## 1 Introduction  
Molecular communication (MC) is a promising communication technique for use in nanoscale machine systems [1]. A transmitter nanomachine emits molecules that propagate in a fluid environment to a receiver nanomachine via diffusion. These molecules are absorbed and decoded by the receiver nanomachine. MC is anticipated to be a key innovative technology for nanoscale machines for healthcare, environmental protection, agriculture, and nanomedicine applications [2; 3]. Compared with traditional electromagnetic communications, MC systems provide the following distinct features: (1) They use molecules as a communication carrier, and signal transmission occurs by changing the molecular emission time, concentration, or type. (2) The emitted molecules propagate via diffusion, and their movement is governed by Brownian motion [3]. (3) Because of the size and power-consumption limitations of nanomachines, applications are limited to slow communication systems with low energy consumption. Consequently, the design of MC systems, including signal modulation, signal detection, synchronization, and transceiver optimization, poses new fundamental challenges [4; 5; 6]. The two most critical challenges of system design are how to design transmitter and receiver nanomachines that can encode and modulate information into signals, and how to detect and decode information from the received diffused signals, respectively. In terms of signal detection, much research on MC assumes that, in nanomachines, perfect time synchronization occurs for modulation and demodulation [7]. Methods based on single-spike feedback signals were proposed [8]. A transmitter estimated the distance by measuring the round-trip time (RTT) or signal attenuation of the received feedback signal. Both schemes employed the distance function of RTT and molecular concentration to calculate the distance. These methods were expensive, and the transmitter and receiver nanomachines had to be tuned for the diffusion coefficient or number of transmitted molecules. However, in real MC systems, automatic synchronization does not occur. In an MC system, in contrast to traditional radio communications, information is transmitted through the slow process of diffusion-based propagation. This process results in intersymbol interference (ISI), which impairs the accurate detection of subsequent symbols. To decode a signal, a maximal-likelihood estimator was proposed in [9] for a clock offset between two nanomachines. A transmitter recorded the sending time of the message and passed it to the receiver. The receiver then used this information to estimate the clock offset. Clock synchronization between a transmitter and receiver in a mobile MC system was investigated in [10] to estimate the clock offset using the least-squares and peak-time methods. A synchronization technique was proposed in [11] that utilized synchronization and information molecules with different diffusion coefficients. The start of the signal was estimated on the basis of the high concentration of synchronization molecules, which had a higher diffusion coefficient than that of the information molecules. A two-way time synchronization scheme was proposed in [12] that considered the use of a bidirectional flow channel for the exchange of forward-feedback messages. Additionally, several studies were conducted that used techniques such as quorum sensing [13], blind synchronization with delay [14], and signal-peak observation [15; 16]. For event detection, a feedback-based method for detecting signal-peak concentration was proposed [17]. Although the time cost was reduced, estimation accuracy was low. Distance-estimation schemes based on molecular concentration were proposed to improve signal detection performance [18; 19]. These studies estimated the distance by measuring either the peak concentration time or the received concentration energy. However, it had a higher requirement in terms of system complexity.