OPTICAL RECEIVING APPARATUS, OPTICAL TRANSMITTING APPARATUS, AND FREQUENCY OFFSET ESTIMATION METHOD

Abstract

Upon receipt of a coherent optical signal that includes a training signal generated using a code sequence constituted by multi-value phase modulation symbols, in which a deviation angle of a vector average of a one-symbol delay differential component of a signal generated on the basis of the code sequence has a prescribed angle and a modulation phase difference between adjacent symbols has a fixed, repeated pattern, a reception training signal corresponding to a training code sequence for frequency offset estimation is detected within a reception signal acquired by converting the received coherent optical signal into an electric signal, a plurality of delay differential components are calculated on the basis of the detected reception training signal and at least two delay signals of the reception training signal, each delay signal having a different number of delay symbols, and an averaged frequency offset amount is calculated using the calculated plurality of delay differential components.

Claims

1. An optical receiving apparatus for receiving a coherent optical signal that includes a training signal, the optical receiving apparatus comprising: a timing detection unit configured to detect a reception training signal corresponding to a training code sequence for frequency offset estimation within a reception signal acquired by converting the received coherent optical signal into an electric signal; a frequency offset estimation unit configured to calculate a plurality of delay differential components on the basis of the reception training signal detected by the timing detection unit and at least two delay signals of the reception training signal, each delay signal having a different number of delay symbols, and calculates an averaged frequency offset amount using the calculated plurality of delay differential components; and a frequency offset compensation processing unit configured to perform frequency offset compensation on the reception signal using the frequency offset amount calculated by the frequency offset estimation unit, wherein the training code sequence for frequency offset estimation is a code sequence constituted by multi-value phase modulation symbols, in which a deviation angle of a vector average of a one-symbol delay differential component of the training signal generated on the basis of the code sequence has a prescribed angle, and a modulation phase difference between adjacent symbols has a fixed, repeated pattern; wherein each of the timing detection unit, the frequency offset estimation unit and the frequency offset compensation processing unit is implemented by: i) computer executable instructions executed by at least one processor, ii) at least one circuitry or iii) a combination of computer executable instructions executed by at least one processor and at least one circuitry.

2. The optical receiving apparatus according to claim 1, wherein a sequence length of the training code sequence for frequency offset estimation is a multiple of a number of elements included in the fixed, repeated pattern of the modulation phase difference between adjacent symbols.

3. The optical receiving apparatus according to claim 1, wherein, when the frequency offset estimation unit calculates a one-symbol delay differential component and a two-symbol delay differential component of the reception training signal, the frequency offset estimation unit calculates a first vector of a differential component between a vector average of the one-symbol delay differential component of the reception training signal and the vector average of the one-symbol delay differential component of the training signal, calculates a second vector in which a phase component of a predetermined angle, determined in advance on the basis of the prescribed angle and a total angle of the elements of the modulation phase difference included in the repeated pattern, has been removed from a vector of a differential component between respective vector averages of the one-symbol delay differential component and the two-symbol delay differential component of the reception training signal, and calculates the frequency offset amount by averaging the calculated first and second vectors.

4. The optical receiving apparatus according to claim 3, wherein, when the frequency offset estimation unit calculates a p (where p is an integer of at least 2) symbol delay differential component and a (p+1)-symbol delay differential component of the reception training signal, the frequency offset estimation unit calculates a third vector in which a phase component of a predetermined angle, determined in advance on the basis of the prescribed angle, has been removed from a vector of a differential component between respective vector averages of the p-symbol delay differential component and the (p+1) symbol delay differential component of the reception training signal, calculates the frequency offset amount by averaging the first vector, the second vector, and the third vector when p includes 2, and calculates the frequency offset amount by averaging the first vector and the third vector when p does not include 2.

5. The optical receiving apparatus according to claim 4, wherein, when the number of elements included in the fixed, repeated pattern of the modulation phase difference between adjacent symbols is set as M, p takes a value of M−1, or M, or M+1, or all of these values.

6. The optical receiving apparatus according to claim 1, wherein the timing detection unit, when detecting the reception training signal corresponding to the training code sequence for frequency offset estimation within the reception signal, detects, as the reception training signal, an interval of the reception signal including all or a part of the training code sequence for frequency offset estimation, the interval having a length that corresponds to the sequence length of the training code sequence for frequency offset estimation.

7. An optical transmitting apparatus comprising: a frame generation unit configured to generate a transmission frame by writing, to a preamble, a training code sequence that includes a training code sequence for frequency offset estimation, the training code sequence for frequency offset estimation being a code sequence constituted by multi-value phase modulation symbols, in which a deviation angle of a vector average of a one-symbol delay differential component of a signal generated on the basis of the code sequence has a prescribed angle, and a modulation phase difference between adjacent symbols has a fixed, repeated pattern; an IQ signal generation unit configured to generate an I component and a Q component of the transmission frame generated by the frame generation unit; and an optical coherent transmission unit configured to transmit a coherent optical signal acquired by performing modulation on the basis of the I component of the transmission frame and the Q component of the transmission frame, generated by the IQ signal generation unit, wherein each of the frame generation unit, the IQ signal generation unit and the optical coherent transmission unit is implemented by: i) computer executable instructions executed by at least one processor, ii) at least one circuitry or iii) a combination of computer executable instructions executed by at least one processor and at least one circuitry.

8. A frequency offset estimation method comprising: receiving a coherent optical signal that includes a training signal generated using a code sequence constituted by multi-value phase modulation symbols, in which a deviation angle of a vector average of a one-symbol delay differential component of a signal generated on the basis of the code sequence has a prescribed angle, and a modulation phase difference between adjacent symbols has a fixed, repeated pattern; detecting a reception training signal corresponding to a training code sequence for frequency offset estimation within a reception signal acquired by converting the received coherent optical signal into an electric signal; and calculating a plurality of delay differential components on the basis of the detected reception training signal and at least two delay signals of the reception training signal, each delay signal having a different number of delay symbols, and calculating an averaged frequency offset amount, which is used to compensate for a frequency offset in the reception signal, using the calculated plurality of delay differential components.

Description

BRIEF DESCRIPTION OF DRAWINGS

[0071] FIG. 1 is a block diagram showing a configuration of an optical transmission system according to a first embodiment of the present invention.

[0072] FIG. 2 is a block diagram showing an internal configuration of a frequency offset compensation unit of the first embodiment.

[0073] FIG. 3 is a view illustrating a training code sequence for frequency offset estimation applied to the first embodiment.

[0074] FIG. 4 is a flowchart showing a flow of processing executed by the frequency offset compensation unit of the first embodiment.

[0075] FIG. 5 is a block diagram showing a configuration of an optical transmission system according to a second embodiment of the present invention.

[0076] FIG. 6 is a block diagram showing an internal configuration of a frequency offset compensation unit of the second embodiment.

[0077] FIG. 7 is a flowchart showing a flow of processing executed by the frequency offset compensation unit of the second embodiment.

[0078] FIG. 8 is a block diagram showing a configuration of a PON system.

[0079] FIG. 9 is a block diagram showing a configuration of an optical transmission system for implementing the method disclosed in NPL 4.

[0080] FIG. 10 is a view showing a configuration of a burst frame generated by an optical transmission device.

[0081] FIG. 11 is a block diagram showing an internal configuration of a frequency offset compensation unit provided in an optical reception device shown in FIG. 9.

[0082] FIG. 12 is a view (1) illustrating a frequency offset amount on an IQ plane.

[0083] FIG. 13 is a view (2) illustrating a frequency offset amount on an IQ plane.

DESCRIPTION OF EMBODIMENTS

First Embodiment

[0084] Embodiments of the present invention will be described below with reference to the figures. FIG. 1 is a block diagram showing a configuration of an optical transmission system S according to a first embodiment. The optical transmission system S includes an optical transmission device (optical transmitting apparatus) 1, an optical reception device (optical receiving apparatus) 2, and an optical transmission path 3. For example, the optical transmission device 1 and the optical reception device 2 are provided respectively in the ONUs 310-1 to 310-3 and the OLT 320 of the optical transmission system 300 of the PON system shown in FIG. 8. The optical transmission path 3 connects the optical transmission device 1 to the optical reception device 2 so as to transmit optical signals transmitted by the optical transmission device 1 to the optical reception device 2.

[0085] The optical transmission device 1 includes a frame generation unit 10, an IQ signal generation unit 11, and an optical coherent transmission unit 12. The frame generation unit 10 takes in transmission data supplied from the outside and writes the transmission data to the payload 602 of the burst frame 600 shown in FIG. 10. Further, the frame generation unit 10 generates a burst frame 10out by writing a training code sequence for frequency offset estimation of the first embodiment, which is stored in advance in an internal storage area, to the preamble 601.

