  In a cell-free cloud radio access network (C-RAN) architecture, uplink
channel estimation is carried out by a centralized baseband processing unit
(BBU) connected to distributed remote radio heads (RRHs). When the RRHs have
multiple antennas and limited radio front-end resources, the design of uplink
channel estimation is faced with the challenges posed by reduced radio
frequency (RF) chains and one-bit analog-to-digital converters (ADCs) at the
RRHs. This work tackles the problem of jointly optimizing the pilot sequences
and the pre-RF chains analog combiners with the goal of minimizing the sum of
mean squared errors (MSEs) of the estimated channel vectors at the BBU. The
problem formulation models the impact of the ADC operation by leveraging
Bussgang's theorem. An efficient solution is developed by means of an iterative
alternating optimization algorithm. Numerical results validate the advantages
of the proposed joint design compared to baseline schemes that randomly choose
either pilots or analog combiners.
