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I was wondering what is the operating frequency of different antenna's in a MIMO system? Do they work in the same band or separate band that the LTE(22 bands) assigned with? Thank you.

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If you are refering to "E-UTRA operating bands" defined by 3GPP standands (section 5.5), the answer is NO.

In LTE access network, an operating band is assigned to a physical cell and MIMO is a signal processing method in the band. Currently, MIMO in LTE uses frequency between sub-carriers and space diversity (SFBC, spatial multiplexing and beamforming) and channel code (turbo code + tail bitting convolution code) add time diversity.

PS: just wonder where you found the number "22 bands".

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Operating frequency of an antenna is not related to whether it's a single antenna or in MIMO configuration. Operating frequency is related to the geometry of the antenna. The antenna is designed to be optimal in delivering and radiating power in that frequency. MIMO is a mathematical method to put the signal of interest on the antennas in such a way that maximizes SNR and rate, benefiting from space and time diversity of MIMO configuration.

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