Signal processing device, signal processing method, and recording medium

Abstract

This signal processing device comprises: a plurality of linear filters that remove interference and that include a first linear filter to which a reception signal and an auxiliary first input signal are inputted and which outputs an output signal and an auxiliary first output signal, and a second linear filter to which an auxiliary second input signal is inputted and which outputs an auxiliary second output signal; a signal equalization unit having a nonlinear signal conversion unit that converts a signal to be converted, in accordance with the modulation scheme of a transmission signal corresponding to the reception signal, and a phase shift unit that shifts the phase of a signal to be shifted; and a phase noise removal unit that estimates a phase fluctuation relating to the output signal. The phase shift unit shifts the phase of the signal to be shifted, in accordance with the estimated phase fluctuation, the auxiliary first output signal outputted by the first linear filter is inputted to the nonlinear signal conversion unit via the phase shift unit, the signal outputted by the nonlinear signal conversion unit is inputted as the auxiliary second input signal to the second linear filter via the phase shift unit, and the auxiliary second output signal outputted by the second linear filter is inputted as the auxiliary first input signal to the first linear filter.

Description

Signal processing device, signal processing method, and recording medium

[0001] The present disclosure relates to a signal processing device, a signal processing method, and a recording medium in a transmission system that performs communication using a carrier wave that includes phase fluctuations via a transmission path with interference.

[0002] Demand for information transmission systems using optical fiber transmission technology or wireless transmission technology as communication infrastructure is increasing. As demand for information transmission systems increases, there is a demand for larger transmission capacities. Under these circumstances, transmission technology using multi-core optical fibers having multiple cores is attracting attention in optical fiber transmission. Coupled multi-core fiber (MCF) technology increases communication capacity by allowing crosstalk (XT) between cores and increasing core density. There are expectations for the introduction of MCF technology into long-distance transmission systems such as optical submarine cables.

[0003] In coupled MCF transmission, a digital signal processing technique is essential to estimate with high accuracy the transmitted signal corresponding to the received signal from the received signal affected by various noises, thereby enabling a reduction in the bit error rate (BER). This is similar to the digital signal processing in multi-antenna signal transmission, which simultaneously uses multiple antennas to perform high-capacity wireless transmission.

[0004] Various noises include signal interference, typified by XT between cores, and phase fluctuations. In high-capacity communication systems, equalization processing plays a major role in removing the effects of various types of interference during signal transmission, and improving its accuracy significantly contributes to increasing the capacity and reach of transmission systems. One known equalization processing technique for interference removal is an adaptive linear filter, which adaptively controls filter coefficients according to the interference conditions on the transmission path. Patent Document 1 discloses, as an example of nonlinear equalization technology that contributes to extending the reach of coupled MCF transmission, an adaptive nonlinear equalization technology consisting of a linear filter group and a nonlinear transformation, in which the tap coefficients of the linear filter group are adaptively controlled to match the transmission path.

[0005] Japanese Patent Application Laid-Open No. 2023-035921

[0006] Nonlinear equalization, which involves nonlinear signal processing, significantly improves the immunity of transmission signals to interference. However, there is a problem in that its accuracy deteriorates when there is phase fluctuation in the transmission signal. Phase fluctuation is phase noise, which is the modulation of oscillator noise. In particular, to apply nonlinear equalization, which adaptively controls filter tap coefficients to match the transmission path, it is necessary to estimate the phase in advance and remove the effects of phase noise.

[0007] However, in some systems, such as optical fiber transmission, it may be difficult to remove the effects of phase noise before equalization processing that removes interference. For this reason, it is common to perform phase noise removal after interference removal. This processing order is not a problem when equalization processing is performed using a linear filter, but it becomes an issue that must be resolved when nonlinear equalization processing is used. Note that similar issues exist not only in optical fiber transmission systems, but also in transmission systems that perform wireless communication. An object of this disclosure is to provide a signal processing device, a signal processing method, and a recording medium that can solve the above-mentioned technical problems.

[0008] One aspect of a signal processing device includes a first linear filter that receives a received signal and an auxiliary first input signal and outputs an output signal and an auxiliary first output signal, and a second linear filter that receives an auxiliary second input signal and outputs an auxiliary second output signal, and is equipped with a plurality of linear filters that remove interference, a signal equalization unit that has a nonlinear signal conversion unit that converts a signal to be converted in accordance with a modulation method of a transmission signal corresponding to the received signal, and a phase shift unit that shifts the phase of the signal to be shifted, and a phase noise removal unit that estimates a phase fluctuation related to the output signal, wherein the phase shift unit shifts the phase of the signal to be shifted in accordance with the estimated phase fluctuation, the auxiliary first output signal output by the first linear filter is input to the nonlinear signal conversion unit via the phase shift unit, the signal output by the nonlinear signal conversion unit is input to the second linear filter via the phase shift unit as the auxiliary second input signal, and the auxiliary second output signal output by the second linear filter is input to the first linear filter as the auxiliary first input signal.

[0009] One aspect of the signal processing method includes estimating a phase fluctuation for a signal output by a linear filter, shifting the phase of the signal output by the pre-linear filter in accordance with the phase fluctuation, converting the shifted signal in accordance with a modulation scheme of a transmission signal corresponding to a received signal input to the pre-linear filter, shifting the phase of the converted signal in accordance with the phase fluctuation, and inputting the shifted signal to the linear filter.

[0010] One aspect of the recording medium has recorded thereon a computer program that causes a computer to execute a signal processing method, including estimating a phase fluctuation related to a signal output by a linear filter, shifting the phase of the signal output by the pre-linear filter in accordance with the phase fluctuation, converting the shifted signal in accordance with a modulation method of a transmission signal corresponding to a received signal input to the pre-linear filter, shifting the phase of the converted signal in accordance with the phase fluctuation, and inputting the shifted signal to the linear filter.

[0011] According to each aspect of the above-described signal processing device, signal processing method, and recording medium, it is possible to improve the accuracy of estimating a transmitted signal.

[0012] Fig. 1 is a block diagram showing the configuration of a transmission system in this embodiment. Fig. 2 is a block diagram showing the configuration of a signal processing device in this embodiment. Fig. 3 is a block diagram showing the configuration of a signal processing device in this embodiment. Fig. 4 is a diagram showing the relationship between input and output in a nonlinear function. Fig. 5 is a block diagram showing the configuration of a signal processing device in this embodiment. Fig. 6 is a block diagram showing the configuration of a signal processing device in this embodiment. Fig. 7 is a block diagram showing the configuration of a signal processing device in this embodiment. Fig. 8 is a diagram showing the relationship between input and output in a nonlinear function.

