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In this paper, low complexity linear network coordinated beamforming (N-CBF) algorithms under a zero inter-user interference constraint are proposed for the multi-cell downlink channel. We consider a downlink scenario with three base stations (BSs) equipped with one transmit antenna each and three mobile users, each of which has more than one receive antenna and is located on the cell-boundary. A single data stream is transmitted to all three cell-boundary users where each user receives his/her own independent data stream (called full broadcast channel), or where two users receive the same data stream while the third user receives a different data stream (called clustered broadcast channel). For the full and clustered broadcast channel scenarios, we propose low complexity linear N-CBF algorithms approaching the sum capacity realized by multi-cell dirty paper coding. Monte Carlo simulations are carried out to verify the proposed algorithms.