This paper investigates the influence of channel estimation error on the precoding matrix selection and signal detection for MIMO multiplexing using precoding in the downlink OFDM radio access. In a simulation, we assume codebook-based unitary precoding and signal detection that employs a minimum mean squared error (MMSE) based interference suppression filter. The simulation results clarify the effect of the channel estimation error with respect to the precoding matrix selection and signal detection from the viewpoints of the number of streams, i.e., rank order, the number of transmit antennas, the modulation scheme and channel coding rate, and codebook size, i.e., quantization for precoding matrix feedback information.