[0013] Hereinafter, embodiments of a signal processing device, a signal processing method, and a recording medium will be described with reference to the drawings. However, this disclosure is not limited to the embodiments described below. [1: First Embodiment]

[0014] A first embodiment of a signal processing device, a signal processing method, and a computer program will be described. [1-1: Configuration of the transmission system SYS]

[0015] First, the overall configuration of the transmission system SYS in this embodiment will be described with reference to Fig. 1. Fig. 1 is a block diagram showing the configuration of the transmission system SYS in this embodiment.

[0016] As shown in Fig. 1, the transmission system SYS includes a transmitter 1 and a receiver 2. The transmitter 1 transmits a transmission signal to the receiver 2 via a transmission path 3. The receiver 2 receives the transmission signal transmitted from the transmitter 1 as a received signal y via the transmission path 3. The transmission signal is made up of a pre-set number of quadrature amplitude modulation (QAM) signal points.

[0017] To receive the reception signal y, the receiving device 2 includes a signal processing device 10 and a storage device 4. The signal processing device 10 may include at least one of a CPU (Central Processing Unit), a GPU (Graphic Processing Unit), and an FPGA (Field Programmable Gate Array). The signal processing device 10 may load a computer program. For example, the signal processing device 10 may load a computer program stored in the storage device 4. For example, the signal processing device 10 may load a computer program stored in a computer-readable recording medium using a recording medium reading device (not shown). The signal processing device 10 may acquire (i.e., download or load) the computer program from a device (not shown) located outside the receiving device 2 via a communication device (not shown). The signal processing device 10 executes the loaded computer program. As a result, a logical functional block for executing the operation to be performed by the receiving device 2 is realized within the signal processing device 10. Specifically, a logical functional block for executing the receiving operation of receiving the received signal y is realized within the signal processing device 10. In other words, the signal processing device 10 can function as a controller for realizing the logical functional block for executing the operation to be performed by the receiving device 2.

[0018] The storage device 4 can store desired data. For example, the storage device 4 may temporarily store a computer program executed by the signal processing device 10. The storage device 4 may temporarily store data that the signal processing device 10 temporarily uses when the signal processing device 10 is executing a computer program. The storage device 4 may store data that the receiving device 2 stores for a long period of time. The storage device 4 may include at least one of a RAM (Random Access Memory), a ROM (Read Only Memory), a hard disk device, a magneto-optical disk device, an SSD (Solid State Drive), and a disk array device.

[0019] In order to transmit a transmission signal, the transmitting device 1 may include a signal processing device and a storage device. The signal processing device included in the transmitting device 1 may function in the same manner as the signal processing device 10 described above. The storage device included in the transmitting device 1 may function in the same manner as the storage device 4 described above.

[0020] The transmission system SYS according to this embodiment transmits information by means of a carrier wave containing phase fluctuations over a transmission path with interference and noise.

[0021] The receiving device 2 performs signal estimation processing to estimate a transmitted signal from the received signal y as at least a part of the receiving operation. [1-2: Configuration of the receiving device 2 (signal processing device 10)]

[0022] The configuration of the receiving device 2 that performs the signal estimation process (particularly the configuration of the signal processing device 10) will be described with reference to Fig. 2. Fig. 2 is a block diagram showing logical functional blocks realized in the signal processing device 10 for performing the signal estimation process.

[0023] As shown in FIG. 2, the signal processing device 10 includes, as logical functional blocks for performing signal estimation processing, a nonlinear equalization unit 101, which is a specific example of a "signal equalization unit" described in the appendix below, and a phase noise elimination unit 140. The nonlinear equalization unit 101 includes a linear filter 110-1, a linear filter 110-2, a nonlinear signal conversion unit 120, a phase shift unit 130-, and a phase shift unit 130+. The linear filter 110-1 and the linear filter 110-2 included in the nonlinear equalization unit 101 remove interference from the received signal. The linear filter 110-1 and the linear filter 110-2 are connected in a ring shape. The nonlinear signal conversion unit 120 is provided between the linear filter 110-1 and the linear filter 110-2. The nonlinear signal conversion unit 120, the phase shift unit 130-, and the phase shift unit 130+ may be collectively referred to as the nonlinear conversion unit 121.

[0024] The phase noise elimination unit 140 estimates and compensates for phase fluctuations related to the output signal output from the nonlinear equalization unit 101. The phase noise elimination unit 140 outputs phase information related to the phase fluctuations to the nonlinear equalization unit 101. The phase information may include a phase shift amount. The phase noise elimination unit 140 also outputs an estimated transmission signal obtained by removing the phase fluctuations from the output signal output from the nonlinear equalization unit 101.

[0025] The phase shift unit 130- shifts the phase of the signal input to the nonlinear signal converter 120. The phase shift unit 130- may rotate the phase of the signal input to the nonlinear signal converter 120. The phase shift unit 130- adjusts the phase of the signal input to the nonlinear signal converter 120 in accordance with phase information provided from the phase noise elimination unit 140. The phase shift unit 130+ shifts the phase of the signal output from the nonlinear signal converter 120. The phase shift unit 130+ may rotate the phase of the signal output from the nonlinear signal converter 120. The phase shift unit 130+ adjusts the phase of the signal output from the nonlinear signal converter 120 in accordance with phase information provided from the phase noise elimination unit 140.

[0026] The linear filter 110-1, phase shift unit 130-, nonlinear signal conversion unit 120, phase shift unit 130+, and linear filter 110-2 are connected in a ring. The nonlinear equalization unit 101 is configured to perform iterative processing. In other words, FIG. 2 shows an example of the configuration of an iterative processing type nonlinear equalization mechanism. The nonlinear equalization unit 101 has as its basic component a repetition of the linear filter 110 and the nonlinear signal conversion unit 120 following the linear filter 110.

[0027] In order to avoid complexity, components not directly related to this embodiment are omitted from Fig. 2. Fig. 2 merely shows conceptually (in other words, simply) logical functional blocks for performing signal estimation processing. In other words, the functional blocks shown in Fig. 2 do not need to be implemented as they are in the signal processing device 10, and the configuration of the functional blocks implemented in the signal processing device 10 is not limited to the configuration shown in Fig. 2 as long as the signal processing device 10 can perform the signal estimation processing performed by the functional blocks shown in Fig. 2. [1-3: Flow of Equalization Processing and Phase Noise Removal Processing]

[0028] The flow of the equalization process in this embodiment will be described with reference to FIG.

[0029] A received signal transmitted by a carrier wave containing phase fluctuation (represented as θ(t)) via an interference-affected transmission path is input to the nonlinear equalizer 101. In the following, to clearly show the effect of the phase fluctuation, the received signal will be represented by the symbol y(t, y(t, θ(t))). Note that t is an index representing time, but in the following, the notation of the time index (t) may be omitted to avoid complexity. Also, the received signal is represented by a complex number. Note that what can be observed as the received signal is y(t, θ(t)), and when observing the received signal, the phase fluctuation θ(t) is unknown.

