In emerging Internet-of-Nano-Thing (IoNT), information will be embedded and conveyed in the form of molecules through complex and diffusive medias. One main challenge lies in the long-tail nature of the channel response causing inter-symbol-interference (ISI), which deteriorates the detection performance. If the channel is unknown, existing coherent schemes (e.g., the state-of-the-art maximum a posteriori, MAP) have to pursue complex channel estimation and ISI mitigation techniques, which will result in either high computational complexity, or poor estimation accuracy that will hinder the detection performance. In this paper, we develop a novel high-dimensional non-coherent detection scheme for molecular signals. We achieve this in a higher-dimensional metric space by combining different non-coherent metrics that exploit the transient features of the signals. By deducing the theoretical bit error rate (BER) for any constructed high-dimensional non-coherent metric, we prove that, higher dimensionality always achieves a lower BER in the same sample space, at the expense of higher complexity on computing the multivariate posterior densities. The realization of this high-dimensional non-coherent scheme is resorting to the Parzen window technique based probabilistic neural network (Parzen-PNN), given its ability to approximate the multivariate posterior densities by taking the previous detection results into a channel-independent Gaussian Parzen window, thereby avoiding the complex channel estimations. The complexity of the posterior computation is shared by the parallel implementation of the Parzen-PNN. Numerical simulations demonstrate that our proposed scheme can gain 10dB in SNR given a fixed BER as $10^{-4}$ , in comparison with other state-of-the-art methods.

中文翻译：

---

用于非相干分子信号检测的高维度量组合

在新兴的纳米物联网 (IoNT) 中，信息将通过复杂的扩散介质以分子的形式嵌入和传输。一个主要挑战在于信道响应的长尾特性会导致符号间干扰 (ISI)，这会降低检测性能。如果信道未知，现有的相干方案（例如，最先进的后验最大值，MAP）必须采用复杂的信道估计和 ISI 缓解技术，这将导致计算复杂度高或估计精度差这将阻碍检测性能。在本文中，我们开发了一种新的分子信号高维非相干检测方案。我们通过组合利用信号瞬态特征的不同非相干度量，在更高维的度量空间中实现了这一点。通过推导出任何构造的高维非相干度量的理论误码率 (BER)，我们证明，在相同的样本空间中，更高的维度总是可以实现更低的 BER，但代价是计算多元后验密度的复杂性更高. 这种高维非相干方案的实现是依靠基于 Parzen 窗口技术的概率神经网络 (Parzen-PNN)，因为它能够通过将先前的检测结果转化为与通道无关的高斯 Parzen 来近似多元后验密度窗口，从而避免复杂的信道估计。Parzen-PNN 的并行实现共享后验计算的复杂性。数值模拟表明，与其他最先进的方法相比，我们提出的方案可以在固定 BER 为 $10^{-4}$ 的情况下获得 10dB 的 SNR。