Title of Invention: Communication apparatus, demodulation apparatus, carrier reproduction apparatus, phase error compensation apparatus, phase error compensation method, and storage medium on which phase error compensation program has been stored Abstract: To enable a large-capacity, high-quality data communication that is excellent in bit error rate characteristic even in an adverse noise environment mainly caused by phase noises or thermal noises. [Solution] Included are: a first phase error detection filter that generates, on the basis of a forward sequence of received symbols, a first phase difference value and a first phase error estimated value; a second phase error detection filter that generates, on the basis of a backward sequence of received symbols, a second phase difference value and a second phase error estimated value; a phase error combination means that generates a third phase error estimated value on the basis of the first and second phase error estimated values and one of the first and second phase difference values; and a phase error compensation means that compensates the phase error of the received symbols in accordance with the third phase error estimated value. Detailed Description: Part general_description_paragraphs: Part CROSS-REFERENCE TO RELATED APPLICATIONS: This application is a national stage application of International Application No. PCT/JP2015/000160 entitled “COMMUNICATION APPARATUS, DEMODULATION APPARATUS, CARRIER REPRODUCTION APPARATUS, PHASE ERROR COMPENSATION APPARATUS, PHASE ERROR COMPENSATION METHOD, AND STORAGE MEDIUM ON WHICH PHASE ERROR COMPENSATION PROGRAM HAS BEEN STORED,” filed on Jan. 15, 2015, which claims the benefit of the priority of Japanese Patent Application No. 850-986-2094 filed on Jan. 16, 2014, the disclosures of each of which are hereby incorporated by reference in their entirety. Part TECHNICAL FIELD: The present invention relates to a communication apparatus, a demodulation apparatus, a carrier reproduction apparatus, a phase error compensation apparatus, a control method for the phase error compensation apparatus, and a storage medium stored with a control program for the phase error compensation apparatus. Part BACKGROUND ART: In digital communication, as a modulation and demodulation method for performing efficient data transmission, a quadrature amplitude modulation (QAM) method in which both of phase information and amplitude information are used for data identification is well-known. In recent years, as a demand for capacity enlargement in a communication system, there has been a demand for increasing the modulation multi-level number. However, there is a problem that increasing the modulation multi-level number may increase a transmission error probability caused by noise, and lower noise resistance. In particular, phase noise mainly caused by a reference oscillator (LO; Local Oscillator) in a transmission apparatus and in a receiving apparatus may increase uncertainty of phase information, and may considerably deteriorate a bit error rate (BER). In view of the above, in order to perform data communication with enhanced reliability by a multi-level QAM method in which the number of signal points is e.g. 256 or larger, it is necessary to estimate a phase error caused by the phase noise with high precision, and to compensate the phase error. Concurrently, it is necessary to improve resistance against an error caused by other factors such as thermal noise. In the aforementioned technical field, there is known a demodulation apparatus, in which a phase error is compensated by a phase locked loop, and a QAM symbol demapping apparatus for outputting a bit sequence reflecting likelihood information, and an error correction decoder for inputting the likelihood information and performing an error correction process are provided in the post-stage of the phase locked loop to implement improvement of error resistance. PTL 1 describes an example of the QAM symbol demapping apparatus. However, it may be impossible to obtain a sufficiently improved bit error rate depending on a magnitude of phase noise included in a baseband signal to be output from a detector, or due to deterioration of precision of phase detection resulting from thermal noise or the like. In view of the above, there is known a technique for improving precision of phase error compensation by adaptively adjusting a bandwidth of a loop filter in a phase locked loop. PTL 2, PTL 3, and PTL 4 disclose the aforementioned technique. Error resistance, however, may yet be insufficient. Further, there is known a demodulation method, in which a smoothing phase locked loop (S-PLL), which is an improved phase locked loop, is used in order to improve precision of phase error compensation. For instance, NPL 1 and NPL 2 disclose a principle on phase noise compensation by averaging as described above. Part CITATION LIST: Part Patent Literature: [PTL 1] Re-publication of PCT International Publication No. WO2011/068119 [PTL 2] Japanese Laid-open Patent Publication No. 2000-101666 [PTL 3] Japanese Translation of PCT International Application Publication No. 2003-531523 [PTL 4] Japanese Laid-open Patent Publication No. 2011-101177 Part Non Patent Literature: [NPL 1] J. Yang, B. Geller, C. Herzet, J. M. Brossier, “Smoothing PLLs for QAM Dynamical Phase Estimation,” IEEE ICC 2009 Proceedings, Jun. 14, 2009 [NPL 2] J. Yang, B. Geller, “Near Optimal Low Complexity Smoothing Loops for Dynamical Phase Estimation-Application to BPSK Modulated Signal,” IEEE Transactions on Signal Processing, Sep. 1, 2009 Part SUMMARY OF INVENTION: Part Technical Problem: However, in the technique described in the aforementioned literatures, the effect of phase noise compensation by a phase locked loop is limited. Specifically, when the level of phase noise included in a baseband signal to be output from a detector is large, as compared with a multi-level number of a signal by a QAM method, it is impossible to obtain a sufficiently improved bit error rate, and it is difficult to perform large-capacity and high-quality data communication. Further, the same problem as described above may be applied to a smoothing phase locked loop. In particular, when a signal-to-noise ratio (SNR) is large, improvement cannot be expected, as compared with a phase locked loop. Therefore, it is impossible to obtain