Receiving device, receiving method, program, and optical communication system

Abstract

A receiving device (120) receives a digital received signal (80) including a plurality of data frames including a pilot signal and a payload. The pilot signal is composed of two or more constant amplitude zero autocorrelation waveform (CAZAC) sequences. The receiving device (120) includes a determining unit (122) that determines a head position and a frequency offset of each of the data frames by calculating a correlation sequence for each of the candidate frequency offsets, where the correlation sequence for the candidate frequency offset is a sequence of cross-correlations between the pilot signal and sub-blocks of the digital received signal under a frequency shift represented by the candidate frequency offset having various head positions, determining two or more peaks for each of the correlation sequences, and determining the head position and frequency offset of the data frame based on the peaks of the correlation sequence.

Description

[Technical Field]

[0001] The present disclosure generally relates to a receiving apparatus, a receiving method, a non-transitory computer-readable storage medium, and an optical communication system. [Background technology]

[0002] In an optical communication system, a message is transmitted from a transmitter to a receiver over an optical communication channel, such as an optical fiber medium. The transmitter divides the message into multiple payloads and generates a data frame for each payload, thereby generating a data frame sequence that forms an optical signal transmitted from the transmitter.

[0003] The receiving device receives an optical signal through an optical communication channel, converts the optical signal into a digital signal, and detects each data frame from the digital signal to obtain a message. To enable the receiving device to detect each data frame from the received signal, the data frame includes a predefined pilot signal as an indicator of the head position of the data frame. In this way, the receiving device detects each data frame by detecting the pilot signal of each data frame from the received signal.

[0004] Since some frequency shift may be induced in the received signal during transmission over the optical communication channel, it is also necessary to determine the amount of frequency shift induced in the data frame (i.e., frequency offset) in order to correctly obtain each data frame.

[0005] In this regard, Patent Document 1 discloses a technique for detecting both the head position and frequency offset of a data frame in a wireless communication system. The receiver disclosed in Patent Document 1 includes multiple matched filters with different expected frequency offsets. Each matched filter correlates a received signal with a pilot signal having a corresponding frequency offset, and outputs a correlation output signal. The receiver detects peaks from each correlation output signal and selects the head position and frequency offset corresponding to the maximum peak. [Prior art documents] [Patent documents]

[0006] [Patent Document 1] US Patent Publication No. 2008 / 0267303 Summary of the Invention [Problem to be solved by the invention]

[0007] In Patent Document 1, the pilot signal consists of a single CAZAC sequence. The purpose of this disclosure is to provide a novel technique for detecting both the head position and the frequency offset of a data frame transferred over an optical communication channel. [Means for solving the problem]

[0008] The present disclosure provides a receiving device comprising at least one memory configured to store instructions and at least one processor, the processor being configured to execute instructions for acquiring a digital received signal obtained by converting an optical received signal into a digital signal, the digital received signal including a plurality of data frames, each including a pilot signal and a payload, the pilot signal being composed of two or more constant amplitude zero autocorrelation waveform (CAZAC) sequences, and instructions for determining a head position and a frequency offset of each of the data frames, the determining of the head position and the frequency offset of the data frames comprising: calculating a correlation sequence for each of candidate frequency offsets, the correlation sequences for the candidate frequency offsets being a sequence of cross-correlations between the pilot signal and a sub-block of the digital received signal under a frequency shift represented by the candidate frequency offset, the head position of the sub-block being selected from a plurality of candidate head positions; determining two or more peaks for each of the correlation sequences; and determining the head position and the frequency offset of the data frame based on the determined peaks of the correlation sequence.

[0009] The present disclosure further provides a computer-implemented receiving method, the receiving method including: obtaining a digital received signal obtained by converting an optical received signal into a digital signal, the digital received signal including a plurality of data frames, each including a pilot signal and a payload, the pilot signal being composed of two or more constant amplitude zero autocorrelation waveform (CAZAC) sequences; determining a head position and a frequency offset of each of the data frames, the determining the head position and the frequency offset of the data frames including calculating a correlation sequence for each of candidate frequency offsets, the correlation sequences for the candidate frequency offsets being a sequence of cross-correlations between the pilot signal and a sub-block of the digital received signal under a frequency shift represented by the candidate frequency offset, the head position of the sub-block being selected from a plurality of candidate head positions; determining two or more peaks for each of the correlation sequences; and determining the head position and the frequency offset of the data frames based on the determined peaks of the correlation sequences.

[0010] The present disclosure further provides a non-transitory computer-readable storage medium storing a program, the program causing a computer to: acquire a digital received signal obtained by converting an optical received signal into a digital signal, the digital received signal including a plurality of data frames, each including a pilot signal and a payload, the pilot signal being composed of two or more constant amplitude zero autocorrelation waveform (CAZAC) sequences; determine a head position and a frequency offset of each of the data frames; the determination of the head position and the frequency offset of the data frames includes calculating a correlation sequence for each of candidate frequency offsets, the correlation sequences for the candidate frequency offsets being a sequence of cross-correlations between the pilot signal and a sub-block of the digital received signal under a frequency shift represented by the candidate frequency offset, the head position of the sub-block being selected from a plurality of candidate head positions; determine two or more peaks for each of the correlation sequences; and determine the head position and the frequency offset of the data frames based on the determined peaks of the correlation sequences.

[0011] The present disclosure further provides an optical communication system comprising a transmitting device and a receiving device. The transmitting device is configured to obtain a source signal, divide the source signal into two or more payloads, generate a data frame for each of the payloads to generate a sequence of the data frames, the data frame including a pilot signal and a payload, the pilot signal being composed of two or more constant amplitude zero autocorrelation waveform (CAZAC) sequences, and transmit an optical signal obtained by converting the sequence of the data frames over an optical communication channel. The receiving device is configured to receive the optical signal through the optical communication channel, convert the received optical signal into a digital received signal, and determine a head position and a frequency offset of each of the data frames included in the digital received signal. The determining of the head position and the frequency offset of the data frame includes calculating a correlation sequence for each of candidate frequency offsets, where the correlation sequences for the candidate frequency offsets are sequences of cross-correlations that are each a cross-correlation between the pilot signal and a sub-block of the digital received signal under a frequency shift represented by the candidate frequency offset, and the head position of the sub-block is selected from a plurality of candidate head positions; determining two or more peaks for each of the correlation sequences; and determining the head position and the frequency offset of the data frame based on the determined correlation sequence peaks. [Effects of the Invention]

[0012] According to the present disclosure, a novel technique is provided for detecting both the head position and frequency offset of a data frame transferred over an optical communication channel. [Brief explanation of the drawings]