[0086] The IQ signal generation unit 11 takes in the burst frame 10out generated by the frame generation unit 10 and generates a modulation signal 11out, which is constituted by an I component and a Q component, by QSPK.

[0087] The optical coherent transmission unit 12 generates a transmission signal constituted by a coherent optical signal by modulating light output by an internally provided light source using the modulation signal having the I component and the Q component, generated by the IQ signal generation unit 11. The optical coherent transmission unit 12 transmits the generated transmission signal to the optical reception device 2 on the optical transmission path 3.

[0088] The optical reception device 2 includes an optical coherent reception unit 20, a local oscillator 21, an ADC 22, a digital signal processing unit 23, and an output unit 24.

[0089] The optical coherent reception unit 20 performs coherent reception for measuring an interference waveform between reception light received via the optical transmission path 3 by a phase diversity method and local light output by the local oscillator 21, and outputs an analog signal having an I component and a Q component.

[0090] The ADC 22 converts the analog signal having the I component and the Q component from the optical coherent reception unit 20 to a digital signal. The digital signal processing unit 23 is constituted by a DSP, for example, and includes an equalizer 31, a frequency offset compensation unit 32, and a phase offset compensation unit 33. The equalizer 31 performs adaptive equalization processing on the digital signal output by the ADC 22 and outputs a reception signal 31out in which waveform distortion occurring during propagation, such as chromatic dispersion, polarization mode dispersion, and polarization rotation, for example, has been compensated for.

[0091] The frequency offset compensation unit 32 calculates a frequency offset amount using a training signal included in the reception signal 31out output by the equalizer 31. Further, the frequency offset compensation unit 32 performs a reverse rotation calculation on the reception signal 31out output by the equalizer 31 using the calculated frequency offset amount, and outputs a reception signal 32out from which phase rotation of the frequency offset has been removed.

[0092] The phase offset compensation unit 33 removes a temporally fixed phase offset component from the reception signal 32out output by the frequency offset compensation unit 32 and outputs a reception signal 33out that reproduces the constellation of the transmission signal. The output unit 24 decodes the reception signal 33out and outputs the decoded signal to the outside.

[0093] FIG. 2 is a block diagram showing an internal configuration of the frequency offset compensation unit 32. The frequency offset compensation unit 32 includes a training signal analysis unit 40, a frequency offset estimation unit 50, a timing detection unit 60, and a frequency offset compensation processing unit 61.

[0094] The training signal analysis unit 40 includes a training signal generation unit 41, a deviation angle calculation unit 42, and a phase difference totaling unit 43. In the training signal analysis unit 40, the training signal generation unit 41 stores, in advance in an internal storage area, the training code sequence for frequency offset estimation of the first embodiment, which is identical to the code sequence written to the preamble 601 by the frame generation unit 10 of the optical transmission device 1.

[0095] Here, the training code sequence for frequency offset estimation of the first embodiment will be described. FIG. 3(a) shows an example of the training signal t(n) generated from the training code sequence for frequency offset estimation of the first embodiment. As shown in FIG. 3(a), the modulation phase difference 401(n) between adjacent symbols of the training code sequence for frequency offset estimation of the first embodiment has a repeated pattern constituted by three elements, namely “(½)π”, “it”, and “−(½)π”. Note that the sequence length of the training code sequence for frequency offset estimation is set at L.

[0096] Further, the training signal generation unit 41 stores “3”, which represents the number of elements included in the repeated pattern of the modulation phase difference 401(n), as described above, in advance in the internal storage area together with the training code sequence for frequency offset estimation. Furthermore, the training signal generation unit 41 generates and outputs the training signal t(n) on the basis of the training code sequence for frequency offset estimation of the first embodiment, stored in the internal storage area.

[0097] Note that the training code sequence for frequency offset estimation of the first embodiment and the number of elements included in the repeated pattern of the modulation phase difference 401(n) are assumed to be stored in advance in the internal storage area of the training signal generation unit 41 by following means. For example, the optical reception device 2 receives the training code sequence for frequency offset estimation and the number of elements from the optical transmission device 1 over a separate communication line having a high communication quality, or the optical reception device 2 takes in information indicating the training code sequence for frequency offset estimation and the number of elements by means such as reading the information from a recording medium. The training signal generation unit 41 writes the information indicating the training code sequence for frequency offset estimation and the number of elements, taken in thereby, to the internal storage area so that the information is stored therein in advance.

[0098] The deviation angle calculation unit 42 includes a one-symbol delay device 101, a complex conjugator 102, a multiplier 103, and a vector averaging device 104. In the deviation angle calculation unit 42, the one-symbol delay device 101, having taken in the training signal t(n+1), outputs the one-symbol delay signal t(n) of the training signal t(n+1). The complex conjugator 102 outputs a signal of a complex conjugate of the signal taken in thereby. The multiplier 103 multiplies the two signals taken in thereby, i.e. t(n+1) and the complex conjugate of t(n), and outputs a multiplication result. The vector averaging device 104 determines and outputs a vector average by calculating the sum of the vectors in the range of the sequence length L of the training code sequence for frequency offset estimation.

[0099] In other words, the deviation angle calculation unit 42 calculates the one-symbol delay difference component Δt.sub.1(n) defined by formula (2) using the one-symbol delay device 101, the complex conjugator 102, and the multiplier 103. The vector averaging device 104 calculates the vector average of the one-symbol delay difference component Δt.sub.1(n), or in other words expj(θ.sub.t), which is a vector in which the predetermined deviation angle θ.sub.t is included in the phase, by performing the calculation shown in formula (9), and outputs the calculation result to the frequency offset estimation unit 50.

[0100] The phase difference totaling unit 43 reads the information indicating the training code sequence for frequency offset estimation and the number of elements included in the repeated pattern of the modulation phase difference Δθ.sub.1(n), which are stored in the internal storage area of the training signal generation unit 41. In the first embodiment, the number of elements is “3”, and therefore the phase difference totaling unit 43 calculates a sum “X” of the modulation phase differences 401(n) of the training code sequence for frequency offset estimation in three consecutive symbols on the basis of formula (13) below. Further, the phase difference totaling unit 43 outputs expj(X), which is a vector in which the calculated value “X” is included in the phase. Note that in formula (13), “c” is a predetermined arbitrary integer, and X takes a fixed value regardless of n. In the case of the training signal t(n) of FIG. 3(a), X=(½)π+π−(½)π=

[00008]$\begin{array}{cc}\left[\mathrm{Formula}13\right]& \\ X=\stackrel{c+2}{\underset{n=c}{.Math.}}{\mathrm{\Delta \theta }}_1\left(n\right)& \left(13\right)\end{array}$

[0101] The timing detection unit 60 takes in the reception signal 31out output by the equalizer 31 and detects, in the reception signal 31out taken in thereby, the start position of the reception training signal r(n) corresponding to the training code sequence for frequency offset estimation written to the preamble 601. Further, the timing detection unit 60 extracts the reception training signal r(n) from the reception signal 31out on the basis of the detected start position and the sequence length L of the training code sequence for frequency offset estimation, and outputs the extracted signal to the frequency offset estimation unit 50.

[0102] The frequency offset estimation unit 50 includes a one-symbol delay differential component vector average calculation unit 51-1, a two-symbol delay differential component vector average calculation unit 51-2, a complex conjugator 52, a multiplier 53, a differential calculation unit 54, an adder 55, and a deviation angle device 56.

[0103] In the frequency offset estimation unit 50, the one-symbol delay differential component vector average calculation unit 51-1 includes a one-symbol delay device 151-1, a complex conjugator 152-1, a multiplier 153-1, and a vector averaging device 154-1. The two-symbol delay differential component vector average calculation unit 51-2 includes a two-symbol delay device 151-2, a complex conjugator 152-2, a multiplier 153-2, and a vector averaging device 154-2.

[0104] In the one-symbol delay differential component vector average calculation unit 51-1, the one-symbol delay device 151-1, having taken in the reception training signal r(n+1), outputs the one-symbol delay signal r(n) of the reception training signal r(n+1). In the two-symbol delay differential component vector average calculation unit 51-2, the two-symbol delay device 151-2, having taken in a reception training signal r(n+2), outputs a two-symbol delay signal r(n) of the reception training signal r(n+2).

[0105] The complex conjugators 152-1 and 152-2 respectively output signals of the complex conjugates of the signals taken in by the one-symbol delay differential component vector average calculation unit 51-1 and the two-symbol delay differential component vector average calculation unit 51-2, i.e. r(n) and r(n). The multiplier 153-1 multiplies the two signals taken in thereby, i.e. r(n+1) and the complex conjugate of r(n), and outputs a multiplication result. 153-2 multiplies the two signals taken in thereby, i.e. r(n+2) and the complex conjugate of r(n), and outputs a multiplication result. The vector averaging devices 154-1, 154-2 determine and output vector averages by calculating the sum of the vectors in the range of the sequence length L of the training code sequence for frequency offset estimation.

