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We consider multichannel deconvolution in a periodic setting with long-memoryerrors under three different scenarios for the convolution operators, i.e.,super-smooth, regular-smooth and box-car convolutions. We investigate globalperformances of linear and hard-thresholded non-linear wavelet estimators forfunctions over a wide range of Besov spaces and for a variety of loss functionsdefining the risk. In particular, we obtain upper bounds on convergence ratesusing the $L^p$-risk $(1 \le p < \infty)$. Contrary to the case where theerrors follow independent Brownian motions, it is demonstrated thatmultichannel deconvolution with errors that follow independent fractionalBrownian motions with different Hurst parameters results in a much moreinvolved situation. An extensive finite-sample numerical study is performed tosupplement the theoretical findings.

Multichannel Deconvolution with Long Range Dependence: Upper bounds on the $L^p$-risk $(1 \le p < \infty)$