[0013] [Figure 1] 1 is a diagram illustrating an optical communication system according to a first embodiment. [Figure 2] FIG. 2 illustrates an exemplary structure of a transmitting device. [Figure 3] FIG. 2 illustrates an exemplary structure of a receiving device. [Figure 4A] FIG. 1 illustrates a peak of a correlation sequence. [Figure 4B] FIG. 1 illustrates a peak of a correlation sequence. [Figure 5] 2 is a block diagram showing an exemplary hardware configuration of a transmitting device and an exemplary hardware configuration of a receiving device. FIG. [Figure 6]4 is a flowchart illustrating an exemplary flow of a process performed by a transmitting device. [Figure 7] 4 is a flowchart illustrating an exemplary flow of a process performed by a receiving device. [Figure 8] 10 is a flowchart illustrating an exemplary flow for simultaneous determination of head position and frequency offset of a data frame. [Figure 9] FIG. 2 illustrates an example of the functional configuration of a determination unit 122. DETAILED DESCRIPTION OF THE INVENTION

[0014]

[0023] The embodiments according to the present disclosure will be described below with reference to the drawings. The same elements are assigned the same reference numerals throughout the drawings, and redundant descriptions will be omitted as necessary. Furthermore, unless otherwise specified, predetermined information (e.g., predetermined values ​​or predetermined threshold values) is pre-stored in a storage device accessible by a computer that uses the information.

[0015] First embodiment <Summary> 1 shows an optical communication system 100 according to a first embodiment. The optical communication system 100 includes a transmitting device 110 and a receiving device 120, which are connected to each other via a communication channel 130. Note that the communication channel 130 is not necessarily included in the optical communication system 100.

[0016] The transmitting device 110 transmits an optical signal to the receiving device 120 through a communication channel 130. The communication channel 130 includes an optical fiber through which the optical signal is transmitted from the transmitting device 110 to the receiving device 120. Hereinafter, the optical signals transmitted from the transmitting device 110 and received by the receiving device 120 are referred to as the "optical transmitted signal" and the "optical received signal," respectively.

[0017] 2 shows an exemplary structure of the transmitting device 110. The transmitting device 110 includes a frame generator 111 and an optical transmitter 112. The frame generator 111 receives a source signal 10 that may represent an encoded message to be conveyed from the transmitting device 110 to the receiving device 120, and generates a sequence of data frames 20 from the source signal 10. Specifically, the frame generator 111 divides the source signal 10 into multiple payloads 30 and generates a data frame 20 for each payload 30, thereby converting the source signal 10 into a frame sequence 50.

[0018] The data frame 20 includes a pilot signal 40 and a payload 30, and the pilot signal 40 precedes the payload 30. The pilot signal 40 serves to indicate the position of the head of the corresponding data frame 20.

[0019] The content of the pilot signal 40 is common to all data frames 20. Specifically, the frame generation unit 111 obtains the pilot signal 40 stored in advance in a storage unit accessible to the frame generation unit 111, and uses the obtained pilot signal 40 for all data frames 20.

[0020] In the optical communication system 100, the pilot signal 40 is constructed using two or more CAZAC (Constant Amplitude Zero AutoCorrelation waveform) sequences. An exemplary type of CAZAC sequence applicable to the optical communication system 100 is a Zadoff-Chu (ZC) sequence. However, the type of CAZAC sequence applicable to the optical communication system 100 is not limited to a ZC sequence. In the following, unless otherwise specified, a ZC sequence will be used as an example of a CAZAC sequence in the optical communication system 100.

[0021] In some embodiments, the pilot signal 40 can be expressed as:

number

[0022] The optical transmitter 112 converts the frame sequence 50 into an optical transmit signal 60 and transmits the optical transmit signal 60 over the communication channel 130. Note that there are various well-known techniques for converting a digital signal representing a sequence of data frames into an optical signal and outputting the optical signal, any of which may be applied to the optical communication system 100.

[0023] 3 shows an exemplary structure of the receiving device 120. The receiving device 120 includes an optical receiving unit 121 and a decision unit 122. The optical receiving unit 121 receives an optical receiving signal 70 from a communication channel 130 and converts the optical receiving signal 70 into a digital signal called a "digital receiving signal 80." It should be noted that there are various well-known techniques for converting an optical signal received from an optical communication channel into a digital signal, and any of these techniques can be applied to the optical communication system 100.

[0024] The decision unit 122 takes the digital received signal 80 and generates a frame sequence 90, which is a reproduction of the frame sequence 50, by detecting the pilot signal 40 for each data frame 20 using a coherent detection device. Note that before the digital received signal 80 is input to the decision unit 122, one or more types of compensation other than frequency shift compensation may be performed on the digital received signal 80, such as chromatic dispersion (CD) compensation.

[0025] Some frequency shift may be induced in the digital received signal 80 due to differences in the carrier frequencies of the local oscillators used in the transmitter 110 and receiver 120. Therefore, to correctly acquire each data frame 20, it is also necessary to determine the amount of frequency shift (i.e., frequency offset) induced in the data frame 20. The optical signal also experiences delay due to signal propagation in the channel.

[0026] For this purpose, the determiner 122 simultaneously determines the head position of the pilot signal 40 and the frequency offset of the data frame 20. Specifically, for each candidate head position k and each candidate frequency offset w, the determiner 122 calculates the cross-correlation f(k,w) of the sub-blocks of the pilot signal 40 and the digital received signal 80 with the head position k, assuming a frequency offset w. This can be formulated as follows:

number

[0027] In equation (2), exp^-j*w*n is applied to compensate for the frequency shift. Note that the frequency shift compensation may be performed on the pilot signal 40 or on the digital received signal 80. In the former case, for each w in the set of candidate frequency offsets, the pilot signal 40 (i.e., p[n]*exp^-j*w*n) that has been frequency shift compensated by the frequency offset w can be input to the calculation block that calculates the cross-correlation. In the latter case, for each w in the set of candidate frequency offsets, the digital received signal 80 (i.e., x[n]*exp^-j*w*n) that has been frequency shift compensated by the frequency offset w can be input to the calculation block that calculates the cross-correlation.

[0028] For each data frame 20, the determiner 122 determines the most suitable head position ko and the most suitable frequency offset wo for the data frame 20 from among the candidate head positions and candidate frequency offsets, and treats ko and wo as the head position and frequency offset of the data frame 20, respectively. Specifically, for each candidate frequency offset w in a predetermined set W of candidate frequency offsets, the determiner 122 calculates f(k,w) with possible head positions {k1,K2,...,kM}, thereby obtaining a correlation sequence g(w), which is a sequence of cross-correlations with frequency offset w: g(w)={f(k1,w), f(k2,w),..., f(kM,w)}.

[0029] As will be described in detail later, the pilot signal 40 is composed of two or more CAZAC sequences, and therefore the correlation sequence g(w) has two or more peaks. Therefore, the determiner 122 determines two or more peaks of the correlation sequence g(w) for each candidate frequency w, and determines the head position ko of the pilot signal 40 and the frequency offset wo of the data frame 20 based on the determined peaks.

[0030] Figure 4 shows the peaks of the correlation sequence. Figure 4A shows the correlation sequence when the pilot signal does not consist of two or more CAZAC sequences. In this case, the correlation sequence has only a single peak. Therefore, the head position and frequency offset of the data frame can be determined by detecting this single peak for each possible frequency offset.