[0106] In other words, the one-symbol delay differential component vector average calculation unit 51-1 calculates the one-symbol delay differential component Δr.sub.1(n) of the reception training signal r(n) by performing the calculation shown in formula (5) using the one-symbol delay device 151-1, the complex conjugator 152-1, and the multiplier 153-1. The vector averaging device 154-1 calculates the sum of Δr.sub.1(n) added over the sequence length L as the vector average of the one-symbol delay differential component Δr.sub.1(n).

[0107] Further, the two-symbol delay differential component vector average calculation unit 51-2 calculates a two-symbol delay differential component Δr.sub.2(n) of the reception training signal r(n) using the two-symbol delay device 151-2, the complex conjugator 152-2, and the multiplier 153-2. The vector averaging device 154-2 calculates the sum of the two-symbol delay differential component Δr.sub.2(n) added over the sequence length L as the vector average of the two-symbol delay differential component Δr.sub.2(n).

[0108] The complex conjugator 52 takes in the output value expj(θ.sub.t) output by the deviation angle calculation unit 42 of the training signal analysis unit 40, and outputs expj(−θ.sub.t) as the complex conjugate of the output value. The multiplier 53 performs the calculation shown in formula (11) by multiplying the output value of the one-symbol delay differential component vector average calculation unit 51-1 by the output value of the complex conjugator 52, and in so doing calculates a vector in which the frequency offset amount is included in the phase.

[0109] The differential calculation unit 54 takes in the output value of the one-symbol delay differential component vector average calculation unit 51-1, the output value of the two-symbol delay differential component vector average calculation unit 51-2, expj(X), output by the phase difference totaling unit 43, and the output value expj(θ.sub.t) output by the deviation angle calculation unit 42. Further, the differential calculation unit 54 calculates a vector in which a predetermined angle, which is determined in advance on the basis of expj(X), output by the phase difference totaling unit 43, and the output value expj(θ.sub.t) output by the deviation angle calculation unit 42, is included in the phase. Furthermore, the differential calculation unit 54 calculates a differential component between the output value of the one-symbol delay differential component vector average calculation unit 51-1 and the output value of the two-symbol delay differential component vector average calculation unit 51-2. Moreover, the differential calculation unit 54 removes the aforesaid predetermined angle from the differential component by multiplying the complex conjugate of the vector in which the predetermined angle is included in the phase by the calculated differential component, and in so doing calculates a vector in which the frequency offset amount is included in the phase.

[0110] The adder 55 adds the output value of the multiplier 53 to the output value of the differential calculation unit 54 and outputs an addition value. The deviation angle device 56 calculates the deviation angle of the addition value output by the adder 55, or in other words the frequency offset amount, and outputs the result to the frequency offset compensation processing unit 61. The frequency offset compensation processing unit 61 performs frequency offset compensation on the reception signal using the frequency offset amount output by the frequency offset estimation unit 50.

[0111] (Principles of Frequency Offset Amount Estimation According to First Embodiment)

[0112] Here, the principles by which the frequency offset estimation unit 50 estimates the frequency offset amount in the first embodiment will be described. The two-symbol delay differential component Δt.sub.2(n) of the training signal t(n) is defined by formula (14), shown below, similarly to formula (2) for calculating the one-symbol delay differential component.

[00009]$\begin{array}{cc}\left[\mathrm{Formula}14\right]& \\ \begin{array}{c}\Delta t_2\left(n\right)=t\left(n+2\right).Math.{t\left(n\right)}^{*}\\ =\exp j\left({\phi }_m\left(n+2\right)-{\phi }_m\left(n\right)\right)\\ =\exp j\left({\mathrm{\Delta \theta }}_2\left(n\right)\right)\end{array}& \left(14\right)\end{array}$

[0113] The two-symbol delay differential component t.sub.2(n) can also be expressed by formula (15) below.

[00010]$\begin{array}{cc}\left[\mathrm{Formula}15\right]& \\ \begin{array}{c}\Delta t_2\left(n\right)=\left\{t\left(n+1\right).Math.{t\left(n\right)}^{*}\right\}.Math.\left\{t\left(n+2\right).Math.{t\left(n+1\right)}^{*}\right\}.Math.\\ \left\{t\left(n+3\right).Math.{t\left(n+2\right)}^{*}\right\}.Math.{\left\{t\left(n+3\right).Math.{t\left(n+2\right)}^{*}\right\}}^{*}\\ =\exp j(\Delta {\theta }_1\left(n\right)+\Delta {\theta }_1\left(n+1\right)+\Delta {\theta }_1\left(n+2\right)-\Delta {\theta }_1\left(n+2\right)\end{array}& \left(15\right)\end{array}$

[0114] Here, a relationship shown below in formula (16) is established by formula (13).

[00011]$\begin{array}{cc}\left[\mathrm{Formula}16\right]& \\ \exp j\left(X\right)=\exp j\left(\underset{n=c}{\overset{c+2}{.Math.}}\Delta {\theta }_1\left(n\right)\right)& \left(16\right)\end{array}$

[0115] When c=n is set in formula (16), formula (16) becomes formula (17) below.

[Formula 17]

expj(X)=expj(Δθ.sub.1(n)+Δθ.sub.1(n+1)+Δθ.sub.1(n+2))  (1)

[0116] Formula (18), shown below, can be derived from formula (15) and formula (17).

[Formula 18]

Δt.sub.2(n)=expj(X−Δθ.sub.1(n+2))=expj(Δθ.sub.2(n))  (18)

[0117] The two-symbol delay differential component Δr.sub.2(n) of the reception training signal including the frequency offset, resulting from formula (4), is defined by formula (19), shown below.

[00012]$\begin{array}{cc}\left[\mathrm{Formula}19\right]& \\ \begin{array}{c}\Delta r_2\left(n\right)=r\left(n+2\right).Math.{r\left(n\right)}^{*}\\ =\exp j(\left(n+2\right)2\pi f_{\mathrm{IF}}T+{\phi }_m\left(n+2\right)-\\ \left\{\left(n2\pi f_{\mathrm{IF}}T+{\phi }_m\left(n\right)\right\}\right)\\ =\exp j\left(2.Math.2\pi f_{\mathrm{IF}}T+{\mathrm{\Delta \theta }}_2\left(n\right)\right)\end{array}& \left(19\right)\end{array}$

[0118] From formula (18) and formula (19), formula (20), shown below, is established in relation to the two-symbol delay differential component Δr.sub.2(n).

[Formula 20]

Δr.sub.2(n)=expj(2.Math.2πf.sub.IFT+X−Δθ.sub.1(n+2))  (20)

[0119] When the vector average is calculated as the sum of the two-symbol delay differential component Δr.sub.2(n) shown in formula (20) added over the length of the sequence length L, formula (21), shown below, can be derived from similar considerations to formula (10).

[00013]$\begin{array}{cc}\left[\mathrm{Formula}21\right]& \\ \underset{n=0}{\overset{L}{.Math.}}\Delta r_1\left(n\right)\cong \exp j\left(-{\theta }_t+X\right).Math.\exp j\left(2.Math.2\pi f_{\mathrm{IF}}T\right)& \left(21\right)\end{array}$

[0120] As n increases, the third term “Δθ.sub.1(n+2)” of the phase in formula (20) shows identical variation to the one-symbol delay differential component Δt.sub.1(n) of the training signal t(n). Therefore, the third term in parentheses following expj, when added over a sufficiently long sequence length L, takes the value acquired by adding the one-symbol delay differential component Δt.sub.1(n) over the sequence length L, or in other words, according to formula (9), “θ.sub.t”. Thus, formula (21) can be derived.

[0121] The differential component between the vector average of the two-symbol delay differential component, calculated using formula (21), and the vector average of the one-symbol delay differential component, calculated using formula (10), is expj(2πf.sub.IFT+X−2θ.sub.t). Here, the predetermined angle is set as (X−2θ.sub.t), and by multiplying a vector expj(−X+2θ.sub.t), which is the complex conjugate of the vector in which the predetermined angle is included in the phase, by the differential component, as shown below in formula (22), the predetermined angle (X−2θ.sub.t) is removed from the differential component.