[0030] The received signal y(t, θ(t)) input to the nonlinear equalization unit 101 is input to the linear filter 110-1. The input signals to the linear filter 110-1 include the received signal y and the signal output by the linear filter 110-2. In the first iterative process, the signal output by the linear filter 110-2 is assumed to be initialized to zero. Therefore, in the first iterative process, the received signal y(t, θ(t)) can be considered as the signal input to the linear filter 110-1.

[0031] The filter action of the linear filter 110-1 is represented as f(·). In this case, the signal output by the linear filter 110-1 can be represented as f(y(t, θ(t))). The received signal from which the influence of phase fluctuation has been removed is represented as y(t, 0). In this case, the signal f(y(t, θ(t))) output by the linear filter 110-1 is generally approximated by the following [Equation 1]. [Equation 1]

[0032] The signal output by the linear filter 110-1 can be regarded as a signal obtained by multiplying a signal f(y(t,0)) obtained by inputting a signal y(t,0) that is not affected by phase fluctuation into the linear filter by the phase fluctuation term exp(jθ(t)). Here, j represents the imaginary unit √-1, and exp represents an exponential function with Napier's constant as the base. The signal output from the linear filter 110-1 has its phase shifted by the phase shift unit 130-, and is input to the nonlinear signal conversion unit 120. The phase shift unit 130- shifts the phase in accordance with the phase information output from the phase noise elimination unit 140.

[0033] The phase noise elimination unit 140 outputs an estimated value of the phase fluctuation θ(t). Hereinafter, the estimated value of the phase fluctuation θ(t) will be referred to as θ － The signal input to the nonlinear signal transform unit 120 is expressed as exp(j(θ(t))-θ － f(y(t), 0). Furthermore, θ(t) ≈ θ － When f(y(t), the signal input to the nonlinear signal transformer 120 can be approximated to f(y(t), 0). Furthermore, the signal output from the nonlinear signal transformer 120 is subjected to a phase rotation by the phase shifter 130+ in the opposite direction to the phase rotation by the phase shifter 130-. The signal output from the phase shifter 130+ is approximately equal to the signal expressed in the following [Equation 2]. [Equation 2]

[0034] In the above [Equation 2], π(•) represents the action of the nonlinear signal conversion unit 120. The signal output from the phase shift unit 130+ expressed in the above [Equation 2] is input to the linear filter 110-2. Therefore, similar to the case of the signal output from the linear filter 110-1, the signal input to the linear filter 110-2 can be considered to be approximately equal to the signal obtained by multiplying the signal π(f(y(t,0))) obtained as a result of processing the received signal y(t,0) that is not affected by phase fluctuation, by the phase fluctuation term exp(jθ(t)).

[0035] Next, when the action of the linear filter 110-2 is denoted as g(·), the signal output from the linear filter 110-2 is the signal shown on the left side of the following [Equation 3]. Due to the linearity of the linear filter 110-2, the signal output from the linear filter 110-2 is approximately equal to the right side of the following [Equation 3]. [Equation 3]

[0036] The signal output from linear filter 110-2 shown in [Equation 3] above is input to linear filter 110-1. This is the first iterative process in nonlinear equalization unit 101. Note that the signal output from linear filter 110-2 shown in [Equation 3] above can also be regarded as a signal obtained by multiplying the result of processing a signal without phase fluctuation by the phase fluctuation term exp(jθ(t)).

[0037] In the second iterative process, in addition to the received signal y(t, θ(t)), the signal output from the linear filter 110-2 is used. When the linear filter 110-1 is applied to the result of adding the received signal y(t, θ(t)) and the signal output from the linear filter 110-2, the signal output from the linear filter 110-1 can be approximated as shown in the following [Equation 4], for example. [Equation 4]

[0038] Similarly, the signal shown in the above [Equation 4] can be regarded as a signal obtained by multiplying the result of processing a signal without phase fluctuation by the phase fluctuation term exp(jθ(t)). Similarly, the output signal obtained after performing the process a predetermined number of times can be regarded as a signal obtained by multiplying the result of processing a signal without phase fluctuation by the phase fluctuation term exp(jθ(t)). This can be realized by providing a phase shift unit 130- that shifts the phase of the signal input to the nonlinear signal conversion unit 120, and a phase shift unit 130+ that shifts the phase of the signal output from the nonlinear signal conversion unit 120. The phase shift units 130- and 130+ shift the phase according to the phase information output by the phase noise elimination unit 140.

[0039] In this way, the signal undergoing equalization processing can be regarded as a signal obtained by multiplying the result of processing a signal without phase fluctuation by a term of phase fluctuation. Therefore, the desired result can be obtained. [2: Second embodiment]

[0040] A second embodiment of a signal processing device, a signal processing method, and a recording medium will be described below. Hereinafter, the second embodiment of a signal processing device, a signal processing method, and a recording medium will be described using a signal processing device 20 according to this disclosure. [2-1: Configuration of the signal processing device 20]

[0041] The configuration of the signal processing device 20 that performs the signal estimation processing will be described with reference to Fig. 3. Fig. 3 is a block diagram showing logical functional blocks realized in the signal processing device 20 for performing the signal estimation processing.

[0042] As shown in FIG. 3, the signal processing device 20 has a linear filter 210, a nonlinear signal conversion unit 220, a phase shift unit 230−, a phase shift unit 230+, and a phase noise elimination unit 240. Each of the linear filters 210 receives a received signal and an auxiliary input signal, and outputs an output signal and an auxiliary output signal. Each of the linear filters 210 may be a combination of the linear filter 110-1 and the linear filter 110-2 described above. As shown in FIG. 3, the linear filter 210, the nonlinear signal conversion unit 220, and the phase noise elimination unit 240 included in the signal processing device 20 are connected alternately in tandem. The second embodiment shows an example of a pipeline processing type configuration.

[0043] The signal processing device 20 includes a phase shift unit 230- on the input side of the nonlinear signal conversion unit 220, and a phase shift unit 230+ on the output side of the nonlinear signal conversion unit 220. The phase shift unit 230- adjusts the phase of the signal input to the nonlinear signal conversion unit 220 in accordance with phase information provided from the phase noise elimination unit 240. The phase shift unit 230+ adjusts the phase of the signal output from the nonlinear signal conversion unit 220 in accordance with phase information provided from the phase noise elimination unit 240. The nonlinear signal conversion unit 220, the phase shift unit 230-, and the phase shift unit 230+ may be collectively referred to as the nonlinear conversion unit 221. In the second embodiment, the basic components are a linear filter 210, and a repetition of a nonlinear conversion unit 221 and a phase noise elimination unit 240 following the linear filter 210.