[0031] 4B shows a correlation sequence when the pilot signal is composed of two CAZAC sequences. In this case, the correlation sequence has two peaks. As described above, the determination unit 122 determines the head position ko and frequency offset wo of the data frame 20 by detecting the two peaks of the correlation sequence for each frequency offset candidate.

[0032] <Examples of beneficial effects> The optical communication system 100 uses a pilot signal 40 that is composed of multiple CAZAC sequences, which results in a cross-correlation sequence between the pilot signal 40 and the digital received signal 80 having two or more peaks. Thus, the receiver 120 performs simultaneous determination of the head position and frequency offset of a data frame 20, which, unlike that performed by [1], involves determining two or more peaks of the correlation sequence. This means that the present disclosure introduces a novel technique for simultaneous determination of the head position and frequency offset of a data frame transmitted over an optical communication channel.

[0033] This simultaneous determination of the head position and frequency offset of the data frame 20 is particularly useful when the communication channel 130 is comprised of bonded multi-core fiber (MCF), where detection of a pilot signal from the digital received signal is important to enable accurate data-aided equalization.

[0034] In systems where the pilot signal does not consist of two or more CAZAC sequences, the correlation sequence peak appears or is inaccurate only when the expected frequency offset is within a very limited synchronization range, e.g., within ±10 MHz of the frequency offset induced in the received signal. Therefore, it is necessary to simultaneously determine the data frame head position and frequency offset using a large number of candidate frequency offsets. For example, an optical communication system with a carrier frequency offset of up to 150 MHz, i.e., [-150 MHz, 150 MHz], may require at least 30 (150 / 5) candidate frequency offsets. The greater the number of candidate frequency offsets, the greater the number of correlation calculations between the pilot signal and subblocks of the digital received signal. This increases implementation complexity and processing time.

[0035] In this regard, pilot signals constructed using CAZAC sequences result in the appearance of two main peaks in correlation plots under all frequency offset conditions. This is due to the CAZAC sequence's characteristic of allowing the correlation peak to shift under the influence of frequency offset. Information about the shifted peaks allows for the calculation of frequency offset and head position within a large, uncompensated frequency offset range, greater than the limited synchronization range of other pilot signals (e.g., ±10 MHz).

[0036] The optical communication system 100 will now be described in more detail.

[0037] <Example of hardware configuration of transmitting device and receiving device> The transmitting device 110 may be implemented by one or more computers, each of which may be a special-purpose computer manufactured for implementing the transmitting device 110, or may be a general-purpose computer. The same is true for the receiving device 120.

[0038] 5 is a block diagram showing an exemplary hardware configuration of the transmitting device 110 and an exemplary hardware configuration of the receiving device 120. The upper part of FIG. 5 shows the transmitting device 110. In FIG. 5, the transmitting device 110 includes a computer 200 and an optical front end 300. The computer 200 is used to implement the frame generating unit 111. The computer 200 may be a microprocessor chip such as a digital signal processor (DSP).

[0039] The computer 200 includes a bus 210, a processor 220, a memory 230, and an input / output (I / O) interface 240. The bus 210 is a data transmission channel through which the processor 220, the memory 230, and the I / O interface 240 send and receive data to and from each other. The processor 220 is any type of processing device that executes programs (i.e., instructions) stored in the memory 230.

[0040] Memory 230 is any type of memory component that stores programs executed by processor 220. In addition, memory 230 also stores data referenced by processor 220 (e.g., pilot signal 40) and data generated by processor 220.

[0041] I / O interface 240 includes any type of interface used to receive source signal 10 and output frame sequence 50 .

[0042] The frame generating unit 111 may be realized by installing an application on the computer 200. The application is implemented by a program that causes the computer 200 to function as the frame generating unit 111.

[0043] The optical front end 300 is used to implement the optical transmitting unit 112. The optical front end 300 may include a digital-to-analog (D / A) converter that converts the frame sequence 50 into an analog electronic signal, a light source (e.g., a laser diode) that outputs an optical carrier wave, and an optical modulator that generates the optical transmit signal 60 by modulating the optical carrier wave based on the analog electronic signal output from the D / A converter.

[0044] The hardware configuration of the transmission device 110 is not limited to that shown in Fig. 5. For example, the computer 200 may be realized by a plurality of computers.

[0045] The lower part of Fig. 5 shows the receiving device 120. In Fig. 5, the receiving device 120 includes a computer 400 and an optical front end 500. The computer 400 is used to implement the decision unit 122. Like the computer 200, the computer 400 may be a microprocessor chip such as a DSP.

[0046] 5, the computer 400 includes a bus 410, a processor 420, a memory 430, and an I / O interface 440. The bus 410 is a data transmission channel through which the processor 420, the memory 430, and the I / O interface 440 transmit and receive data to and from each other. The processor 420 is any type of processing device that executes programs (in other words, instructions) stored in the memory 430.

[0047] Memory 430 is any type of memory component that stores programs executed by processor 420. Memory 430 also stores data referenced by processor 420 (e.g., lookup tables, described in detail below, and pilot signals 40) and data generated by processor 420.

[0048] I / O interface 440 includes any type of interface that can be used to receive digital receive signal 80 and output frame sequence 90 .

[0049] The decision unit 122 may be realized by installing an application on the computer 400. The application is implemented by a program that causes the computer 400 to function as the decision unit 122.

[0050] The optical front end 500 is used to realize the optical receiving unit 121. The optical front end 500 may include a light source (e.g., a laser diode) that outputs local light, an optical demodulator that generates an analog electronic signal by demodulating the optical received signal 70 using the local light, and an analog-to-digital converter that converts the analog electronic signal output from the optical demodulator into a digital received signal 80.

[0051] The hardware configuration of the receiving device 120 is not limited to that shown in Fig. 5. For example, the computer 400 may be realized by a plurality of computers.

[0052] <Process flow> 6 is a flowchart showing an exemplary flow of a process performed by the transmitting device 110. The frame generating unit 111 acquires the source signal 10 (S102). The frame generating unit 111 converts the source signal 10 into a frame sequence 50 (S104). The optical transmitting unit 112 converts the frame sequence 50 into an optical transmission signal 60 (S106). The optical transmitting unit 112 transmits the optical transmission signal 60 through the communication channel 130 (S108).

[0053] 7 is a flowchart showing an exemplary flow of a process performed by the receiving device 120. The optical receiving unit 121 receives an optical receiving signal 70 from the communication channel 130 (S202). The optical receiving unit 121 converts the optical receiving signal 70 into a digital receiving signal 80 (S204). The determining unit 122 performs simultaneous determination of the head position and frequency offset for each data frame 20 (S206).

