In cooperative cognitive radio networks (CRNs), multiple secondary base stations are managed by a central unit (CU) via finite-capacity backhaul links, which performs joint encoding and precoding of the messages intended for the secondary users (SUs). In this paper, the limitation of backhaul links is handled with the implementation of compression strategies, by which precoding is followed at the CU. In particular, focusing on underlay cooperative CRNs, we propose the joint optimal design of precoding and backhaul quantization with the aim of maximizing the sum throughput of the secondary network under limited backhaul capacity, transmit power, and interference power constraints. Furthermore, both perfect and imperfect channel state information (CSI) available at the CU are considered. In the imperfect-CSI case, the uncertainty of the channels is explicitly accounted for via a robust or worst-case optimization formulation. The proposed algorithmic solutions leverage rank relaxation and majorization-minimization programming, whose performances are evaluated via numerical results.