As an important part of the channel fading, large scale fading should be considered in downlink massive multiple-input multipleoutput(MIMO) systems. This paper investigates the downlink massive MIMO system over a large scale fading channel, when the base station takes advantage of maximum-radio transmission(MRT) precoding. The cases when the base station has perfect and imperfect channel state information(CSI) are considered respectively. Specially, through the analysis of single user’s ergodic achievable rate, some novel and approximate expressions for the spectral efficiency(SE) are derived. Based on the approximate SE, the effect of the channel estimation error is analyzed intuitively. In addition, the average SE of all the users with different large-scale fading parameters is carefully investigated. Simulations validate that all the theoretical results coincide with numerical results and the large scale fading factors have little influence on SE reduction resulted from channel estimation. As an important part of the channel fading, large scale fading should be considered in downlink massive multiple-input multiple output (MIMO) systems. This paper investigates the downlink massive MIMO system over a large scale fading channel, when the base station takes advantage of maximum The cases when the base station has perfect and imperfect channel state information (CSI) are considered respectively. Specially, through the analysis of single user’s ergodic achievable rate, some novel and approximate expressions for the spectral efficiency (MRT) SE) are derived. Based on the approximate SE, the effect of the channel estimation error is analyzed intuitively. Simultaneously the average SE of all the users with different large-scale fading parameters is carefully investigated. coincide with numerical results and the large scale fading factors have little influence on SE reduction due from channel esti mation.