Abstract:
Disclosed is a transmission device capable of reducing quantization errors in nonlinear quantization of IQ signals. In the device, a standard deviation measuring unit measures a standard deviation σ of the amplitude distribution of input signals. A kurtosis measuring unit measures the kurtosis of the amplitude distribution of the input signals. A correction coefficient determining unit determines a correction coefficient α corresponding to the kurtosis of the amplitude distribution of the input signals. A quantization unit quantizes the input signals using the correction coefficient α and calculates quantization data. A multiplexing unit multiplexes the quantization data and quantization control information with each other.

Description:
TECHNICAL FIELD 
     The present disclosure relates to a transmission apparatus and a quantization method. 
     BACKGROUND ART 
     For interfaces complying with ORI (Open Radio equipment Interface) which is an international standard, data compression techniques have been studied for the purpose of reducing the transfer rate of the IQ signal between the REC (Radio Equipment Control) and the RE (Radio Equipment) (see, for example, Non-PTLS 1 to 3). 
     Data compression techniques of the IQ signal include down-sampling (reduction of sampling rate), and non-linear quantization (reduction of transmission bit number). 
     By utilizing the characteristics in which the distribution of the signal amplitude of the real part and the imaginary part (hereinafter referred to as IQ) is a regular distribution (see, for example,  FIG. 1( a ) ), the non-linear quantization employs an algorithm for reducing the transmission bit number of each sample by use of the cumulative distribution function (CDF) of the amplitude of the IQ signal (see, for example,  FIG. 1( b ) ). To be more specific, in non-linear quantization, the quantization threshold is set such that the sample value corresponding to the amplitude having a higher occurrence probability is more correctly indicated (the quantization error is reduced) in comparison with the sample value corresponding to the amplitude having a lower occurrence probability in consideration of the frequency of generation (occurrence probability) of the amplitude of the input signal. That is, in the amplitude distribution of the IQ signal, the interval of the quantization threshold of the amplitude having a high occurrence probability (the amplitudes around the average value) is set to a value smaller than the interval of the quantization threshold of the amplitude having a low occurrence probability (see, for example,  FIG. 1( c ) ). 
     Cumulative distribution function g(x) of the regular distribution can be expressed with error function (erf) as in Expression (1). 
     
       
         
           
             
               
                 
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     In Expression (1), x is an integer value representing the IQ signal for compression (that is, the input signal), which falls within the range of [−2 N−1 , . . . , 2 N−1 −1] (N is a natural number). For example, a sample value of input signal x is represented by N=15 bits, for example. In addition, σ represents a standard deviation. 
     Next, the value of function g(x) expressed by Expression (1) is associated with sample value h(x) (that is, quantization data) of the IQ signal after compression in accordance with Expression (2).
 
[Expression 2]
 
 h ( x )=| g ( x )*(2 M −1)|  (2)
 
     In Expression (2), h(x) is an integer value representing quantization data, which falls within the range of [0, . . . , 2 M−1 ] (M is a natural number smaller than N). The sample value of the quantization data is represented by M=10 bits, for example. In addition, the right side of Expression (2) is a minimum integer of g(x)*(2 M−1 ) or greater. 
     That is, in the above-mentioned example, the input signal of N=15 bits is compressed into quantization data of M=10 bits by non-linear quantization. 
     CITATION LIST 
     Non-PTLs 
     
         
         Non-PTL 1 
         ETSI GS ORI 001 V4.1.1 (2014-10) 
         Non-PTL 2 
         ETSI GS ORI 002-1 V4.1.1 (2014-10) 
         Non-PTL 3 
         ETSI GS ORI 002-2 V4.1.1 (2014-10) 
       
