In the present paper, we investigate the design and optimization for fronhaul links in cloud radio access networks (C-RAN). Existing C-RAN designs rely on the instantaneous network-wide channel state information (CSI), which might impose a significant overhead due to the potential large-scale of C-RAN. To overcome this limitation, we optimize C-RAN based on the average performance metrics which only require the second-order statistics of the fading channels. Firstly, a tight upper bound of the block error rate (BLER) over Rayleigh fading channels is derived in closed-form expression, through which some insights on C-RAN are drawn: i) full diversity order, which is equal to the number of RRHs, is achievable with respect to the signal to compression plus noise ratio; and ii) the BLER is limited below by either compression or Gaussian noises. Secondly, based on the derived bound, a compression optimization is proposed to minimize the fronthaul transmission rate while satisfying some predefined BLER constraints. The premise of the proposed optimization originates from practical scenarios where most applications tolerate a non-zero BLER. Finally, a fronthaul rate allocation scheme is proposed to minimize the system BLER. It is proved that the proposed allocation scheme, which imposes uniform compression noise across the RRHs, approaches the optimal allocation as the total fronthauls' bandwidth increases.