Wavelet Packet Modulation (WPM) is an emerging Multi-Carrier Modulation (MCM) technique regarded as a potential alternative to widely used Orthogonal Frequency Division multiplexing (OFDM). OFDM uses Cyclic Prex (CP) and can rely on one-tap equalization. Since WPM has overlapping symbols in the time domain, equalization cannot depend on the use of CP. This paper considers time-domain Minimum Mean-Square Error (MMSE) equalization for WPM with unknown Channel State Information (CSI), where equalizer filter coefficients are computed using known training sequences. The infuence of the transmission overhead due to training sequences on the Bit Error Rate (BER) performance is investigated considering quasistatic time-varying Rayleigh fading channels. Numerical results from computer simulations show that, with moderate overhead due to training sequences, BER performances are comparable with the case of known CSI. Furthermore, WPM is compared to OFDM with one-tap equalization, and is shown to provide better BER performances as compared to OFDM. Finally, this paper demonstrates improvement in Peak-to-Average Power Ratio (PAPR) of the transmitted signal using subcarrier combining for WPM in heterogeneous communication environments, where low-rate and high-rate devices share the same transmission resources.