Patent Publication Number: US-10763973-B2

Title: Phase noise compensation apparatus, demodulation apparatus, communication apparatus, communication system, and phase noise compensation method

Description:
This application is a National Stage Entry of PCT/JP2017/018310 filed on May 16, 2017, which claims priority from Japanese Patent Application 2016-160081 filed on Aug. 17, 2016, the contents of all of which are incorporated herein by reference, in their entirety. 
     TECHNICAL FIELD 
     The present disclosure relates to a phase noise compensation apparatus and method. Specifically, the present disclosure relates to a phase noise compensation apparatus and method used in a communication scheme for transmitting information using phase information. 
     The present disclosure also relates to a demodulation apparatus, a communication apparatus, and a communication system including the phase noise compensation apparatus. 
     BACKGROUND ART 
     In digital communication, a Quadrature Amplitude Modulation (QAM) scheme that uses both phase information and amplitude information to identify data is known as a modulation/demodulation scheme for efficient data transmission. Recently, an increase in a modulation multilevel number has been desired along with a demand for increasing a capacity of a communication system. However, there is a problem that when the modulation multilevel number is increased, a transmission error probability increases due to noise, thereby decreasing the noise immunity. In particular, in a transmission apparatus and a reception apparatus employing a modulation scheme such as the QAM scheme, phase noise mainly caused by a Local Oscillator (LO) becomes a factor to increase uncertainty of phase information and remarkably degrade a Bit Error Rate (BER). 
     For example, if a phase error occurs due to phase noise in a communication system using a multilevel QAM scheme having 256 or more signal points, the bit error rate increases, and the reliability of data communication decreases. In such a communication system, it is necessary to estimate the phase error caused by the phase noise with high accuracy and then compensate it in order to perform highly reliable data communication. Further, in a communication system using a multilevel QAM scheme or the like, it is necessary to improve tolerance to errors caused by factors other than the phase noise such as thermal noise. 
     As a demodulation apparatus that can improve error tolerance, a demodulation apparatus that includes a QAM symbol demapping apparatus which performs phase error compensation using a Phase Lock Loop (PLL) and outputs a bit sequence reflecting likelihood information at a subsequent stage of the PLL, and an error correction decoder which inputs likelihood information and performs error correction processing is known. An example of the QAM symbol demapping apparatus is disclosed in, for example, Patent Literature 1. 
     However, in the above demodulation apparatus, a sufficiently and satisfactory bit error rate characteristic may not be achieved because of a magnitude of the phase noise included in a baseband signal output from a detector or deteriorated accuracy of phase detection due to thermal noise etc. In order to address this problem, Patent Literature 2 and 3 discloses a technique for improving the accuracy of phase error compensation by adaptively adjusting a bandwidth of a loop filter in a phase lock loop. 
     In addition to the above-described method of using the phase lock loop, a method of periodically embedding a known signal (a pilot signal) in a transmission signal and compensating the phase noise using this known signal is known. A general principle related to improvement of communication reliability using a pilot signal is described in, for example, Non Patent Literature 1. A method of using the pilot signal to improve the accuracy of the phase noise compensation method is described in, for example, Non Patent Literature 2, 3, and 4. 
       FIG. 10  is a block diagram showing a configuration example of a phase noise compensation apparatus which compensates phase noise using a pilot signal. Referring to  FIG. 10 , a phase noise compensation apparatus  200  includes a FIFO (First-In First-Out) memory  201 , a phase detector  202 , an interpolation filter  203 , a phase rotator  204 , and a switch  205 . 
     In the phase noise compensation apparatus  200 , a reception symbol corresponding to a reception baseband signal is input to the FIFO memory  201 . When the reception symbol is a pilot symbol corresponding to a known pilot signal inserted at a transmission side, the reception symbol is also input to the phase detector  202  through the switch  205 . The phase detector  202  detects a phase component of the reception pilot symbol and outputs it to the interpolation filter  203 . 
     The interpolation filter  203  includes a selector  206 , a register  207 , a multiplier  208 , and a tap coefficient update apparatus  209 . The interpolation filter  203  performs weighted interpolation processing on a plurality of reception pilot symbols and estimates phase noise in the reception symbol between the pilot symbols. The phase rotator  204  rotates a phase of the reception symbol based on phase information output by the interpolation filter  203  to compensate the phase noise in the reception symbol. A phase noise compensation method using such a pilot signal is disclosed in, for example, Patent Literature 4. 
     CITATION LIST 
     Patent Literature 
     
         
         Patent Literature 1: International Patent Publication No. WO2011/068119 
         Patent Literature 2: Japanese Unexamined Patent Application Publication No. 2000-101666 
         Patent Literature 3: Japanese Unexamined Patent Application Publication No. 2011-101177 
         Patent Literature 4: International Patent Publication No. WO2013/161801 
       
    
     Non Patent Literature 
     
         
         Non Patent Literature 1: J. Cavers, “An analysis of pilot symbol assisted modulation for Rayleigh fading channel,” IEEE Transactions on Vehicular Technology, vol.40, no.4, pp.686-693, November 1991. 
         Non Patent Literature 2: A. Spalvieri and L. Barletta, “Pilot-aided carrier recovery in the presence of phase noise,” IEEE Transactions on Communications, vol.59, no.7, pp.1966-1974, July 2011. 
         Non Patent Literature 3: N. Kamiya and E. Sasaki, “Pilot-symbol assisted and code-aided phase error estimation for high-order QAM transmission,” IEEE Transactions on Communications, vol.61, no.10, pp.4396-4380, October 2013. 
         Non Patent Literature 4: V. Simon, A. Senst, M. Speth and H. Meyr, “Phase noise estimation through adapted interpolation,” IEEE Global Telecommunications Conference (Globecom), Proceedings, pp.3297-3301, November 2001. 
       