a sufficient bit error rate, and it is difficult to perform large-capacity and high-quality data communication. An object of the present invention is to provide a technique for solving the aforementioned problems. Part Solution to Problem: To achieve the object described above, a phase error compensation apparatus comprises: a first phase error detection filter which generates a first phase difference value and a first phase error estimation value on the basis of received symbols in a forward sequence; a second phase error detection filter which generates a second phase difference value and a second phase error estimation value on the basis of the received symbols in a reverse sequence; a phase error combination means which generates a third phase error estimation value on the basis of the first phase error estimation value and the second phase error estimation value, and one of the first phase difference value and the second phase difference value; and a phase error compensation means which compensates a phase error in the received symbols in association with the third phase error estimation value. To achieve the object described above, a carrier reproduction apparatus comprises: the phase error compensation apparatus of any one of claims 1 to 5; a symbol demapping means which demaps received symbols whose phase error is compensated by the phase error compensation apparatus; and an error correction decoding means which corrects an error included in the received symbols whose phase error is compensated on the basis of an output of the symbol demapping means, and outputs demodulated data. To achieve the object described above, a demodulation apparatus comprises: the carrier reproduction apparatus; a reference oscillator which outputs a reference signal of a fixed frequency; a detector which orthogonally detects an input signal of an intermediate frequency, and generates an Ich baseband signal and a Qch baseband signal; and an analog-to-digital converter which converts a generated baseband signal into a digital signal, and inputs the digital signal to the carrier reproduction apparatus as the received symbols. To achieve the object described above, a communication apparatus comprises: at least the demodulation apparatus; a receiving circuit which selects a radio wave of a predetermined frequency band from radio waves to be received by an antenna to convert the selected radio wave into a signal of an intermediate frequency, and inputs the converted signal to the demodulation apparatus; and a received data decoding means which decodes demodulated data input by the demodulation apparatus, and generates received data. To achieve the object described above, a phase error compensation method comprises: generating a sequence of phase difference values φ(1), φ(2), . . . , φ(M) (where M is a positive integer) between a sequence of received symbols and a sequence of reference symbols; successively calculating first phase error estimation values θ+(1), θ+(2), . . . , θ+(M), θ+(M+1) caused by phase noise included in the sequence of phase difference values on the basis of the sequence of phase difference values; successively calculating second phase error estimation values θ−(M), θ−(M−1), . . . , θ−(1) on the basis of the sequence of phase difference values φ(M), φ(M−1), φ(1) by setting θ+(M+1) as an initial value; calculating third phase error estimation values θ±(1), θ±(2), . . . , θ±(M) by linear computation of the first phase error estimation values θ+(1), θ+(2), . . . , θ+(M), the second phase error estimation values θ−(1), θ−(2), . . . , θ−(M), and the phase difference values φ(1), φ(2), . . . , φ(M); successively calculating the first phase error estimation values, the second phase error estimation values, and the third phase error estimation values included in phase difference values φ(kM+1), φ(kM+2), . . . , φ((k+1)M) regarding a positive integer k by the calculation processes; and compensating a phase error by subtracting the third phase error estimation values θ±(kM+1), θ±(kM+2), . . . , θ±((k+1)M) from the phase difference values φ(kM+1), φ(kM+2), . . . , φ((k+1)M). To achieve the object described above, a storage medium stored with a phase error compensation program which causes a computer to execute the processes of: generating a sequence of phase difference values φ(1), φ(2), . . . , φ(M) (where M is a positive integer) between a sequence of received symbols and a sequence of reference symbols; successively calculating first phase error estimation values θ+(1), θ+(2), . . . , θ+(M), θ+(M+1) caused by phase noise included in the sequence of phase difference values on the basis of the sequence of phase difference values; successively calculating second phase error estimation values θ−(M), θ−(M−1), . . . , θ−(1) on the basis of the sequence of phase difference values φ(M), φ(M−1), . . . , φ(1) by setting θ+(M+1) as an initial value; calculating third phase error estimation values θ±(1), θ±(2), . . . , θ±(M) by linear computation of the first phase error estimation values θ+(1), θ+(2), . . . , θ+(M), the second phase error estimation values θ−(1), θ−(2), . . . , θ−(M), and the phase difference values φ(1), φ(2), . . . , φ(M); successively calculating the first phase error estimation values, the second phase error estimation values, and the third phase error estimation values included in phase difference values φ(kM+1), φ(kM+2), . . . , φ((k+1)M) regarding a positive integer k by the calculation processes; and compensating a phase error by subtracting the third phase error estimation values θ±(kM+1), θ±(kM+2), . . . , θ±((k+1)M) from the phase difference values φ(kM+1), φ(kM+2), . . . , φ((k+1)M). Part Advantageous Effects of Invention: According to the present invention, it is possible to perform large-capacity and high-quality data communication with an improved bit error rate even in an adverse noise environment mainly caused by phase noise or thermal noise. Part DESCRIPTION OF EMBODIMENTS: In the following, exemplary embodiments of the present invention are illustratively described in detail referring to the drawings. Note that constituent elements described in the following exemplary embodiments are merely exemplary elements, and the technical scope of the present invention is not limited only to those elements. Part First Exemplary Embodiment: A phase error compensation