    
     SUMMARY OF INVENTION 
     Technical Problem 
     In the case where the amplitude distribution of the IQ signal varies, however, the amplitude distribution of the IQ signal may possibly not be a regular distribution. In this case, with the above-described non-linear quantization, the quantization error may possibly be increased. 
     An object of the present disclosure is to provide a transmission apparatus and a quantization method which can reduce quantization error in non-linear quantization of an IQ signal. 
     Solution to Problem 
     A transmission apparatus according to a mode of the present disclosure includes: a kurtosis measurement section that measures a degree of kurtosis of an amplitude distribution of an input signal; a determination section that determines correction coefficient α in accordance with the degree of kurtosis; and a quantization section that quantizes the input signal and calculates quantization data by use of the correction coefficient α in accordance with Expression (2) and Expression (3). 
     A transmission apparatus according to a mode of the present disclosure includes: a skewness measurement section that measures a degree of skewness of an amplitude distribution of an input signal; a determination section that determines correction coefficient β in accordance with the degree of skewness; and a quantization section that quantizes the input signal and calculates quantization data by use of the correction coefficient β in accordance with Expression (2) and Expression (4). 
     A transmission apparatus according to a mode of the present disclosure includes: a kurtosis measurement section that measures a degree of kurtosis of an amplitude distribution of an input signal; a skewness measurement section that measures a degree of skewness of the amplitude distribution of the input signal; a determination section that determines correction coefficient α in accordance with the degree of kurtosis and determines correction coefficient β in accordance with the degree of skewness; and a quantization section that quantizes the input signal and calculates quantization data by use of the correction coefficient α and the correction coefficient β in accordance with Expression (2) and Expression (5). 
     A quantization method according to a mode of the present disclosure includes: measuring a degree of kurtosis of an amplitude distribution of an input signal; determining correction coefficient α in accordance with the degree of kurtosis; and quantizing the input signal and calculating quantization data by use of the correction coefficient α in accordance with Expression (2) and Expression (3). 
     A quantization method according to a mode of the present disclosure includes: measuring a degree of skewness of an amplitude distribution of an input signal; determining correction coefficient β in accordance with the degree of skewness; and quantizing the input signal and calculating quantization data by use of the correction coefficient β in accordance with Expression (2) and Expression (4). 
     A quantization method according to a mode of the present disclosure includes: measuring a degree of kurtosis of an amplitude distribution of an input signal; measuring a degree of skewness of the amplitude distribution of the input signal; determining correction coefficient α in accordance with the degree of kurtosis and determining correction coefficient β in accordance with the degree of skewness; and quantizing the input signal and calculating quantization data by use of the correction coefficient α and the correction coefficient β in accordance with Expression (2) and Expression (5). 
     Advantageous Effects of Invention 
     According to embodiments of the present disclosure, quantization error in non-linear quantization of an IQ signal can be reduced. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  illustrates examples of (a) a distribution of an IQ signal, (b) a cumulative distribution function, and (c) a quantization threshold in a non-linear quantization process of ORI; 
         FIG. 2  is a block diagram illustrating an example configuration of a communication system according to Embodiment 1; 
         FIG. 3  is used for describing the degree of kurtosis; 
         FIG. 4  illustrates an example kurtosis table according to Embodiment 1; 
         FIG. 5A  illustrates a relationship between input signal x and quantization value h(x); 
         FIG. 5B  illustrates a squared error of an intermediate value of input signal x and quantization value h(x); 
         FIG. 5C  illustrates a quantization error in the case where the amplitude distribution of the input signal is the regular distribution; 
         FIG. 6  illustrates an optimum value of correction coefficient α of the case where the amplitude distribution of the input signal is the regular distribution according to Embodiment 1; 
         FIG. 7  is used for describing reduction of quantization error with correction coefficient α according to Embodiment 1; 
         FIG. 8  is used for describing adjustment of a quantization zone with correction coefficient α according to Embodiment 1; 
         FIG. 9  is a sequence diagram illustrating a notification operation of correction coefficient α according to Embodiment 1; 
         FIG. 10  is a block diagram illustrating an example configuration of a communication system according to Embodiment 2; 
         FIG. 11  is used for describing the degree of skewness; 
         FIG. 12  illustrates an example skewness table according to Embodiment 2; 
         FIG. 13  is a sequence diagram illustrating a notification operation of correction coefficient α according to Embodiment 2; 
         FIG. 14  is used for describing adjustment of a quantization zone with correction coefficient α according to Embodiment 2; 