    
     SUMMARY OF INVENTION 
     Technical Problem 
     Recently, there has been a growing demand for increasing a capacity of a wireless communication system, and an expansion of the modulation multilevel number has been required, which poses a problem about compensation of phase noise in an LO signal that greatly affects a transmission characteristic. The effect of phase noise compensation using carrier wave reproduction PLL according to the related art is limited regarding this problem. For example, when a level of the phase noise included in the baseband signal output by the detector is larger than a signal multilevel number of the QAM scheme, a sufficient BER characteristic cannot be achieved, and large-capacity and high-quality data communication becomes difficult. 
     On the other hand, the phase noise compensation apparatus using a pilot signal can compensate the phase noise with high accuracy. However, the phase noise compensation apparatus using a pilot signal has a problem in a trade-off between compensation accuracy and an apparatus size and a calculation amount. In order to improve the compensation accuracy, it is necessary to increase the number of taps of the interpolation filter  203 . An increase in the number of taps involves an increase in the selector  206 , the register  207 , the multiplier  208 , and the tap coefficient update apparatus  209 , thereby increasing the apparatus size and the calculation amount. In particular, the tap coefficient update apparatus  209  includes a register, a multiplier, and an adder, and thus an increase of the tap coefficient update apparatus  209  greatly affects the increase in the apparatus size. A large number of taps are required in order to perform highly accurate phase noise compensation under a transmission condition with a low Carrier-to-Noise Ratio (C/N ratio), which increases an apparatus size of the interpolation filter compared with the case where a phase lock loop is used. 
     In view of the above circumstances, an object of the present disclosure is to provide a phase noise compensation apparatus and method capable of compensating phase noise with high accuracy without requiring a large increase in a calculation amount and an apparatus size. 
     Solution to Problem 
     In order to address the above problem, the present disclosure provides a phase noise compensation apparatus used for a demodulation apparatus for demodulating a transmission signal modulated by a modulation scheme that uses phase information for data identification. The phase noise compensation apparatus includes: a phase detector configured to section reception symbols including a reception data symbol and a reception pilot symbol included in the transmission signal into a block of predetermined number of symbols and detect a phase error of a reception pilot symbol sequence obtained by extracting the reception pilot symbol included in the sectioned reception symbol sequence; a first filter including an infinite impulse response filter configured to refer to the phase error in order in a time series manner and sequentially estimate a first phase noise component of the reception pilot symbol; a second filter including an infinite impulse response filter configured to refer to the phase error in order in a reverse time series manner and sequentially estimate a second phase noise component of the reception pilot symbol; synthesis processing means for estimating a phase noise component of the reception symbol included in the reception symbol sequence based on the first phase noise component, the second phase noise component, and the phase error; and a phase rotator configured to rotate a phase of the reception symbol based on the estimated phase noise component of the reception symbol. 
     The present disclosure further provides a demodulation apparatus including: the above phase noise compensation apparatus; a local oscillator configured to output a signal having a predetermined frequency; and a detector configured to detect the transmission signal using the signal output from the local oscillator and output it to the phase noise compensation apparatus. 
     The present disclosure further provides a reception apparatus including: the above demodulation apparatus; and a reception circuit configured to receive the transmission signal and supply it to the demodulation apparatus. 
     The present disclosure further provides a communication system including: the above reception apparatus; a modulation apparatus configured to modulate transmission data and output a modulated signal to the reception apparatus; and a transmission apparatus including a transmission circuit that transmits the modulated signal to the reception apparatus. 
     The present disclosure further provides a phase noise compensation method including: sectioning a reception symbol sequence including a data symbol and a pilot symbol included in a transmission signal modulated by a modulation scheme that uses phase information for data identification into a block of a predetermined number of symbols and detecting a phase error of a reception pilot symbol sequence obtained by extracting the reception pilot symbol included in the sectioned reception symbol sequence; referring to the phase error in order in a time series manner and sequentially estimating a first phase noise component of the reception pilot symbol using an infinite impulse response filter; referring to the phase error in order in a reverse time series manner and sequentially estimating a second phase noise component of the reception pilot symbol using an infinite impulse response filter; estimating a phase noise component of a reception symbol included in the reception symbol sequence based on the first phase noise component, the second phase noise component, and the phase error; and rotating a phase of the reception symbol based on the estimated phase noise component of the reception symbol. 
     Advantageous Effects of Invention 
     The phase noise compensation apparatus, the demodulation apparatus, the communication apparatus, the communication system, and the phase noise compensation method according to the present disclosure can compensate phase noise with high accuracy without requiring a large increase in a calculation amount and an apparatus size. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a block diagram showing a phase noise compensation apparatus according to the present disclosure; 
         FIG. 2  is a block diagram showing a configuration of the phase noise compensation apparatus according to an embodiment of the present disclosure; 
         FIG. 3  is a block diagram showing an example of a transmission frame structure; 
         FIG. 4  is a view showing an example of a phase noise spectrum of a local oscillator; 
         FIG. 5  is a flowchart showing an operation procedure of the phase noise compensation apparatus; 
         FIG. 6  is a graph showing a relationship between a mean square error and a carrier-to-noise power ratio of a transmission path; 
         FIG. 7  is a block diagram showing a demodulation apparatus; 
         FIG. 8  is a block diagram showing a communication apparatus; 
         FIG. 9  is a block diagram showing a communication system; and 
         FIG. 10  is a block diagram showing a phase noise compensation apparatus according to related art. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     An outline of the present disclosure will be described prior to describing an embodiment according to the present disclosure.  FIG. 1  shows a phase noise compensation apparatus according to the present disclosure. A phase noise compensation apparatus  10  includes a phase detector  11 , a first filter  12 , a second filter  13 , a synthesis processing unit (synthesis processing means)  14 , and a phase rotator  15 . 
     The phase noise compensation apparatus  10  is used in a demodulation apparatus that demodulates a transmission signal modulated by a modulation scheme that uses phase information for data identification. The transmission signal includes data symbols and pilot symbols. The phase detector  11  sections reception symbols included in the transmission signal into a block of a predetermined number of symbols and detects a phase error of a reception pilot symbol sequence which is obtained by extracting reception pilot symbols included in a sectioned reception symbol sequence. 
     The first filter  12  and the second filter  13  each include an infinite impulse response filter. The first filter  12  refers to a phase error detected by the phase detector  11  in a time series manner and sequentially estimates first phase noise components of the reception pilot symbols. The second filter  13  refers to the phase error in a reverse time series manner and sequentially estimates second phase noise components of the reception pilot symbols. The time series here indicates a time sequence in a temporal direction in which the time passes from the past to the present, whereas the reverse time series means a time sequence in a direction on a time axis opposite to the time series. The first filter  12  and the second filter  13  refer to the phase errors in directions on the time axis opposite to each other and estimate the phase noise components. 
     The synthesis processing unit  14  estimates a phase noise component of the reception symbol included in the reception symbol sequence based on the first phase noise component estimated by the first filter  12 , the second phase noise component estimated by the second filter  13 , and the phase error of the reception pilot symbol. The phase rotator  15  rotates a phase of the reception symbol based on the phase noise component of the reception symbol estimated by the synthesis processing unit  14 . 
     Here, the phase noise has a time correlation, and when an attempt is made to estimate the phase noise at a certain point of time, the phase noise can be estimated by making an estimation in a time series manner using past observation values before the point of time. Additionally, phase noise at the same point of time can be estimated in a reverse time series manner using observation values preceding the point of time. In the present disclosure, the phase noise component is estimated in a time series manner using the first filter, and the phase noise component is estimated in a reverse time series manner using the second filter. It can be considered that by using these two estimation results, estimation accuracy higher than when only one estimation result is used can be achieved. Further, in the present disclosure, an infinite impulse response filter is used for the first filter and the second filter, which makes it possible to estimate the phase noise component with high accuracy without requiring a large increase in the calculation amount and the apparatus size. 
     Hereinafter, an embodiment according to the present disclosure will be described in detail with reference to the drawings. However, the components described in the following embodiments are merely examples, and the technical scope of the present disclosure is not limited to them. 
       FIG. 2  shows a phase noise compensation apparatus according to the embodiment of the present disclosure. A phase noise compensation apparatus  100  includes an FIFO (First-In First-Out) memory  101 , a phase rotator  103 , a phase detector  104 , an LIFO (Last-In First-Out) memory  105 , an Infinite Impulse Response (IIR) filter  106 , an IIR filter  108 , and a synthesis processing unit  109 . The phase noise compensation apparatus  100  compensates degradation of a transmission signal caused by phase noise and/or thermal noise generated in a local oscillator. 
     The phase noise compensation apparatus  100  according to the present embodiment is used in a signal reception apparatus in a communication system that performs communication using a modulation scheme that uses phase information for data identification. The communication system may be a wireless communication system that transmits and receives radio signals or may be an optical communication system that transmits and receives optical signals. In the following descriptions, the case in which the modulation scheme is QAM (Quadrature Amplitude Modulation) will be mainly described, but the modulation scheme is not limited to QAM. The modulation scheme may be other modulation schemes that use phase information for data identification such as a PSK (Phase Shift Keying) scheme or an APSK (Amplitude and phase-shift keying) scheme. 
