Perturbation Stability of Various Coherent Riesz Families
نویسندگان
چکیده
We compare three types of coherent Riesz families (Gabor systems, Wilson bases, and wavelets) with respect to their perturbation stability under convolution with elements of a family of typical channel functions. This problem is of key relevance in the design of modulation signal sets for digital communication over time–invariant channels. Upper and lower bounds on the orthogonal perturbation are formulated in terms of spectral spread and temporal support of the prototype, and by the approximate design of worst case convolution kernels. Among the considered bases, the Weyl–Heisenberg structure which generates Gabor systems turns out to be optimal.
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Perturbation Stability of Coherent Riesz Systems under Convolution Operators
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