apparatus 100 as a first exemplary embodiment of the present invention is described using FIG. 1. The phase error compensation apparatus 100 is an apparatus for compensating phase noise generated in a reference oscillator, or thermal noise. As illustrated in FIG. 1, the phase error compensation apparatus 100 includes a first phase error detection filter 101, a second phase error detection filter 102, a phase error combination unit 103, and a phase error compensation unit 104. The first phase error detection filter 101 generates a first phase difference value 101b and a first phase error estimation value 101a on the basis of received symbols in a forward sequence. The second phase error detection filter 102 generates a second phase difference value 102b and a second phase error estimation value 102a on the basis of the received symbols in a reverse sequence. A third phase error estimation value 103a is generated on the basis of the first phase error estimation value 101a and the second phase error estimation value 102a, and one of the first phase difference value 101b and the second phase difference value 102b. The phase error compensation unit 104 compensates phase error in received symbols according to the third phase error estimation value 103a. According to the exemplary embodiment, a phase error is compensated by combining a phase error estimation value and a phase difference value generated on the basis of received symbols in a forward sequence and in a reverse sequence. Therefore, the aforementioned configuration makes it possible to perform large-capacity and high-quality data communication with an improved bit error rate, even in an adverse noise environment mainly caused by phase noise or thermal noise. Part Second Exemplary Embodiment: Next, a phase error compensation apparatus in a second exemplary embodiment of the present invention is described. The phase error compensation apparatus in the exemplary embodiment compensates a phase error by combining a phase error estimation value and a phase difference value generated on the basis of received symbols in a forward sequence and in a reverse sequence. Further, in the exemplary embodiment, description is made regarding a carrier reproduction apparatus including a phase error compensation apparatus, a demodulation apparatus including the carrier reproduction apparatus, and a communication apparatus including the demodulation apparatus. In the exemplary embodiment, a modulation method using phase information for data identification is used. In the exemplary embodiment, a QAM method is described as an example of a modulation method. It is possible to apply the exemplary embodiment, as far as the modulation method is a modulation method using phase information for data identification. Further, in the exemplary embodiment, a quasi-synchronous detection method, in which detection is performed on the basis of a periodic signal of a fixed frequency to be generated by a demodulation circuit itself, and a phase error is subtracted after the detection, is used as a detection method for a demodulation method. This detection method is advantageous because it is not necessary to generate a signal that is completely synchronous with a carrier wave. In the exemplary embodiment, a phase error compensation apparatus for compensating a phase error caused by phase noise by a quasi-synchronous detection method is provided. Note that description is simplified regarding an entire configuration of a demodulation apparatus by a quasi-synchronous detection method. Hereinafter, a section relating to phase error estimation, which is a core feature of the exemplary embodiment, is mainly described. In a QAM method as a modulation and demodulation method, when the number of signal points is 2m (where m is a positive integer), a bit sequence to be transmitted on the transmission side is divided per m-bit, and each m-bit is mapped at one of the 2m signal points. It is possible to express mapped signal points in terms of complex numbers, which are referred to as transmitted symbols. A baseband signal detected on the receiving side and subsequently converted into a digital signal is received symbols associated with transmitted symbols. It is possible to express each of an Ich baseband signal and a Qch baseband signal in terms of complex numbers associated with a real part and an imaginary part. Hereinafter, the aforementioned complex numbers are referred to as received symbols. Received symbols serve as an input to the phase error compensation apparatus in the exemplary embodiment. <<Configuration of Communication Apparatus>> FIG. 2A is a block diagram illustrating a configuration of a communication apparatus including a phase error compensation apparatus 241 in the exemplary embodiment. It is possible to use the communication apparatus in the exemplary embodiment for providing a backhaul line indispensable for mobile phone services, digital data fixed line services, or the like. In particular, it is possible to use the communication apparatus in the exemplary embodiment as a high-quality and large-capacity digital communication line for connecting between base stations for providing mobile phone services. Note that the configuration of the communication apparatus is not limited to the configuration illustrated in FIG. 2A. The communication apparatus in the exemplary embodiment includes, as a receiving system, a receiving circuit 202, a demodulation apparatus 200, and a received data decoding unit 203. The receiving circuit 202 selects a radio wave of a predetermined frequency band from radio waves received by an antenna 201 for converting into a signal of an intermediate frequency, and outputs the signal to the demodulation apparatus 200 in the exemplary embodiment. The received data decoding unit 203 decodes demodulated data to be output by the demodulation apparatus 200, and generates received data. Further, the communication apparatus in the exemplary embodiment may include, as a transmission system, a transmitted data encoding unit 205, a modulation apparatus 204, and a transmission circuit 206. The transmitted data encoding unit 205 encodes transmitted data. The modulation apparatus 204 modulates the encoded transmitted data in association with a demodulation method for the demodulation apparatus 200, and generates a signal of an