     The phase noise compensation apparatus  100  is implemented by hardware such as LSI (Large-Scale Integration). The phase noise compensation apparatus  100  may be configured as a part of an LSI that implements a signal reception apparatus or another circuit part included in the LSI, for example, as a part of an LSI that implements a demodulation apparatus or the like. At least a part of the processing performed by the phase noise compensation apparatus  100  may be carried out by software processing using a processor. 
     In the phase noise compensation apparatus  100 , a reception symbol corresponding to a reception baseband signal is input to the FIFO memory  101 . The FIFO memory  101  stores a reception symbol sequence obtained by sectioning the reception symbols into a block of a predetermined number of symbols. The FIFO memory  101  outputs each reception symbol included in the stored reception symbol sequence in a time series manner. 
     In the phase noise compensation apparatus  100 , a control circuit (not shown) closes the switch  102  only during a time slot of a reception pilot symbol corresponding to a known pilot signal inserted in a transmission signal on a transmission side. A reception pilot symbol sequence composed of the reception pilot symbols included in the reception symbol sequence is input to the phase detector  104  through the switch  102 . The phase detector  104  detects a phase component (a phase error) of each reception pilot symbol included in the reception pilot sequence. The phase detector  104  outputs the detected phase error to the LIFO memory  105  and the first IIR filter  106 . The phase detector  104  corresponds to the phase detector  11  in  FIG. 1 . 
     The first IIR filter  106  is configured as an infinite impulse response filter having two taps. The first IIR filter  106  refers to the phase error detected by the phase detector  104  in a time series manner and sequentially estimates first phase noise components of the reception pilot symbols. The first IIR filter  106  corresponds to the first filter  12  in  FIG. 1 . 
     The first IIR filter  106  includes multipliers  161  and  162 , an adder  163 , and a register  164 . The multiplier  161  multiplies the phase error detected by the phase detector  104  by a predetermined coefficient (a tap coefficient) stored in a ROM (Read Only Memory)  115 . The register  164  is a delay element. The multiplier  162  multiplies an output of the register  164  by a predetermined coefficient (a tap coefficient) stored in the ROM  114 . The adder  163  adds an output of the multiplier  161  and an output of the multiplier  162 . An output of the adder  163  is stored in the register  164 . The data stored in the register  164  corresponds to the first phase noise component estimated by the first IIR filter  106 . The first IIR filter  106  outputs the first phase noise component from the register  164 . 
     The LIFO memory  105  stores the phase error detected by the phase detector  104 . When the LIFO memory  105  stores the phase error of each reception pilot symbol included in the reception pilot symbol sequence, it outputs the phase error of each reception pilot symbol to the second IIR filter  108  in a reverse order of an input order. The LIFO memory  105  outputs the phase error of each reception pilot symbol also to the synthesis processing unit  109  through the switch  117  and the multiplier  116 . The multiplier  116  multiplies the phase error of the reception pilot symbol input from the LIFO memory  105  through the switch  117  by a predetermined coefficient stored in the ROM  118  and outputs it to the synthesis processing unit  109 . 
     The second IIR filter  108  is configured as an infinite impulse response filter having two taps. The second IIR filter  108  refers to the phase error detected by the phase detector  104  in a reverse time series manner, and sequentially estimates second phase noise components of the reception pilot symbols. When the second IIR filter  108  refers to the phase error in a reverse time series manner, it may use a value calculated using the first phase noise component, which is estimated by the first IIR filter  106 , as an initial value. The second IIR filter  108  corresponds to the second filter  13  in  FIG. 1 . 
     The second IIR filter  108  includes multipliers  181  and  182 , an adder  183 , and a register  184 . The multiplier  181  multiplies a predetermined coefficient stored in the ROM  115  by the phase error input through the LIFO memory  105 . The register  184  is a delay element. The multiplier  182  multiplies an output of the register  184  by a predetermined coefficient stored in the ROM  114 . The adder  183  adds an output of the multiplier  181  and an output of the multiplier  182 . An output of the adder  183  is stored in the register  184 . The data stored in the register  184  corresponds to the second phase noise component estimated by the second IIR filter  108 . The second IIR filter  108  outputs the second phase noise component from the register  184 . 
     The first IIR filter  106  outputs the first phase noise component of the reception pilot symbol sequentially estimated in a time series manner to the LIFO memory  107 . The LIFO  107  memory outputs the first phase noise component input from the first IIR filter  106  to the synthesis processing unit  109  in the reverse order to the input order. The second IIR filter  108  outputs the second phase noise components of the reception pilot symbols sequentially estimated in a reverse time series manner to the synthesis processing unit  109 . The phase error of the reception pilot multiplied by the predetermined coefficient output from the LIFO memory  105  and stored in the ROM  118  by the multiplier  116  is also input to the synthesis processing unit  109 . 
     The synthesis processing unit  109  estimates the phase noise component of each reception symbol included in the reception symbol sequence based on an estimated value of the first phase noise component estimated by the first IIR filter  106 , an estimated value of the second phase noise component estimated by the second IIR filter  108 , and the phase error detected by the phase detector  104 . The synthesis processing unit  109  estimates the phase noise component of each data symbol included in the reception symbol sequence based on, for example, the estimated first phase noise component and second phase noise component. The synthesis processing unit  109  also estimates the phase noise component of the pilot symbol included in the reception symbol sequence based on the estimated first phase noise component and second phase noise component and the phase error of the reception pilot symbol. The synthesis processing unit  109  corresponds to the synthesis processing unit  14  in  FIG. 1 . 
     The synthesis processing unit  109  includes multipliers  191  and  192 , adders  193  and  194 , and a ROM  196 . The multiplier  191  multiplies the output (the estimated first phase noise component) of the first IIR filter  106  input through the LIFO memory  107  by a predetermined coefficient stored in the ROM  196 . The multiplier  192  multiplies the output (the estimated second phase noise component) of the second IIR filter  108  by a predetermined coefficient stored in the ROM  196 . The adder  193  adds an output of the multiplier  191  and an output of the multiplier  192 . In other words, the adder  193  weights and adds the first phase noise component and the second phase noise component with the coefficients (weights) stored in the ROM  196 . 
     The adder  194  adds an output of the adder  193  and the phase error multiplied by the predetermined coefficient in the multiplier  116 . In other words, the adder  194  weights and adds a result of the weighted addition of the first phase noise component and the second phase noise component with the phase error detected by the phase detector  104 . An output of the adder  194  corresponds to the phase noise component estimated by the synthesis processing unit  109 . The predetermined coefficients stored in the ROMs  115 ,  114 ,  118 , and  196  are determined based on a phase noise spectrum of the local oscillator used to demodulate the transmission signal. A specific example of the predetermined coefficients will be described later. 
     The synthesis processing unit  109  outputs the estimated phase noise component to the LIFO memory  110 . The LIFO memory  110  outputs the phase noise component input from the synthesis processing unit  109  to the phase rotator  103  in the reverse order to the input order. The phase rotator  103  rotates the phase of the reception symbol output from the FIFO memory  101  by an amount corresponding to output data of the LIFO memory  110 . The phase rotator  103  compensates the phase noise by rotating the phase of each reception symbol in a direction that cancels the phase noise component estimated by the synthesis processing unit  109 . The phase rotator  103  corresponds to the phase rotator  15  in  FIG. 1 . 
     In the present embodiment, the FIFO memory and LIFO memories are used to control the order of reference and calculation etc. The configuration shown in  FIG. 2  is an example, and the arrangement of the FIFO memory and the LIFO memories is not limited to that shown in  FIG. 2 . Instead of using the FIFO memory, the LIFO memories etc., the order of reference and calculation may be controlled in such a way that the reception symbol sequence, the detection result of the phase error, and the estimation result of the phase noise components are stored in normal memories, and the stored data is read in a specified order by each unit. 
     Further, in the present embodiment, although an example in which each coefficient is stored in the ROM has been described, the present disclosure is not limited to this. Each coefficient may be stored in any type of storage device and is not limited to being stored in a particular type of storage device. 
       FIG. 3  shows an example of a transmission frame. A transmission frame  300  is composed of data symbols  301  and pilot symbols  302 . In the transmission frame  300 , the pilot symbols  302  are arranged, for example, at regular intervals of N symbols, where N is a positive integer. The transmission frame  300  is sectioned into a block of, for example, every MN reception symbols, where M is a positive integer. The MN sectioned reception symbols include M pilot symbols  302 . The phase noise compensation apparatus  100  performs phase noise estimation and phase noise compensation in units of MN reception symbols. 
     In  FIG. 3 , although the pilot symbols are arranged at regular intervals in the reception symbols, the present disclosure is not limited to this. The pilot symbols may be arranged in any way, and the pilot symbols are not necessarily arranged at regular intervals. Hereinafter, an example in which the pilot symbols are arranged at regular intervals will be described for the convenience of descriptions. 
     In the phase noise compensation apparatus  100 , for example, the transmission frame  300  composed of MN reception symbols including the data symbols  301  and the pilot symbols  302  is input. An example of the transmission frame  300  is shown in  FIG. 3 . Hereinafter, the reception symbols are denoted by r(1), r(2), . . . , and r(MN), and transmission symbols corresponding to the reception symbols are denoted by s(1), s(2), . . . , and s(MN). Further, phase noise caused by the local oscillator in each reception symbol is denoted by θ(1), θ(2), . . . , and θ(MN), and noise components caused by thermal noise are denoted by w(1), w(2), . . . , and w(MN). When n is an integer more than or equal to 1 and less than or equal to MN, the reception symbol r(n) can be expressed by the following equation.
 