         FIG. 15  is a block diagram illustrating an example configuration of a communication system according to Embodiment 3; 
         FIG. 16  is a sequence diagram illustrating a notification operation of correction coefficients α and β according to Embodiment 3; and 
         FIG. 17  is used for describing adjustment of a quantization zone with correction coefficients α and β according to Embodiment 3. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     Embodiments of the present disclosure are described in detail below with reference to the accompanying drawings. 
     (Embodiment 1) 
     [Configuration of Communication System] 
       FIG. 2  illustrates an example configuration of a communication system according to the present embodiment. 
     Communication system  10  illustrated in  FIG. 2  includes transmission apparatus  100  and reception apparatus  200 . 
     Transmission apparatus  100  performs non-linear quantization on an input signal (IQ signal), and transmits the quantization data to reception apparatus  200  through an optical line. Transmission apparatus  100  is an REC, and is a BBU (Base Band Unit), for example. Further, transmission apparatus  100  may convert (down-sampling) the data rate of an input signal (which is not illustrated in the drawing). 
     Reception apparatus  200  performs inverse quantization on quantization data transmitted from transmission apparatus  100 , and obtains a signal (output signal) after the inverse quantization. Reception apparatus  200  is an RE and is an RRH (Remote Radio Head), for example. Further, reception apparatus  200  may convert (up sampling) the data rate of the received signal (which is not illustrated in the drawing). 
     [Configuration of Transmission Apparatus  100 ] 
     Transmission apparatus  100  includes standard deviation measurement section  101 , kurtosis measurement section  102 , correction coefficient determination section  103 , control section  104 , quantization section  105 , multiplex section  106 , and optical device  107 . 
     Standard deviation measurement section  101  measures standard deviation σ of an input signal, and outputs the measured standard deviation σ to kurtosis measurement section  102  and control section  104 . 
     Kurtosis measurement section  102  uses an input signal, and standard deviation σ input from standard deviation measurement section  101  to measure the “degree of kurtosis” which represents the degree of concentration of the amplitude distribution of the input signal. Kurtosis measurement section  102  outputs information representing the measured degree of kurtosis to correction coefficient determination section  103 . 
       FIG. 3  is used for describing the characteristics of the degree of kurtosis. As illustrated in  FIG. 3 , when the amplitude distribution of an input signal is a regular distribution, the degree of kurtosis is 0. In addition, as illustrated in  FIG. 3 , in the amplitude distribution of an input signal, the degree of kurtosis has a large value (in  FIG. 3 , 0.5) on the positive side when the degree of concentration around the average value is high relative to the regular distribution, and the degree of kurtosis has a large value (in  FIG. 3 , −0.5) on the negative side when the degree of concentration around the average value is low relative to the regular distribution. 
     Correction coefficient determination section  103  determines correction coefficient (Scaling Factor) α of a cumulative distribution function which is used for the non-linear quantization in accordance with the degree of kurtosis represented by the information input from kurtosis measurement section  102 . Correction coefficient determination section  103  outputs the determined correction coefficient α to control section  104 . 
     Correction coefficient determination section  103  preliminarily holds the relationship (kurtosis table) of the value of the degree of kurtosis and the value of correction coefficient α. For example, in the kurtosis table representing the relationship of the value of the degree of kurtosis and the value of correction coefficient α, correction coefficient determination section  103  preliminarily sets correction coefficient α of the case where the degree of kurtosis is 0 (the case of the regular distribution) as the reference value. The reference value of correction coefficient α is determined by a calculation simulation and the like (details will be described later), for example. The value of the degree of kurtosis and the value of correction coefficient α are associated in the kurtosis table such that, as the degree of kurtosis increases to the positive side (degree of kurtosis&gt;0), correction coefficient α decreases in a range smaller than the reference value, and that, as the degree of kurtosis increases to the negative side (degree of kurtosis&lt;0), correction coefficient α increases in a range greater than the reference value (see, for example,  FIG. 4 ). 
     Control section  104  generates quantization control information including a input from standard deviation measurement section  101  and correction coefficient α input from correction coefficient determination section  103 , and outputs the quantization control information to quantization section  105  and multiplex section  106 . 
     By use of the quantization control information (σ, α) input from control section  104 , quantization section  105  performs the non-linear quantization on the input signal, and calculates quantization data. Quantization section  105  outputs the calculated quantization data to multiplex section  106 . To be more specific, quantization section  105  performs the non-linear quantization on the input signal in accordance with cumulative distribution function g(x) expressed by Expression (3), and Expression (2). Expression (3) differs from Expression (1) in that correction coefficient α is additionally provided. 
     