[00014]$\begin{array}{cc}\left[\mathrm{Formula}22\right]& \\ \underset{n=0}{\overset{L}{.Math.}}\Delta r_2\left(n\right).Math.{\left\{\underset{n=0}{\overset{L}{.Math.}}\Delta r_1\left(n\right)\right\}}^{*}.Math.\exp {j\left(X\right)}^{*}.Math.\exp j\left(2{\theta }_t\right)=\underset{n=0}{\overset{L}{.Math.}}\Delta r_2\left(n\right).Math.{\left\{\underset{n=0}{\overset{L}{.Math.}}\Delta r_1\left(n\right)\right\}}^{*}.Math.\exp j\left(-X+2{\theta }_t\right)=\exp j\left(2\pi f_{\mathrm{IF}}T\right)& \left(22\right)\end{array}$

[0122] By performing the calculation of formula (22), similarly to formula (11), a vector in which the frequency offset amount is included in the phase can be calculated.

[0123] To acquire a vector in which the frequency offset amount is included in the phase on the basis of formula (22), the training code sequence for frequency offset estimation must take the following form.

[0124] The code sequence must be set so that when the vector average of the one-symbol delay differential component Δr.sub.1(n) of the reception training signal r(n) is calculated on the basis of formula (10), the calculated vector average does not reach zero, that is, a vector remains.

[0125] Further, to acquire a vector in which the frequency offset amount is included in the phase on the basis of formula (11), the training code sequence for frequency offset estimation must take the following form. That is, the deviation angle of the vector average of the one-symbol delay differential component Δt.sub.1(n) of the training signal t(n) must not be zero. The deviation angles must strengthen each other rather than canceling each other out on an IQ plane. The deviation angle must have a prescribed angle of θ.sub.t. In addition, the code sequence must be constituted by a repeated, fixed pattern. When the vector average of the one-symbol delay differential component Δt.sub.1(n) reaches zero, a noise component caused by an error included in the reception training signal r(n) increases, and as a result, θ.sub.r1 in formula (12) takes a random value, making it difficult to calculate the frequency offset amount by calculation.

[0126] In the training code sequence for frequency offset estimation of the first embodiment, an example of which is shown in FIG. 3(a), a pattern in which the modulation phase difference Δθ.sub.1(n) between adjacent symbols is constituted by three elements, namely “(½)π”, “it”, and “−(½)π”, occurs repeatedly. In other words, as shown in FIG. 3(b), the one-symbol delay differential component Δt.sub.1(n) of the training signal t(n), shown in FIG. 3(a), takes a form in which the fixed code sequence “(½)π”, “it”, “−(½)π” occurs repeatedly. Accordingly, the training code sequence for frequency offset estimation is also a fixed, repeated pattern constituted by six elements, namely “0”, “(½)π”, “−(½)π”, “π”, “−(½)π”, and “(½)π”.

[0127] In the case of this code sequence, when the sequence length L is a multiple of “3”, i.e. the number of elements in the repeated pattern of the modulation phase difference Δθ.sub.1(n), or is sufficiently large, as shown in FIG. 3(b), the deviation angle of the vector average of the one-symbol delay differential component Δt.sub.1(n) of the training signal t(n), or in other words the prescribed deviation angle θ.sub.t, does not reach zero, and instead equals “it” such that a vector remains. Accordingly, a vector remains likewise in the vector average of the one-symbol delay differential component Δr.sub.1(n) of the reception training signal r(n) shown in formula (10), and as a result, a vector in which the frequency offset amount is included in the phase is acquired on the basis of formula (11) and formula (22).

[0128] When noise is ignored, formula (11) and formula (22) are vectors having identical deflection angles. In actuality, however, formula (11) and formula (22) include different noise components. Therefore, by adding together formula (11) and formula (22) and averaging the result, the noise component can be reduced. Thus, the frequency offset can be estimated with a higher precision than when only formula (11) is used, or in other words when the method of NPL 4, which employs only the one-symbol delay differential component, is used.

[0129] Therefore, when the frequency offset is estimated with a similar degree of precision to the method of NPL 4 using the frequency offset compensation unit 32 of the first embodiment, the length of the training code sequence for frequency offset estimation can be shortened in comparison with the method of NPL 4.

[0130] (Processing of Frequency Offset Estimation Unit of First Embodiment)

[0131] Next, the processing performed by the frequency offset estimation unit 50 of the first embodiment will be described. FIG. 4 is a flowchart showing the flow of the processing performed by the frequency offset estimation unit 50. It is assumed that prior to the start of the processing shown in FIG. 4, the deviation angle calculation unit 42 of the training signal analysis unit 40 calculates expj(θ.sub.t) as a vector in which the prescribed deviation angle θ.sub.t is included in the phase on the basis of the training signal t(n) generated by the training signal generation unit 41, and outputs the calculation result to the frequency offset estimation unit 50. It is also assumed that the phase difference totaling unit 43 of the training signal analysis unit 40 calculates X on the basis of formula (13), calculates expj(X) as a vector in which X is included in the phase, and outputs expj(X) to the frequency offset estimation unit 50. As noted above, in the case of the training signal t(n) shown in FIG. 3(a), θ.sub.t=π and X=π.

[0132] The one-symbol delay differential component vector average calculation unit 51-1 and the two-symbol delay differential component vector average calculation unit 51-2 of the frequency offset estimation unit 50 take in the reception training signals r(n) output successively by the timing detection unit 60 (step S1).

[0133] The one-symbol delay device 151-1, complex conjugator 152-1, and multiplier 153-1 of the one-symbol delay differential component vector average calculation unit 51-1, having taken in the reception training signal r(n+1), calculate the one-symbol delay differential component Δr.sub.1(n) of the reception training signal by performing the calculation of formula (5). The vector averaging device 154-1 calculates the sum of the one-symbol delay differential component Δr.sub.1(n) of the reception training signal added over the sequence length L as the vector average of the one-symbol delay differential component of the reception training signal. The vector averaging device 154-1 outputs the calculated vector average of the one-symbol delay differential component of the reception training signal to the multiplier 53 and the differential calculation unit 54 (step S2-1).

[0134] The two-symbol delay device 151-2, complex conjugator 152-2, and multiplier 153-2 of the two-symbol delay differential component vector average calculation unit 51-2, having taken in the reception training signal r(n+2), calculate the two-symbol delay differential component Δr.sub.2(n) of the reception training signal by performing the calculation of formula (19). The vector averaging device 154-2 calculates the sum of the two-symbol delay differential component Δr.sub.2(n) of the reception training signal added over the sequence length L as the vector average of the two-symbol delay differential component of the reception training signal. The vector averaging device 154-2 outputs the calculated vector average of the two-symbol delay differential component of the reception training signal to the differential calculation unit 54 (step S2-2).

[0135] The complex conjugator 52 outputs the complex conjugate expj(−θ.sub.t) of expj(θ.sub.t), output by the deviation angle calculation unit 42 of the training signal analysis unit 40, to the multiplier 53. The multiplier 53 performs the calculation of formula (11) on the basis of the vector average of the one-symbol delay differential component of the reception training signal, output by the one-symbol delay differential component vector average calculation unit 51-1, and expj(−θ.sub.t), output by the complex conjugator 52, and outputs the calculation result to the adder 55 (step S3-1).

[0136] The differential calculation unit 54 takes in the output value of the one-symbol delay differential component vector average calculation unit 51-1, the output value of the two-symbol delay differential component vector average calculation unit 51-2, expj(X), output by the phase difference totaling unit 43, and the output value expj(θ.sub.t) output by the deviation angle calculation unit 42.

[0137] The differential calculation unit 54 calculates a vector in which a predetermined angle (X−2θ.sub.t), which is determined in advance on the basis of expj(X), output by the phase difference totaling unit 43, and the output value expj(θ.sub.t) output by the deviation angle calculation unit 42, is included in the phase. The differential calculation unit 54 performs the calculation shown in formula (22), or in other words calculates the differential component between the output value of the one-symbol delay differential component vector average calculation unit 51-1 and the output value of the two-symbol delay differential component vector average calculation unit 51-2. The differential calculation unit 54 removes the predetermined angle from the differential component by multiplying expj(−X+2θ.sub.t), which is the complex conjugate of the vector in which the predetermined angle is included in the phase, by the calculated differential component, and in so doing calculates a vector in which the frequency offset amount is included in the phase (step S3-2).

[0138] The adder 55 performs a calculation shown below on the left side of formula (23) to add the output value of the multiplier 53 to the output value of the differential calculation unit 54, and outputs an addition value (step S4).

[00015]$\begin{array}{cc}\left[\mathrm{Formula}23\right]& \\ \underset{n=0}{\overset{L}{.Math.}}\Delta r_2\left(n\right).Math.{\left\{\underset{n=0}{\overset{L}{.Math.}}\Delta r_1\left(n\right)\right\}}^{*}.Math.\exp j\left(-X+2{\theta }_t\right)+\exp j\left(-{\theta }_t\right).Math.\underset{n=0}{\overset{L}{.Math.}}\Delta r_1\left(n\right)=2.Math.\exp j\left(2\pi f_{\mathrm{IF}}T\right)& \left(23\right)\end{array}$

[0139] The deviation angle device 56 performs a calculation shown below in formula (24) to calculate the deviation angle of the addition value output by the adder 55, thereby calculating the frequency offset amount, and outputs the calculated frequency offset amount to the frequency offset compensation processing unit 61 (step S5).

