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A robust technique for array interpolation using second-order cone programming

We consider Friedlander's(1993) array interpolation technique, whose main shortcoming in multi-source scenarios is that it does not provide sufficient robustness against sources arriving outside specified interpolation sectors. We propose a new interpolation approach which incorporates such robustness property. Our technique minimizes the interpolation error inside the sector of interest while setting multiple "stopband" constraints outside this sector to prevent performance degradation effects caused by out-of-sector sources. Based on such robust approach to array interpolation, we develop convex formulations of the interpolation matrix design problem using second-order cone (SOC) programming.