High-dimensional metric combining for non-coherent molecular signal detection

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.