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 (<inline-formula> <tex-math notation="LaTeX">${\mathrm{Exp}}_{\mathrm{amse}}$ </tex-math></inline-formula>) and variance of AMSE (<inline-formula> <tex-math notation="LaTeX">${\mathrm{Var}}_{\mathrm{amse}}$ </tex-math></inline-formula>) are acquired, where <inline-formula> <tex-math notation="LaTeX">${\mathrm{Var}}_{\mathrm{amse}}$ </tex-math></inline-formula> is inversely proportional to the number of antennas (<inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula>). As <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> becomes infinite, the PDF of AMSE at <inline-formula> <tex-math notation="LaTeX">${\mathrm{Exp}}_{\mathrm{amse}}$ </tex-math></inline-formula> has an order of root <inline-formula> <tex-math notation="LaTeX">${M}$ </tex-math></inline-formula>. When the pilot power decreases with <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> in a power law, the LS case keeps deteriorating while the MMSE case converges to a constant which basically depends on the Rician <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula>-factor. Next, the spectral efficiency is investigated by considering AMSE. When <inline-formula> <tex-math notation="LaTeX">${\mathrm{Exp}}_{\mathrm{amse}}$ </tex-math></inline-formula> 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.