This paper studies the downlink beamforming for a multi-cell system, where multiple base stations (BSs) each with multiple antennas cooperatively design their respective transmit beamforming vectors to optimize the overall system performance. It is assumed that all mobile stations (MSs) are equipped with a single antenna each, and there is one active MS in each cell at one time. Accordingly, the system of interest can be modeled by a multiple-input single-output (MISO) Gaussian interference channel (IC), termed as MISO-IC, with interference treated as additive Gaussian noise. We are interested in designing a multi-cell cooperative downlink beamforming scheme to achieve different rate-tuples for active MSs on the Pareto boundary of the achievable rate region for the MISO-IC, which is in general a non-convex problem due to the coupled signal structure. By exploring the relationship between the MISO-IC and the cognitive radio (CR) MISO channel, we show that each Pareto-boundary rate-tuple of the MISO-IC can be achieved in a decentralized manner when each of the MSs attains its own channel capacity subject to a certain set of interference-power constraints (also known as interference-temperature constraints in the CR system) at the other MS receivers. Furthermore, we show that this result leads to a decentralized algorithm for implementing the multi-cell cooperative downlink beamforming, where all different pairs of BSs independently search for their mutually desirable interference-temperature constraints, under which their respective beamforming vectors are optimized to maximize the individual transmit rates. It is shown that this algorithm guarantees to improve the rates for a given pair of BSs at each iteration with those for the other BSs unaffected, and converges when there are no further incentives for all the BSs to adjust their mutual interference-temperature constraints.
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