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In this letter, we analyze the convergence rate of loaded sample matrix inversion (LSMI) algorithm in amplitude heterogeneous clutter environment. The probability density function of output signal to interference and noise ratio loss (SINR Loss) is derived. Then we give an approximate expression of average SINR loss. Compared with the case where samples used for estimation of covariance matrix of cell under test (CUT) are independent and identically distributed (i.i.d.) with the snapshot of CUT, if the clutter to noise ratio (CNR) of the training samples is larger than that of CUT, the convergence rate of LSMI is faster and output SINR is higher; conversely, the convergence rate of LSMI is slower and SINR is lower. Simulation validates the theoretical analysis.