[0044] The signal processing device 20 includes M (M is a positive integer) linear filters 210, M phase noise elimination units 240, and M−1 nonlinear conversion units 221 (M−1 sets of phase shift units 230−, nonlinear signal conversion units 220, and phase shift units 230+). That is, the signal processing device 20 is provided with the same number of phase noise elimination units 240 as the linear filters 210. The kth (k is an integer greater than or equal to 1 and less than M) linear filter 210 outputs a signal to the kth phase noise elimination unit 240 and the kth nonlinear conversion unit 221. Furthermore, the phase shift unit 230− arranged on the input side of the kth nonlinear signal conversion unit 220 and the phase shift unit 230+ arranged on the output side perform processing using phase information supplied from the kth phase noise elimination unit 240. Furthermore, the Mth phase noise elimination unit 240, to which the output signal of the Mth linear filter 210 is input, outputs a final transmission signal estimation result.

[0045] In order to avoid complexity, components not directly related to this embodiment are omitted from Fig. 3. Fig. 3 merely shows conceptually (in other words, simply) logical functional blocks for performing nonlinear equalization processing. In other words, the functional blocks shown in Fig. 3 do not need to be implemented as they are in the signal processing device 20, and the configuration of the functional blocks implemented in the signal processing device 20 is not limited to the configuration shown in Fig. 3 as long as the signal processing device 20 can perform the nonlinear equalization processing performed by the functional blocks shown in Fig. 3. [2-2: Nonlinear Signal Conversion]

[0046] Fig. 4 shows an example of the nonlinear signal converter 220. As shown in Fig. 4, the nonlinear signal converter 220 has a nonlinear function 200. A signal input to the nonlinear signal converter 220 is expressed as a complex number. The nonlinear signal converter 220 maps each of the real and imaginary parts of the input signal using the nonlinear function 200. The nonlinear signal converter 220 outputs each of the mapping results as a complex signal with a real part and an imaginary part.

[0047] The relationship between the input and output of the nonlinear function 200 may be determined depending on the modulation method of the transmission signal. In other words, the nonlinear function 200 may be determined depending on the modulation method of the transmission signal. Graphs 202 and 203 illustrated in FIG. 4 are graphs illustrating the relationship between the input signal and the output signal of the nonlinear function 200.

[0048] Graph 202 shows an example of the relationship between input and output in nonlinear signal conversion unit 220 when the modulation method of the transmission signal is QPSK (Quadrature Phase Shift Keying), in which the transmission signal is represented by four points on the complex plane: +1+√(-1), +1-√(-1), -1+√(-1), -1-√(-1). Graph 203 shows an example of the relationship between the input and output of nonlinear signal conversion unit 220 when the modulation method of the transmission signal is 16QAM (Quadrature Amplitude Modulation) method, in which the transmission signal is represented by 16 points on the complex plane: (+3+3√(-1), +3-3√(-1), -3+3√(-1), -3-3√(-1), +3+√(-1), +3-√(-1), -3+√(-1), -3-√(-1), +1+3√(-1), +1-3√(-1), -1+3√(-1), -1-3√(-1), 1+√(-1), 1-√(-1), -1+√(-1), -1-√(-1)). [2-3: Phase Shift]

[0049] The signal processing device 20 is configured by expanding the repetitive processing exemplified in the first embodiment into a pipelined form. The kth phase shift unit 230- shifts the phase of the signal input to the kth nonlinear signal transform unit 220 in accordance with the phase information provided from the kth phase noise elimination unit 240. The kth phase shift unit 230+ shifts the phase of the signal output from the kth nonlinear signal transform unit 220 in accordance with the phase information provided from the kth phase noise elimination unit 240. [3: Third Embodiment]

[0050] A third embodiment of a signal processing device, a signal processing method, and a recording medium will be described below. A third embodiment of a signal processing device, a signal processing method, and a recording medium will be described below using a signal processing device 30 according to this disclosure.

[0051] The configuration of the signal processing device 30 that performs the signal estimation processing will be described with reference to Fig. 5. Fig. 5 is a block diagram showing logical functional blocks realized in the signal processing device 30 for performing the signal estimation processing.

[0052] The third embodiment also has a basic component consisting of a linear filter 310 and a nonlinear signal converter 320 following the linear filter 310, repeated. The third embodiment differs from the second embodiment in the arrangement of the phase noise elimination unit 340. That is, the signal processing device 30 has a phase noise elimination unit 340 arranged only in the final stage. The signal processing device 30 uniformly inputs phase information provided by the phase noise elimination unit 340 arranged in the final stage to each phase shift unit 330. The phase shift unit 330- arranged on the input side of the kth nonlinear signal converter 320 and the phase shift unit 330+ arranged on the output side perform processing according to common phase information supplied from the phase noise elimination unit 340 in the final stage. The nonlinear signal converter 320, the phase shift unit 330-, and the phase shift unit 330+ may be collectively referred to as the nonlinear converter 321. When the time change of the phase fluctuation θ(t) is gradual compared to the signal modulation speed, a configuration in which only one phase noise elimination unit 340 is arranged in the final stage is considered effective.

[0053] In order to avoid complexity, components not directly related to this embodiment are omitted from Fig. 5. Fig. 5 merely shows conceptually (in other words, simply) logical functional blocks for performing nonlinear equalization processing. In other words, the functional blocks shown in Fig. 5 do not need to be implemented as they are in the signal processing device 30, and the configuration of the functional blocks implemented in the signal processing device 30 is not limited to the configuration shown in Fig. 5 as long as the signal processing device 30 can perform the nonlinear equalization processing performed by the functional blocks shown in Fig. 5. [4: Fourth Embodiment]

[0054] A fourth embodiment of a signal processing device, a signal processing method, and a recording medium will be described. Hereinafter, the fourth embodiment of a signal processing device, a signal processing method, and a recording medium will be described using a signal processing device 40 according to this disclosure. [4-1: Configuration of the signal processing device 40]

[0055] The configuration of the signal processing device 40 that performs the signal estimation processing will be described with reference to Fig. 6. Fig. 6 is a block diagram showing logical functional blocks realized in the signal processing device 40 for performing the signal estimation processing.

[0056] 6, the signal processing device 40 includes a nonlinear equalizer 401 and a phase noise elimination unit 440. The phase noise elimination unit 440 may be a configuration example of a phase-locked loop (PLL) device. The phase noise elimination unit 440 includes a phase shift unit 430-2 as a second phase shift unit, a signal determination unit 441, a phase detection unit 442, a filter 443, and an accumulator 444.