 r ( n )= s ( n ) e   jθ(n)   +w ( n )
 
     In the above equation, e represents the Napier&#39;s constant and j represents an imaginary unit. It is assumed that the thermal noise w(n) is white noise with an average of 0 and a variance of σ 2 . The thermal noise has a flat spectrum. On the other hand, the phase noise has a non-flat spectrum.  FIG. 4  shows an example of a phase noise spectrum. In the example shown in  FIG. 4 , the phase noise spectrum is constant at a frequency lower than or equal to the frequency f p  (Hz) and at a frequency higher than or equal to f z  (Hz), and a section between f p  and f z  has a gradient of −20 dBc/dec. The power spectral density at a frequency 0 (Hz) is K 0 . An example of a case where the phase noise has a spectrum shown in  FIG. 4  will be described below. 
     Among the MN transmission symbols transmitted from the transmission side, M transmission symbols s(N), s(2N), . . . , and s(MN) are transmission pilot symbols defined in advance and corresponding to pilot signals known at the reception side. Suppose that power P of the pilot signal matches an average value of transmission symbol power. Among the MN reception symbols input to the phase noise compensation apparatus  100 , reception symbols r(N), r(2N), . . . , and r(MN) are the reception pilot symbols corresponding to the pilot signal. 
     The phase noise compensation apparatus  100  receives the input reception symbols r(1), r(2), . . . , r(MN) and sequentially stores them in the FIFO memory  101 . The M reception pilot symbols r(N), r(2 N), . . . , and r(MN) among the MN reception symbols are input to the phase detector  104  through the switch  102 . When k is an integer more than or equal to 1 and less than or equal to M, the phase detector  104  calculates a phase difference (a phase error) between each reception pilot symbol r(kN) and a known transmission pilot symbol s(kN). More specifically, the phase detector  104  calculates a phase difference φ(kN) between the reception pilot symbol r(kN) and the transmission pilot symbol s(kN) using the equation below, where arg(z) is a function representing an argument of a complex number z.
 
φ( kN )=arg( r ( kN )/ s ( kN ))
 
     The phase difference φ(kN) calculated by the above equation can be expressed by the following equation using the phase noise θ(kN) of the reception pilot symbol and random noise w θ (kN) caused by heat.
 
φ( kN )=θ( kN )+ w   θ ( kN )
 
In this equation, w θ (kN) is a random sequence with an average of 0 and a variance of σ θ   2 . The σ θ   2  can be expressed as σ θ   2 =σ 2 /(2P) using the above-mentioned noise variance σ 2  of the thermal noise and the average signal power P. The phase noise compensation apparatus  100  estimates the phase noise θ(1), θ(2), . . . , and θ(MN) of the MN reception symbols from the M phase differences φ(N), φ(2N), . . . , and φ(MN) detected by the phase detector  104 .
 
     The phase detector  104  outputs the M phase differences φ(N), φ(2N), . . . , and φ(MN) to the first IIR filter  106  and the LIFO memory  105 . After the input of the phase differences φ(N), φ(2 N), . . . , and φ(MN) to the LIFO memory  105  is completed, the LIFO memory  105  outputs the stored phase differences to the second IIR filter  108  in the order of φ(MN), φ((M−1)N), . . . , and φ(N). The presence of the LIFO memory  105  between the phase detector  104  and the second IIR filter  108  makes it possible for the first IIR filter  106  and the second IIR filter  108  to refer to the phase differences φ(N), φ(2N), . . . , and φ(MN) in reverse order to each other. Hereinafter, the first phase noise component estimated by the first IIR filter  106  is represented by θ + , and the second phase noise component estimated by the second IIR filter  108  is represented by θ − . 
     As described above, the first IIR filter  106  includes two multipliers  161  and  162 , one adder  163 , and one register  164 . The first IIR filter  106  estimates the first phase noise component and then outputs the estimated value θ +  thereof. More specifically, the first IIR filter  106  calculates an estimated value θ + ((k+1)N) of the first phase noise component of the k+1th reception pilot symbol using an estimated value θ + (kN) of the first phase noise component of the kth reception pilot symbol and the phase difference φ(kN). 
     Specifically, the first IIR filter  106  sequentially performs the calculation of the following equation to sequentially calculate the estimated values θ + (N), θ + (2N), . . . , θ + (MN), and θ + ((M+1)N) of the first phase noise components of the reception pilot symbols.
 
θ + (( k+ 1) N )← p   1 θ + ( kN )+ p   2 φ( kN ),  k= 1, 2, . . . ,  M  
 
     In this equation, θ + (N) is an initial value of the register  164 . Further, p 1  is a tap coefficient stored in the ROM  114 , and p 2  is a tap coefficient stored in the ROM  115 . Further, p 1  and p 2  are determined based on the phase noise spectrum, a pilot symbol interval N, the noise variance σ θ   2 , and the like, which will be described later. 
     The first IIR filter  106  outputs the estimated values θ + (N), θ + (2N), . . . , and θ + (MN) of the first to Mth reception pilot symbols to the LIFO memory  107 . The estimated value θ + ((M+1)N) of the first phase noise of the M+1th reception pilot symbol calculated by the first IIR filter  106  is an initial value of the register  164  in the processing of the next frame. 
     Although not shown in  FIG. 2  in order to make the drawing simple, the estimated value θ + ((M+1)N) of the phase noise of the M+1th reception pilot symbol is supplied to the second IIR filter  108  and is used to calculate the initial value in the second IIR filter  108 . Specifically, the initial value θ − (MN) of the second IIR filter  108  is calculated by the following equation using the estimated value θ + ((M+1)N) of the first phase noise.
 