[0054] Simultaneous Determination of Head Position and Frequency Offset of Data Frame 20 The determination unit 122 simultaneously determines the head position and frequency offset of the pilot signal 40 of each data frame 20 in the digital received signal 80 (S204). Fig. 8 is a flowchart showing an exemplary flow of simultaneously determining the head position and frequency offset of the data frame 20. The series of processes shown in Fig. 8 is performed for each data frame 20.

[0055] The determiner 122 performs a loop process L1 consisting of steps S302 to S306 for each candidate frequency offset w in the predefined set W. In the loop process L1, the determiner 122 generates a correlation sequence g(w) for the candidate frequency offset w of the current iteration by calculating the cross-correlation with the frequency offset f(k,w) induced for each candidate head position k.

[0056] After generating the correlation sequence g(w) for each candidate frequency offset in the set W, the determiner 122 determines the head position ko and the frequency offset wo based on the set of correlation sequences (S308).

[0057] 9 shows an example of the functional configuration of the decision unit 122. The decision unit 122 may include a frequency offset subunit 122a, a correlation subunit 122b, and a decision subunit 122c. The frequency offset subunit 122a and the correlation subunit 122b may cooperate to implement the loop process L1 shown in FIG.

[0058] Specifically, the frequency offset subunit 122a applies the frequency offset w of the current iteration to the pilot signal 40 at each iteration of the loop process L1, thereby outputting the pilot signal 40 induced by the frequency offset w. The correlation subunit 122b obtains the digital received signal 80 and the pilot signal 40 induced by the frequency offset w, and calculates the cross-correlation f(k,w) for each head position k, thereby generating a correlation sequence g(w).

[0059] The determination subunit 122c obtains the set of correlation sequences, ie, {g(w); w in W}, from the correlation subunit 122b, and determines the head position ko and frequency offset wo based on the set of correlation sequences.

[0060] Note that the configuration of the determination unit 122 is not limited to the configuration shown in Fig. 9. For example, the frequency offset subunit 122a may apply a frequency offset w to the digital received signal 80 instead of the pilot signal 40. In this case, the correlation subunit 122b calculates the correlation sequence g(w) using the pilot signal 40 and the digital received signal 80 induced by the frequency offset w.

[0061] A specific method for determining the head position ko and frequency offset wo based on a set of correlation sequences will now be described in detail.

[0062] In the following description, unless otherwise specified, it is assumed that the pilot signal 40 is composed of two CAZAC sequences. The case where the pilot signal 40 is composed of three or more CAZAC sequences will be described later.

[0063] In the presence of a substantial frequency shift, the number of peaks in the correlation sequence g(w) is the same as the number of CAZAC sequences from which the pilot signal 40 is constructed after taking into account any multipath interference. Thus, if the pilot signal 40 is composed of two CAZAC sequences, the determiner 122 determines the two highest maxima f(K1(w),w) and f(K2(w),w) of the sequence g(w) as the peaks of the sequence g(w), where K1(w) and K2(w) are separated by at least α, and f(K1(w),w)>f(K2(w),w)).

[0064] The parameter α is a predetermined threshold. When the communication channel 130 is configured with MCF, it is preferable to determine α by taking into account the modal dispersion (MD) of the MCF channel. The modal dispersion characteristics (mainly group delay characteristics) can be obtained from the fiber specifications or by observing the length of the optimal tap setting of the adaptive equalization block in the receiver 120.

[0065] As a result of the above calculations, the determiner 122 obtains (w,K1(w),K2(w),f(K1(w),w),f(K2(w),w)) for each w in the set W. Using the obtained data, the determiner 122 determines the head position ko and the frequency offset wo of the data frame 20. The specific method of this determination may depend on the structure of the pilot signal 40. Below, exemplary methods for determining the head position ko and the frequency offset wo are described for some example pilot signals.

[0066] <<Example 1>> In this embodiment, the pilot signal 40 is expressed by equation (1): In this case, the head position ko can be calculated as follows:

number

[0067] If the condition "f(K1(w),w) / f(K2(w),w)<β" is not satisfied, the frequency compensation exp^(-j*w*n) with the assumed frequency offset w will nearly or completely compensate for the frequency shift. In the absence of a substantial frequency shift, the correlation sequence g(w) will have only a single peak in the absence of multipath interference, and therefore f(K1(w),w) will be substantially higher than f(K2(w),w)). In this case, the position K1(w) corresponding to this single peak f(K1(w),w) is estimated as the most suitable head position with frequency offset w.

[0068] The selection of the parameter β may depend on the expected magnitude of the cross-correlation. The magnitude of the cross-correlation calculated by the determiner 122 may depend on the signal transmission power, the received signal-to-noise ratio at the receiver 120, and the mode dependent loss (MDL) characteristics exhibited by the fiber. In a communication system, it is preferable to determine β taking into account the above factors.

[0069] It should be noted that ko may be calculated using other statistical functions other than the mode based on the set S. For example, ko may be calculated as the statistical mean or median of the set S. In another example, the determiner 122 may generate a histogram from the set S, select the most frequently occurring frequency bin (or range) in the histogram, and use this as ko.

[0070] After determining the head position ko, the determination unit 122 determines the frequency offset wo, which can be calculated as follows:

number

[0071] The set Ŵs represents the set of frequency offsets w for which the estimated head position is substantially close to ko and the correlation sequence g(w) has two peaks of substantial magnitude. The set T represents the set of frequency offsets extracted from the lookup table for each w in the set Ŵs.

[0072] A lookup table is created in advance for each pair of R and N, and the lookup table for R=R1, N=N1 associates a candidate frequency offset with a value of (K1-K2) / 2 when the pilot signal 40 is composed of a CAZAC sequence of order R1 and length N1. Therefore, LookUp(a,R1,N1) represents the process of extracting a candidate frequency offset corresponding to (K1-K2) / 2=a from the lookup table for the pair (R=R1,N=N1).

[0073] As represented by equation (4), the determiner 122 obtains candidate frequency offsets for each w in Ŵs and puts the obtained candidate frequency offsets into a set T. Then, the determiner 122 calculates the mode of the values ​​in the set T as wo.

[0074] Note that, similar to the head position ko, the frequency offset wo may be calculated in different ways based on the set T. For example, wo may be calculated as the statistical mean or median of the set T. In another example, the decision unit 122 may generate a probability distribution given by a histogram generated from the set T and select the discrete value corresponding to a high probability.

[0075] Most errors in identifying the head position ko arise due to the magnitude of the side lobes associated with the CAZAC pattern forming the pilot signal exceeding the magnitude of the two expected main correlation peaks. However, in such cases, the value K1-K2 may correspond to the distance between the main peak and the side lobes. The distance between the peak and the side lobe in the correlation plot is a fixed value that depends only on the characteristics of the pilot signal (i.e., the order R and length N). This distance is independent of the frequency offset applied in the optical communication system 100. The mode or statistical operation of equations (3) or (4) may be performed after discarding T or S values ​​where this distance between the identified peaks (|K1-K2|) is equal to the expected distance between the main peak and the side lobes or a multiple thereof. In such cases, considering an even number of correlation peaks greater than two (as in equation (9) described below) can also result in accurate synchronization.