[0057] The phase shift unit 430-2 shifts the phase of the output signal output by the nonlinear equalization unit 401. The signal determination unit 441 determines the nearest transmission signal point from multiple transmission signal points specified by the modulation scheme that is closest to the estimated transmission signal output by the phase shift unit 430-2. The signal determination unit 441 outputs a differential signal indicating the difference between the output signal output by the nonlinear equalization unit 401 and the nearest transmission signal point. The phase detection unit 442 detects the phase of the differential signal. The filter 443 suppresses noise components in the phase detected by the phase detection unit 442. The cumulative addition unit 444 cumulatively adds the output of the filter 443 and outputs phase information.

[0058] In Fig. 6, to avoid complexity, descriptions of components that are not directly related to this embodiment are omitted. Also, Fig. 6 merely shows conceptually (in other words, simply) logical functional blocks for performing signal estimation processing. In other words, the functional blocks shown in Fig. 6 do not need to be implemented as they are in the signal processing device 40, and as long as the signal processing device 40 can perform the signal estimation processing performed by the functional blocks shown in Fig. 6, the configuration of the functional blocks implemented in the signal processing device 40 is not limited to the configuration shown in Fig. 6. [4-2: Estimation result θ of phase fluctuation θ(t+1) － (t+1) Acquisition Flow]

[0059] The phase noise elimination unit 440 estimates and compensates for phase fluctuations in the input signal. The phase noise elimination unit 440 also eliminates noise related to the phase fluctuations. As an example, a configuration example using a phase-locked loop will be described. The input signal to the phase noise elimination unit 440 is the signal output by the nonlinear equalization unit 401. The signal input to the phase noise elimination unit 440 is first input to the phase shift unit 430-2. The phase shift unit 430-2 rotates the phase of the input signal to the phase noise elimination unit 440 in accordance with the estimation result output from the cumulative addition unit 444. The cumulative addition unit 444 outputs the result of estimating the phase fluctuation θ(t) using the input signal prior to time t. Specifically, the cumulative addition unit 444 calculates the estimated value θ of the phase fluctuation described above. － (t) is estimated.

[0060] The phase shift unit 430-2 calculates exp(jθ － The signal obtained by multiplying by (t)) is an estimate of the transmission signal at time t (estimated transmission signal). The transmission signal is a complex value specified by the modulation method used. For example, in the example where the modulation method is the above-mentioned QPSK modulation, the transmission signal is one of the four points {±1±j}, and in the example where the modulation method is the above-mentioned 16-QAM method, the transmission signal is one of the 16 points {±3±3j, ±3±j, ±1±3j, ±1±j}. The phase shift unit 430-2 outputs the phase-shifted result to the signal determination unit 441.

[0061] The signal determination unit 441 calculates the closest transmission signal point (referred to as the "closest transmission signal point") from among multiple transmission signal points specified by the modulation scheme described above, to the estimated transmission signal output by the phase shift unit 430-2. The signal determination unit 441 outputs the closest transmission signal point as the transmission signal estimation result. The signal determination unit 441 outputs the difference between the transmission signal estimation result and the input signal to the phase noise elimination unit 440 (the output signal of the nonlinear equalization unit 401) as a differential signal to the phase detection unit 442.

[0062] The phase detector 442 detects the phase of the input signal and outputs it. That is, the phase detector 442 outputs the phase of the differential signal. The output signal of the phase detector 442 is passed through a filter 443, which suppresses noise components. The output signal of the phase detector 442, from which noise components have been suppressed, is input to the cumulative adder 444. The cumulative adder 444 calculates and outputs a cumulative sum of the input signal in time series. That is, the cumulative adder 444 internally stores the output signal θ － (t), and the input signal and the output signal θ － (t) to obtain the output signal θ － (t+1) is calculated, and the output signal θ － (t+1) is stored in a register.

[0063] As described above, the signal obtained through the phase detector 442, the filter 443, and the cumulative adder 444 is the estimated result θ of the phase fluctuation θ(t+1) at the next time point t+1. － (t+1). [5: Fifth embodiment]

[0064] A fifth embodiment of a signal processing device, a signal processing method, and a recording medium will be described. Hereinafter, a third embodiment of a signal processing device, a signal processing method, and a recording medium will be described using a nonlinear equalizer 501 included in the signal processing device according to this disclosure. [5-1: Configuration of the nonlinear equalizer 501]

[0065] The configuration of the nonlinear equalizer 501 that performs the linear filter coefficient update process will be described with reference to Fig. 7. Fig. 7 is a block diagram showing logical functional blocks realized within the nonlinear equalizer 501 for performing the linear filter coefficient update process. As shown in Fig. 7, the nonlinear equalizer 501 has a linear filter unit 511 and a nonlinear error backpropagation unit 520.

[0066] The linear filter unit 511 includes a linear filter 510, a filter coefficient update unit 512, and an error backpropagation unit 513. The linear filter 510 includes a register 5101, a multiplier 5102, a storage unit 5103, and an adder 5104. The linear filter 510 calculates the filter coefficient (w ０ , w １ , ..., w Ｌ－１ ) and the input signal.

[0067] The filter coefficient update unit 512 updates the filter coefficients of the linear filter 510 based on the output signal error ∇e(t) representing the error of the output signal z(t) of the linear filter 510. The filter coefficient update unit 512 includes a buffer 5121, a multiplier 5122, and a register 5123.

[0068] The error backpropagation unit 513 outputs an input signal error representing the error of the input signal input to the linear filter 510 based on the output signal error ∇e(t). In other words, the error backpropagation unit 513 calculates an error signal for the signal x(t) input to the linear filter 510 based on the error signal for the output signal z(t) of the linear filter 510. The error backpropagation unit 513 may be a device that performs error backpropagation processing using the chain rate of a composite function. Note that the processing performed by the error backpropagation unit 513 is linear processing that does not include nonlinear transformation.

[0069] The nonlinear error backpropagation unit 520 outputs an output signal error ∇e(t) from the output signal z(t) of the linear filter 510 and an error signal ∇E(t) representing the error of the signal output from the nonlinear signal transformation unit included in the nonlinear error backpropagation unit 520. The nonlinear error backpropagation unit 520 has a first nonlinear transformation unit 521 and a second nonlinear transformation unit 522. The first nonlinear transformation unit 521 may have a configuration corresponding to the nonlinear transformation units 121, 221, and 321.

[0070] The first nonlinear transformer 521 performs a first nonlinear transform on the output signal of the linear filter 510 and outputs the result. The first nonlinear transformer 521 includes a first nonlinear signal transformer 523, a phase shifter 531, and a phase shifter 532. The first nonlinear signal transformer 523 transforms the output signal z(t) from the first nonlinear transformer 521 using a nonlinear function.