θ − ( MN )← p   3 θ + (( M+ 1) N )
 
     In this equation, p 3  is a coefficient determined based on the phase noise spectrum, the pilot symbol interval N, the noise variance σ θ   2 , and the like in a manner similar to the above p 1  and p 2 . 
     Like the first IIR filter  106 , the second IIR filter  108  includes two multipliers  181  and  182 , one adder  183 , and one register  184 . The second IIR filter  108  estimates the second phase noise component and outputs an estimated value θ −  thereof. More specifically, the second IIR filter  108  uses the estimated value θ − (kN) of the second phase noise component of the kth reception pilot symbol and the phase difference φ(kN) to calculate an estimated value θ − ((k−1)N) of the second phase noise component of the k−1th reception pilot symbol. 
     Specifically, the second IIR filter  108  sequentially performs the calculation shown in the following equation to sequentially calculate the estimated values θ − (MN), θ + ((M−1)N), . . . , θ + (N), and θ + (0) of the second phase noise components of the reception pilot symbols.
 
θ − (( k− 1) N )← p   1 θ − ( kN )+ p   2 φ( kN ),  k=M, M− 1, . . . , 1
 
     The LIFO memory  107  outputs the estimated values θ + (N), θ + (2N), . . . , and θ + (MN) of the first phase noise components output from the first IIR filter  106  to the synthesis processing unit  109  in the reverse order to the input order. That is, the LIFO memory  107  sequentially outputs the estimated values θ + (MN), θ + ((M−1)N), . . . , and θ + (N) of the first phase noise components. The second IIR filter  108  sequentially outputs the estimated values θ − (MN), θ + ((M−1)N), . . . , θ + (N), and θ + (0) of the second phase noise components to the synthesis processing unit  109 . The LIFO memory  105  sequentially outputs the phase differences φ(MN), φ((M−1)N), . . . , and φ(N) to the synthesis processing unit  109  through the switch  117  and the multiplier  116 . 
     The synthesis processing unit  109  estimates the phase noise component of each reception symbol r(n) including the data symbols  301  and the pilot symbols  302  (see  FIG. 3 ) based on the input data. The phase noise component of each reception symbol estimated by the synthesis processing unit  109  is represented by θ ± (n). 
     The synthesis processing unit  109  calculates the estimated value θ ± (kN) of the phase noise component of the reception pilot symbol using the estimated value θ + (kN) of the first phase noise component, the estimated value θ − (kN) of the second phase noise component, and the phase difference φ(kN). Further, the synthesis processing unit  109  calculates the estimated value θ ± (1+(k−1)N) of the phase noise component of the reception symbol corresponding to the data symbol  301  using the estimated value θ + (kN) of the first phase noise component and the estimated value θ − ((k−1)N) of the second phase noise component, where 1 is an integer more than or equal to 1 and less than or equal to N−1. 
     Specifically, the synthesis processing unit  109  sequentially performs the calculation shown in the following equation to calculate the estimated value θ ± (kN) of the phase noise component of the reception pilot symbol.
 
 ± ( kN )← p   4,N (θ + ( kN )+θ − ( kN ))+ p   5 φ( kN ),  k=M, M− 1, . . . , 1
 
     Furthermore, the synthesis processing unit  109  sequentially performs the calculation shown in the following equation to calculate the estimated value θ ± (1+( k− 1)N) of the phase noise component of the reception symbol corresponding to the data symbol  301  that is sandwiched between the two adjacent reception pilot symbols.
 
θ ± (1+( k− 1) N )← p   4,1 θ + ( kN )+ p   4,N−1 θ − (( k− 1) N ), 1= N− 1,  N− 2, . . . , 1
 
     In this equation, p 4,1  to p 4,N  are coefficients stored in the ROM  196 , and p 5  is a coefficient stored in the ROM  118 . Like p 1  to p 3 , p 4,1  to p 4,N  and p 5  are determined based on the phase noise spectrum, the pilot symbol interval N, the noise variance σ θ   2 , and the like. 
     The synthesis processing unit  109  sequentially outputs the estimated values θ ± (MN), θ ± (MN−1), . . . , and θ ± (1) of the phase noise components of the respective reception symbols. The LIFO memory  110  rearranges the order of the phase noise components output from the synthesis processing unit  109  and sequentially outputs the estimated values θ ± (1), θ ± (2), . . . , and θ ± (MN) to the phase rotator  103 . The phase rotator  103  rotates the phase of the reception symbol r(n) output from the FIFO memory  101  by the estimated value θ ± (n) of the phase noise component to compensate for the phase noise component, and outputs the reception symbol r c (n), the phase noise component of which is compensated. The compensated reception symbol r c (n) can be expressed by the following equation.
 
 r   c ( n )= r ( n ) e   −jθ     ±     (n)    [Equation 1]
 
     Next, a method of calculating each coefficient (a constant) stored in the ROM  114 ,  115 ,  118 , and  196  will be described. Hereinafter, an example of a case where the phase noise spectrum of the local oscillator is modeled as shown in  FIG. 4  will be described. As shown in  FIG. 4 , the phase noise spectrum is constant at a frequency less than or equal to f p (Hz) and at a frequency more than or equal to f z (Hz), and a section between f p (Hz) and f z (Hz) has a gradient of −20 dBc/Dec. The power spectrum density at a frequency 0(Hz) is K 0 , and the transmission symbol rate is f s (Hz). The constants a1, b1, and K1 used to calculate the coefficients stored in the respective ROMs are defined by the following equations. 
                             a   1     =         f   s     -     π   ⁢           ⁢     f   z             f   s     +     π   ⁢           ⁢     f   z             ,               b   1     =         f   s     -     π   ⁢           ⁢     f   p             f   s     +     π   ⁢           ⁢     f   p             ,             K   1     =       K   0     ⁢         f   s     ⁡     (       1   -     b   1         1   -     a   1         )       2                     [     Equation   ⁢           ⁢   2     ]               
In this equation, the circular constant is denoted by π. Using the above constants, different constants α and η are defined by the following equations.
 
     
       
         
           
             
               
                 
                   
                     α 
                     = 
                     
                       
                         
                           
                             K 
                             1 
                           
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                   ⁢ 
                   
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                     = 
                     
                       
                         
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                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     3 
                   
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     The coefficients p 1 , p 2 , p 3 , p 4,1 , and p 5  used for estimating the phase noise components are defined by the following equations respectively using the constants defined above. 
     