[0076] <<Example 2>> In this example, the pilot signal 40 is represented as follows:

number

[0077] In this case, the method of calculating the synchronization point sync(w) differs from the method in embodiment 1. Specifically, the synchronization point sync(w) can be calculated as follows.

number

[0078] The parameters r1 and r2 are predefined scalar values ​​which imply r1+r2=1. They can be determined by test operation of the designed pilot signal under induced frequency offset.

[0079] After calculating the synchronization point sync(w) for each w in the set W using equation (6), the determiner 122 determines ko in the same way as in Example 1, eg, ko=Mode(S).

[0080] Based on the determined head position ko, the determiner 122 determines the frequency offset wo. In this example, the frequency offset wo can be calculated as follows:

number

[0081] Equation (7) differs from equation (4) in the parameters used for extraction from the lookup table. Because the pilot signal 40 is composed of two CAZAC sequences of different orders, a lookup table is created for each possible combination of the order R1 of the first CAZAC sequence, the order R2 of the second CAZAC sequence, and the length N of both CAZAC sequences, i.e., for each (R1, R2, N). Therefore, the determination unit 122 extracts a frequency offset estimate from the lookup table corresponding to (R1, R2, N) of a particular pilot signal 40.

[0082] <<Example 3>> In this example, the pilot signal 40 is represented as follows:

number

[0083] In this case, since the pilot signal 40 is composed of four CAZAC sequences, the determiner 122 detects four peaks of the correlation sequence g(w) for each candidate frequency offset w in the set W. Specifically, the determiner 122 determines the top four maximum values ​​f(K1(w),w), f(K2(w),w), f(K3(w),w), and f(K4(w),w), where |K1(w)-K2(w)|>α, |K3(w)-K4(w)|>α, f(K1(w))>=f(K2(w)), and f(K3(w))>=f(K4(w)).

[0084] Next, similar to the first and second embodiments, the determination unit calculates a synchronization point sync(w) for each candidate frequency offset w and determines ko based on the set of synchronization points S, e.g., ko=Mode(S). In this embodiment, the synchronization point sync(w) is calculated as follows:

number

[0085] After determining the head position ko, the determination unit 122 determines the frequency offset wo, which can be calculated as follows:

number

[0086] As in Example 2, a lookup table is created for each possible combination (R1, R2, N). Additionally, since in this example four peaks in the correlation sequence g(w) are considered, the lookup table associates the combinations (K1(w), K2(w), K3(w), K4(w)) with frequency offset estimates.

[0087] <<Other examples of pilot signals>> Other examples of pilot signals 40 are shown below.

number

[0088] <Using the results of simultaneous decisions> The result of the simultaneous determination of the head position ko and frequency offset wo of the data frame 20 is used to divide the digital received signal 80 into data frames 20 and perform frequency shift compensation for each data frame 20, thereby generating a frame sequence 90 (a reproduction of the frame sequence 50). Further processes such as equalization and decoding can be performed on the frame sequence 90 to obtain the message conveyed from the transmitting device 110.

[0089] The program can be stored and provided to a computer using any type of non-transitory computer-readable medium. Non-transitory computer-readable media include any type of tangible storage medium. Examples of non-transitory computer-readable media include magnetic storage media (e.g., floppy disks, magnetic tapes, hard disk drives, etc.), magneto-optical storage media (e.g., magneto-optical disks), compact disc read-only memory (CD-ROM), compact disc recordable (CD-R), compact disc rewritable (CD-R / W), and semiconductor memory (e.g., mask ROM, programmable ROM (PROM), erasable PROM (EPROM), flash ROM, random access memory (RAM)), etc.). The program can be provided to a computer using any type of temporary computer-readable medium. Examples of temporary computer-readable media include electrical signals, optical signals, and electromagnetic waves. The temporary computer-readable medium can provide the program to a computer via wired communication lines (e.g., electrical wires and optical fibers) or wireless communication lines.

[0090] Although the present disclosure has been described above with reference to the embodiments, the present disclosure is not limited to the above-described embodiments. Various changes that can be understood by those skilled in the art can be made to the arrangements and details of the present disclosure within the scope of the present invention.

