A key problem in the design of cloud radio access networks (CRANs) is to devise effective baseband compression\nstrategies for transmission on the fronthaul links connecting a remote radio head (RRH) to the managing central unit\n(CU). Most theoretical works on the subject implicitly assume that the RRHs, and hence the CU, are able to perfectly\nrecover time synchronization from the baseband signals received in the uplink, and focus on the compression of the\ndata fields. This paper instead does not assume a priori synchronization of RRHs and CU, and considers the problem of\nfronthaul compression design at the RRHs with the aim of enhancing the performance of time and phase\nsynchronization at the CU. The problem is tackled by analyzing the impact of the synchronization error on the\nperformance of the link and by adopting information and estimation-theoretic performance metrics such as the\nrate-distortion function and the Cramer-Rao bound (CRB). The proposed algorithm is based on the Charnes-Cooper\ntransformation and on the Difference of Convex (DC) approach, and is shown via numerical results to outperform\nconventional solutions.
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