Abstract: An optimization model is formulated with respect to the pilot signal in the frequency division duplexing (FDD) massive multiple-input multiple-output (MIMO) downlink system by maximizing the downlink ergodic achievable rate with total power constraint, while jointly considering the effects of the channel spatial correlation, channel estimation accuracy and the data beamforming scheme. Because the original objective function is not in closed form, an approximate analytical is derived by using the deterministic equivalent approximation technology in large-dimensional random matrix theory, which gives the explicit relations between the ergodic achievable rate and the pilot signal matrix. Based on this, the structural characteristic of the pilot signal matrix is deduced firstly by using the majorization theory, which makes the primal problem be an equivalent power allocation problem for the pilot sequence. Then, the closed-form solution of the optimal pilot signal is obtained by utilizing the Lagrangian dual method. Moreover, the actual length as well as the maximum value of pilot sequence is analyzed. Numerical results validate the accuracy and the effectiveness of the proposed analytical of the ergodic rate, and verify the performance gain of our proposed pilot scheme in terms of the ergodic achievable rate and the actual pilot sequence length when compared with the conventional mean square error (MSE) minimization based pilot scheme, and show the difference of the pilot signal power allocation of both schemes.