[0091] A part or all of the above-described embodiments can be described as, but not limited to, the following supplementary notes. <Additional Notes> (Appendix 1) A receiving device, at least one memory configured to store instructions; At least one processor and wherein the processor: instructions for acquiring a digital received signal obtained by converting an optical received signal into a digital signal, the digital received signal including a plurality of data frames each including a pilot signal and a payload, the pilot signal being composed of two or more constant amplitude zero autocorrelation waveform (CAZAC) sequences; instructions for determining a head position and a frequency offset for each of said data frames; The determination of the head position and the frequency offset of the data frame comprises: calculating a correlation sequence for each of the candidate frequency offsets, the correlation sequences for the candidate frequency offsets being a sequence of cross-correlations each being a cross-correlation between the pilot signal and a sub-block of the digital received signal under a frequency shift represented by the candidate frequency offset, the head position of the sub-block being selected from a plurality of candidate head positions; determining two or more peaks for each of the correlation sequences; determining the head position and the frequency offset of the data frame based on the determined peak of the correlation sequence. (Appendix 2) The determination of the head position of the data frame comprises: calculating a synchronization point for each candidate frequency offset based on the peaks of the correlation sequence for the candidate frequency offset, wherein the synchronization point for the candidate frequency offset is a simple average or a weighted average of the head positions corresponding to the peaks of the correlation sequence for the candidate frequency offset; and determining the head position of the data frame based on the calculated synchronization point. (Appendix 3) The determination of the head position of the data frame comprises: calculating a statistic of the calculated synchronization point as the head position of the data frame; or 3. The receiving device of claim 2, further comprising: estimating the head position of the data frame by calculating the frequency of occurrence of the calculated synchronization points. (Appendix 4) The determining of the frequency offset of the data frame comprises: determining one or more candidate frequency offsets having the synchronization point whose absolute difference from the determined head position of the data frame is less than a predefined threshold; obtaining, for each of the determined candidate frequency offsets, an estimate of a frequency offset associated with the pair of peaks of the correlation sequence of the candidate frequency offset according to predefined information; and determining the frequency offset of the data frame based on the obtained frequency offset estimate. (Appendix 5) The determining of the frequency offset of the data frame comprises: calculating a statistic of the frequency offset estimates obtained as the frequency offset of the data frame; or 5. The receiving apparatus of claim 4, further comprising sampling the frequency offset of the data frame as a value from a probability distribution given by a histogram of the obtained frequency offset estimates. (Appendix 6) the predefined information is predefined for each pair of the order of the CAZAC sequence and the length of the CAZAC sequence; 6. The receiving apparatus of claim 5, wherein the estimate of the frequency offset is obtained from the predefined information corresponding to a pair of the order and the length of the CAZAC sequence from which the pilot signal is constructed. (Appendix 7) 4. The receiving device according to any one of Supplementary Notes 1 to 3, wherein the pilot signal is composed of a sum of a CAZAC sequence and a conjugate of the CAZAC sequence or an upsampled version thereof. (Appendix 8) 1. A computer-implemented receiving method, comprising: obtaining a digital received signal obtained by converting an optical received signal into a digital signal, the digital received signal including a plurality of data frames each including a pilot signal and a payload, the pilot signal being composed of two or more constant amplitude zero autocorrelation waveform (CAZAC) sequences; determining a head position and a frequency offset for each of said data frames; The determination of the head position and the frequency offset of the data frame comprises: calculating a correlation sequence for each of the candidate frequency offsets, the correlation sequences for the candidate frequency offsets being a sequence of cross-correlations that are each a cross-correlation between the pilot signal and a sub-block of the digital received signal under a frequency shift represented by the candidate frequency offset, the head position of the sub-block being selected from a plurality of candidate head positions; determining two or more peaks for each of the correlation sequences; determining the head position and the frequency offset of the data frame based on the determined correlation sequence peak. (Appendix 9) The determination of the head position of the data frame comprises: calculating a synchronization point for each candidate frequency offset based on the peaks of the correlation sequence for the candidate frequency offset, wherein the synchronization point for the candidate frequency offset is a simple average or a weighted average of the head positions corresponding to the peaks of the correlation sequence for the candidate frequency offset; and determining the head position of the data frame based on the calculated synchronization point. (Appendix 10) The determination of the head position of the data frame comprises: calculating a statistic of the calculated synchronization point as the head position of the data frame; or 10. The receiving method of claim 9, comprising estimating the head position of the data frame by calculating the frequency of occurrence of the calculated synchronization points. (Appendix 11) The determining of the frequency offset of the data frame comprises: determining one or more candidate frequency offsets having the synchronization point whose absolute difference from the determined head position of the data frame is less than a predefined threshold; obtaining, for each of the determined candidate frequency offsets, an estimate of a frequency offset associated with the pair of peaks of the correlation sequence of the candidate frequency offset according to predefined information; and determining the frequency offset of the data frame based on the obtained frequency offset estimate. (Appendix 12) The determining of the frequency offset of the data frame comprises: calculating statistics of the obtained frequency offset estimates as the frequency offset of the data frame; or 12. The receiving method of claim 11, comprising sampling the frequency offset of the data frame as a value from a probability distribution given by a histogram of the obtained frequency offset estimates. (Appendix 13) the predefined information is predefined for each pair of the order of the CAZAC sequence and the length of the CAZAC sequence; 13. The receiving method of claim 12, wherein the estimate of the frequency offset is obtained from the predefined information corresponding to the pair of the order and the length of the CAZAC sequence from which the pilot signal is constructed. (Appendix 14) 11. The receiving method according to any one of Supplementary Notes 8 to 10, wherein the pilot signal is composed of a sum of a CAZAC sequence and a conjugate of the CAZAC sequence or an upsampled version thereof. (Appendix 15) A non-transitory computer-readable storage medium storing a program, the program being configured to cause a computer to: obtaining a digital received signal obtained by converting an optical received signal into a digital signal, the digital received signal including a plurality of data frames each including a pilot signal and a payload, the pilot signal being composed of two or more constant amplitude zero autocorrelation waveform (CAZAC) sequences; determining a head position and a frequency offset for each of said data frames; The determination of the head position and the frequency offset of the data frame comprises: calculating a correlation sequence for each of the candidate frequency offsets, the correlation sequences for the candidate frequency offsets being a sequence of cross-correlations each being a cross-correlation between the pilot signal and a sub-block of the digital received signal under a frequency shift represented by the candidate frequency offset, the head position of the sub-block being selected from a plurality of candidate head positions; determining two or more peaks for each of the correlation sequences; determining the head position and the frequency offset of the data frame based on the determined correlation sequence peak. (Appendix 16) The determination of the head position of the data frame comprises: calculating a synchronization point for each candidate frequency offset based on the peaks of the correlation sequence for the candidate frequency offset, wherein the synchronization point for the candidate frequency offset is a simple average or a weighted average of the head positions corresponding to the peaks of the correlation sequence for the candidate frequency offset; and determining the head position of the data frame based on the calculated synchronization point. (Appendix 17) The determination of the head position of the data frame comprises: calculating a statistic of the calculated synchronization point as the head position of the data frame; or 17. The storage medium of claim 16, further comprising: estimating the head position of the data frame by calculating a frequency of occurrence of the calculated synchronization points. (Appendix 18) The determining of the frequency offset of the data frame comprises: determining one or more candidate frequency offsets having the synchronization point whose absolute difference from the determined head position of the data frame is less than a predefined threshold; obtaining, for each of the determined candidate frequency offsets, an estimate of a frequency offset associated with the pair of peaks of the correlation sequence of the candidate frequency offset according to predefined information; and determining the frequency offset of the data frame based on the obtained frequency offset estimate. (Appendix 19) The determining of the frequency offset of the data frame comprises: calculating a statistic of the frequency offset estimates obtained as the frequency offset of the data frame; or 19. The storage medium of claim 18, further comprising sampling the frequency offset of the data frame as a value from a probability distribution given by a histogram of the obtained frequency offset estimates. (Appendix 20) the predefined information is predefined for each pair of the order of the CAZAC sequence and the length of the CAZAC sequence; 20. The storage medium of claim 19, wherein the estimate of the frequency offset is obtained from the predefined information corresponding to the pair of the order and the length of the CAZAC sequence from which the pilot signal is constructed. (Appendix 21) 18. The storage medium of any one of appendices 15 to 17, wherein the pilot signal is composed of a sum of a CAZAC sequence and a conjugate of the CAZAC sequence or an upsampled version thereof. (Appendix 22) 1. An optical communication system, comprising: a transmitting device; a receiving device, The transmitting device acquiring a source signal; Splitting the source signal into two or more payloads; generating a data frame for each of the payloads to generate a sequence of the data frames, the data frame including a pilot signal and a payload, the pilot signal being comprised of two or more constant amplitude zero autocorrelation waveform (CAZAC) sequences; transmitting an optical signal obtained by converting the sequence of data frames over an optical communication channel; The receiving device receiving the optical signal over the optical communication channel; converting the received optical signal into a digital received signal; determining a head position and a frequency offset of each of the data frames included in the digital received signal; The determination of the head position and the frequency offset of the data frame comprises: calculating a correlation sequence for each of the candidate frequency offsets, the correlation sequences for the candidate frequency offsets being a sequence of cross-correlations each being a cross-correlation between the pilot signal and a sub-block of the digital received signal under a frequency shift represented by the candidate frequency offset, the head position of the sub-block being selected from a plurality of candidate head positions; determining two or more peaks for each of the correlation sequences; determining the head position and the frequency offset of the data frame based on the determined correlation sequence peak. (Appendix 23) The determination of the head position of the data frame comprises: calculating a synchronization point for each candidate frequency offset based on the peaks of the correlation sequence for the candidate frequency offset, wherein the synchronization point for the candidate frequency offset is a simple average or a weighted average of the head positions corresponding to the peaks of the correlation sequence for the candidate frequency offset; and determining the head position of the data frame based on the calculated synchronization point. (Appendix 24) The determination of the head position of the data frame comprises: calculating a statistic of the calculated synchronization point as the head position of the data frame; or 24. The optical communication system of claim 23, further comprising: estimating the head position of the data frame by calculating a frequency of occurrence of the calculated synchronization points. (Appendix 25) The determining of the frequency offset of the data frame comprises: determining one or more candidate frequency offsets having the synchronization point whose absolute difference from the determined head position of the data frame is less than a predefined threshold; obtaining, for each of the determined candidate frequency offsets, an estimate of a frequency offset associated with the pair of peaks of the correlation sequence of the candidate frequency offset according to predefined information; and determining the frequency offset of the data frame based on the obtained frequency offset estimate. (Appendix 26) The determining of the frequency offset of the data frame comprises: calculating a statistic of the frequency offset estimates obtained as the frequency offset of the data frame; or 26. The optical communication system of claim 25, further comprising sampling the frequency offset of the data frame as a value from a probability distribution given by a histogram of the obtained frequency offset estimates. (Appendix 27) the predefined information is predefined for each pair of the order of the CAZAC sequence and the length of the CAZAC sequence; 27. The optical communication system of claim 26, wherein the estimate of the frequency offset is obtained from the predefined information corresponding to the pair of the order and the length of the CAZAC sequence from which the pilot signal is constructed. (Appendix 28) 25. The optical communication system according to any one of appendixes 22 to 24, wherein the pilot signal is composed of a sum of a CAZAC sequence and a conjugate of the CAZAC sequence or an upsampled version thereof. [Explanation of symbols]

