In this work we analyze the performance of a new scheme combining 2x512/19-phase shift keying Wavelet Coding with a maximum a posteriori receiver on varying multipath channels in terms of bit-error rate. Considering COST 207based power delay profiles for urban environments, we find that a maximum a posteriori receiver can provide a gain of nearly 1.5 dB in relation to Euclidean based Wavelet Coded systems on fading channels with low frequency selectivity. We also investigate in which extent a state-of-the-art equation for error probability of Wavelet-Coded systems is valid for varying multipath channels. Our findings show moderate mismatch between those equations and Monte-Carlo simulations, indicating that channel memory should be considered for the formulation of upper-bound solutions. Nevertheless, the results suggest that the wavelet coding shows considerable resilience to channels with memory, making it a suitable candidate for the use of mm-wave frequencies in future generation mobile communications.