       
         
           
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     
                       p 
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                     ⁢ 
                     
                         
                     
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                     ⁢ 
                     
                         
                     
                     ⁢ 
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                     ⁢ 
                     
                         
                     
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                     6 
                   
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                     Equation 
                     ⁢ 
                     
                         
                     
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                     7 
                   
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                     ⁢ 
                     
                         
                     
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                     8 
                   
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     The inventor of the present disclosure has derived the coefficients defined by the above respective equations as the coefficient in which the mean square error of the estimation result of the phase noise component becomes minimum when the frequency spectrum of the phase noise of the local oscillator is the one shown in  FIG. 4 . The value of each coefficient does not have to be exactly the same as the value defined by the above equation as long as the mean square error of the estimation result of the phase noise component is within an allowable range, and may be an approximate value defined by the above equation. When the frequency spectrum of the phase noise of the local oscillator differs from that shown in  FIG. 4 , a value of the coefficient that can keep the mean square error of the estimation result of the phase noise component within the allowable range may be searched for, while repeatedly setting values of the respective coefficients and verifying them. 
     Next, an operation procedure of the phase noise compensation apparatus  100  will be described.  FIG. 5  shows the operation procedure of the phase noise compensation apparatus  100 . The FIFO memory  101  stores the reception symbols r(n) constituting the transmission frame  300  (see  FIG. 3 ) that are sequentially input to the phase noise compensation apparatus  100 . The reception pilot symbols corresponding to the pilot symbols  302  among the input reception symbols r(n) are sequentially input to the phase detector  104  through the switch  102 . The phase detector  104  detects the phase error (the phase difference φ(kN)) of each reception pilot symbol (Step A 1 ). The phase detector  104  sequentially outputs the M phase differences φ(kN) of the detected reception pilot symbols to the first IIR filter  106  and the LIFO memory  105  in the order along the time series. The LIFO memory  105  outputs the M phase differences φ(kN) of the reception pilot symbols to the second IIR filter  108  and the switch  117  in the reverse order to the input order. 
     The first IIR filter  106  sequentially estimates the first phase noise components θ + ((k+1)N) of the reception pilot symbols using the phase differences φ(kN) of the reception pilots sequentially output by the phase detector  104  (Step A 2 ). The first IIR filter  106  starts processing in a state where the initial value θ + (N) is stored in the register  164 . The first IIR filter  106  calculates the estimated value θ + ((k+1)N) of the first phase noise of the k+1th reception pilot symbol from the phase difference φ(kN) of the kth reception pilot symbol input along the time series and the estimated value θ + (kN) of the previous first phase noise component delayed by the register  164  and stores the estimated value θ + ((k+1)N)in the register  164 . In the processing of consecutive transmission frames, the initial value θ + (N) is given from a processing result of the previous transmission frame. In the case of the first frame having no preceding frame, a predetermined value, for example, 0 is given as the initial value θ + (N). The first IIR filter  106  outputs the estimated values θ + (N), θ+(2N), . . . , and θ+(MN) of the first phase noise components including the initial value θ + (N). The estimated value θ + ((M+1)N) of the first phase noise component of the k+1th reception pilot symbol becomes the initial value of the next transmission frame and is used to calculate the initial value of the second IIR filter  108 . 
     The phase differences φ(kN) of the reception pilots sequentially output by the phase detector  104  are input to the second IIR filter  108  through the LIFO memory  105  in a reverse time series manner. That is, the phase differences φ(MN), φ((M−1)N), . . . , and φ(N) are sequentially input to the second IIR filter  108 . Although not shown in  FIG. 2 , the estimated value θ + ((M+1)N) of the first phase noise component of the k+1th reception pilot symbol output from the first IIR filter  106  is also input to the second IIR filter  108 , and the initial value determined based on the estimated value θ + ((M+1)N) of the first phase noise component is stored in the register  184 . 
     The second IIR filter  108  sequentially estimates the second phase noise components θ − ((k−1)N) of the reception pilot symbols using the phase differences φ(kN) input in a reverse time series manner (Step A 3 ). The second IIR filter  108  calculates the estimated value θ − ((k−1)N) of the second phase noise of the k−1th reception pilot symbol from the phase difference φ(kN) of the kth reception pilot symbol input in a reverse time series manner and the estimated value θ − (kN) of the previous second phase noise component delayed by the register  184  and stores the estimated value θ − ((k−1)N) in the register  184 . The second IIR filter  108  outputs the estimated values θ − (MN), θ − ((M−1)N), . . . , θ − (1), and θ − (0) including the initial value θ − (MN) of the second phase noise components. 
     The estimated value θ + (MN), θ + ((M−1)N), . . . , and θ + (N) of the first phase noise components are sequentially input to the synthesis processing unit  109  through the LIFO memory  107 , and the estimated values θ − (MN), θ − ((M−1)N), . . . , θ − (1), and θ − (0) of the second phase noise components are sequentially input to the to the synthesis processing unit  109  through the LIFO memory  107 . Further, the phase differences φ(MN), φ((M−1)N), . . . , and φ(N) of the reception pilot symbols are sequentially input to the synthesis processing unit  109  through the switch  117  and the multiplier  116 . The synthesis processing unit  109  estimates the phase noise component of each reception symbol r(n) based on the phase difference of the reception pilot symbol input from the multiplier  116 , the first phase noise component input from the first IIR filter  106 , and the second phase noise component input from the second IIR filter  108  (Step A 4 ). 
     In Step A 4 , the switch  117  is closed at the timing when the synthesis processing unit  109  calculates the estimated value θ ± (kN) of the phase noise component of the reception pilot symbol. In Step A 4 , when n is an integer multiple of N (n=kN), that is, when the reception symbol is a reception pilot symbol corresponding to the pilot symbol  302 , the synthesis processing unit  109  calculates the estimated value θ ± (kN) of the phase noise component based on the first phase noise component θ + (kN), the second phase noise component θ − (kN), and the phase difference φ(kN) of the reception pilot symbol. When n is larger than (k−1)N and smaller than kN, i.e., ((k−1) N&lt;n&lt;kN), specifically, when the reception symbol is a symbol corresponding to the data symbol  301 , the synthesis processing unit  109  calculates the estimated value θ ± (n) of the phase noise component based on the first phase noise component θ + (kN) and the second phase noise component θ − ((k−1)N). The synthesis processing unit  109  sequentially calculates the estimated values θ ± (MN), θ ± (MN−1), θ ± (MN−2), . . . , and θ ± (1) of the phase noise components of the respective reception symbols and outputs them. 
     The phase noise component of each reception symbol estimated by the synthesis processing unit  109  is input to the phase rotator  103  through the LIFO memory  110 . The phase rotator  103  rotates the phase of the reception symbol r(n) output from the FIFO memory  101  by the estimated phase noise component of each reception symbol (Step A 5 ). The phase noise component included in each reception symbol can be removed by rotating the phase of the reception symbol r(n) by the estimated phase noise component. 
     In the present embodiment, the phase noise compensation apparatus  100  includes the first IIR filter  106  and the second IIR filter  108  that estimate the phase noise components of the reception pilot symbols. The first IIR filter  106  refers to the phase errors of the reception pilot symbols in a time series manner, whereas the second IIR filter  108  refers to the phase errors of the reception pilot symbols in a reverse time series manner. It is known that there is time correlation in phase noise. When estimation results of two phase noise components obtained using time correlation in two time directions are used for estimating the phase noise component of the reception symbol, the estimation accuracy of the phase noise component is expected to improve more than when only one estimation result is used. The phase noise compensation apparatus  100  according to the present embodiment can compensate phase noise with high accuracy, and when used in a multilevel QAM transmission scheme having a large number of transmission multilevels, it is possible to achieve data communication with a large capacity and high quality. 
     In the present embodiment, the first IIR filter  106  and the second IIR filter  108  are used for estimating the phase noise components of the respective reception pilot symbols. In the phase noise compensation apparatus  200  (see  FIG. 10 ) according to the related art using the pilot symbol and the interpolation filter, it is necessary to increase the number of taps of the interpolation filter  203  in order to improve the compensation accuracy. In the phase noise compensation apparatus  200  according to the related art, the increase in the number of taps causes the apparatus size and the calculation amount to increase. In the present embodiment, each of the first IIR filter  106  and the second IIR filter  108  is configured as the IIR filter having two taps, and thus they can estimate the phase noise component with less number of taps as compared with the phase noise compensation apparatus  200  according to the related art. Therefore, the phase noise compensation apparatus  100  according to the present embodiment can achieve highly accurate phase compensation with a smaller apparatus size and calculation amount as compared with the phase noise compensation apparatus  200  according to the related art. 
     An effect of the phase noise compensation apparatus according to the above embodiment will be described with reference to numerical examples. The inventor carried out a simulation and obtained a mean square error that remains after the phase noise is compensated for each of the phase noise compensation apparatus  100  according to the above embodiment and the phase noise compensation apparatus  200  according to the related art shown in  FIG. 10 . In the simulation, the parameters f p , f z , and K 0  in the phase noise spectrum of the local oscillator shown in  FIG. 4  were set such that f p =100 Hz, f z =5 MHz, and K 0 =−35 dBc/Hz, and the symbol rate was set to f s =24 MHz. Further, the pilot signal interval was set to N=50 symbols, and one transmission frame was set to MN=500 symbols. The modulation scheme was 256 QAM scheme. In the phase noise compensation apparatus  200  according to the related art, the number of taps of the interpolation filter  203  was set to 11. 
     The results of the simulation are shown in  FIG. 6 . In the graph shown in  FIG. 6 , the horizontal axis represents a carrier-to-noise power ratio (CNR) caused by thermal noise, and the vertical axis represents the mean square error with respect to the remaining phase noise in decibels. In  FIG. 6 , the mean square error of the phase noise compensation apparatus  100  according to the present embodiment is plotted with circular symbols, and the mean square error of the phase noise compensation apparatus  200  according to the related art is plotted with triangular symbols. The broken line shown in  FIG. 6  shows a lower limit value of the mean square error. 
     Referring to  FIG. 6 , when the carrier-to-noise power ratio is relatively large, for example, when the CNR is equal to or greater than 30 dB, the mean square error almost reaches the lower limit value both in the phase noise compensation apparatus  100  according to the present embodiment and in the phase noise compensation apparatus  200  according to the related art. On the other hand, when the carrier-to-noise power ratio is small, the mean square error in the phase noise compensation apparatus  100  according to the present embodiment exhibits a characteristic better than that of the phase noise compensation apparatus  200  according to the related art by a few dB, even though it deviates from the lower limit value. 
     Furthermore, the number of multipliers necessary for the filter in the phase noise compensation apparatus  100  according to the present embodiment is about ⅓ of that of the phase noise compensation apparatus  200  according to the related art. Considering the case in which the phase noise compensation apparatus is implemented as an IC (Integrated Circuit) etc., it is preferable that the number of multipliers be small, because the multiplier has a particularly large influence on the apparatus size. The phase noise compensation apparatus  100  according to the present embodiment can reduce the number of the multipliers and the apparatus size as compared with the phase noise compensation apparatus  200  according to the related art. 
