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We have developed a new multifractal modelling framework, called complex multifractal dimension, for characterizing the HF channel. Using the wavelet packet decomposition, and a special fractal dimension algorithm, the complex multifractal dimension provides a local characterization and a coherent physical interpretation, contrarily to others multifractal spectrums. We have adopted the scattering function as a tool for the ionosphere channel characterization. The non-homogeneity of the scattering function expressed according to the propagation time and Doppler shift led us to split it into two one dimensional vectors. Our analysis was performed over both theoretical examples and experimental scattering functions of the ionospheric channel obtained with an experimental support: STUDIO station.