Multi-Carrier Modulation (MCM) is attractive for copper wire access technology in high-performance communication networks e.g. Asymmetric Digital Subscriber Line (ADSL). In digital implementations of MCM, subcarrier generation and data modulation are accomplished digitally using orthogonal transformations of data blocks. These implementations are particularly efficient with regard to bandwidth utilization and transceiver complexity. In this thesis a high-performance digital MCM was used, which is called Discrete Wavelet Multi-Tone (DWMT) Transmission. DWMT is based on the application of wavelet filter bank. The traditional wavelet system uses real basis. However, it is shown in the work that complex wavelet system is very attractive for MCM. It is usually implemented using parallel filter bank, which has strict design constraints. Instead, two design methods based on complex wavelet packets are proposed depending on the orthogonality condition between the subcarriers. Two multicarrier systems were simulated: DWMT system and the standard Discrete Multi-Tone (DMT) system. Their performances were examined under different channel and noise conditions in an ADSL environment. Two baseband modulations were simulated: Qaudrature Amplitude Modulation (QAM) and Pulse Amplitude Modulation (PAM) corresponding to complex and real basis respectively, using both ordinary and Gray mapping. A general simulation program was designed to generate Gray coded QAM symbols and verified successfully. Computer simulation tests show that up to 8.5 dB SNR improvement at 10-4 BER is achieved with DWMT if compared to the conventional DMT system, hi addition, the performance of single carrier QAM was compared with MCM over the twisted-pair channel to verify the more applicable for ADSL modem.