Microwave linear analog computers (MiLACs) have recently emerged as a promising solution for future gigantic multiple-input multiple-output (MIMO) systems, enabling beamforming with greatly reduced hardware and computational cost. However, channel estimation for MiLAC-aided systems remains an open problem. Conventional least squares (LS) and minimum mean square error (MMSE) estimation rely on intensive digital computation, which undermines the computational advantage offered by MiLACs. In this letter, we propose efficient LS and MMSE channel estimation schemes for MiLAC-aided MIMO systems. By designing the training precoder and combiner implemented by lossless and reciprocal MiLACs, the proposed schemes perform LS and MMSE estimation in the analog domain, leaving only simple digital scaling. They achieve identical estimation performance to their digital counterparts while significantly reducing computational complexity. Numerical results verify the effectiveness of the proposed schemes.

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