intermediate frequency. The transmission circuit 206 generates a radio wave of a predetermined frequency band for transmission on the basis of a signal of an intermediate frequency, and transmits the radio wave from the antenna 201. <<Configuration and Operation of Demodulation Apparatus>> FIG. 2B is a block diagram illustrating a configuration of the demodulation apparatus 200 including the phase error compensation apparatus 241 in the exemplary embodiment. The demodulation apparatus 200 is an apparatus for demodulating a data signal that is modulated and transmitted by a QAM method. The demodulation apparatus 200 is provided with a reference oscillator 220, a detector 210, an analog-to-digital converter (hereinafter, referred to as an A/D converter) 230, and a carrier reproduction apparatus 240. The reference oscillator 220 inputs a reference signal of a fixed frequency to the detector 210. The detector 210 orthogonally detects an input signal of an intermediate frequency (IF), and generates a baseband signal of a same phase component (Ich) and a baseband signal of an orthogonal component (Qch). Generated baseband signals are converted into digital signals by the A/D converter 230, and are input to the carrier reproduction apparatus 240 as received symbols. The carrier reproduction apparatus 240 is provided with the phase error compensation apparatus 241 in the exemplary embodiment, a QAM symbol demapping unit 242, and an error correction decoder 243. The QAM symbol demapping unit 242 receives received symbols whose phase error is compensated by the phase error compensation apparatus 241, and generates input data to the error correction decoder 243, which is provided in the post-stage of the QAM symbol demapping unit 242. The error correction decoder 243 performs a process for correcting a bit error included in received symbols on the basis of data input from the QAM symbol demapping unit 242. Data after an error correction process serves as demodulated data, which is an output of the demodulation apparatus 200. In this case, when the number of times of performing phase error compensation by the phase error compensation apparatus 241 reaches a predetermined specific number of times, or when the error correction decoder 243 determines that there is no error, an output of the error correction decoder 243 is output as demodulated data of the demodulation apparatus 200. Otherwise, the phase error compensation apparatus 241 repeatedly compensates a phase error in received symbols to improve precision of compensation. In the aforementioned configuration, it may be configured such that the carrier reproduction apparatus 240 temporarily holds input received symbols in a buffer, and compensates a phase error in the received symbols held in the buffer by using the phase error compensation apparatus 241 a plural number of times. <<Phase Error Compensation Apparatus>> Next, a configuration of the phase error compensation apparatus 241 in the exemplary embodiment is described. A premise technique relating to a configuration of a phase error compensation apparatus is described in order to clarify the features of the phase error compensation apparatus 241. <<Configuration of Phase Error Compensation Apparatus as Premise Technique>> FIG. 4A is a block diagram illustrating a configuration of a phase error compensation apparatus 241A as a premise technique. By replacing the phase error compensation apparatus 241 illustrated in FIG. 2B with the phase error compensation apparatus 241A illustrated in FIG. 4A, a demodulation apparatus as a premise technique is configured. The phase error compensation apparatus 241A illustrated in FIG. 4A is provided with a phase locked loop (PLL) constituted by a rotation matrix multiplier 411, a phase detection unit 412, a loop filter 413, a cumulative adder unit 414, and a data conversion unit 415, which are connected in a loop. The rotation matrix multiplier 411 rotates a phase of received symbols associated with each of an Ich baseband signal and a Qch baseband signal, which are digitized by the A/D converter 230 according to output information of the data conversion unit 415, to compensate a phase error. An output signal of the rotation matrix multiplier 411 is input to the phase detection unit 412. The phase detection unit 412 detects a phase error remaining in the received symbols, and inputs the detected phase error to the loop filter 413. The loop filter 413 removes an unnecessary high frequency component included in a phase error, and inputs a phase error after removal of a high frequency component to the cumulative adder unit 414. The cumulative adder unit 414 generates phase error information for designating a phase rotation amount in the rotation matrix multiplier 411 on the basis of an input by the loop filter 413, and inputs the generated phase error information to the data conversion unit 415. The data conversion unit 415 converts the phase error information input by the cumulative adder unit 414 into sine data and cosine data associated with the input phase error information, and inputs the converted data to the rotation matrix multiplier 411. As described above, it is possible to implement a stable phase locked state by an operation of a phase locked loop constituted by the rotation matrix multiplier 411, the phase detection unit 412, the loop filter 413, the cumulative adder unit 414, and the data conversion unit 415, which are connected in a loop, thereby compensating a phase error. Note that the received symbols whose phase error is compensated by the rotation matrix multiplier 411 are also input to the QAM symbol demapping unit 242 in the carrier reproduction apparatus 240, as well as to the phase detection unit 412. As described above, the phase error compensation apparatus 241A illustrated in FIG. 4A performs phase error compensation by a phase locked loop, and implements improvement of error resistance by an error correction process to be performed in the post-stage. However, it may be difficult to obtain a sufficiently improved bit error rate depending on a magnitude of phase noise included in a baseband signal to be output from the detector 210, or due to deterioration of precision of the phase detection unit 412 caused by thermal noise or the like. FIG. 4B is a block diagram illustrating a configuration of a phase error compensation