[0071] The second nonlinear conversion unit 522 performs a second nonlinear conversion corresponding to the differentiation of the first nonlinear conversion. The second nonlinear conversion unit 522 includes a second nonlinear signal conversion unit 524, a phase shift unit 533, a phase shift unit 534, a phase shift unit 535, and a complex multiplication operation unit 550. The second nonlinear signal conversion unit 524 converts the output signal z(t) of the linear filter 510, which has passed through the phase shift unit 533, using the derivative of the nonlinear function used by the first nonlinear signal conversion unit 523. [5-2: Nonlinear Signal Conversion]

[0072] Fig. 8 shows an example of the second nonlinear signal converter 524. As shown in Fig. 8, the second nonlinear signal converter 524 has a nonlinear function 500. A signal input to the second nonlinear signal converter 524 is expressed as a complex number. The second nonlinear signal converter 524 inputs each of the real part and imaginary part of the input signal to the nonlinear function 500. The second nonlinear signal converter 524 outputs each output signal as a complex signal with a real part and an imaginary part.

[0073] The nonlinear function 500 is determined depending on the modulation method of the transmission signal. Graphs 502 and 503 are graphs illustrating the relationship between the input signal and the output signal in the nonlinear function 500.

[0074] Graph 502 shows an example when the modulation method is QPSK modulation. The graph of the nonlinear function illustrated by graph 502 corresponds to the derivative obtained by differentiating the nonlinear function of graph 202 illustrated in FIG. 4. Graph 503 shows an example when the modulation method is 16-QAM. The graph of the nonlinear function illustrated by graph 503 corresponds to the derivative obtained by differentiating the nonlinear function of graph 203 illustrated in FIG. 4.

[0075] The complex multiplication operation unit 550 multiplies the signal converted by the second nonlinear signal conversion unit 524 by a signal obtained by shifting the phase of the error signal ∇E(t) representing the error of the signal output from the first nonlinear conversion unit 521 by the phase of the error signal ∇E(t) by the phase shift unit 534. In other words, the complex multiplication operation unit 550 generates a signal to be input to the filter coefficient update unit 512 from the error signal ∇E(t) related to the output signal from the first nonlinear signal conversion unit 523 and the output signal from the second nonlinear signal conversion unit 524.

[0076] The phase shift unit 531 adjusts the phase of the input signal to the first nonlinear signal converter 523 in accordance with phase information provided from a phase noise elimination unit (not shown). The phase shift unit 532 adjusts the phase of the output signal from the first nonlinear signal converter 523 in accordance with phase information provided from the phase noise elimination unit. The phase shift unit 533 adjusts the phase of the input signal to the second nonlinear signal converter 524 in accordance with phase information provided from the phase noise elimination unit. The phase shift unit 534 adjusts the phase of the output signal from the second nonlinear signal converter 524 in accordance with phase information provided from the phase noise elimination unit. [5-3: Flow of Linear Filter Coefficient Update Process]

[0077] The filter coefficient update process for the linear filter 510 will be described with reference to Fig. 7. The nonlinear equalization unit 501 shown in Fig. 7 includes a linear filter 510 obtained by extracting the basic components of the nonlinear equalization unit in the first to fourth embodiments, a first nonlinear conversion unit 521, a filter coefficient update unit 512 which was omitted in the first to fourth embodiments because it would be complicated, and a second nonlinear conversion unit 522.

[0078] As an example, the linear filter 510 may be a typical linear filter that performs a convolution operation between the input signal x(t) and the filter coefficients stored in the storage unit 5103 and outputs the result. The input signal to the linear filter 510 is represented by a time series x(t-L+1), x(t-L+2), ..., x(t-1), x(t), and the filter coefficients are represented by w ０ , w １ ,...w Ｌ－１When the output signal of the linear filter 510 is expressed as follows, the output signal of the linear filter 510 obtained by the convolution operation is expressed as z(t). [Equation 6]

[0079] The output signal z(t) is processed by a first nonlinear signal transformer 523, which has a phase shifter 531 arranged on the input side and a phase shifter 532 arranged on the output side. The signal u(t) output by the first nonlinear transformer 521 can be written as shown in the following [Equation 7]. [Equation 7]

[0080] Meanwhile, the second nonlinear transformer 522 outputs an output signal error ∇e(t) for the output signal z(t) of the linear filter 510 based on the error signal for the signal u(t) output by the first nonlinear transformer 521, the phase information provided by the phase noise elimination unit, and the output signal z(t) of the linear filter 510. In other words, the second nonlinear transformer 522 plays the role of an error backpropagation device.

[0081] The error signal related to the signal output from the first nonlinear conversion unit 521 is denoted as ∇E(t), and the phase information shared from the phase noise elimination unit is denoted as θ － The second nonlinear transform unit 522 calculates the output signal error ∇e(t) for the output signal z(t) of the linear filter 510 using the following [Equation 8]. [Equation 8]

[0082] In the above [Equation 8], ψ(·) represents the action of the second nonlinear signal converter 524. As described above, ψ(·) corresponds to the derivative of π(·), which is the action of the first nonlinear signal converter 523. Furthermore, the symbol "@" in [Equation 8] represents the operation (a+jb)@(c+jd)=ac+jbd for two complex numbers a+jb and c+jd.

[0083] The output signal error ∇e(t) is input to the filter coefficient update unit 512. The filter coefficient update unit 512 calculates the filter coefficients (w as shown in the following [Equation 9]) from the signal sequence x(t-L+1), x(t-L+2), ..., x(t-1), x(t) input to the linear filter 510 and the output signal error ∇e(t). ０ , w１ , ..., w Ｌ－１ ) is updated [Formula 9].

[0084] In the above [Equation 9], μ is a parameter set in advance. ＊ (ti) represents the complex conjugate of the input signal x(ti). The filter coefficient (w ０ , w １ , ..., w Ｌ－１ ) may be updated at every time point t. Alternatively, as shown below, it may be updated by averaging every time interval N (N is an integer equal to or greater than 1). In this case, the filter coefficients may be updated, for example, as shown in [Formula 10] below. [Formula 10]

[0085] The above describes the flow of the filter coefficient update process for the linear filter 510. [Technical Effects]