       
         
           
             
               
                 
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     Multiplex section  106  multiplexes the quantization data input from quantization section  105  with the quantization control information input from control section  104  to generate a multiplex signal. Multiplex section  106  outputs the generated multiplex signal to optical device  107 . 
     Optical device  107  transmits the multiplex signal input from multiplex section  106  to reception apparatus  200  through an optical line. 
     It is to be noted that the quantization control information (σ, α) may be notified simultaneously with the quantization data, or may be preliminarily notified to reception apparatus  200  before the non-linear quantization/inverse quantization. In addition, transmission apparatus  100  may notify the quantization control information (updated σ or α) to reception apparatus  200  every time when standard deviation σ or correction coefficient α is updated. Details of the way of the notification of the quantization control information will be described later. 
     [Configuration of Reception Apparatus  200 ] 
     Reception apparatus  200  includes optical device  201 , separation section  202 , control section  203 , and inverse quantization section  204 . 
     Optical device  201  receives through an optical line a signal transmitted from transmission apparatus  100 , and outputs the received signal to separation section  202 . The received signal contains quantization data or quantization control information. 
     Separation section  202  separates the received signal input from optical device  201  into quantization data and quantization control information, and outputs the quantization control information and the quantization data to control section  203  and inverse quantization section  204 , respectively. 
     Control section  203  extracts a parameter which is used for the non-linear inverse quantization from the quantization control information input from separation section  202 . The parameter used for the non-linear inverse quantization includes standard deviation σ and correction coefficient α. Control section  203  outputs standard deviation σ and correction coefficient α to inverse quantization section  204 . 
     By use of the parameters (σ, α) input from control section  203 , inverse quantization section  204  performs the non-linear inverse quantization on the quantization data input from separation section  202 . That is, by use of the non-linear quantization data and the notification parameter in quantization section  105  of transmission apparatus  100 , inverse quantization section  204  performs restoration of the IQ signal, and outputs the obtained signal. 
     [Way of Setting Correction Coefficient α] 
     Next, details of the way of setting correction coefficient α used in transmission apparatus  100  and reception apparatus  200  are described. 
     First, setting of the reference value of correction coefficient α, that is, correction coefficient α for the case where the amplitude distribution of the input signal is the regular distribution (degree of kurtosis: 0) is described. 
       FIG. 5A  to  FIG. 5C  are used for describing an quantization error in the case where correction coefficient α is not used (which corresponds to correction coefficient α=1). 
       FIG. 5A  illustrates a relationship (the thick solid line in the drawing) between input signal x and quantization value h(x) which is obtained in accordance with Expression (1) and Expression (2) (note that M=4 bits). The setting interval of the quantization threshold is shortened as the generation frequency of input signal x increases, and the setting interval of the quantization threshold is widened as the generation frequency of input signal x decreases. In this manner, probability of the generation is substantially uniformized among the values of quantization value h(x). 
     Each of the markers (the circles in the drawing) illustrated in  FIG. 5A  represents a point on Expression (1) corresponding to the intermediate value of adjacent quantization values h(x), and the projection of the markers to input signal x represents a representative value of each quantization zone. The non-linear inverse quantization is conversion of quantization value h(x) to the representative value of the quantization zone represented by the quantization value h(x). 
       FIG. 5B  illustrates the squared error of input signal x and the representative value of the quantization zone corresponding to the input signal x in the case where the non-linear quantization having the characteristics illustrated in  FIG. 5A  is performed. That is,  FIG. 5B  illustrates the square of the error caused by performing the non-linear quantization and the non-linear inverse quantization on input signal x (which is hereinafter referred to as “quantization error”). As illustrated in  FIG. 5B , the quantization error is increased as the quantization zone is widened. 
       FIG. 5C  illustrates a result obtained by multiplying the squared error of input signal x and the representative value of the quantization zone corresponding to the input signal x, by the occurrence probability (generation frequency) of the input signal x in the case where the occurrence probability of input signal x is the regular distribution and the non-linear quantization having the characteristics illustrated in  FIG. 5A  is performed. That is,  FIG. 5C  illustrates a result obtained by multiplying the quantization error by the occurrence probability (generation frequency) of the input signal x (hereinafter referred to as “weighted quantization error”). The weighted quantization error integrated with respect to input signal x represents the average quantization error. 