apparatus 241B as a premise technique. By replacing the phase error compensation apparatus 241 illustrated in FIG. 2B with the phase error compensation apparatus 241B illustrated in FIG. 4B, a demodulation apparatus as a premise technique is configured. The phase error compensation apparatus 241B illustrated in FIG. 4B employs a demodulation method in which a smoothing phase locked loop (S-PLL) being an improved phase locked loop is used in order to improve precision of phase error compensation. The phase error compensation apparatus 241B employing a smoothing phase locked loop is constituted by a buffer 421, two phase locked loops 422 and 423, and an averaging unit 424. The buffer 421 temporarily holds an input to the phase error compensation apparatus 241B, and inputs one of two types of data sequences i.e. a data sequence in an input order and a data sequence whose order is reversed to the input order to one of the phase locked loops 422 and 423, and inputs the other of the two types of data sequences to the other of the phase locked loops 422 and 423. Each of the phase locked loops 422 and 423 processes the input data, and inputs a processing result to the averaging unit 424. The averaging unit 424 calculates an average of the two data which are processed in different orders, and outputs a calculation result. However, the aforementioned smoothing phase locked loop may have a problem that when an SNR relating to thermal noise is large, precision of phase error compensation for thermal noise becomes substantially equal to precision obtained by an ordinary phase locked loop, and improvement appropriate for the increased amount of calculation is not observed. <<Configuration of Phase Error Compensation Apparatus in Exemplary Embodiment>> FIG. 3 is a block diagram illustrating a configuration of the phase error compensation apparatus 241 in the exemplary embodiment. The phase error compensation apparatus 241 in the exemplary embodiment receives received symbols, estimates a phase error caused by phase noise of a reference oscillator, and outputs received symbols whose phase error is compensated. The phase error compensation apparatus 241 illustrated in FIG. 3 is provided with a phase error detection filter 301 for received symbols in a forward sequence, a phase error detection filter 302 for received symbols in a reverse sequence, FILO buffers 303 and 304, and a phase error combination unit 300. Further, the phase error compensation apparatus 241 is provided with a data conversion unit 306, a rotation matrix multiplier 305, an FILO buffer 307, and a parameter generation unit 308. The phase error detection filter 301 receives received symbols in a forward sequence, and outputs a difference between a phase of the received symbols in a forward sequence and a phase of estimated transmitted symbols generated inside the phase error compensation apparatus 241, and an estimated value of phase error generated in a phase of received symbols caused by phase noise. The phase error detection filter 302 receives received symbols in a reverse sequence, and outputs a difference between a phase of the received symbols in a reverse sequence and a phase of estimated transmitted symbols generated inside the phase error compensation apparatus 241, and an estimated value of phase error generated in a phase of received symbols caused by phase noise. Each of the FILO buffers 303 and 304 is a first in/last out temporary storage unit which holds received symbols and an output data sequence of the phase error detection filter 301 by a predetermined fixed number of times, and outputs the received symbols and the output data sequence in the order reverse to an input order. Further, the FILO buffer 307 is a first in/last out temporary storage unit which converts received symbols in a reverse sequence whose phase error is compensated into received symbols in a forward sequence. Note that a storage unit of a predetermined capacity may be connected, in place of the FILO buffer 307, to control write addresses and read addresses. The phase error combination unit 300 outputs an estimated value of phase error generated in a phase of received symbols caused by phase noise on the basis of an input from the phase error detection filters 301 and 302. A phase error estimation value 304a, whose sequence is reversed with respect to a phase error estimation value 301a from the phase error detection filter 301 by the FILO buffer 304, and a phase error estimation value 302a and a phase difference value 302b from the phase error detection filter 302 are input to the phase error compensation apparatus 241 illustrated in FIG. 3. The data conversion unit 306 receives a phase error estimation value 300a, which is output data of the phase error combination unit 300, and outputs phase compensation data constituted by a sine value and a cosine value of an input value. The rotation matrix multiplier 305 receives received symbols, and a sine value and a cosine value, which are an output of the data conversion unit 306, and multiplies a rotation matrix including a sine value and a cosine value as components with received symbols to rotate a phase, and outputs a multiplication result via the FILO buffer 307. The parameter generation unit 308 generates coefficients K1 to K5, which are used in one of the process by the phase error detection filters 301 and 302, and the process by the phase error combination unit 300 on the basis of a phase noise parameter of the reference oscillator 220 and a signal-to-noise ratio. (Operation of Phase Error Compensation Apparatus) Next, an operation of the phase error compensation apparatus 241 illustrated in FIG. 3 is described. The phase error compensation apparatus 241 receives received symbols, compensates a phase error including a phase of the received symbols, and outputs the received symbols after phase error compensation. Received symbols input to the phase error compensation apparatus 241 are r(1), r(2), . . . , r(M) (where M is a positive integer). When it is assumed that transmitted symbols associated with the received symbols are s(1), s(2), . . . , s(M), phase noise caused by an oscillator is θ(1), θ(2), . . . , θ(M), and noise caused by thermal noise is w(1), w(2), . . . , w(M), the received symbols can be expressed by Eq. (1). [Math. 1] r(n)=s(n)ejθ(n)+w(n),n=1,2, . . . ,M (1) Here, e is a Napier's constant, and j is an imaginary unit. Thermal noise is white noise whose spectrum is flat. However, the spectrum of phase noise is not flat. As an example, a case is described in which the spectrum of phase noise has the shape as illustrated in FIG. 8. Symbols for phase reference, which are a further input to the phase error compensation apparatus 241 illustrated in FIG. 3, are indicated by a(1), a(2), . . . , a(M). When transmitted symbols are clear in advance, it is assumed that the symbols for phase reference coincide with the transmitted symbols. When transmitted symbols are not clear, and when it is possible to use estimated transmitted symbols after error correction, which are obtained after an error correction process, it is assumed that the symbols for phase reference coincide with the estimated transmitted symbols. Further, when it is impossible to use transmitted symbols, and estimated transmitted symbols after error correction, estimated transmitted symbols to be generated inside the phase error compensation apparatus 241 are used. Therefore, when transmitted symbols and estimated transmitted symbols after error correction are used, symbols for phase reference are not used, although the symbols for phase reference are input from the outside. When estimated transmitted symbols to be generated inside the phase error compensation apparatus 241 are used, an input of symbols for phase reference is assumed to be NULL. Note that the phase error compensation apparatus 241 illustrated in FIG. 3 uses estimated transmitted symbols to be generated inside the phase error compensation apparatus 241. Symbols input to the phase error compensation apparatus 241 are input to the phase error detection filter 301. The phase error detection filter 301 calculates a phase error estimation value and a phase difference value on the basis of received symbols and estimated transmitted symbols, and outputs a calculation result. Each of the output data is numerical value data representing a phase. Output data relating to a phase error estimation value of the phase error detection filter 301 is indicated by θ+(1), θ+(2), . . . , θ+(M). Output data relating to a phase difference value is indicated by φ(1), φ(2), . . . , φ(M). Note that in the example illustrated in FIG. 3, a phase difference value to be output from the phase error detection filter 301 is not used. Received symbols, and the phase error estimation value 301a from the phase error detection filter 301 are respectively and temporarily held in the FILO buffers 303 and 304, and are output in the order reverse to an input order. Specifically, when received symbols are input in the order of r(1), r(2), . . . , r(M), the received symbols are output in the order of r(M), r(M−1), . . . , r(1). Further, when output data relating to a phase error estimation value is input in the order of θ+(1), θ+(2), . . . , θ+(M), the output data is output in the order of θ+(M), θ+(M−1), . . . , θ+(1). Received symbols respectively output from the FILO buffers 303 and 304 are input to the phase error detection filter 302, and the phase error estimation value 304a is input to the phase error combination unit 300. Similarly to the phase error detection filter 301, the phase error detection filter 302 calculates the phase error estimation value 302a and the phase difference value 302b on the basis of received symbols and estimated transmitted symbols, and outputs a calculation result. The phase error detection filter 302 is different from the phase error detection filter 301 regarding an input order and initial value setting. Received symbols are input from the FILO buffer 303 to the phase error detection filter 302 in the order of r(M), r(M−1), . . . , r(1). Further, an initial value is set on the basis of the coefficient K3. Output data relating to phase error estimation by the phase error detection filter 302 is indicated by θ−(M), θ−(M−1), . . . , θ−(1). An output of a phase difference value is indicated by φ(M), φ(M−1), . . . , φ(1) with use of the same symbols as used in an output of the phase error detection filter 301. Each of outputs of the phase error detection filters 301 and 302 is input to the phase error combination unit 300. The phase error combination unit 300 combines the phase error estimation value 304a or 302a and the phase difference value 302b, and outputs the phase error estimation value 300a. An output of the phase error combination unit 300a is indicated by θ±(M), θ±(M−1), . . . , θ±(1). An output of the phase error combination unit 300 is converted into sine data sin(θ±(M)), sin(θ±(M−1)), . . . , sin(θ±(1)), and cosine data cos(θ±(M)), cos(θ±(M−1)), . . . , cos(θ±(1)). Sine data and cosine data are input to the rotation matrix multiplier 305, and compensate a phase of received symbols. An output of the rotation matrix multiplier 305, whose order is reversed by the FILO buffer 307, is output data of the phase error compensation apparatus 241. The output data can be expressed by Eq. (2) with use of the aforementioned notation. [Math. 2] r(n)e−jθ±(n),n=1,2, . . . ,M (2) (Configuration of Phase Error Detection Filter) FIG. 5 is a block diagram illustrating a configuration of the phase error detection filters 301 and 302 in the exemplary embodiment. Note that the phase error detection filters 301 and 302 have the same configuration except for a point that the phase error detection filter 302 sets an initial value on the basis of the coefficient K3. Therefore, the configurations of the phase error detection filters 301 and 302 are shared by FIG. 5. Each of the phase error detection filters 301 and 302 illustrated in FIG. 5 receives received symbols, and outputs a difference between a phase of the received symbols and a phase of estimated transmitted symbols, and an estimated value of phase error generated in a phase of the received symbols caused by phase noise. Each of the phase error detection filters 301 and 302 illustrated in FIG. 5 is provided with a phase detection unit 503, a one-tap filter 504, a cumulative adder unit 505 provided with a feedback coefficient, a data conversion unit 506, a rotation matrix multiplier 501, and a determination unit 502. The phase detection unit 503 receives output symbols from the rotation matrix multiplier 501, and output symbols from the determination unit 502, and outputs