[00016]$\begin{array}{cc}\left[\mathrm{Formula}24\right]& \\ 2\pi f_{\mathrm{IF}}T=\arg \left[\underset{n=0}{\overset{L}{.Math.}}\Delta r_2\left(n\right).Math.{\left\{\underset{n=0}{\overset{L}{.Math.}}\Delta r_1\left(n\right)\right\}}^{*}.Math.\exp j\left(-X+2{\theta }_t\right)+\exp j\left(-{\theta }_t\right).Math.\underset{n=0}{\overset{L}{.Math.}}\Delta r_1\left(n\right)\right]& \left(24\right)\end{array}$

[0140] Note that in the flowchart shown in FIG. 4, the processing of step S3-2 may be performed after step S3-1, as described above, or the processing of steps S3-1 and S3-2 may be performed in parallel. Alternatively, the processing of step S3-1 may be performed after step S3-2.

[0141] According to the configuration of the first embodiment, described above, in the frequency offset compensation unit 32 of the optical reception device 2, which receives a coherent optical signal that includes a training signal, the timing detection unit 60 detects the reception training signal corresponding to the training code sequence for frequency offset estimation within the reception signal that is acquired by converting the received coherent optical signal into an electric signal. Here, the training code sequence for frequency offset estimation is a code sequence constituted by multi-value phase modulation symbols, in which the deviation angle of the vector average of the one-symbol delay differential component of a training signal generated on the basis of the training code sequence for frequency offset estimation has a prescribed angle and the modulation phase difference between adjacent symbols has a fixed, repeated pattern. The frequency offset compensation unit 32 calculates a plurality of delay differential components on the basis of the reception training signal detected by the timing detection unit 60 and at least two delay signals of the reception training signal, each delay signal having a different number of delay symbols, and calculates an averaged frequency offset amount using the calculated plurality of delay differential components. More specifically, the frequency offset compensation unit 32 calculates the one-symbol delay differential component and the two-symbol delay differential component of the reception training signal, calculates a first vector of a differential component between the vector average of the one-symbol delay differential component of the reception training signal and the vector average of the one-symbol delay differential component of the training signal, calculates a second vector in which the phase component of the predetermined angle, which is determined in advance on the basis of the prescribed angle and the total angle of the elements of the modulation phase difference included in the repeated pattern, has been removed from the vector of the differential component between the respective vector averages of the one-symbol delay differential component and the two-symbol delay differential component of the reception training signal, and calculates the frequency offset amount by averaging the calculated first and second vectors. The frequency offset compensation processing unit 61 performs frequency offset compensation on the reception signal using the frequency offset amount calculated by the frequency offset compensation unit 32.

[0142] By performing the processing for averaging the first and second vectors, or in other words processing for adding together formula (11) and formula (22), the frequency offset compensation unit 32 can reduce the noise component. As a result, the frequency offset can be estimated with a higher precision than when only formula (11) is used, or in other words when the method of NPL 4, which employs only the one-symbol delay differential component, is used.

[0143] Accordingly, as described above, when the frequency offset is estimated with a similar degree of precision to the method of NPL 4 using the frequency offset compensation unit 32 of the first embodiment, the length of the training code sequence for frequency offset estimation can be shortened in comparison with the method of NPL 4. Therefore, in the optical transmission system S of the first embodiment, by employing a training code sequence for frequency offset estimation in which the one-symbol delay differential component Δt.sub.1(n) of the training signal t(n) is a certain fixed, repeated code sequence, the length of the preamble 601 can be reduced. In other words, a frequency offset amount can be estimated with a high degree of precision in a digital coherent system using a training code sequence with a short sequence length.

[0144] Note that although with the configuration of the first embodiment, as described above, the sequence length L of the training code sequence for frequency offset estimation can be shortened in comparison with the method of NPL 4, in actuality, the sequence length L must be set as described below. As illustrated in formula (11) and formula (22), the frequency offset compensation unit 32 of the first embodiment estimates the frequency offset amount by accurately calculating the vector average over the length L from the start n=0.

[0145] In an actual configuration, however, a slight timing error may occur in the timing detection unit 60. For example, when the timing detection unit 60 makes an error of Δn symbols in the start position of the training signal t(n), the interval in which the vector average is calculated becomes n=n+Δn to n=L+Δn such that a vector component is generated from an erronous interval, and as a result, an error occurs in the estimated frequency offset amount.

[0146] Even when a timing error occurs, as long as the sequence length L of the training code sequence for frequency offset estimation is sufficiently longer than the sequence length of the timing error Δn, the vector component of the correct interval is dominant over the vector component of the erronous interval in the interval n+Δn to L+Δn.

[0147] Therefore, as long as the vector component of the correct interval is not zero, the effect of the vector component of the erroneous interval can be ignored. The condition that the vector component of the correct interval is not zero can be satisfied by ensuring that the deviation angle θ.sub.t of the vector average serving as the sum of the one-symbol delay differential component Δt.sub.1(n) of the training signal t(n) added from 0 to L, as described above, is not zero.

[0148] Hence, according to the configuration of the first embodiment, although the sequence length of the training code sequence for frequency offset estimation can be shortened in comparison with the method of NPL 4, the sequence length L must be set at a length corresponding to the allowable timing error Δn of the timing detection unit 60.

Second Embodiment

[0149] FIG. 5 is a block diagram showing a configuration of an optical transmission system Sa according to a second embodiment. In the second embodiment, identical reference symbols have been allocated to configurations that are identical to the first embodiment, and different configurations will be described below.

[0150] In the first embodiment, the modulation phase difference Δθ.sub.1(n) between adjacent symbols of the training code sequence for frequency offset estimation has a repeated pattern constituted by three elements, namely “(½)π”, “π”, and “−(½)π”. In the second embodiment, however, a generalized training code sequence for frequency offset estimation (referred to hereafter as the training code sequence for frequency offset estimation of the second embodiment), in which the modulation phase difference Δθ.sub.1(n) between adjacent symbols has a repeated pattern constituted by M elements, is used.

[0151] Further, in the first embodiment, the frequency offset amount is estimated using the one-symbol delay differential component and the two-symbol delay differential component of the reception training signal, whereas the second embodiment is generalized so that a plurality of delay differential components from the one-symbol delay differential component to a P-symbol delay differential component are used (note that P is an integer of 2 or more).

[0152] The optical transmission system Sa of the second embodiment includes an optical transmission device 1a, an optical reception device 2a, and the optical transmission path 3. The optical transmission device 1a includes a frame generation unit 10a, the IQ signal generation unit 11, and the optical coherent transmission unit 12. The frame generation unit 10a generates a burst signal 10aout by writing the training code sequence for frequency offset estimation of the second embodiment, which is stored in advance in an internal storage area, to the preamble 601.

[0153] The optical reception device 2a includes the optical coherent reception unit 20, the local oscillator 21, the ADC 22, a digital signal processing unit 23a, and the output unit 24. The digital signal processing unit 23a includes the equalizer 31, a frequency offset compensation unit 32a, and the phase offset compensation unit 33.

[0154] The frequency offset compensation unit 32a has an internal configuration shown in FIG. 6, and includes a training signal analysis unit 40a, a frequency offset estimation unit 50a, the timing detection unit 60, and the frequency offset compensation processing unit 61.

[0155] The training signal analysis unit 40a includes a training signal generation unit 41a, the deviation angle calculation unit 42, and a phase difference totaling unit 43a. The training signal generation unit 41a stores, in advance in an internal storage area, the training code sequence for frequency offset estimation of the second embodiment, and “M”, which represents the number of elements in the repeated pattern of the modulation phase difference 4θ.sub.1(n). Further, the training signal generation unit 41a generates and outputs the training signal t(n) on the basis of the training code sequence for frequency offset estimation of the second embodiment, stored in the internal storage area.

[0156] Note that the training code sequence for frequency offset estimation of the second embodiment and the number of elements included in the repeated pattern of the modulation phase difference Δθ.sub.1(n) are assumed to be stored in advance in the internal storage area of the training signal generation unit 41a by the following means. For example, the optical reception device 2a receives the training code sequence for frequency offset estimation and the number of elements from the optical transmission device 1a over a separate communication line having a high communication quality, or the optical reception device 2a takes in information indicating the training code sequence for frequency offset estimation and the number of elements by means such as reading the information from a recording medium. The training signal generation unit 41a writes the information indicating the training code sequence for frequency offset estimation and the number of elements, taken in thereby, to the internal storage area so that the information is stored therein in advance.

