  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, we cannot easily achieve traditional coherent
channel estimation and cancellation, and the impact of ISI will be more severe.
In this paper, we develop a novel high-dimensional non-coherent scheme for
blind detection of 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.
Then, we design a generalised blind detection algorithm that utilizes the
Parzen approximation and its probabilistic neural network (Parzen-PNN) to
detect information bits. Taking advantages of its fast convergence and parallel
implementation, our proposed scheme can meet the needs of detection accuracy
and real-time computing. Numerical simulations demonstrate that our proposed
scheme can gain 10dB BER compared with other state of the art methods.