     As illustrated in  FIG. 5C , even after the assignment of weights of the occurrence probability of the input signal x, the weighted quantization error of the region where the quantization zone is wide has a large value, and the average quantization error is large. As a way for reducing the average quantization error, it is conceivable to optimally set the quantization threshold such that the weighted quantization error in each quantization zone is small. However, under an environment where the occurrence probability (generation frequency) of the input signal varies, it is extremely difficult to perform real-time optimization of the quantization threshold. 
     In view of this, in the present embodiment, transmission apparatus  100  and reception apparatus  200  correct the characteristics of cumulative distribution function g(x) used for the non-linear quantization by use of correction coefficient α. 
       FIG. 6  illustrates a result of a calculator simulation conducted by the present inventors, which shows a relationship between the quantization error and the value of correction coefficient α in cumulative distribution function g(x) expressed by Expression (3) in the case where the amplitude distribution of the input signal is the regular distribution. In  FIG. 6 , the number of bits M after quantization is 10 as with the ORI. 
     As illustrated in  FIG. 6 , in the area around correction coefficient α=1.6, the average quantization error is minimized (about −56 dB). In contrast, in the case of correction coefficient α=1 (that is, in the case of no correction, which corresponds to the ORI), the average quantization error is about −41 dB. 
     That is, in the case where the input signal is the regular distribution, the quantization error in the non-linear quantization average can be minimized by setting α of cumulative distribution function g(x) expressed by Expression (3) to 1.6. 
       FIG. 7  illustrates the weighted quantization error obtained by multiplying, by the occurrence probability of the input signal (note that M=4 bits), the squared error of input signal x and quantization value h(x) of the case where the non-linear quantization is performed in accordance with Expression (3) with a correction coefficient α of 1.6 when the input signal is the regular distribution. 
     In comparison with  FIG. 5C  (the case of no correction), in  FIG. 7 , the weighted quantization error in the region where the generation frequency of input signal x is high is slightly high, but the weighted quantization error is reduced as a whole including the region where the generation frequency of input signal x is low. 
     That is, it can be said that the average quantization error can be further reduced by appropriately setting correction coefficient α and by performing the non-linear quantization in accordance with Expression (3) (with correction), in comparison with the case where the non-linear quantization is performed in accordance with Expression (1) (no correction). 
     It is to be noted that correction coefficient α=1.6 illustrated in  FIG. 6  is an optimum value which is obtained under the condition assumed in the above-mentioned calculator simulation, and the optimum value of correction coefficient α of the case where the amplitude distribution of the input signal is the regular distribution is not limited to 1.6. The optimum value of correction coefficient α of the case where the amplitude distribution of the input signal is the regular distribution may be appropriately set in accordance with the conditions. 
     The following describes the way of setting correction coefficient α in accordance with the degree of kurtosis of the amplitude distribution of the input signal by use of correction coefficient α in the case where the amplitude distribution of the input signal is the regular distribution as the reference value. 
     As illustrated in  FIG. 3 , as the degree of kurtosis of the amplitude distribution of the input signal increases, the degree of concentration at the average value of the amplitude distribution increases and the distribution around the average value becomes steep. On the other hand, as illustrated in  FIG. 3 , as the degree of kurtosis of the amplitude distribution of the input signal decreases, the degree of concentration at the average value of the amplitude distribution decreases and the distribution around the average value becomes gradual. 
     On the other hand, as expressed in Expression (3), correction coefficient α is a parameter by which standard deviation σ as the denominator of the error function (erf) corresponding to the cumulative distribution function of the regular distribution is multiplied. That is, the distribution in cumulative distribution function g(x) expressed by Expression (3) becomes gradual in the case of correction coefficient α&gt;1, and the distribution in cumulative distribution function g(x) expressed by Expression (3) becomes steep in the case of correction coefficient α&lt;1. 
     That is, correction coefficient α serves to adjust the degree of variation of the distribution in cumulative distribution function g(x). In other words, correction coefficient α serves to adjust the setting interval (quantization zone) of the quantization threshold in the non-linear quantization and the representative value of each quantization zone in the non-linear inverse quantization. To be more specific, the setting interval of the quantization threshold increases as correction coefficient α increases in the range greater than 1, and the setting interval of the quantization threshold decreases as correction coefficient α decreases in the range smaller than 1. 