[0157] The phase difference totaling unit 43a reads the information indicating the training code sequence for frequency offset estimation of the second embodiment and the number of elements “M” included in the repeated pattern of the modulation phase difference 4θ.sub.1(n), which are stored in the internal storage area of the training signal generation unit 41. Further, the phase difference totaling unit 43a calculates the sum “X” of the modulation phase differences Δθ.sub.1(n) of the training code sequence for frequency offset estimation in M consecutive symbols on the basis of formula (25) shown below, which is acquired by generalizing formula (13). Further, the phase difference totaling unit 43a outputs expj(X), which is a vector in which the calculated value “X” is included in the phase. Note that in formula (25), “c” is a predetermined arbitrary integer, and X takes a fixed value regardless of n.

[00017]$\begin{array}{cc}\left[\mathrm{Formula}25\right]& \\ X=\underset{n=c}{\overset{c+M-1}{.Math.}}{\mathrm{\Delta \theta }}_1\left(n\right)& \left(25\right)\end{array}$

[0158] The frequency offset estimation unit 50a includes the one-symbol delay differential component vector average calculation unit 51-1, the two-symbol delay differential component vector average calculation unit 51-2, . . . , a P-symbol delay differential component vector average calculation unit 51-N, the complex conjugator 52, the multiplier 53, a differential calculation unit 54a, the adder 55, and the deviation angle device 56.

[0159] Here, the internal configuration will be described using a p-symbol delay differential component vector average calculation unit 51-N, where p is an integer from 2 to P, to represent the two-symbol delay differential component vector average calculation unit 51-2, . . . , and the P-symbol delay differential component vector average calculation unit 51-N. Each p-symbol delay differential component vector average calculation unit 51-N includes a p-symbol delay device 151-p, a complex conjugator 152-p, a multiplier 153-p, and a vector averaging device 154-p.

[0160] In the p-symbol delay differential component vector average calculation unit 51-p, the p-symbol delay device 151-p, having taken in a reception training signal r(n+p), outputs a p-symbol delay signal r(n). The complex conjugator 152-p outputs a signal of the complex conjugate of the signal taken in thereby. The multiplier 153-p multiplies the two signals taken in thereby and outputs the multiplication result. The vector averaging device 154-p determines a vector average by calculating the sum of the vectors in the range of the sequence length L of the training code sequence for frequency offset estimation, and outputs the determined vector average.

[0161] Here, formulae generalizing the vector average of the p-symbol delay differential components Δr.sub.p(n) serving as the outputs of the respective p-symbol delay differential component vector average calculation units 51-p will be described. First, a p-symbol delay differential component Δt.sub.p(n) of the training signal t(n) is defined by formula (26) below, which is acquired by generalizing formula (15).

[Formula 26]

Δt.sub.p(n)=t(n+p).Math.t(n)*=expj(φ.sub.m(n+p)−φ.sub.m(n))=expj(Δθ.sub.p(n))  (26)

[0162] Further, by dividing the p-symbol delay differential component t.sub.p(n) of the training signal t(n) by case, the p-symbol delay differential component t.sub.p(n) can be expressed as follows.

[0163] When M<p, the p-symbol delay differential component t.sub.p(n) can be expressed by formula (27) below.

[00018]$\left[\mathrm{Formula}27\right]$$\begin{array}{cc}\begin{array}{c}\Delta t_p\left(n\right)=\underset{k=n}{\overset{n+M-1}{.Math.}}t\left(k+1\right).Math.{t\left(k\right)}^{*}.Math.\underset{k=n+M}{\overset{n+M+D-1}{.Math.}}t\left(k+1\right).Math.{t\left(k\right)}^{*}\\ =\exp j\left(X\right).Math.\underset{k=n+M}{\overset{n+M+D-1}{.Math.}}t\left(k+1\right).Math.{t\left(k\right)}^{*}\end{array}& \left(27\right)\end{array}$

[0164] When M>p, the p-symbol delay differential component t.sub.p(n) can be expressed by formula (28) below.

[00019]$\left[\mathrm{Formula}28\right]$$\begin{array}{cc}\begin{array}{c}\Delta t_p\left(n\right)=\underset{k=n}{\overset{n+M-1}{.Math.}}t\left(k+1\right).Math.{t\left(k\right)}^{*}.Math.\underset{k=n+M-\left(M-p\right)}{\overset{n+M-\left(M-p\right)+D-1}{.Math.}}{\left\{t\left(k+1\right).Math.{t\left(k\right)}^{*}\right\}}^{*}\\ =\exp j\left(X\right).Math.\underset{k=n+p}{\overset{n+p+D-1}{.Math.}}{\left\{t\left(k+1\right).Math.{t\left(k\right)}^{*}\right\}}^{*}\end{array}& \left(28\right)\end{array}$

[0165] When M=p, the p-symbol delay differential component t.sub.p(n) can be expressed by formula (29) below.

[Formula 29]

Δt.sub.p(n)=expj(X)  (29)

[0166] Note that D in formulae (27) and (28) is D=M−p.

[0167] Here, the p-symbol delay differential component Δr.sub.p(n) of the reception training signal r(n) is defined by formula (30) below, which is acquired by generalizing formula (19).

[00020]$\left[\mathrm{Formula}30\right]$$\begin{array}{cc}\begin{array}{c}\Delta r_p\left(n\right)=r\left(n+p\right).Math.{r\left(n\right)}^{*}\\ =\exp j\left(\left(n+p\right)2\pi f_{\mathrm{IF}}T+{\phi }_m\left(n+p\right)-\left\{n2\pi f_{\mathrm{IF}}T+{\phi }_m\left(n\right)\right\}\right)\\ =\exp j\left(p.Math.2\pi f_{\mathrm{IF}}T+{\mathrm{\Delta \theta }}_p\left(n\right)\right)\end{array}& \left(30\right)\end{array}$

[0168] Further, by dividing the p-symbol delay differential component Δr.sub.p(n) by case, the p-symbol delay differential component Δr.sub.p(n) can be expressed as follows.

[0169] (i) When p=M+1, formula (31) is acquired from formula (27).

[00021]$\left[\mathrm{Formula}31\right]$$\begin{array}{cc}\Delta r_p\left(n\right)=\exp j\left(p.Math.2\pi f_{\mathrm{IF}}T\right).Math.\exp j\left(X\right).Math.\underset{k=n+M}{\overset{n+M+D-1}{.Math.}}t\left(k+1\right).Math.{t\left(k\right)}^{*}& \left(31\right)\end{array}$

[0170] When the vector average of formula (31) is calculated, formula (32), shown below, is acquired.

[00022]$\left[\mathrm{Formula}32\right]$$\begin{array}{cc}\underset{n=0}{\overset{L}{.Math.}}\Delta r_p\left(n\right)\cong \exp j\left({\theta }_t+X\right).Math.\exp j\left(p.Math.2\pi f_{\mathrm{IF}}T\right)& \left(32\right)\end{array}$

[0171] (ii) When p=M−1, formula (33) is acquired from formula (28).

[00023]$\left[\mathrm{Formula}33\right]$$\begin{array}{cc}\Delta r_p\left(n\right)=\exp j\left(p.Math.2\pi f_{\mathrm{IF}}T\right).Math.\exp j\left(X\right).Math.\underset{k=n+p}{\overset{n+p+D-1}{.Math.}}{\left\{t\left(k+1\right).Math.{t\left(k\right)}^{*}\right\}}^{*}& \left(33\right)\end{array}$

[0172] When the vector average of formula (33) is calculated, formula (34), shown below, is acquired.

[00024]$\left[\mathrm{Formula}34\right]$$\begin{array}{cc}\underset{n=0}{\overset{L}{.Math.}}{r}_p\left(n\right)\cong \exp j\left(-{\theta }_t+X\right).Math.\exp j\left(p.Math.2\pi f_{\mathrm{IF}}T\right)& \left(34\right)\end{array}$

[0173] (iii) When M=p, formula (35) is acquired from formula (29).

[Formula 35]

Δr.sub.p(n)=expj(p.Math.2πf.sub.IFT+X)  (35)

[0174] When the vector average of formula (35) is calculated, formula (36), shown below, is acquired.