[0086] According to the above-mentioned Patent Document 1, by applying nonlinear equalization processing, the resistance to interference of the transmission signal is improved and the estimation accuracy of the transmission signal is improved, but on the other hand, when there is phase fluctuation in the transmission signal, the estimation accuracy of the transmission signal deteriorates significantly. As disclosed in the above-mentioned Patent Document 1, many nonlinear equalization methods are configured by combining a linear filter and a nonlinear transformation, and by applying this disclosure and applying a multiplication process that performs phase rotation before and after the nonlinear transformation, the problem of phase fluctuation can be solved and the estimation accuracy can be improved by applying nonlinear equalization even when there is phase fluctuation in the carrier wave. [6: Supplementary Note] The following supplementary note is further disclosed with respect to the above-described embodiment. [Supplementary Note 1] A signal processing device comprising: a first linear filter that receives a received signal and an auxiliary first input signal and outputs an output signal and an auxiliary first output signal; and a second linear filter that receives an auxiliary second input signal and outputs an auxiliary second output signal, the signal equalization unit having a plurality of linear filters that remove interference; a nonlinear signal conversion unit that converts a signal to be converted in accordance with a modulation method of a transmission signal corresponding to the received signal; and a phase shift unit that shifts the phase of the signal to be shifted; and a phase noise reduction unit that estimates a phase fluctuation related to the output signal, wherein the phase shift unit shifts the phase of the signal to be shifted in accordance with the estimated phase fluctuation, the auxiliary first output signal output by the first linear filter is input to the nonlinear signal conversion unit via the phase shift unit, the signal output by the nonlinear signal conversion unit is input to the second linear filter via the phase shift unit as the auxiliary second input signal, and the auxiliary second output signal output by the second linear filter is input to the first linear filter as the auxiliary first input signal. [Supplementary Note 2] The signal processing device according to Supplementary Note 1, wherein the phase noise elimination unit outputs an estimated transmission signal obtained by eliminating the phase fluctuation from the output signal, and outputs phase information related to the phase fluctuation.[Supplementary Note 3] The signal equalization unit has M (M is a positive integer) linear filters and M-1 sets of the nonlinear signal conversion units and the phase shift units, and is equipped with M phase noise elimination units, wherein the linear filter receives the received signal and an auxiliary input signal and outputs the output signal and an auxiliary output signal, the auxiliary output signal output from the kth (k is an integer greater than or equal to 1 and less than M) linear filter among the M linear filters passes through the kth phase shift unit and is input to the kth nonlinear signal conversion unit, the signal output from the kth nonlinear signal conversion unit passes through the kth phase shift unit and is input to the k+1th linear filter as the auxiliary input signal, and the output signal output from the kth linear filter is input to the kth phase noise elimination unit, The kth phase shift unit shifts the phase of the signal input to the kth nonlinear signal converter and the signal output from the kth nonlinear signal converter in accordance with the phase information output from the kth phase noise elimination unit, and the Mth phase noise elimination unit to which the output signal of the Mth linear filter is input outputs the final estimated transmission signal.[Supplementary Note 4] The signal equalization unit has M (M is a positive integer) linear filters and M-1 sets of the nonlinear signal conversion units and the phase shift units, and is provided with one phase noise elimination unit, wherein the linear filter receives the received signal and an auxiliary input signal and outputs the estimated transmission signal and an auxiliary output signal, the auxiliary output signal output from the kth (k is an integer equal to or greater than 1 and less than M) linear filter among the M linear filters passes through the kth phase shift unit and is input to the kth nonlinear signal conversion unit, the signal output from the kth nonlinear signal conversion unit passes through the kth phase shift unit and is input to the k+1th linear filter as the auxiliary input signal, and the kth phase shift unit shifts the phase of the signal input to the kth nonlinear signal conversion unit and the signal output from the kth nonlinear signal conversion unit according to the phase information output from the phase noise elimination unit, the output signal output by the Mth linear filter is input to the phase noise elimination unit, and the phase noise elimination unit outputs the estimated transmission signal. [Supplementary Note 5] The signal processing device according to any one of Supplementary Notes 2 to 4, wherein the phase noise elimination unit includes: a second phase shift unit that shifts the phase of the output signal, a signal determination unit that determines a most recent transmission signal point that is closest to the signal output by the second phase shift unit from a plurality of transmission signal points specified by the modulation scheme, and outputs a differential signal that indicates a difference between the output signal and the most recent transmission signal point, a phase detection unit that detects the phase of the differential signal, a filter that suppresses noise components of the phase detected by the phase detection unit, and an accumulator that accumulates and adds outputs of the filters, and outputs the phase information.and a linear filter unit including: the linear filter; a filter coefficient update unit that updates filter coefficients of the linear filter based on an output signal error that represents an error in the output signal; and an error backpropagation unit that outputs an input signal error that represents an error in an input signal input to the linear filter based on the output signal error; and a nonlinear error backpropagation unit that includes the nonlinear signal conversion unit and the phase shift unit and outputs the output signal error from the output signal and an error signal that represents an error in the signal output from the nonlinear signal conversion unit, wherein the nonlinear error backpropagation unit multiplies a converted signal obtained by converting the output signal, the phase of which is shifted by the phase shift unit, and the error signal, the phase of which is shifted by the phase shift unit, by a shifted signal obtained by shifting the phase of the error signal, and shifts the phase of the multiplication result by the phase shift unit to calculate the output signal error. [Supplementary Note 7] The signal processing device according to Supplementary Note 6, wherein the nonlinear error backpropagation unit has: a first nonlinear conversion unit including a first nonlinear signal conversion unit that converts the output signal that has passed through the phase shift unit using the nonlinear function, a second nonlinear signal conversion unit that converts the output signal that has passed through the phase shift unit into the converted signal using the derivative, and a second nonlinear conversion unit including a multiplication unit that multiplies the converted signal by the shifted signal. [Supplementary Note 8] A signal processing method comprising: estimating a phase fluctuation related to a signal output by a linear filter, shifting the phase of the signal output by the linear filter in accordance with the phase fluctuation, converting the shifted signal in accordance with a modulation scheme of a transmission signal corresponding to a received signal input to the linear filter, shifting the phase of the converted signal in accordance with the phase fluctuation, and inputting the shifted signal to the linear filter.[Supplementary Note 9] A recording medium having recorded thereon a computer program for causing a computer to execute a signal processing method, the method including: estimating a phase fluctuation related to a signal output by a linear filter; shifting the phase of the signal output by the linear filter in accordance with the phase fluctuation; converting the shifted signal in accordance with a modulation method of a transmission signal corresponding to a reception signal input to the linear filter; shifting the phase of the converted signal in accordance with the phase fluctuation; and inputting the shifted signal to the linear filter.

[0087] The present invention can be modified as appropriate within the scope that does not contradict the gist or idea of ​​the invention that can be read from the claims and the entire specification, and signal processing devices, signal processing methods, and recording media that involve such modifications are also included in the technical idea of ​​the present invention.

