exactly, the BS does multiplex pilots for the users in the downlink which indeed results in a large overhead. To avoid this, a scheme where orthogonal pilot sequences are employed helps in this case. This is implemented via the LTE Uplink pilot pattern. Here, pilot symbols for users are allocated overlapping in the time-frequency resource grid and orthogonal sequences are used for channel estimation. This reduces the overhead significantly.
When doing so, the orthogonal pilot sequence length has to be longer than the number of scheduled users in the multi-user MIMO cell to ensure orthogonality in between the user pilot symbols.