In this article, we investigate the training optimization for multiple-input-multiple-output (MIMO)-Aided Internet of Things (IoTs) systems that employ subarray-based intelligent reflecting surface (IRS). In order to overcome the nonlinear relationship between two cascaded channel matrices, the IRS can be divided into a series of subarrays, for which only an equivalent cascaded channel matrix should be estimated in each subarray. Correspondingly, the training sequence should be divided into multiple segments. By sufficiently utilizing the available statistical channel state information (CSI), either mean-square error (MSE) minimization or mutual information (MUI) maximization can be taken as the performance metric for optimizing the training sequence. A variety of fairnesses among different subarray channel estimations has been taken into account. Furthermore, in order to reduce the hardware cost of the power amplifier, we propose a two-stage training sequence structure, including a fully digital filter and a constant modulus sequence. To further reduce computational complexity, various low-complexity water-filling solutions are proposed. Numerical results demonstrate the accuracy and efficiency of the proposed solutions.