Wireless communication system, relay device, and receiving device

A radio communication system comprising:

• a reception device;
• and
• a relay device configured to relay a signal stream transmitted by a transmission device through MIMO transmission to the reception device,
• wherein the relay device includes
• a lattice base reduction processing unit configured to transform bases of the signal stream transmitted by the transmission device through MIMO transmission, to increase orthogonality of a lattice of the signal stream,
• a MIMO equalization unit configured to detect, by equalization, reception symbols in the signal stream with the bases transformed by the lattice base reduction processing unit,
• a symbol quantization unit configured to perform quantization by mapping the reception symbols detected by the MIMO equalization unit, to a region on a complex plane delimited by quantization threshold values, and
• a transmission unit configured to transmit, to the reception device, at least a signal quantized by the symbol quantization unit, and
• the reception device includes
• a reception unit configured to receive the signal transmitted by the transmission unit and
• a signal detection unit configured to detect the signal stream with the bases transformed by the lattice base reduction processing unit, in the signal received by the reception unit.