In this paper, by considering the average mean squared error (AMSE) of channel estimation, we primarily obtain the closed-from expressions of the probability density function (PDF) and cumulative distribution function of AMSE for the least squares (LS)/minimum mean squared error (MMSE) estimation method as the line-of-sight (LOS) component is known, where the asymptotic analysis is executed in Rayleigh fading and strong LOS conditions. Secondly, the closed-form expressions for the expectation of AMSE ( Exp _amse ) and variance of AMSE ( Var _amse ) are acquired, where Var _amse is inversely proportional to the number of antennas ( M). As M becomes infinite, the PDF of AMSE at Exp _amse has an order of root M. When the pilot power decreases with M in a power law, the LS case keeps deteriorating while the MMSE case converges to a constant which basically depends on the Rician K-factor. Next, the spectral efficiency is investigated by considering AMSE. When Exp _amse accelerates, the spectral efficiency of the LS method keeps dropping and that of the MMSE method firstly is degraded and then is improved to a constant except Rayleigh fading. Finally, all results are validated via simulations.