[0092] 10 Source Signals 20 Data Frames 30 Payload 40 Pilot Signal 50 frame sequence 60 Optical transmission signal 70 Optical receiving signal 80 digital received signals 90 frame sequence 100 Optical Communication System 110 Transmitting device 111 Frame Generation Unit 112 Optical transmitter 120 receiving device 121 Optical receiver 122 Decision Section 122a Frequency Offset Sub-part 122b Correlation subsection 122c Decision Subdivision 130 communication channels 200 computers 210 Bus 220 processors 230 memory 240 Input / Output Interface 300 Optical Front End 400 computers 410 Bus 420 processor 430 memory 440 Input / Output Interface 500 Optical Front End 1000 computers 1020 Bus 1040 processor 1060 memory 1080 storage device 1100 Input / Output Interface 1120 Network Interface 2000 receiving device 2020 First Training Division 2040 Second Training Division 2060 Third Training Division

Claims

1. A receiving device, at least one memory configured to store instructions; at least one processor; wherein the processor: instructions for acquiring a digital received signal obtained by converting an optical received signal into a digital signal, the digital received signal including a plurality of data frames each including a pilot signal and a payload, the pilot signal being composed of two or more constant amplitude zero autocorrelation waveform (CAZAC) sequences; instructions for determining a head position and a frequency offset for each of said data frames; The determination of the head position and the frequency offset of the data frame comprises: calculating a correlation sequence for each of the candidate frequency offsets, the correlation sequences for the candidate frequency offsets being a sequence of cross-correlations each being a cross-correlation between the pilot signal and a sub-block of the digital received signal under a frequency shift represented by the candidate frequency offset, the head position of the sub-block being selected from a plurality of candidate head positions; determining two or more peaks for each of the correlation sequences; determining the head position and the frequency offset of the data frame based on the determined peak of the correlation sequence.

2. The determination of the head position of the data frame comprises: calculating a synchronization point for each candidate frequency offset based on the peaks of the correlation sequence for the candidate frequency offset, wherein the synchronization point for the candidate frequency offset is a simple average or a weighted average of the head positions corresponding to the peaks of the correlation sequence for the candidate frequency offset; and determining the head position of the data frame based on the calculated synchronization point.

3. The determination of the head position of the data frame comprises: calculating a statistic of the calculated synchronization point as the head position of the data frame; or 3. The receiving device of claim 2, further comprising estimating the head position of the data frame by calculating a frequency of occurrence of the calculated synchronization points.

4. The determining of the frequency offset of the data frame comprises: determining one or more candidate frequency offsets having the synchronization point whose absolute difference from the determined head position of the data frame is less than a predefined threshold; obtaining, for each of the determined candidate frequency offsets, an estimate of a frequency offset associated with the pair of peaks of the correlation sequence of the candidate frequency offset according to predefined information; and determining the frequency offset of the data frame based on the obtained frequency offset estimate.

5. The determining of the frequency offset of the data frame comprises: calculating a statistic of the frequency offset estimates obtained as the frequency offset of the data frame; or 5. The receiving device of claim 4, further comprising sampling, as the frequency offset of the data frame, a value from a probability distribution given by a histogram of the obtained frequency offset estimates.

6. the predefined information is predefined for each pair of the order of the CAZAC sequence and the length of the CAZAC sequence; 6. The receiving device of claim 5, wherein the estimate of the frequency offset is obtained from the predefined information corresponding to the pair of the order and the length of the CAZAC sequence from which the pilot signal is constructed.

7. 4. The receiving device according to claim 1, wherein the pilot signal is composed of a sum of a CAZAC sequence and a conjugate of the CAZAC sequence or an upsampled version thereof.

8. 1. A computer-implemented receiving method, comprising: obtaining a digital received signal obtained by converting an optical received signal into a digital signal, the digital received signal including a plurality of data frames each including a pilot signal and a payload, the pilot signal being composed of two or more constant amplitude zero autocorrelation waveform (CAZAC) sequences; determining a head position and a frequency offset for each of said data frames; The determination of the head position and the frequency offset of the data frame comprises: calculating a correlation sequence for each of the candidate frequency offsets, the correlation sequences for the candidate frequency offsets being a sequence of cross-correlations that are each a cross-correlation between the pilot signal and a sub-block of the digital received signal under a frequency shift represented by the candidate frequency offset, the head position of the sub-block being selected from a plurality of candidate head positions; determining two or more peaks for each of the correlation sequences; determining the head position and the frequency offset of the data frame based on the determined correlation sequence peak.

9. The determination of the head position of the data frame comprises: calculating a synchronization point for each candidate frequency offset based on the peaks of the correlation sequence for the candidate frequency offset, wherein the synchronization point for the candidate frequency offset is a simple average or a weighted average of the head positions corresponding to the peaks of the correlation sequence for the candidate frequency offset; and determining the head position of the data frame based on the calculated synchronization point.

