The concentration of molecules in the medium can provide us very useful information about the medium. In this paper, we use this information and design a molecular flow velocity meter using a molecule releasing node and a receiver that counts these molecules. We first assume $M$ hypotheses according to $M$ possible medium flow velocity values and an $L$-sample decoder at the receiver and obtain the flow velocity detector using maximum-a-posteriori (MAP) method. To analyze the performance of the proposed flow velocity detector, we obtain the error probability, and its Gaussian approximation and Chernoff information (CI) upper bound. We obtain the optimum sampling times which minimize the error probability and the sub-optimum sampling times which minimize the Gaussian approximation and the CI upper bound. When we have binary hypothesis, we show that the sub-optimum sampling times which minimize the CI upper bound are equal. When we have $M$ hypotheses and $L \rightarrow \infty$, we show that the sub-optimum sampling times that minimize the CI upper bound yield to $M \choose 2$ sampling times with $M \choose 2$ weights. Then, we assume a randomly chosen constant flow velocity and obtain the MAP and minimum mean square error (MMSE) estimators for the $L$-sample receiver. We consider the mean square error (MSE) to investigate the error performance of the flow velocity estimators and obtain the Bayesian Cramer-Rao (BCR) and expected Cramer-Rao (ECR) lower bounds on the MSE of the estimators. Further, we obtain the sampling times which minimize the MSE. We show that when the flow velocity is in the direction of the connecting line between the releasing node and the receiver with uniform distribution for the magnitude of the flow velocity, and $L \rightarrow \infty$, two different sampling times are enough for the MAP estimator.

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关于分子流速计

培养基中分子的浓度可以为我们提供关于培养基的非常有用的信息。在本文中，我们使用这些信息并使用分子释放节点和对这些分子进行计数的接收器来设计分子流速计。我们首先根据 $M$ 可能的介质流速值和接收器处的 $L$ 样本解码器假设 $M$ 假设，并使用最大后验 (MAP) 方法获得流速检测器。为了分析所提出的流速检测器的性能，我们获得了错误概率及其高斯近似和切尔诺夫信息 (CI) 上限。我们获得了最小化错误概率的最佳采样时间和最小化高斯近似和 CI 上限的次优采样时间。当我们有二元假设时，我们表明，最小化 CI 上限的次优采样时间是相等的。当我们有 $M$ 假设和 $L \rightarrow \infty$ 时，我们表明最小化 CI 上限的次优采样时间会产生 $M \choose 2$ 采样时间和 $M \choose 2$ 权重。然后，我们假设随机选择的恒定流速并获得 $L$ 样本接收器的 MAP 和最小均方误差 (MMSE) 估计量。我们考虑均方误差 (MSE) 来研究流速估计器的误差性能，并获得估计器 MSE 的贝叶斯 Cramer-Rao (BCR) 和预期 Cramer-Rao (ECR) 下限。此外，我们获得了最小化 MSE 的采样时间。