  Movable antenna (MA) is a new technology with great potential to improve
communication performance by enabling local movement of antennas for pursuing
better channel conditions. In particular, the acquisition of complete channel
state information (CSI) between the transmitter (Tx) and receiver (Rx) regions
is an essential problem for MA systems to reap performance gains. In this
paper, we propose a general channel estimation framework for MA systems by
exploiting the multi-path field response channel structure. Specifically, the
angles of departure (AoDs), angles of arrival (AoAs), and complex coefficients
of the multi-path components (MPCs) are jointly estimated by employing the
compressed sensing method, based on multiple channel measurements at designated
positions of the Tx-MA and Rx-MA. Under this framework, the Tx-MA and Rx-MA
measurement positions fundamentally determine the measurement matrix for
compressed sensing, of which the mutual coherence is analyzed from the
perspective of Fourier transform. Moreover, two criteria for MA measurement
positions are provided to guarantee the successful recovery of MPCs. Then, we
propose several MA measurement position setups and compare their performance.
Finally, comprehensive simulation results show that the proposed framework is
able to estimate the complete CSI between the Tx and Rx regions with a high
accuracy.
