  We propose a novel resource efficient analog over-the-air (OTA) computation
framework to address the demanding requirements of the uplink (UL) fronthaul
between the access points (APs) and the central processing unit (CPU) in
cell-free massive multiple-input multiple-output (MIMO) systems. We discuss the
drawbacks of the wired and wireless fronthaul solutions, and show that our
proposed mechanism is efficient and scalable as the number of APs increases. We
present the transmit precoding and two-phase power assignment strategies at the
APs to coherently combine the signals OTA in a spectrally efficient manner. We
derive the statistics of the APs locally available signals which enable us to
to obtain the analytical expressions for the Bayesian and classical estimators
of the OTA combined signals. We empirically evaluate the normalized mean square
error (NMSE), symbol error rate (SER), and the coded bit error rate (BER) of
our developed solution and benchmark against the state-of-the-art wired
fronthaul based system
