We have proposed an intruder detection method by using multiple-input multiple-output (MIMO) channels. Although the channel capacity for MIMO transmission is severely degraded in time-variant channels, we can take advantage of this feature in MIMO sensor applications. For MIMO sensors, the accurate estimation of channel state information (CSI) is essential. Moreover, the transceiver should be simplified from the viewpoint of saving power. Narrowband signals such as minimum shift keying (MSK) and offset quaternary phase shift keying signals are effective and are used in sensor network systems. However, because the timing and carrier offsets between the transmitter and receiver are relatively large compared to the symbol rate, accurate CSI estimation is impossible given the severe constraints imposed by the timing and carrier offsets. To solve this issue, a signal synchronization method for the CSI estimation using a narrowband MSK signal has been proposed. In this paper, we propose a new CSI estimation method for arbitrary amplitude and phase modulation schemes for the MIMO sensor. The key point of the proposed method is that control signals (unique words) are mapped so as not to pass through the origin of the complex I/Q plane. The estimation accuracy of the proposed method is evaluated via a computer simulation. Moreover, the basic performance by the proposed CSI estimation method is verified when considering intruder detection by MIMO sensor.