     In view of this, as illustrated in  FIG. 4 , correction coefficient determination section  103  sets the value of correction coefficient α such that the value decreases relative to the reference value as the degree of kurtosis of the amplitude distribution of the input signal increases. In this manner, as illustrated in  FIG. 8 , quantization section  105  performs non-linear quantization in which the setting interval of the quantization threshold is narrow (the quantization zone is set to steep). 
     On the other hand, as illustrated in  FIG. 4 , correction coefficient determination section  103  sets the value of correction coefficient α such that the value increases relative to the reference value as the degree of kurtosis of the amplitude distribution of the input signal decreased. In this manner, as illustrated in  FIG. 8 , quantization section  105  performs non-linear quantization in which the setting interval of the quantization threshold is wide (the quantization zone is set to gradual). 
     As described, transmission apparatus  100  appropriately adjust the interval of the quantization threshold in the non-linear quantization in accordance with the amplitude distribution of the input signal. In this manner, even in the case where the occurrence probability of the input signal varies, non-linear quantization (non-linear inverse quantization) using the quantization threshold in accordance with the amplitude distribution of the input signal is performed, and thus the quantization error can be reduced. 
     [Notification of Correction Coefficient α] 
     Next, details of notification of quantization control information from transmission apparatus  100  (REC) to reception apparatus  200  (RE) are described. 
       FIG. 9  is a sequence diagram illustrating an operation of exchanging signals of transmission apparatus  100  and reception apparatus  200 . 
     In  FIG. 9 , at step (hereinafter referred to simply as “ST”)  101 , transmission apparatus  100  transmits quantization control information including standard deviation σ and correction coefficient α used for the non-linear quantization to reception apparatus  200 . 
     For example, in C&amp;M (Control and Management) of ORI, OBJECT CREATION REQUEST message is used for parameter notification from the REC (which corresponds to transmission apparatus  100 ) to the RE (reception apparatus  200 ). In addition, in ORI, standard deviation σ used for the non-linear quantization (that is, data compression) is notified in the field represented by TxSigPath object in OBJECT CREATION REQUEST message. 
     In view of this, transmission apparatus  100  may notify standard deviation σ and correction coefficient α by use of TxSigPath object, for example. That is, correction coefficient α is notified to reception apparatus  200  as a parameter of TxSigPath object of C&amp;M of ORI. 
     At ST 102 , in response to reception of an OBJECT CREATION REQUEST message including quantization control information at ST 101 , reception apparatus  200  generates an OBJECT CREATION RESPONSE message, and transmits the OBJECT CREATION RESPONSE message to transmission apparatus  100 . The response includes information on whether success or failure of the reception of the quantization control information and the like, for example. 
     When success of the reception of the quantization control information is indicated in the OBJECT CREATION RESPONSE message at ST 102 , transmission apparatus  100  and reception apparatus  200  perform, at ST 103 , non-linear quantization and non-linear inverse quantization by use of the standard deviation σ and the correction coefficient α notified at ST 101 . 
     Thereafter, when the amplitude distribution of the input signal in transmission apparatus  100  is varied and the standard deviation σ or the correction coefficient α is updated, transmission apparatus  100  transmits quantization control information including the updated standard deviation σ or correction coefficient α to reception apparatus  200  at ST 104 . 
     For example, in ORI, OBJECT PARAMETER MODIFICATION REQUEST message is used for notification of the parameter update from the REC (which corresponds to transmission apparatus  100 ) to the RE (reception apparatus  200 ). In addition, in C&amp;M of ORI, updated standard deviation σ is notified in the field represented by TxSigPath object in the message. 
     In view of this, transmission apparatus  100  may notify updated standard deviation σ or correction coefficient α by use of TxSigPath object, for example. 
     At ST 105 , in response to reception of an OBJECT PARAMETER MODIFICATION REQUEST message including quantization control information at ST 104 , reception apparatus  200  generates an OBJECT PARAMETER MODIFICATION RESPONSE message, and transmits the OBJECT PARAMETER MODIFICATION RESPONSE message to transmission apparatus  100 . The response includes information on whether success or failure of the reception of the quantization control information and the like, for example. 
     When success of reception of the quantization control information is indicated in the OBJECT PARAMETER MODIFICATION RESPONSE message at ST 105 , transmission apparatus  100  and reception apparatus  200  perform, at ST 106 , non-linear quantization and non-linear inverse quantization by use of the updated standard deviation σ or correction coefficient α notified at ST 104 . 
     As described, in  FIG. 9 , correction coefficient α is newly added in addition to the existing standard deviation σ in TxSigPath object of C&amp;M of ORI. 
