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In this paper, we study cooperative precoder design in two-tier networks, consisting of a macro-cell (MC) and several small-cells (SCs). By exploiting multiuser Vandermonde-subspace frequency division multiplexing (VFDM) transmission, an MC downlink can co-exist with cognitive SCs. In this paper, we first propose a cooperative cross-tier precoder (CTP) among the transmitters in the SCs to increase the transmitted dimension. The cooperative CTP allows us to use more efficient intra-tier precoder (ITP) in SCs to handle intracell interference and improve the throughput of the cognitive system. And then, three ITPs, a block-diagonal zero-forcing (BD-ZF) ITP, a capacity-achieving (CA) ITP, and a generalized MMSE channel inversion (GMI) ITP, are developed. Complexities of all CTPs and ITPs are discussed and compared. The overhead of channel state information (CSI) exchange is analyzed. Numerical results are …