, the filter is overfitted to the chosen set of measurement points, thus providing insufficient robustness. A remedy to these two problems is proposed, based on a constrained MSE design and a method for clustering of RTF zeros. The outcome is a mixed phase compensator with a time-domain performance preferable to that of the original unconstrained design.
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