  In this letter, we study the channel estimation for wireless communications
with movable antenna (MA), which requires to reconstruct the channel response
at any location in a given region where the transmitter/receiver is located
based on the channel measurements taken at finite locations therein, so as to
find the MA's location for optimizing the communication performance. To reduce
the pilot overhead and computational complexity for channel estimation, we
propose a new successive transmitter-receiver compressed sensing (STRCS) method
by exploiting the efficient representation of the channel responses in the
given transmitter/receiver region (field) in terms of multi-path components.
Specifically, the field-response information (FRI) in the angular domain,
including the angles of departure (AoDs)/angles of arrival (AoAs) and complex
coefficients of all significant multi-path components are sequentially
estimated based on a finite number of channel measurements taken at
random/selected locations by the MA at the transmitter and/or receiver.
Simulation results demonstrate that the proposed channel reconstruction method
outperforms the benchmark schemes in terms of both pilot overhead and channel
reconstruction accuracy.
