论文标题
带有内存的高斯通道的反馈能力
Feedback capacity of Gaussian channels with memory
论文作者
论文摘要
我们考虑了MIMO通道的反馈容量，其通道输出由通道输入和高斯过程驱动的线性状态空间模型给出。我们的状态空间模型的一般性集成了所有先前研究的模型，例如具有彩色高斯噪声的加性通道，以及对先前的通道输入或输出的任意依赖性的通道。主要结果是可计算的反馈能力表达式，该表达式作为凸优化问题，但要有可检测性条件。我们证明了自动回归高斯噪声通道的能力结果，在那里我们表明，即使反馈的单个时间效率延迟也会大大降低固定态度的反馈能力。另一方面，对于大回归参数（在非平稳制度中），可以通过延迟反馈来接近反馈能力。最后，我们表明对标量模型满足可检测性条件，并猜想对MIMO模型是正确的。
We consider the feedback capacity of a MIMO channel whose channel output is given by a linear state-space model driven by the channel inputs and a Gaussian process. The generality of our state-space model subsumes all previous studied models such as additive channels with colored Gaussian noise, and channels with an arbitrary dependence on previous channel inputs or outputs. The main result is a computable feedback capacity expression that is given as a convex optimization problem subject to a detectability condition. We demonstrate the capacity result on the auto-regressive Gaussian noise channel, where we show that even a single time-instance delay in the feedback reduces the feedback capacity significantly in the stationary regime. On the other hand, for large regression parameters (in the non-stationary regime), the feedback capacity can be approached with delayed feedback. Finally, we show that the detectability condition is satisfied for scalar models and conjecture that it is true for MIMO models.
