Full duplex radio wireless systems and methods and especially transceivers for full duplex radio wireless systems with reduction of self-interference are described. MIMO (=multiple input multiple output several antennas for output and input) is used within one device with multiple antennas to remove self-interference in a proactive way. For example, a transceiver is described having self-interference suppression, comprising, within one transceiver device: two or more transmitters comprising one or more signal generators for transmitting transmit signals having transmit center frequencies in a selected first subchannel; and one or more receivers having receiver inputs for simultaneously receiving a desired receive signal in a second subchannel and an undesired accumulated interference signal due to said transmitted signals; and at least one of said transmitters also comprising a precompensation circuit that modifies the transmit signals such that said accumulated interference signal at the receiver(s) inputs is reduced.