     It is to be noted that, as expressed in Expression (3), correction coefficient α is a parameter by which standard deviation σ is multiplied. In view of this, transmission apparatus  100  may notify a result (σ′=σ*α) obtained by multiplying standard deviation σ by correction coefficient α to reception apparatus  200  instead of individually notifying standard deviation σ and correction coefficient α as illustrated in  FIG. 9 . In this case, parameter σ′ may be notified by use of the notification field corresponding to standard deviation σ of the existing notification field defined in C&amp;M of ORI. With this configuration, it is unnecessary to newly define the notification field for correction coefficient α. 
     While the way of adjusting the quantization threshold and the representative value of each quantization zone with correction coefficient α has been described above, it is also possible to correct input signal x and the signal after the inverse quantization with correction coefficient α. 
     Hereinabove, the way of notifying the quantization control information has been described. 
     In the above-mentioned manner, in the present embodiment, transmission apparatus  100  determines correction coefficient α in accordance with the degree of kurtosis of the amplitude distribution of the IQ signal, and adjusts the interval of the quantization threshold in the non-linear quantization. In this manner, the quantization threshold is appropriately set in accordance with the variation of the amplitude distribution of the IQ signal, and thus the quantization error in the non-linear quantization can be reduced. 
     (Embodiment 2) 
     In Embodiment 1, the non-linear quantization is performed by use of the correction coefficient corresponding to the degree of kurtosis of the amplitude distribution of the input signal. In contrast, in the present embodiment, the non-linear quantization is performed by use of a correction coefficient corresponding to the degree of skewness of the amplitude distribution of the input signal. 
     [Configuration of Communication System] 
       FIG. 10  illustrates an example configuration of a communication system according to the present embodiment. 
     Communication system  20  illustrated in  FIG. 10  includes transmission apparatus  300  and reception apparatus  400 . It is to be noted that, in  FIG. 10 , the components similar to those of Embodiment 1 ( FIG. 2 ) are denoted with the same reference numerals, and the description thereof will be omitted. Transmission apparatus  300  includes skewness measurement section  301  in place of kurtosis measurement section  102  of transmission apparatus  100  ( FIG. 2 ). 
     Skewness measurement section  301  of transmission apparatus  300  measures “degree of skewness” which indicates the bilateral symmetry in the amplitude distribution of the input signal by use of the input signal and standard deviation σ input from standard deviation measurement section  101 . Skewness measurement section  301  outputs information representing the measured degree of skewness to correction coefficient determination section  302 . 
       FIG. 11  is used for describing characteristics of the degree of skewness. As illustrated in  FIG. 11 , when the amplitude distribution of the input signal is the regular distribution, the degree of skewness is 0. In addition, as illustrated in  FIG. 11 , in the amplitude distribution of the input signal, as deflection to the positive side relative to the regular distribution increases, the degree of skewness increases on the positive side (in  FIG. 11 , 0.5), and as deflection to the negative side relative to the regular distribution increases, the degree of skewness increases on the negative side (in  FIG. 11 , −0.5). 
     Correction coefficient determination section  302  determines correction coefficient β of the cumulative distribution function used for the non-linear quantization in accordance with the degree of skewness indicated in information input from skewness measurement section  301 . Correction coefficient determination section  302  outputs the determined correction coefficient β to control section  104 . 
     Correction coefficient determination section  302  preliminarily holds the relationship (skewness table) of the degree of skewness and the value of correction coefficient β. For example, in the skewness table, correction coefficient β is set to 0 (that is, no correction) when the degree of skewness is 0 (in the case of a regular distribution). The degree of skewness and the value of correction coefficient β are associated in the skewness table such that the correction coefficient β increases to the positive side as the degree of skewness increases to the positive side (degree of skewness&gt;0), and that the correction coefficient β increases to the negative side as the degree of skewness increases to the negative side (degree of skewness&lt;0) (see, for example,  FIG. 12 ). 
     The quantization control information output from control section  104  includes standard deviation σ and correction coefficient β. 
     By use of the quantization control information (σ, β) input from control section  104 , quantization section  303  performs the non-linear quantization on the input signal, and calculates quantization data. To be more specific, quantization section  303  performs the non-linear quantization on the input signal in accordance with cumulative distribution function g(x) expressed by Expression (4), and Expression (2). Expression (4) differs from Expression (1) in that correction coefficient β is additionally provided. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Expression 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     4 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     g 
                     ⁡ 
                     
