A terminal device notifies a base station device about control information associated with a receive quality of the terminal device. The base station device performs data modulation on a plurality of pieces of transmit data for the terminal device, by using a plurality of different data modulation schemes one by one, based on the control information, and spatially multiplexes the plurality of pieces of transmit data after the data modulation over a single wireless resource and transmits a spatially multiplexed signal. The terminal device receives the signal with the plurality of pieces of transmit data spatially multiplexed, and detects desirable transmit data from the receive signal, based on a first channel matrix which represents channel state information between the base station device and the terminal device and a second channel matrix in which the first channel matrix is multiplied by a transform matrix. Accordingly, an adaptive modulation technology is applied even to MIMO spatial multiplexing transmission using a LR technology, and hence a wireless communication system and so forth that can contribute to improvement in frequency utilization efficiency can be provided.