1. A precoding weight generation method of generating precoding weights by which transmission data is multiplied, the transmission data being transmitted from a base station apparatus to a mobile station apparatus with a plurality of streams by using Multi Input Multi Output (MIMO) transmission, the method comprising: in the mobile station apparatus, calculating a throughput expectation value for each of the plurality of streams based on a channel state of each of the plurality of streams, performing the calculating for each of predetermined precoding matrices, and selecting a precoding matrix indicator (PMI) associated with a precoding matrix of the predetermined precoding matrices, the precoding matrix including matrix elements that maximize a throughput expectation value in the calculated throughput expectation values; transmitting the selected PMI to the base station apparatus as channel information; in the base station apparatus, extracting the matrix elements that maximize the throughput expectation value from the precoding matrix associated with the PMI transmitted from the mobile station apparatus as feedback; and generating precoding weights based on the extracted matrix elements.