10. The determination of the head position of the data frame comprises: calculating a statistic of the calculated synchronization point as the head position of the data frame; or 10. The receiving method of claim 9, further comprising estimating the head position of the data frame by calculating a frequency of occurrence of the calculated synchronization points.

11. The determining of the frequency offset of the data frame comprises: determining one or more candidate frequency offsets having the synchronization point whose absolute difference from the determined head position of the data frame is less than a predefined threshold; obtaining, for each of the determined candidate frequency offsets, an estimate of a frequency offset associated with the pair of peaks of the correlation sequence of the candidate frequency offset according to predefined information; and determining the frequency offset of the data frame based on the obtained frequency offset estimate.

12. The determining of the frequency offset of the data frame comprises: calculating statistics of the obtained frequency offset estimates as the frequency offset of the data frame; or 12. The receiving method of claim 11, comprising sampling as the frequency offset of the data frame a value from a probability distribution given by a histogram of the obtained frequency offset estimates.

13. the predefined information is predefined for each pair of the order of the CAZAC sequence and the length of the CAZAC sequence; 13. The receiving method of claim 12, wherein the estimate of the frequency offset is obtained from the predefined information corresponding to the pair of the order and the length of the CAZAC sequence from which the pilot signal is constructed.

14. Receiving method according to any one of claims 8 to 10, wherein the pilot signal consists of a sum of a CAZAC sequence and a conjugate of the CAZAC sequence or an upsampled version thereof.

15. A non-transitory computer-readable storage medium storing a program, the program being configured to cause a computer to: obtaining a digital received signal obtained by converting an optical received signal into a digital signal, the digital received signal including a plurality of data frames each including a pilot signal and a payload, the pilot signal being composed of two or more constant amplitude zero autocorrelation waveform (CAZAC) sequences; determining a head position and a frequency offset for each of said data frames; The determination of the head position and the frequency offset of the data frame comprises: calculating a correlation sequence for each of the candidate frequency offsets, the correlation sequences for the candidate frequency offsets being a sequence of cross-correlations each being a cross-correlation between the pilot signal and a sub-block of the digital received signal under a frequency shift represented by the candidate frequency offset, the head position of the sub-block being selected from a plurality of candidate head positions; determining two or more peaks for each of the correlation sequences; determining the head position and the frequency offset of the data frame based on the determined correlation sequence peak.

16. The determination of the head position of the data frame comprises: calculating a synchronization point for each candidate frequency offset based on the peaks of the correlation sequence for the candidate frequency offset, wherein the synchronization point for the candidate frequency offset is a simple average or a weighted average of the head positions corresponding to the peaks of the correlation sequence for the candidate frequency offset; and determining the head position of the data frame based on the calculated synchronization point.

17. The determination of the head position of the data frame comprises: calculating a statistic of the calculated synchronization point as the head position of the data frame; or 17. The storage medium of claim 16, further comprising estimating the head position of the data frame by calculating a frequency of occurrence of the calculated synchronization points.

18. The determining of the frequency offset of the data frame comprises: determining one or more candidate frequency offsets having the synchronization point whose absolute difference from the determined head position of the data frame is less than a predefined threshold; obtaining, for each of the determined candidate frequency offsets, an estimate of a frequency offset associated with the pair of peaks of the correlation sequence of the candidate frequency offset according to predefined information; and determining the frequency offset of the data frame based on the obtained frequency offset estimate.

19. The determining of the frequency offset of the data frame comprises: calculating a statistic of the frequency offset estimates obtained as the frequency offset of the data frame; or 20. The storage medium of claim 18, further comprising sampling as the frequency offset of the data frame a value from a probability distribution given by a histogram of the obtained frequency offset estimates.

20. the predefined information is predefined for each pair of the order of the CAZAC sequence and the length of the CAZAC sequence; 20. The storage medium of claim 19, wherein the estimate of the frequency offset is obtained from the predefined information corresponding to the pair of the order and the length of the CAZAC sequence from which the pilot signal is constructed.

21. 18. The storage medium of claim 15, wherein the pilot signal consists of a sum of a CAZAC sequence and a conjugate of the CAZAC sequence or an upsampled version thereof.

22. 1. An optical communication system, comprising: a transmitting device; a receiving device, The transmitting device acquiring a source signal; Splitting the source signal into two or more payloads; generating a data frame for each of the payloads to generate a sequence of the data frames, the data frame including a pilot signal and a payload, the pilot signal being comprised of two or more constant amplitude zero autocorrelation waveform (CAZAC) sequences; transmitting an optical signal obtained by converting the sequence of data frames over an optical communication channel; The receiving device receiving the optical signal over the optical communication channel; converting the received optical signal into a digital received signal; determining a head position and a frequency offset of each of the data frames included in the digital received signal; The determination of the head position and the frequency offset of the data frame comprises: calculating a correlation sequence for each of the candidate frequency offsets, the correlation sequences for the candidate frequency offsets being a sequence of cross-correlations each being a cross-correlation between the pilot signal and a sub-block of the digital received signal under a frequency shift represented by the candidate frequency offset, the head position of the sub-block being selected from a plurality of candidate head positions; determining two or more peaks for each of the correlation sequences; determining the head position and the frequency offset of the data frame based on the determined correlation sequence peak.

23. The determination of the head position of the data frame comprises: calculating a synchronization point for each candidate frequency offset based on the peaks of the correlation sequence for the candidate frequency offset, wherein the synchronization point for the candidate frequency offset is a simple average or a weighted average of the head positions corresponding to the peaks of the correlation sequence for the candidate frequency offset; and determining the head position of the data frame based on the calculated synchronization point.

24. The determination of the head position of the data frame comprises: calculating a statistic of the calculated synchronization point as the head position of the data frame; or 24. The optical communication system of claim 23, further comprising estimating the head position of the data frame by calculating a frequency of occurrence of the calculated synchronization points.

25. The determining of the frequency offset of the data frame comprises: determining one or more candidate frequency offsets having the synchronization point whose absolute difference from the determined head position of the data frame is less than a predefined threshold; obtaining, for each of the determined candidate frequency offsets, an estimate of a frequency offset associated with the pair of peaks of the correlation sequence of the candidate frequency offset according to predefined information; and determining the frequency offset of the data frame based on the obtained frequency offset estimate.

26. The determining of the frequency offset of the data frame comprises: calculating a statistic of the frequency offset estimates obtained as the frequency offset of the data frame; or 26. The optical communication system of claim 25, comprising sampling the frequency offset of the data frame as a value from a probability distribution given by a histogram of the obtained frequency offset estimates.

27. the predefined information is predefined for each pair of the order of the CAZAC sequence and the length of the CAZAC sequence; 27. The optical communication system of claim 26, wherein the estimate of the frequency offset is obtained from the predefined information corresponding to the pair of the order and the length of the CAZAC sequence from which the pilot signal is constructed.

28. An optical communication system according to any one of claims 22 to 24, wherein the pilot signal consists of a sum of a CAZAC sequence and a conjugate of the CAZAC sequence or an upsampled version thereof.

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