  In ambient re-scatter communications, devices convey information by
modulating and re-scattering the radio frequency signals impinging on their
antennas. In this correspondence, we consider a system consisting of a legacy
modulated continuous carrier multiple-input-multiple-output (MIMO) link and a
multi-antenna modulated re-scatter (MRS) node, where the MRS node modulates and
re-scatters the signal generated by the legacy transmitter. The receiver seeks
to decode both the original message and the information added by the MRS. We
show that the achievable sum rate of this system exceeds that which the legacy
system could achieve alone. We further consider the impact of channel
estimation errors under the least squares channel estimation and study the
achievable rate of the legacy and MRS systems, where a linear minimum mean
square error receiver with successive interference cancellation is utilized for
joint decoding.