a phase difference value between the output symbols. Output data serves as an input to the one-tap filter 504, which is provided in the subsequent-stage of the phase detection unit 503. The output data is added to an output of the cumulative adder unit 505 provided with a feedback coefficient by the adder 507. Then, the addition result serves as a phase difference value 301b or 302b, which is one of outputs of the phase error detection filter 301 or 302. The one-tap filter 504 is a filter whose number of taps is one for removing a high frequency component. The one-tap filter 504 is constituted by a multiplier 541. The one-tap filter 504 receives an output of the phase detection unit 503, multiplies the output with the tap coefficient K2, and outputs a multiplication result. The tap coefficient K2 is given by the parameter generation unit 308. Note that the tap coefficient K2 represents a degree of reflecting suddenly generated noise to phase error compensation, and is a value significantly smaller than 1. The cumulative adder unit 505 provided with a feedback coefficient is constituted by an adder 551, a flip-flop 552, and a multiplier 553. The cumulative adder unit 505 receives an output of the one-tap filter 504, and outputs data held in the flip-flop 552. Note that in the phase error detection filter 302, a value on the basis of the initial coefficient K3 is set in the flip-flop 552, as an initial value. An output of the cumulative adder 505 provided with a feedback coefficient is the phase error estimation value 301a or 302a, which is one of outputs of the phase error detection filter 301 or 302, and serves as an input to the data conversion unit 506 and to the adder 507. Further, the feedback coefficient K1 of the multiplier 553 is given by the parameter generation unit 308. Note that the feedback coefficient K1 represents a degree of reflecting an influence of previously received symbols on phase error compensation, and is a value smaller than 1. The data conversion unit 506 receives a phase error estimation value output by the cumulative adder unit 505, and outputs a sine value and a cosine value associated with the phase error estimation value. The rotation matrix multiplier 501 multiplies a rotation matrix including, as components, a sine value and a cosine value, which are an output of the data conversion unit 506, with received symbols displayed in terms of complex numbers, and rotates a phase of the received symbols by a numerical value corresponding to an output of the cumulative adder unit 505 to compensate a phase. The determination unit 502 receives received symbols whose phase is compensated by the rotation matrix multiplier 501, and inputs transmitted symbols closest to the input received symbols to the phase detection unit 503. (Operation of Phase Error Detection Filter) Next, an operation of each of the phase error detection filters 301 and 302 is described. Although the phase error compensation apparatus 241 is provided with the phase error detection filters 301 and 302, an operation of generating output data according to input data is the same between the phase error detection filters 301 and 302. Therefore, an operation of the phase error detection filter 301 is described as an example. Note that as initial setting, it is necessary to set an initial value of the flip-flop 552 in the cumulative adder unit 505 provided with a feedback coefficient to a determined appropriate value. Unless otherwise specifically designated, the initial value is set to “b 0”. Received symbols input to the phase error detection filter 301 are input to the rotation matrix multiplier 501. Similarly to the rotation matrix multiplier 305, the rotation matrix multiplier 501 rotates a phase of received symbols according to output data from the data conversion unit 506. When it is assumed that input received symbols at the point of time n are indicated by r(n), and data held in the flip-flop 552 is indicated by θ+(n) (where n is an integer of not smaller than 1 but not larger than M), an output of the rotation matrix multiplier 501 can be expressed by Eq. (3). [Math. 3] r(n)e−jθ+(n),n=1,2, . . . ,M (3) An output of the rotation matrix multiplier 501 expressed by Eq. (3) is input to the determination unit 502 and to the phase detection unit 503. The determination unit 502 outputs transmitted symbols closest to the data expressed by Eq. (3). An output of the determination unit 502 is input to the phase detection unit 503. The phase detection unit 503 calculates a phase difference between two input symbols, and outputs a calculation result. When it is assumed that a phase difference between received symbols, and output symbols of the determination unit 502 is indicated by φ(1), φ(2), . . . , φ(M), an output of the phase detection unit 503 at the point of time n is numerical value data expressed by Eq. (4) on the basis of Eq. (3). [Math. 4] θ(n)−θ+(n),n=1,2, . . . ,M (4) An output of the phase detection unit 503 is input to the one-tap filter 504 and to the adder 507. The other input to the adder 507 is a phase error output θ+(1), θ+(2), . . . , θ+(M). Therefore, by Eq. (4), an output of the adder 507 is phase difference values φ(1), φ(2), . . . , φ(M). On the other hand, in the one-tap filter 504, an output of the phase detection unit 503, and the tap coefficient K2 to be supplied from the parameter generation unit 308 are multiplied by the multiplier 541. Then, the multiplication result is input to the cumulative adder unit 505 provided with a feedback coefficient. The adder 551 in the cumulative adder unit 505 provided with a feedback coefficient adds an output of the one-tap filter 504, and data of the flip-flop 552, which is multiplied by the multiplier 553 with the feedback coefficient K1 to be supplied from the parameter generation unit 308. Then, data of the flip-flop 552 is updated on the basis of the addition result. Data θ+(n) of the flip-flop 552, which is held at the point of time n, is updated at the next point of time (n+1) as expressed by Eq. (5). [Math. 5] θ+(n)←K1θ+(n)+K2(φ(n)−θ+(n)) (5) Output data of the flip-flop 552 is output from the phase error detection filter 301 as the phase error estimation value 301a, and is used for rotating a phase of input received symbols r(n+1) at the point of time (n+1) by the data conversion unit 506. Thereafter, by the same