     Moreover, when comparing the calculation amount required for deriving the phase noise estimated value necessary for one symbol in the phase noise compensation apparatus  100  according to the present embodiment with that in the phase noise compensation apparatus  200  according to the related art, the calculation amount in the phase noise compensation apparatus  100  according to the present embodiment is about ¼ of that in the phase noise compensation apparatus  200  according to the related art. As described above, it has been confirmed that the phase noise compensation apparatus  100  according to the present embodiment is capable of compensating the phase noise with high accuracy while reducing the apparatus size and the calculation amount as compared with the phase noise compensation apparatus according to the related art. 
     Next, a demodulation apparatus including the phase noise compensation apparatus  100  will be described.  FIG. 7  shows the demodulation apparatus including the phase noise compensation apparatus  100 . A demodulation apparatus  120  includes the phase noise compensation apparatus  100 , a detector  121 , an oscillator  122 , an A/D convertor (analog to digital convertor)  123 , an interference removal apparatus  124 , and an error correction apparatus  125 . The detector  121  detects a signal modulated by a modulation scheme that uses the phase information for data identification using a signal of a predetermined frequency output by the oscillator  122  that is a local oscillator. The A/D convertor  123  converts the detection signal output by the detector  121  from an analog signal to a digital signal. 
     The interference removal apparatus  124  removes an interference component from the detection signal output from the A/D convertor  123 . As described in the above embodiment, the phase noise compensation apparatus  100  estimates the first phase noise component and the second phase noise component of each reception pilot symbol, estimates the phase noise component of each reception symbol using these phase noise components and the phase error of each reception pilot symbol, and compensates the phase noise component of each reception symbol. The error correction apparatus  125  performs predetermined error correction processing on the signal in which the phase noise component is compensated. The error correction apparatus  125  outputs a demodulated signal obtained by demodulating the signal modulated on the transmission side. 
     Next, a communication apparatus including the demodulation apparatus  120  will be described.  FIG. 8  shows a communication apparatus  130  including the demodulation apparatus  120 . The communication apparatus  130  includes the demodulation apparatus  120 , a modulation apparatus  131 , a high frequency transmission circuit  132 , a high frequency reception circuit  133 , and an antenna  134 . The communication apparatus  130  is configured as a digital wireless communication apparatus that, for example, transmits and receives radio signals having frequencies in a microwave band or a millimeter wave band. The communication apparatus  130  may be configured as an optical communication apparatus that transmits and receives optical signals by, for example, the WDM (Wavelength Division Multiplexing) scheme. 
     The modulation apparatus  131  modulates transmission data input from a signal processing circuit (not shown) by a modulation scheme that uses phase information for data identification. The high frequency transmission circuit  132  transmits the signal modulated by the modulation apparatus  131  to another communication apparatus  130  through the antenna  134 . The high frequency reception circuit  133  receives the signal transmitted from the other communication apparatus  130  through the antenna  134 . The demodulation apparatus  120  demodulates the data modulated on the transmission side from the signal received by the high frequency reception circuit  133 . The demodulation apparatus  120  outputs the demodulated data to a signal processing circuit (not shown) etc. In the demodulation apparatus  120 , the phase noise component can be compensated with high accuracy, and thus the data modulated on the transmission side can be demodulated with high accuracy. 
       FIG. 9  shows a communication system including the communication apparatus  130 . A communication system  140  includes two communication apparatuses  130  connected to each other through a transmission path  141 . The transmission path  141  may be a wireless transmission path or a wired transmission path. The wired transmission path includes, for example, an electric communication line that performs signal transmission using an electric signal and an optical communication line that performs signal transmission using an optical signal. The communication system  140  is not limited to the one in which the two communication apparatuses  130  are connected to each other through the transmission path  141  and instead may have a configuration in which a plurality of the communication apparatuses  130  are connected to one another through a network. Highly reliable data transmission can be achieved in the communication system  140 , because the communication apparatus  130  can modulate the data modulated on the transmission side with high accuracy. 
     It should be noted that, although the example in which the communication apparatus  130  includes the demodulation apparatus  120  and the high frequency reception circuit  133 , and the modulation apparatus  131  and the high frequency transmission circuit  132  has been described with reference to  FIG. 8 , the present disclosure is not limited to this. For example, when the data transmission in the communication system  140  shown in  FIG. 9  only needs to be one way from one communication apparatus  130  to the other communication apparatus  130 , the communication apparatus  130  may include only a circuit necessary for transmission or reception. For example, the communication apparatus  130  on the transmission side may include the modulation apparatus  131  and the high frequency transmission circuit  132 , and the communication apparatus  130  on the reception side may include the demodulation apparatus  120  and the high frequency reception circuit  133 . 
     Although the present disclosure has been described with reference to the embodiment, the present disclosure is not limited by the above description. Various changes that can be understood by those skilled in the art within the scope of the disclosure can be made to the components and details of the present disclosure. 
     For example, the whole or part of the embodiments disclosed above can be described as, but not limited to, the following supplementary notes. 
     [Supplementary Note 1] 
     A phase noise compensation apparatus used for a demodulation apparatus for demodulating a transmission signal modulated by a modulation scheme that uses phase information for data identification, the phase noise compensation apparatus comprising: 
     a phase detector configured to section reception symbols including a reception data symbol and a reception pilot symbol included in the transmission signal into a block of a predetermined number of symbols and detect a phase error of a reception pilot symbol sequence obtained by extracting the reception pilot symbols included in the sectioned reception symbol sequence; 
     a first filter including an infinite impulse response filter and configured to refer to the phase error in order in a time series manner and sequentially estimate a first phase noise component of the reception pilot symbol; 
     a second filter including an infinite impulse response filter and configured to refer to the phase error in order in a reverse time series manner and sequentially estimate a second phase noise component of the reception pilot symbol; 
     synthesis processing means configured to estimate a phase noise component of the reception symbol included in the reception symbol sequence based on the first phase noise component, the second phase noise component, and the phase error; and 
     a phase rotator configured to rotate a phase of the reception symbol based on the estimated phase noise component of the reception symbol. 
     [Supplementary Note 2] 
     The phase noise compensation apparatus according to Supplementary note 1, wherein each of the infinite impulse response filter included in the first filter and the infinite impulse response filter included in the second filter includes one delay element. 
     [Supplementary Note 3] 
     The phase noise compensation apparatus according to Supplementary note 1 or 2, wherein the synthesis processing means comprises an adder configured to weight and add the first phase noise component and the second phase noise component. 
     [Supplementary Note 4] 
     The phase noise compensation apparatus according to Supplementary note 3, wherein the adder further weights and adds the phase error. 
     [Supplementary Note 5] 
     The phase noise compensation apparatus according to Supplementary note 3 or 4, wherein the adder performs weighting and adding with weights determined based on a phase noise spectrum of a local oscillator used to demodulate the transmission signal. 
     [Supplementary Note 6] 
     The phase noise compensation apparatus according to any one of Supplementary notes 1 to 5, wherein in the second filter, an initial value of the infinite impulse response filter is set based on the first phase noise component estimated by the first filter. 
     [Supplementary Note 7] 
     The phase noise compensation apparatus according to any one of Supplementary notes 1 to 6, wherein the synthesis processing means estimates the phase noise component of the reception data symbol included in the reception symbol sequence based on the first phase noise component and the second phase noise component. 
     [Supplementary Note 8] 
     The phase noise compensation apparatus according to any one of Supplementary notes 1 to 7, wherein the synthesis processing means estimates the phase noise component of the reception pilot symbol included in the reception symbol sequence based on the first phase noise component, the second phase noise component, and the phase error. 
     [Supplementary Note 9] 
     The phase noise compensation apparatus according to any one of Supplementary notes 1 to 8, wherein the synthesis processing means estimates the phase noise component of each reception data symbol included between a k−1th reception pilot symbol and a kth reception pilot symbol based on the first phase noise component of the kth reception pilot symbol and the second phase noise component of the k−1th reception pilot symbol, when the reception pilot symbol sequence includes M reception pilot symbols, where M is a positive integer, and k is a positive integer of more than or equal to 1 and less than or equal to M. 
     [Supplementary Note 10] 
     The phase noise compensation apparatus according to Supplementary note 9, wherein the synthesis processing means estimates the phase noise component of the kth reception pilot symbol based on the first phase noise component of the kth reception pilot symbol, the second phase noise component of the kth reception pilot symbol, and the phase error of the kth reception pilot symbol. 
     [Supplementary Note 11] 
     A demodulation apparatus comprising: 
     the phase noise compensation apparatus according to any one of Supplementary notes 1 to 10; 
     a local oscillator configured to output a signal having a predetermined frequency; and 
     a detector configured to detect the transmission signal using the signal output from the local oscillator and output it to the phase noise compensation apparatus. 
     [Supplementary Note 12] 
     A reception apparatus comprising: 
     the demodulation apparatus according to Supplementary note 11; and 
     a reception circuit configured to receive the transmission signal and supply it to the demodulation apparatus. 
     [Supplementary Note 13] 
     A communication system comprising: 
     the reception apparatus according to Supplementary note 12; 
     a modulation apparatus configured to modulate transmission data and output a modulated signal to the reception apparatus; and 
     a transmission apparatus including a transmission circuit configured to transmit the modulated signal to the reception apparatus. 
     [Supplementary Note 14] 
     A phase noise compensation method comprising: 
     sectioning a reception symbol sequence including a data symbol and a pilot symbol included in a transmission signal modulated by a modulation scheme that uses phase information for data identification into a block of a predetermined number of symbols and detecting a phase error of a reception pilot symbol sequence obtained by extracting the reception pilot symbols included in the sectioned reception symbol sequence; 
     referring to the phase error in order in a time series manner and sequentially estimating a first phase noise component of the reception pilot symbol using an infinite impulse response filter; 
     referring to the phase error in order in a reverse time series manner and sequentially estimating a second phase noise component of the reception pilot symbol using an infinite impulse response filter; 
     estimating a phase noise component of a reception symbol included in the reception symbol sequence based on the first phase noise component, the second phase noise component, and the phase error; and 
     rotating a phase of the reception symbol based on the estimated phase noise component of the reception symbol. 
     The present application is based upon and claims the benefit of priority from Japanese Patent Application No. 2016-160081, filed on Aug. 17, 2016, the entire contents of which are hereby incorporated by reference. 
     REFERENCE SIGNS LIST 
     