[00025]$\left[\mathrm{Formula}36\right]$$\begin{array}{cc}\underset{n=0}{\overset{L}{.Math.}}\Delta r_p\left(n\right)\cong \exp j\left(X\right).Math.\exp j\left(p.Math.2\pi f_{\mathrm{IF}}T\right)& \left(36\right)\end{array}$

[0175] The differential calculation unit 54a performs a calculation in accordance with a predetermined arithmetic expression on the output values of each of the one-symbol delay differential component vector average calculation unit 51-n, . . . , and the P-symbol delay differential component vector average calculation unit 51-P using expj(θ.sub.t), output by the deviation angle calculation unit 42, and expj(X), output by the phase difference totaling unit 43a. Further, by performing this calculation, the differential calculation unit 54a calculates expj (2πf.sub.IFT), in which the frequency offset amount of each output value of the one-symbol delay differential component vector average calculation unit 51-n, . . . , and the P-symbol delay differential component vector average calculation unit 51-P is included in the phase.

[0176] (Processing of Frequency Offset Estimation Unit According to Second Embodiment)

[0177] Next, the processing performed by the frequency offset estimation unit 50a of the second embodiment will be described. FIG. 7 is a flowchart showing a flow of processing executed by the frequency offset estimation unit 50a. It is assumed that prior to the start of the processing shown in FIG. 7, the deviation angle calculation unit 42 of the training signal analysis unit 40a calculates expj(θ.sub.t) as a vector in which the prescribed deviation angle θ.sub.t is included in the phase on the basis of the training signal t(n) generated by the training signal generation unit 41a, and outputs the calculation result to the frequency offset estimation unit 50a. It is also assumed that the phase difference totaling unit 43a of the training signal analysis unit 40a calculates X on the basis of formula (25), calculates expj(X) as a vector in which X is included in the phase, and outputs expj(X) to the frequency offset estimation unit 50a.

[0178] Furthermore, an example in which M=3 and P=4 will be described below as an example.

[0179] The one-symbol delay differential component vector average calculation unit 51-1, the two-symbol delay differential component vector average calculation unit 51-2, a three-symbol delay differential component vector average calculation unit 51-3, and a four-symbol delay differential component vector average calculation unit 51-4 of the frequency offset estimation unit 50a take in the reception training signal r(n) output by the timing detection unit 60 (step Sa1).

[0180] The one-symbol delay differential component vector average calculation unit 51-1 performs similar processing to that of step S2-1 of the first embodiment so as to calculate the vector average of the one-symbol delay differential component of the reception training signal and output the result to the multiplier 53 and the differential calculation unit 54a (step Sa2-1).

[0181] In the two-symbol delay differential component vector average calculation unit 51-2, the two-symbol delay device 151-2, complex conjugator 152-2, and multiplier 153-2 calculate the two-symbol delay differential component Δr.sub.2(n) of the reception training signal on the basis of the reception training signal r(n+2) taken in thereby. The vector averaging device 154-2 calculates the sum of the two-symbol delay differential component Δr.sub.2(n) of the reception training signal added over the sequence length L as the vector average of the two-symbol delay differential component of the reception training signal. Here, since M=3 and p=2, p=M−1, and therefore formula (34) is applied. The two-symbol delay differential component vector average calculation unit 51-2 outputs the calculated vector average of the two-symbol delay differential component of the reception training signal to the multiplier 53 and the differential calculation unit 54a (step Sa2-2).

[0182] In the three-symbol delay differential component vector average calculation unit 51-3, a three-symbol delay device 151-3, a complex conjugator 152-3, and a multiplier 153-3 calculate a three-symbol delay differential component Δr.sub.3(n) of the reception training signal on the basis of a reception training signal r(n+3) taken in thereby. A vector averaging device 154-3 calculates the sum of the three-symbol delay differential component Δr.sub.3(n) of the reception training signal added over the sequence length L as the vector average of the three-symbol delay differential component of the reception training signal. Here, since M=3 and p=3, M=p, and therefore formula (36) is applied. The vector averaging device 154-3 outputs the calculated vector average of the three-symbol delay differential component of the reception training signal to the multiplier 53 and the differential calculation unit 54a (step Sa2-3).

[0183] In the four-symbol delay differential component vector average calculation unit 51-4, a four-symbol delay device 151-4, a complex conjugator 152-4, and a multiplier 153-4 calculate a four-symbol delay differential component Δr.sub.4(n) of the reception training signal on the basis of a reception training signal r(n+4) taken in thereby. A vector averaging device 154-4 calculates the sum of the four-symbol delay differential component Δr.sub.4(n) of the reception training signal added over the sequence length L as the vector average of the four-symbol delay differential component of the reception training signal. Here, since M=3 and p=4, p=M+1, and therefore formula (32) is applied. The vector averaging device 154-4 outputs the calculated vector average of the four-symbol delay differential component of the reception training signal to the multiplier 53 and the differential calculation unit 54a (step Sa2-4).

[0184] The complex conjugator 52 outputs the complex conjugate expj(−θ.sub.t) of expj(θ.sub.t), output by the deviation angle calculation unit 42 of the training signal analysis unit 40a, to the multiplier 53. The multiplier 53 performs the calculation of formula (11) on the basis of the vector average of the one-symbol delay differential component of the reception training signal, output by the one-symbol delay differential component vector average calculation unit 51-1, and expj(−θ.sub.t), output by the complex conjugator 52, and outputs the calculation result to the adder 55 (step Sa3-1).

[0185] The differential calculation unit 54a calculates (X−2θ.sub.t) as the predetermined angle determined in advance on the basis of expj(θ.sub.t) output by the deviation angle calculation unit 42 and expj (X) output by the phase difference totaling unit 43. The differential calculation unit 54a calculates the differential component between the vector average of the one-symbol delay differential component of the reception training signal, output by the one-symbol delay differential component vector average calculation unit 51-1, and the vector average of the two-symbol delay differential component of the reception training signal, output by the two-symbol delay differential component vector average calculation unit 51-2. The differential calculation unit 54a performs a calculation shown below in formula (37) to remove the predetermined angle from the differential component by multiplying expj(−X+2θ.sub.t), which is the complex conjugate of the vector in which the predetermined angle is included in the phase, by the calculated differential component. The differential calculation unit 54a outputs the calculation result to the adder 55 (step Sa3-2).

[00026]$\left[\mathrm{Formula}37\right]$$\begin{array}{cc}\underset{n=0}{\overset{L}{.Math.}}\Delta r_2\left(n\right).Math.{\left\{\underset{n=0}{\overset{L}{.Math.}}\Delta r_1\left(n\right)\right\}}^{*}.Math.\exp {j\left(X\right)}^{*}.Math.\exp j\left(2{\theta }_t\right)=\exp j\left(2\pi f_{\mathrm{IF}}T\right)& \left(37\right)\end{array}$

[0186] Note that formula (37) is identical to formula (22) of the first embodiment.

[0187] The differential calculation unit 54a sets (θ.sub.t), which is the deviation angle of expj(θ.sub.t) output by the deviation angle calculation unit 42, as the predetermined angle determined in advance. The differential calculation unit 54a calculates a differential component between the vector average of the two-symbol delay differential component of the reception training signal, output by the two-symbol delay differential component vector average calculation unit 51-2, and the vector average of the three-symbol delay differential component of the reception training signal, output by the three-symbol delay differential component vector average calculation unit 51-3. The differential calculation unit 54a performs a calculation shown below in formula (38) to remove the predetermined angle (θ.sub.t) from the differential component by multiplying expj(−θ.sub.t), which is the complex conjugate of the vector in which the predetermined angle is included in the phase, by the calculated differential component. The differential calculation unit 54a outputs the calculation result to the adder 55 (step Sa3-3).

[00027]$\left[\mathrm{Formula}38\right]\begin{array}{cc}\underset{n=0}{\overset{L}{.Math.}}\Delta r_3\left(n\right).Math.\exp {j\left({\theta }_t\right)}^{*}.Math.{\left\{\underset{n=0}{\overset{L}{.Math.}}\Delta r_2\left(n\right)\right\}}^{*}=\exp j\left(2\pi f_{\mathrm{IF}}T\right)& \left(38\right)\end{array}$

[0188] The differential calculation unit 54a sets (θ.sub.t), which is the deviation angle of expj(θ.sub.t) output by the deviation angle calculation unit 42, as the predetermined angle determined in advance. The differential calculation unit 54a calculates a differential component between the vector average of the three-symbol delay differential component of the reception training signal, output by the three-symbol delay differential component vector average calculation unit 51-3, and the vector average of the four-symbol delay differential component of the reception training signal, output by the four-symbol delay differential component vector average calculation unit 51-4. The differential calculation unit 54a performs a calculation shown below in formula (39) to remove the predetermined angle from the differential component by multiplying expj(−θ.sub.t), which is the complex conjugate of the vector in which the predetermined angle is included in the phase, by the calculated differential component. The differential calculation unit 54a outputs the calculation result to the adder 55 (step Sa3-4).

