Synchronization for VHF Data Exchange System

In wireless communications, rapid acquisition of synchronization parameters is essential. Very High Frequency (VHF) Data Exchange System (VDES), a new maritime communication system developed on the basis of traditional Automatic Identification System (AIS), uses time division multiple access (TDMA) and belongs to burst communication. Therefore, synchronization is the top priority of VDES research. VDES includes the terrestrial part and satellite part, named as VDE-TER and VDE-SAT, and the two parts have different channel conditions. This paper studies synchronization algorithms for VDE-TER and VDE-SAT respectively on the basis of different channel conditions and focuses on the derivation, the theoretic analysis and performance simulation of the algorithms.


Introduction
Very High Frequency (VHF) Data Exchange System (VDES) is developed on the basis of traditional maritime Automatic Identification System (AIS) and integrates AIS, Application Specific Message (ASM) and VHF Data Exchange (VDE), of which VDE is divided into terrestrial and satellite part, i.e., VDE-TER and VDE-SAT [1] [2]. Under this framework, AIS has the highest priority for transmitting safety-related messages including ship identification, location reporting and tracking, search and rescue [3]. Some application specific messages such as meteorology and hydrology are transferred from AIS channels to new ASM channels to protect AIS from heavy load pressure to ensure its normal operation. As the core of VDES, VDE has larger bandwidth, supports information that is richer in content and more flexible in format and makes adjustments in frame structure and modem technology for terrestrial and satellite communication scenarios. VDE-TER provides greater communication capabilities for ships in the nearshore zone and VDE-SAT uses satellites to provide data exchange service for ships outside the coverage of shore stations, and even allows ships in the polar region to access VDES channels. In summary, VDES is a globally maritime space-ground communication system. The system architecture and of VDES is shown in Figure 1.  Fig.1 System Architecture of VDES VDES belongs to burst communication and thus synchronization is one of the most important research issues. Moreover, terrestrial and satellite part have different channel conditions. This paper studies the applicable synchronization algorithms for VDE-TER and VDE-SAT, respectively. The following of this paper is organized as follows. Firstly, section II derives the double barker synchronization algorithm for VDE-TER, focuses on the frequency offset estimation and analyzes its performance using MATLAB. Secondly, section III proposes the differential detection algorithm for VDE-SAT scenario with large delay and frequency offset, optimizes the algorithms and simulates its performance. Finally, section IV concludes the paper.

VDE-TER synchonization
In VDES, data is transferred using a transmission packet as shown in [4], in which Sync word (training sequence) is fixed for all transmissions and known to the transceivers and used for timing and carrier frequency synchronization, thereby preparing for decoding and demodulation of data symbols. The Sync word for VDE-TER is .
(1) This training sequence is called double barker codes, as it is the combination of a 1 and 13-bit barker codes and its inverted codes. The sequence has nice autocorrelation features, furthermore, frequency offset can be obtained on the basis of phase difference between barker codes and its inverted codes. The reminder of this section focuses on its frequency offset estimation algorithms and performance.
At the transmitter side, training sequence applies following mapping: 1 maps to symbol 3 (1,1), 0 maps to symbol 0 (0,0), as shown in Figure II. And The first symbol of the training sequence is mapped to the constellation defined by points (constellation 1); the next symbol is mapped to the constellation defined by points (constellation 2); and so on.
At the receiver side, the training sequence symbols received can be expressed as [5] (2) is the local training sequence, is frequency offset, is phase offset， is symbol period， is the noise， is the length of training sequence. We convert the received sequences into a new sequences by (3) phase difference of barker code and its inverted codes is then (4) here . Given (5) Substituting (5) into (4), we obtain (6) When the noise can be neglected, (6) is simplified as (7) By averaging the phase differences of 13 bits barker codes and its inverted codes, the frequency offset estimation formula can be deduced as   Fig.4 MSE of normalized frequency estimation error periodically shifts the value by to limit it to the range of . In order to verify the effectiveness and study the performance of the algorithm, we carry on the simulation by MATLAB, observe its frequency offset estimation range and performance under various SNR. The simulation parameters are set to as follows: channel bandwidth is 25 kHz with a roll-off factor of 0.3, sampling rate is 19200 samples per second [4]. Figure III shows the frequency offset estimation range under 10 dB Es/N0 (the energy per symbol to noise power spectral density ratio), in which the normalized frequency offset refers to the offset normalized to sampling rate. According to [4](7), the theoretical estimation range is , i.e., normalized values. Simulation results are consistent with theoretical results. Furthermore, we simulates the mean-square error (MSE) of frequency offset estimates under various SNR, assuming the normalized frequency offset of received signal is 0.03. Simulation results are shown in Figure IV, it can be seen that even under low SNR, the double barker algorithm gets small MSE of normalized frequency error estimates.
According to [6], ships reach an average speed of 23 nautical miles per hour, i.e., 11.8 meters per second, Doppler shift is no more than 10 Hz. With the addition of 3 ppm transmitter frequency error, overall frequency error is lower than 500 Hz. Therefore, the estimation range meets actual demand. Moreover, the algorithm shows high estimation accuracy, in combination with its low computing complexity and no strict need of coherent carrier, the double barker synchronization algorithm can be used in VDE-TER scenario.