         
           10 : PHASE NOISE COMPENSATION APPARATUS 
           11 : PHASE DETECTOR 
           12 ,  13 : FILTER 
           14 : SYNTHESIS PROCESSING UNIT 
           15 : PHASE ROTATOR 
           100 : PHASE NOISE COMPENSATION APPARATUS 
           101 : FIFO MEMORY 
           102 ,  117 : SWITCH 
           103 : PHASE ROTATOR 
           104 : PHASE DETECTOR 
           105 ,  107 ,  110 : LIFO MEMORY 
           106 ,  108 : INFINITE IMPULSE RESPONSE FILTER (IIR FILTER) 
           109 : SYNTHESIS PROCESSING UNIT 
           161 ,  162 ,  181 ,  182 : MULTIPLIER 
           163 ,  183 : ADDER 
           164 ,  184 : REGISTER 
           114 ,  115 ,  118 ,  196 : ROM 
           200 : PHASE NOISE COMPENSATION APPARATUS 
           201 : FIFO MEMORY 
           205 : SWITCH 
           204 : PHASE ROTATOR 
           202 : PHASE DETECTOR 
           203 : INTERPOLATION FILTER 
           206 : SELECTOR 
           209 : TAP COEFFICIENT UPDATE APPARATUS 
           300 : TRANSMISSION FRAME 
           301 : DATA SYMBOL 
           302 : PILOT SYMBOL