[0088] 10, 20, 30, 40 Signal processing device 101, 401, 501 Nonlinear equalization unit 110, 210, 310, 410, 510 Linear filter 120, 220, 320 Nonlinear signal conversion unit 121, 221, 321 Nonlinear conversion unit 130, 230, 330, 430, 531, 532, 533, 534, 535 Phase shift unit 140, 240, 340, 440 Phase noise elimination unit 200, 500 Nonlinear function 441 Signal determination unit 442 Phase detection unit 443 Filter 444 Accumulation addition unit 511 Linear filter unit 5101 Register 5102 Multiplier 5103 Storage unit 5104 Addition unit 512 Filter coefficient update unit 5121 Buffer 5122 Multiplier 5123 Register 513 Error back propagation unit 520 Nonlinear error back propagation unit 521 First nonlinear conversion unit 522 Second nonlinear conversion unit 523 First nonlinear signal conversion unit 524 Second nonlinear signal conversion unit 550 Complex multiplication operation unit

Claims

1. A signal processing device comprising: a first linear filter that receives a received signal and an auxiliary first input signal and outputs an output signal and an auxiliary first output signal; and a second linear filter that receives a supplementary second input signal and outputs an auxiliary second output signal, the signal equalization unit having a plurality of linear filters that remove interference; a nonlinear signal conversion unit that converts a signal to be converted in accordance with a modulation method of a transmission signal corresponding to the received signal; and a phase shift unit that shifts the phase of the signal to be shifted; and a phase noise reduction unit that estimates a phase fluctuation related to the output signal, wherein the phase shift unit shifts the phase of the signal to be shifted in accordance with the estimated phase fluctuation, the auxiliary first output signal output by the first linear filter is input to the nonlinear signal conversion unit via the phase shift unit, the signal output by the nonlinear signal conversion unit is input to the second linear filter via the phase shift unit as the auxiliary second input signal, and the auxiliary second output signal output by the second linear filter is input to the first linear filter as the auxiliary first input signal.

2. The signal processing device according to claim 1, wherein the phase noise elimination unit outputs an estimated transmission signal in which the phase fluctuation has been removed from the output signal, and outputs phase information relating to the phase fluctuation.

3. The signal equalization unit has M (M is a positive integer) linear filters and M-1 sets of the nonlinear signal conversion unit and the phase shift unit, and is equipped with M phase noise elimination units, wherein the linear filter receives the received signal and an auxiliary input signal and outputs the output signal and an auxiliary output signal, the auxiliary output signal output from the kth (k is an integer greater than or equal to 1 and less than M) linear filter among the M linear filters passes through the kth phase shift unit and is input to the kth nonlinear signal conversion unit, the signal output from the kth nonlinear signal conversion unit passes through the kth phase shift unit and is input to the k+1th linear filter as the auxiliary input signal, and the output signal output from the kth linear filter is input to the kth phase noise elimination unit, 3. The signal processing device according to claim 2, wherein the kth phase shift unit shifts the phase of the signal input to the kth nonlinear signal converter and the signal output from the kth nonlinear signal converter according to the phase information output from the kth phase noise elimination unit, and the Mth phase noise elimination unit to which the output signal of the Mth linear filter is input outputs the final estimated transmission signal.

4. The signal equalization unit has M (M is a positive integer) linear filters and M-1 sets of the nonlinear signal conversion units and the phase shift units, and is equipped with one phase noise elimination unit, wherein the linear filter receives the received signal and an auxiliary input signal and outputs the estimated transmission signal and an auxiliary output signal, the auxiliary output signal output from the kth (k is an integer greater than or equal to 1 and less than M) linear filter among the M linear filters passes through the kth phase shift unit and is input to the kth nonlinear signal conversion unit, the signal output from the kth nonlinear signal conversion unit passes through the kth phase shift unit and is input to the k+1th linear filter as the auxiliary input signal, and the kth phase shift unit shifts the phase of the signal input to the kth nonlinear signal conversion unit and the signal output from the kth nonlinear signal conversion unit according to the phase information output from the phase noise elimination unit, The signal processing device according to claim 2 , wherein the output signal output from the M-th linear filter is input to the phase noise elimination unit, and the phase noise elimination unit outputs the estimated transmission signal.

5. The signal processing device according to any one of claims 2 to 4, wherein the phase noise elimination unit comprises: a second phase shift unit that shifts the phase of the output signal; a signal determination unit that determines, from a plurality of transmission signal points specified by the modulation method, a most recent transmission signal point that is closest to the signal output by the second phase shift unit, and outputs a differential signal indicating the difference between the output signal and the most recent transmission signal point; a phase detection unit that detects the phase of the differential signal; a filter that suppresses noise components in the phase detected by the phase detection unit; and an accumulator that accumulates and adds outputs of the filter and outputs the phase information.

6. The signal processing device according to any one of claims 1 to 4, comprising: a linear filter unit having the linear filter, a filter coefficient update unit that updates the filter coefficients of the linear filter based on an output signal error that represents an error in the output signal, and an error backpropagation unit that outputs an input signal error that represents an error in an input signal input to the linear filter based on the output signal error; and a nonlinear error backpropagation unit that includes the nonlinear signal conversion unit and the phase shift unit and outputs the output signal error from the output signal and an error signal that represents the error of the signal output from the nonlinear signal conversion unit, wherein the nonlinear error backpropagation unit multiplies a converted signal obtained by converting the output signal, the phase of which is shifted by the phase shift unit, and the error signal, the phase of which is shifted by the phase shift unit, by a shifted signal obtained by shifting the phase of the error signal, and shifts the phase of the multiplication result by the phase shift unit to calculate the output signal error.

7. The signal processing device according to claim 6, wherein the nonlinear error backpropagation unit comprises: a first nonlinear conversion unit including a first nonlinear signal conversion unit that converts the output signal that has passed through the phase shift unit using the nonlinear function; a second nonlinear signal conversion unit that converts the output signal that has passed through the phase shift unit into the converted signal using the derivative function; and a second nonlinear conversion unit that includes a multiplication unit that multiplies the converted signal by the shifted signal.

8. A signal processing method comprising: estimating a phase fluctuation of a signal output by a linear filter; shifting the phase of the signal output by the linear filter in accordance with the phase fluctuation; converting the shifted signal in accordance with a modulation method of a transmission signal corresponding to a received signal input to the linear filter; shifting the phase of the converted signal in accordance with the phase fluctuation; and inputting the shifted signal to the linear filter.

9. A recording medium having recorded thereon a computer program that causes a computer to execute a signal processing method, the method including: estimating a phase fluctuation related to a signal output by a linear filter; shifting the phase of the signal output by the linear filter in accordance with the phase fluctuation; converting the shifted signal in accordance with a modulation method of a transmission signal corresponding to a received signal input to the linear filter; shifting the phase of the converted signal in accordance with the phase fluctuation; and inputting the shifted signal to the linear filter.

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