Age of information (AoI) is a powerful metric to evaluate the freshness of information, where minimization of average statistics, such as the average AoI and average peak AoI, currently prevails in guiding freshness optimization for related applications. Although minimizing the statistics does improve the received information's freshness for status update systems in the sense of average, the time-varying fading characteristics of wireless channels often cause uncertain yet frequent age violations. The recently-proposed statistical AoI metric can better characterize more features of AoI dynamics, which evaluates the achievable minimum peak AoI under the certain constraint on age violation probability. In this paper, we study the statistical AoI minimization problem for status update systems over multi-state fading channels, which can effectively upper-bound the AoI violation probability but introduce the prohibitively-high computing complexity. To resolve this issue, we tackle the problem with a two-fold approach. For a small AoI exponent, the problem is approximated via a fractional programming problem. For a large AoI exponent, the problem is converted to a convex problem. Solving the two problems respectively, we derive the near-optimal sampling interval for diverse status update systems. Insightful observations are obtained on how sampling interval shall be tuned as a decreasing function of channel state information (CSI). Surprisingly, for the extremely stringent AoI requirement, the sampling interval converges to a constant regardless of CSI's variation. Numerical results verify effectiveness as well as superiority of our proposed scheme.

翻译：信息年龄是评估信息新鲜度的有力指标，其中平均统计量（如平均信息年龄和峰值平均信息年龄）的最小化目前主导着相关应用的新鲜度优化。尽管最小化这些统计量确实能从平均意义上提升状态更新系统中接收信息的新鲜度，但无线信道的时变衰落特性常常导致不确定且频繁的年龄违规。最近提出的统计信息年龄度量能更好地刻画信息年龄动态的更多特征，它评估在年龄违规概率的特定约束下可达到的最小峰值年龄。本文研究多状态衰落信道下状态更新系统的统计信息年龄最小化问题，该方法能有效限定信息年龄违规概率，但会引入极高的计算复杂度。为解决此问题，我们采用双管齐下的方法：对于较小的信息年龄指数，该问题通过分式规划进行近似；对于较大的信息年龄指数，该问题则转化为凸优化问题。通过分别求解这两个问题，我们推导出不同状态更新系统的近最优采样间隔。我们获得了一些有洞察力的结论：采样间隔应作为信道状态信息的递减函数进行调整。令人惊讶的是，对于极其严格的信息年龄要求，采样间隔会收敛到一个与信道状态信息变化无关的常数。数值结果验证了我们所提方案的有效性和优越性。