VDE-SAT Synchronization
VDE-SAT communication has characteristics of low SNR, large delay, large Doppler shift, fading, etc., nevertheless, traditional correlation method for synchronization is susceptible to large frequency offset. Differential is a mainstream technology for eliminating the effect of large frequency offset. This section studies the differential detection synchronization algorithm for VDE-SAT and focuses on the formula derivation and performance simulation.
There are two kinds of training sequences under consideration for VDE-SAT, one of which has length of 27 bits and is modulated by , the other has a length of 48 bits and is modulated by BPSK and CDMA, as shown in Table I. Both have best autocorrelation for differential detection. Since there are much difference between them, it is necessary to study separately. is conjugate operation, indicates different delays, is the received samples, is the local training sequence, and is the length of training sequence. When frequency offset exists, the correlation function is (10) is sampling rate, and . In the absence of noise, the correlation value at correct timing is  The above equation reflects that the maximum correlation value is not affected by frequency offset. Furthermore, after locating the starting position of received training sequence, considering the Doppler shift in the range of to 4 kHz [1], we obtain the coarse frequency offset estimate by (12) and (13) is the received training sequence. After compensating the coarse estimate, the fine estimation is achieved by (14) The final estimate is (16) For a VDE-SAT satellite at the altitude of 600 km, the distance between satellite and ships is between 600 and 2830 km [1], hence the differential delay between the shortest and the longest propagation time with the coverage area is 8 ms. Given the 8ms maximum delay and to 4 kHz frequency offset, we simulate the performance of differential detection in MATLAB. The simulation parameters are set to as follows: signal bandwidth is 42 kHz with a roll-off factor of 0.25 [4], sampling rate is 33600 samples per second.
The statistical results of the timing estimation accuracy rate are shown in Table II. When Es/N0 is less than or equal to 3dB, the differential detection algorithm has poor timing performance. When Es/N0 is greater than or equal to 4 dB, accuracy rate is about 95% or more. When the Es/N0 is 5dB, the timing accuracy is 98%, which is generally consistent with the "Based on search looses 0.3% of packets at ES/N0 of 5 dB" in the VDES recommendation [4]. Furthermore, we simulate the frequency offset estimation performance of differential algorithm when Es/N0 equals to 4, 5, 6, and 7dB, and count the estimation error of 5000 sample frames [4]. Figure V shows the cumulative distribution function (CDF) of frequency offset estimation error. Obviously, the larger the SNR is, the greater the frequency error estimation performance is. When Es/N0 equals to 5 dB, the range of estimation error can be controlled within , i.e., about 1 ppm. At the receiver side, for every possible timing point, we take 48 sets of spread sequence to perform despread. After despreading, the correlation function of differential algorithm is (17) is the length of training sequence, and is length of spreading codes. The correlation value at correct timing is then (18) and is a constant. Obviously, frequency offset estimate can be obtained by calculating the phase of correlation peak , i.e.,

Summary
The above content studies the applicability of differential detection synchronization algorithm for VDE-SAT scenario. Study shows that the correlation peak of sequence 1 is not influenced by frequency offset and after finding the correct timing via correlation peak, frequency offset can be obtained through only two differential operations. In terms of the problem faced by sequence 2 that the correct correlation peak is likely flooded in the noise when the initial frequency offset is more than 1 kHz, we propose means of hypothesis estimation in advance which effectively improves algorithm performance. Simulation results show that sequence 1 has 98.1% timing accuracy rate and less than 200 Hz (1 ppm) frequency estimation error at Es/N0=5 dB, and sequence 2 has 99.7% timing accuracy rate and less than 200 Hz frequency estimation error at Es/N0= dB (Es here means the energy per chip). Therefore, the differential detection can be applied to VDE-SAT synchronization and can achieve good performance. Moreover, sequence 2 is of greater robustness and applies to lower SNR environment.

Conclusion
This paper studies the applicable synchronization algorithms for VDE-TER and VDE-SAT respectively. The double barker algorithm for VDE-TER relies on the training sequence structure and its specific modulation and has the advantages of sufficient estimation range, great performance and no need for strict coherent carrier information. The differential detection for VDE-SAT overcomes the nonapplicability of traditional correlation detection under large frequency offset, the correlation peak is not sensitive to frequency offset, and the algorithm has great timing and frequency offset estimation performance.