In one embodiment, a wireless device for a wireless data communication system including the wireless device and a base station. The base station includes a plurality of first groups and a signal-processing unit. Each first group includes a receiver and at least one antenna connected to the receiver. The signal-processing unit includes memory and a processor adapted to process signals received by the first groups using a Maximum Likelihood Detection (MLD) method. The wireless device includes a plurality of second groups, each second group adapted to transmit a wireless signal to at least one first group via a corresponding communication channel. Each second group further includes a transmitter and at least one antenna connected to the transmitter. The signal-processing unit is adapted to store, in the memory, information corresponding to one or more transfer functions, each transfer function corresponding to transmission of a wireless signal from an antenna of the second groups to an antenna of the first groups. The transmitters and receivers are adapted to operate at essentially the same frequency or frequency band. Two or more of the communication channels are generated simultaneously. Each transmitter is adapted to modulate an information signal on a radio-frequency signal according to a Quadrature Amplitude Modulation (QAM) method to transmit QAM symbols. Each receiver is adapted to demodulate information signals from a received radio-frequency signal according to the QAM method.