Cognitive backscatter communication enables wireless powered backscatter devices (BDs) to transmit information by modulating ambient radio frequency (RF) carriers, which shares both the same spectrum and the same radio-frequency (RF) source as the legacy (ambient) system, thus has become a promising technology for energy-and spectrum-efficient Internet-of-things (IoT) communications. In this paper, we consider a cooperative cognitive backscatter network (CCBN) consisting of a multi-antenna RF-Source, multiple (ambient) BDs, and a multi-antenna cooperative receiver (C-RX). We derive the achievable rates for the CRX decoding the direct-link signal from the RF-Source and the backscatter-link signal from all BDs, respectively. We further formulate an optimization problem to maximize the backscatter-link sum rate by optimizing the beamforming weights (i.e., the precoding matrix) subject to the RF-Source's minimum rate requirement and the BDs' minimum energy requirements. Based on the sequential parametric convex approximation (SPCA) method, we propose an algorithm to find the optimal solution to the original non-convex problem, by using a sequence of semidefinite programming (SDP) problems to approximate the original problem iteratively. Finally, extensive numerical results show that the optimal beamforming solution enhances the BDs' sum rate significantly compared to the omnidirectional transmission, and demonstrate the tradeoff among the direct-link rate of the RF-Source, the sum rate of all BDs, as well as the energy requirements at the BDs.