发表机构
Chalmers University of Technology（查尔姆斯理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出占用域计算（ODC）及其平衡变体BOC，利用共享资源的静默承载求和，无需CSI和相位对齐，实现非相干空中计算，并给出估计器、最优负载及误差界，仿真验证其优于现有非相干方法。
AI 中文摘要
空中计算（AirComp）通过无线多址信道聚合分布式数据，但相干实现需要信道状态信息（CSI）、相位对齐和功率控制，而非相干能量方法仍受衰落影响。接收天线处的信号叠加是线性的但需要相干性，能量叠加仅在期望意义上对衰落是线性的。我们引入占用域计算（ODC），其可观测量既不是接收幅度也不是能量：总和由共享资源的静默承载。采用指数伯努利激活时，个体静默概率相乘，服务器仅利用二元活动决策即可从空闲比例恢复总和，因此一旦检测到激活，产生该激活的幅度便不进入估计。我们刻画了最大似然估计器、最优负载以及针对未知动态范围非自适应操作的尺度积分费雪信息界。随后我们引入平衡占用计算（BOC），其中每个设备形成基于数据的随机突发放置配额。这消除了伯努利激活的随机放置计数波动；在理想检测下，BOC的前导渐近均方根误差在任何负载下都不大于伯努利ODC，并随着设备数量相对于资源元素数M变小而趋近于$1/\sqrt{2M}$。我们进一步分析了未知尺度操作、有限帧偏差和异构检测遗漏。仿真验证了理论，并将ODC/BOC与仿射非相干能量聚合和REED进行了比较。
英文摘要
Over-the-air computation (AirComp) aggregates distributed data through the wireless multiple-access channel, but coherent implementations require channel state information (CSI), phase alignment, and power control, whereas non-coherent energy methods remain affected by fading. Signal superposition at the receive antenna is linear but requires coherence, and energy superposition is linear only in expectation over fading. We introduce occupancy-domain computation (ODC), whose observable is neither a received amplitude nor an energy: the sum is carried by the silence of the shared resources. With exponential Bernoulli activation, the individual silence probabilities multiply, and the server recovers the sum from the idle fraction using binary activity decisions alone, so that once an activation is detected the amplitude that produced it does not enter the estimate. We characterize the maximum-likelihood estimator, optimal load, and a scale-integrated Fisher-information bound for non-adaptive operation over unknown dynamic ranges. We then introduce balanced occupancy computation (BOC), where each device forms a data-dependent quota of random burst placements. This removes the random placement-count fluctuation of Bernoulli activation; under ideal detection, the leading-order asymptotic root-mean-square error of BOC is no larger than that of Bernoulli ODC at any load and approaches $1/\sqrt{2M}$, where $M$ is the number of resource elements, as the number of devices becomes small relative to $M$. We further analyze unknown-scale operation, finite-frame deviations, and heterogeneous detection misses. Simulations validate the theory and compare ODC/BOC with affine non-coherent energy aggregation and REED.