operation as described above, phase error estimation values θ+(1), θ+(2), . . . , θ+(M), and phase difference values φ(1), φ(2), . . . , φ(M) are generated and output. Note that data θ+(M+1) is generated by the aforementioned procedure defined by using Eq. (5) from the M-th input received symbol r(M), and data θ+(M) of the flip-flop 552 at the point of time M. Then, the data θ+(M+1) is used as an initial value of the flip-flop 552 in the phase error detection filter 302. The phase error detection filter 302 generates and outputs phase error estimation values θ−(M), θ−(M−1), . . . , θ−(1) according to the procedure expressed by Eq. (6). [Math. 6] θ−(n−1)←K1θ−(n)+K2(φ(n)−θ−(n)) (6) (Configuration of Phase Error Combination Unit) FIG. 6 is a block diagram illustrating a configuration of the phase error combination unit 300 in the exemplary embodiment. The phase error combination unit 300 receives an output from the phase error detection filter 301 or 302, and outputs an estimated value of phase error generated in a phase of received symbols caused by phase noise. The phase error combination unit 300 illustrated in FIG. 6 is provided with two adders 601 and 604, and two multipliers 602 and 603. The adder 601 adds the phase error estimation value 304a in a reverse sequence from the phase error detection filter 301, and the phase error estimation value 302a from the phase error detection filter 302, and inputs the addition result to the multiplier 602. The multiplier 602 multiplies the addition result by the adder 601 with the multiplication coefficient K4 generated by the parameter generation unit 308, and inputs the multiplication result to the adder 604. The multiplier 603 multiplies the multiplication coefficient K5 generated by the parameter generation unit 308 with the phase difference value 302b from the phase error detection filter 302, and inputs the multiplication result to the adder 604. The adder 604 adds an input by the multiplier 602 and an input by the multiplier 603, and sets the addition result as an output of the phase error combination unit 300. (Operation of Phase Error Combination Unit) Next, an operation of the phase error combination unit 300 is described. The phase error combination unit 300 receives an output of the phase error detection filters 301 and 302, and outputs the phase error estimation value 300a. The adder 601 successively calculates θ+(n)+θ−(n), where n=M, M−1, . . . , 1 on the basis of the phase error estimation value 301a i.e. θ+(1), θ+(2), . . . , θ+(M), and the phase error estimation value 302a i.e. θ−(M), θ−(M−1), . . . , θ−(1). Then, the multiplier 602 multiplies the multiplication coefficient K4 to be supplied from the parameter generation unit 308 with θ+(n)+θ−(n), and obtains K4×(θ+(n)+θ−(n)), where n=M, M−1, . . . , 1. On the other hand, the multiplier 603 multiplies the multiplication coefficient K5 to be supplied from the parameter generation unit 308 with the phase difference value 302b from the phase error detection filter 302, and obtains K5×φ(M), K5×φ(M−1), . . . , K5×φ(1). An output of the multiplier 602 and an output of the multiplier 603 are added by the adder 604, and the phase error estimation value 300a i.e. θ±(M), θ±(M−1), . . . , θ±(1) as expressed by Eq. (7) is obtained. Specifically, the multiplication coefficients K4 and K5 play a role of a weighting factor which reflects one of a phase error estimation value output from the phase error detection filter 301 or 302, and a phase difference value according to reliability with respect to the phase error estimation value 300a. [Math. 7] θ±(n)←K4(θ+(n)+θ−(n))+K5φ(n),n=1,2, . . . ,M (7) (Configuration of Parameter Generation Unit) FIG. 7A is a block diagram illustrating a configuration of the parameter generation unit 308 in the present exemplary embodiment. The parameter generation unit 308 illustrated in FIG. 7A is provided with a noise characteristic value acquisition unit 710, a coefficient calculation unit 720, a table 730 for coefficient calculation, and a coefficient holding unit 740. The noise characteristic value acquisition unit 710 acquires a noise characteristic value of the reference oscillator 220. Note that a noise characteristic value of the reference oscillator 220 may be manually input by an operator, or may be automatically detected by an apparatus. The coefficient calculation unit 720 calculates the coefficients K1 to K5 according to a predetermined algorithm with use of the table 730 for coefficient calculation. The coefficient holding unit 740 holds the coefficients K1 to K5 calculated by the coefficient calculation unit 720. Note that it may be configured such that calculation of the coefficients K1 to K5 is performed by an additionally prepared computer, and the calculation result is held in the coefficient holding unit 740. (Table for Coefficient Calculation) FIG. 7B is a diagram illustrating a configuration of the table 730 for coefficient calculation in the present exemplary embodiment. The table 730 for coefficient calculation is used for generating the coefficients K1 to K5 by the coefficient calculation unit 720 on the basis of a noise characteristic value of the reference oscillator 220. In the table 730 for coefficient calculation, an intermediate value storage unit 732 and a coefficient storage unit 733 are stored in association with a noise characteristic value storage unit 731. The noise characteristic value storage unit 731 stores fp, fz, fs, Kpn, and σw2, which are noise characteristic values of the reference oscillator 220 necessary for coefficient calculation. The intermediate value storage unit 732 stores e.g. a0, a1, b1, α, γ, λ, and η, which are intermediate values for coefficient calculation. The coefficient storage unit 733 stores the calculated coefficients K1, K2, K3, K4, and K5. (Operation of Parameter Generation Unit) Next, calculation of the coefficients K1 to K5 is described. FIG. 8 is a diagram
{'bibliographic_information': "{'country': 'US', 'doc-number': '15110451', 'kind': 'B2', 'date': '20150115', 'invention_title': 'Communication apparatus, demodulation apparatus, carrier reproduction apparatus, phase error compensation apparatus, phase error compensation method, and storage medium on which phase error compensation program has been stored'}", 'source_file': './grant/2018/ipg180123.xml', 'source_data': 'USPTO-Grant'}