In this paper, we study an optimized block-diagonal zeroforcing (BD-ZF) precoder in two-tiered cognitive networks, consisting of a macro-cell (MC) and a small-cell (SC). By exploiting multi-user multiple input multiple outputVandermonde-subspace frequency division multi-plexing (MIMO-VFDM) transmission, a cognitive SC can coexist with an MC. We first devise a cross-tier precoder (CTP) based on the idea of Vandermonde-subspace frequency division multiplexing (VFDM) to cancel the interference from SC to MC. And then, we adopt BD-ZF intra-tier precoder (ITP) to suppress the multi-user interference among SC. In the case that the dimension of the provided null space is larger than what BD-ZF ITP requires, we develop an optimized ITP. By optimizing the rotating and selecting matrix, all limited channel gain is collected, which results in a good performance of throughput. Numerical results are presented to demonstrate the throughput improvement of the proposed optimized BDZF ITP and to discover the impact of imperfect channel state information (CSI).