[00028]$\left[\mathrm{Formula}39\right]$$\begin{array}{cc}\underset{n=0}{\overset{L}{.Math.}}\Delta r_4\left(n\right).Math.\exp {j\left({\theta }_t\right)}^{*}.Math.{\left\{\underset{n=0}{\overset{L}{.Math.}}\Delta r_3\left(n\right)\right\}}^{*}=\exp j\left(2\pi f_{\mathrm{IF}}T\right)& \left(39\right)\end{array}$

[0189] The adder 55 adds the output value of the multiplier 53 to the output values of the differential calculation unit 54a. More specifically, the adder 55 adds together the calculation result generated by the right side of formula (11), the calculation result generated by the left side of formula (37), the calculation result generated by the left side of formula (38), and the calculation result generated by the left side of formula (39), and outputs the resulting addition value to the deviation angle device 56 (step Sa4). The deviation angle device 56 calculates the deviation angle of the addition value output by the adder 55 and outputs the calculated deviation angle to the frequency offset compensation processing unit 61 as the frequency offset amount (step Sa5).

[0190] Note that the processing of steps Sa3-1, Sa3-2, . . . , and Sa3-P may be performed either in parallel or in order of steps Sa3-1, Sa3-2, . . . , and Sa3-P.

[0191] According to the configuration of the second embodiment, described above, the frequency offset compensation unit 32a of the optical reception device 2a, which receives a coherent optical signal that includes a training signal, further calculates a p (where p is an integer of at least 2) symbol delay differential components and a (p+1)-symbol delay differential component of the reception training signal, and calculates a third vector in which the phase component of the predetermined angle, which is determined in advance on the basis of the prescribed angle, has been removed from the vector of the differential component between the respective vector averages of the p-symbol delay differential component and the (p+1)-symbol delay differential component of the reception training signal.

[0192] The frequency offset compensation unit 32a calculates the frequency offset amount by averaging the first vector and the second vector, which are described below, and the calculated third vector. The first vector is the vector of the differential component between the vector average of the one-symbol delay differential component of the reception training signal and the vector average of the one-symbol delay differential component of the training signal. The second vector is a vector in which the phase component of the predetermined angle, which is determined in advance on the basis of the prescribed angle and the total angle of the elements of the modulation phase difference included in the repeated pattern, has been removed from the vector of the differential component between the respective vector averages of the one-symbol delay differential component and the two-symbol delay differential component of the reception training signal.

[0193] Hence, in the second embodiment, the number of vectors subjected to averaging is larger than in the first embodiment, and therefore the noise component can be further reduced, with the result that the frequency offset amount can be calculated with an even higher degree of precision. Therefore, in the second embodiment, when the frequency offset amount is estimated with a similar degree of precision to the first embodiment, the length of the training code sequence for frequency offset estimation can be shortened in comparison with the first embodiment. As a result, likewise in the second embodiment, a frequency offset amount can be estimated with a high degree of precision in a digital coherent system using a training code sequence with a short sequence length.

[0194] Note that in the second embodiment, described above, when p>M, the p-symbol delay differential component Δt.sub.p(n) of the training signal can be generalized as shown below in formula (40).

[00029]$\left[\mathrm{Formula}40\right]$$\begin{array}{cc}\Delta t_p\left(n\right)=\exp j\left(\underset{k=0}{\overset{p-M}{.Math.}}{\mathrm{\Delta \theta }}_1\left(n+M+k\right)\right)& \left(40\right)\end{array}$

[0195] The vector average of the p-symbol delay differential component Δt.sub.p(n) of the training signal is expressed as shown below in formula (41).

[00030]$\left[\mathrm{Formula}41\right]$$\begin{array}{cc}\underset{n=0}{\overset{L}{.Math.}}\Delta t_p\left(n\right)=\underset{n=0}{\overset{L}{.Math.}}\exp j\left(\underset{k=0}{\overset{p-M}{.Math.}}{\mathrm{\Delta \theta }}_1\left(n+M+k\right)\right)=\exp j\left({\theta }_p\right)& \left(41\right)\end{array}$

[0196] In formula (41), θ.sub.p is the deviation angle of the vector acquired when the p-symbol delay differential component Δt.sub.p(n) of the training signal is added over the sequence length L of the training code sequence for frequency offset estimation.

[0197] Here, formula (42) is defined as follows.

[00031]$\left[\mathrm{Formula}42\right]$$\begin{array}{cc}\underset{n=0}{\overset{L}{.Math.}}\Delta t_q\left(n\right)=\exp j\left({\theta }_{\mathrm{tq}}\right)& \left(42\right)\end{array}$

[0198] In the case of M+1, θ.sub.p becomes “θ.sub.p=X+θ.sub.t”. Further, in the case of M+2, θ.sub.p becomes “θ.sub.p=X+θ.sub.t2”. Furthermore, in the case of M−2, θ.sub.p becomes “θ.sub.p=X−θ.sub.t2”.

[0199] In other words, when p>M, by setting q=p−M, “θ.sub.p” can be expressed by formula (43) below.

[Formula 43]

θ.sub.p=X+θ.sub.tq  (43)

[0200] When formula (43) is used, formula (32) in a case where p=M+1 can be generalized to p>M and expressed by formula (44) below.

[00032]$\left[\mathrm{Formula}44\right]$$\begin{array}{cc}\underset{n=0}{\overset{L}{.Math.}}\Delta r_p\cong \exp j\left({\theta }_p\right).Math.\exp j\left(q.Math.2\pi f_{\mathrm{IF}}T\right)=\exp j\left(X+{\theta }_{\mathrm{tq}}+q.Math.2\pi f_{\mathrm{IF}}T\right)& \left(44\right)\end{array}$

[0201] Furthermore, in the second embodiment, the frequency offset amount is averaged by adding together formula (11), formula (37), formula (38), and formula (39), but the configuration of the present invention is not limited to this embodiment, and the frequency offset amount may be averaged using any desired combination of formulae, for example by adding together only formula (11) and formula (38), adding together only formula (11) and formula (39), and so on.

[0202] Moreover, in the first and second embodiments described above, the training signal generation unit 41, 41a stores the number of elements included in the repeated pattern of the modulation phase difference Δθ.sub.1(n) in an internal storage area, but instead, the phase difference totaling unit 43, 43a may detect the number of elements.

[0203] Furthermore, in the first and second embodiments described above, the frequency offset compensation unit 32, 32a includes the training signal analysis unit 40, 40a, but the configuration of the present invention is not limited to this embodiment. Instead, for example, the vector expj(θ.sub.t) in which θ.sub.t is included in the phase and the vector expj(X) in which X is included in the phase may be calculated and stored in advance in an internal storage area of the frequency offset estimation unit 50, 50a. Then, when the frequency offset estimation unit 50, 50a performs the processing for estimating the frequency offset amount, the complex conjugator 52 and the differential calculation unit 54, 54a may refer to the vectors expj(θ.sub.t) and expj(X) stored in the internal storage area. By employing this configuration, the frequency offset compensation unit 32, 32a can be formed without the training signal analysis unit 40, 40a.

[0204] In the embodiments described above, the frame generation unit 10, 10a of the optical transmission device 1, la and the digital signal processing unit 23, 23a of the optical reception device 2, 2a may be realized by a computer. In this case, a program for realizing the functions thereof may be recorded on a computer-readable recording medium, and the aforesaid units may be realized by causing a computer system to read and execute the program recorded on the recording medium. Note that here, the “computer system” is assumed to include an OS and hardware such as peripheral devices. Further, the “computer-readable recording medium” is a portable medium such as a flexible disk, a magneto-optical disk, a ROM, or a CD-ROM, or a storage device such as a hard disk installed in the computer system. The “computer-readable recording medium” may also be a medium that holds the program dynamically for a short time, such as a communication line in a case where the program is transmitted over a network such as the Internet or a communication line such as a telephone line, or a medium that holds the program for a fixed time, such as a volatile memory installed in the computer system of a server or a client in the aforesaid case. Furthermore, the program may be a program for realizing some of the functions described above or a program that can realize the functions described above in combination with a program already recorded on the computer system, and may also be realized using a programmable logic device such as an FPGA (Field Programmable Gate Array).

[0205] Embodiments of this invention were described in detail above with reference to the figures, but the specific configurations are not limited to these embodiments and also include designs and the like within a scope that does not depart from the spirit of the invention.

REFERENCE SIGNS LIST

[0206] 1 Optical transmission device [0207] 2 Optical reception device [0208] 3 Optical transmission path [0209] 10 Frame generation unit [0210] 11 IQ signal generation unit [0211] 12 Optical coherent transmission unit [0212] 20 Optical coherent reception unit [0213] 21 Local oscillator [0214] 22 ADC [0215] 23 Digital signal processing unit [0216] 24 Output unit [0217] 31 Equalizer [0218] 32 Frequency offset compensation unit [0219] 33 Phase offset compensation unit