解开稳健MISO下行传输优化的秩一解之谜：一个新对偶结果的可验证充分条件
Unraveling the Rank-One Solution Mystery of Robust MISO Downlink Transmit Optimization: A Verifiable Sufficient Condition via a New Duality Result
摘要：
针对多用户多输入单输出（MISO）下行链路，研究了在信道状态信息（CSI）不准确情况下的鲁棒传输优化问题。这个鲁棒的问题处理一般秩的发送协方差设计，它遵循一个安全的速率约束下的球形有界CSI的不确定性制定。奇怪的是，在以前的作品中的仿真结果表明，鲁棒问题承认在大多数情况下，秩一最佳传输协方差。这样的数值发现是有吸引力的，因为具有秩一协方差的传输可以通过单流发射波束成形容易地实现。这就产生了一个根本性的重要问题，即，我们是否可以在理论上确定的条件下，鲁棒问题承认一个秩一的解决方案。在本文中，我们确定了一个这样的条件。简单地说，我们证明了鲁棒性问题是保证承认秩一的解决方案，如果CSI的不确定性不是太大，多用户信道是不是太差的条件。为了建立上述条件，我们开发了一个新的对偶框架，通过它的鲁棒问题和相关的极大极小问题之间的密切关系被揭示。我们的条件只涉及一个简单的表达式，相对于多用户信道和其他系统参数。特别是，与文献中出现的其他充分秩一条件不同，我们的条件是可验证的。我们的分析框架，其他几个CSI不确定性模型的应用进行了讨论。
英文摘要：
This paper concentrates on a robust transmit optimization problem for the multiuser multi-input single-output (MISO) downlink scenario and under inaccurate channel state information (CSI). This robust problem deals with a general-rank transmit covariance design, and it follows a safe rate-constrained formulation under spherically bounded CSI uncertainties. Curiously, simulation results in previous works suggested that the robust problem admits rank-one optimal transmit covariances in most cases. Such a numerical finding is appealing because transmission with rank-one covariances can be easily realized by single-stream transmit beamforming. This gives rise to a fundamentally important question, namely, whether we can theoretically identify conditions under which the robust problem admits a rank-one solution. In this paper, we identify one such condition. Simply speaking, we show that the robust problem is guaranteed to admit a rank-one solution if the CSI uncertainties are not too large and the multiuser channel is not too poorly conditioned. To establish the aforementioned condition, we develop a novel duality framework, through which an intimate relationship between the robust problem and a related maximin problem is revealed. Our condition involves only a simple expression with respect to the multiuser channel and other system parameters. In particular, unlike other sufficient rank-one conditions that have appeared in the literature, ours is verifiable. The application of our analysis framework to several other CSI uncertainty models is also discussed.
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