                       ( 
                       x 
                       ) 
                     
                   
                   = 
                   
                     
                       1 
                       2 
                     
                     ⁢ 
                     
                       ( 
                       
                         1 
                         + 
                         
                           erf 
                           ⁡ 
                           
                             ( 
                             
                               
                                 x 
                                 - 
                                 β 
                               
                               
                                 
                                   2 
                                 
                                 ⁢ 
                                 σ 
                               
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     In reception apparatus  400  illustrated in  FIG. 10 , inverse quantization section  401  performs the non-linear inverse quantization on the quantization data input from separation section  202  by use of the parameters (σ, β) input from control section  203 . That is, inverse quantization section  401  performs a process that is opposite to the non-linear quantization process in quantization section  303  of transmission apparatus  300 , and performs restoration of the IQ signal. 
     It is to be noted that quantization control information (σ, β) may be notified simultaneously with the quantization data, or may be preliminarily notified to reception apparatus  400  before the non-linear quantization/inverse quantization. In addition, transmission apparatus  300  may notify the quantization control information (updated σ or β) to reception apparatus  400  every time when standard deviation σ or correction coefficient β is updated. 
       FIG. 13  a sequence diagram illustrating an operation of exchanging signals of transmission apparatus  300  and reception apparatus  400 . In  FIG. 13 , the operations identical to those of Embodiment 1 ( FIG. 9 ) are denoted with the same reference numerals, and the description thereof will be omitted. To be more specific, this differs from Embodiment 1 ( FIG. 9 ) only in that correction coefficient β is notified by use of the field represented by TxSigPath object at ST 101   a  and  104   a  illustrated in  FIG. 13 . That is, correction coefficient β is notified to reception apparatus  400  as a parameter of TxSigPath object of C&amp;M of ORI. 
     [Way of Setting Correction Coefficient β] 
     Next, details of the way of setting correction coefficient β used in the above-described transmission apparatus  300  and reception apparatus  400  are described. 
     As illustrated in  FIG. 11 , the amplitude distribution deflects to the positive side relative to the regular distribution as the degree of skewness of the amplitude distribution of the input signal increases, and the amplitude distribution deflects to the negative side relative to the regular distribution as the degree of skewness of the amplitude distribution of the input signal decreases. 
     On the other hand, as expressed in Expression (4), correction coefficient β is a parameter which is subtracted from input signal x as a molecule of error function (erf) corresponding to the cumulative distribution function of the regular distribution. That is, in the case of correction coefficient β&gt;0, cumulative distribution function g(x) expressed by Expression (4) deflects to the positive side relative to the distribution of the cumulative distribution function g(x) expressed by Expression (1). In addition, in the case of correction coefficient β&lt;0, the distribution in the cumulative distribution function g(x) expressed by Expression (4) deflects to the negative side relative to the distribution of the cumulative distribution function g(x) expressed by Expression (1). 
     That is, correction coefficient β serves to adjust the degree of the deviation of the distribution in cumulative distribution function g(x). In other words, correction coefficient β serves to shift the position of the quantization threshold in the non-linear quantization. To be more specific, the quantization threshold of the case of β=0 is shifted to the positive side as correction coefficient β increases in a range greater than 0, and the quantization threshold of the case of β=0 is shifted to the negative side as correction coefficient β decreases in a range of smaller than 0. 
     In view of this, as illustrated in  FIG. 12 , correction coefficient determination section  302  sets the value of correction coefficient β such that the value increases to the positive side as the degree of skewness of the amplitude distribution of the input signal increases to the positive side. In this manner, as illustrated in  FIG. 14 , quantization section  303  performs non-linear quantization in which quantization threshold is shifted to the positive side. 
     On the other hand, as illustrated in  FIG. 12 , correction coefficient determination section  302  sets the value of correction coefficient β such that the value increases to the negative side as the degree of skewness of the amplitude distribution of the input signal increases to the negative side. In this manner, as illustrated in  FIG. 14 , quantization section  303  performs non-linear quantization in which quantization threshold is shifted to the negative side. 
     As described, transmission apparatus  300  appropriately adjusts the position of the quantization threshold in the non-linear quantization in accordance with the amplitude distribution of the input signal. In this manner, even in the case where the occurrence probability of the input signal varies, the non-linear quantization (non-linear inverse quantization) using the quantization threshold in accordance with the amplitude distribution of the input signal is performed, and thus quantization error can be reduced. 
     In the above-mentioned manner, in the present embodiment, transmission apparatus  300  determines correction coefficient β in accordance with the degree of skewness of the amplitude distribution of the IQ signal, and adjusts the position of the quantization threshold in the non-linear quantization. In this manner, the quantization threshold is appropriately set in accordance with variation of the amplitude distribution of the IQ signal, and thus the quantization error in the non-linear quantization can be reduced. 
     While the way of adjusting the quantization threshold and the representative value of each quantization zone with correction coefficient β has been described above, input signal x and the signal after the inverse quantization may be corrected with correction coefficient β. 
     (Embodiment 3) 
     In the present embodiment, non-linear quantization using both of the correction coefficient α described in Embodiment 1 and the correction coefficient β described in Embodiment 2 is described. 
     [Configuration of Communication System] 
       FIG. 15  illustrates an example configuration of a communication system according to the present embodiment. 
     Communication system  30  illustrated in  FIG. 15  includes transmission apparatus  500  and reception apparatus  600 . It is to be noted that, in  FIG. 15 , the components similar to those of Embodiment 1 ( FIG. 2 ) and Embodiment 2 ( FIG. 10 ) are denoted with the same reference numerals, and the description thereof will be omitted. 
     Correction coefficient determination section  501  of transmission apparatus  500  determines correction coefficient α of the cumulative distribution function used for the non-linear quantization in accordance with the degree of kurtosis indicated in information input from kurtosis measurement section  102 , and determines correction coefficient β of the cumulative distribution function used for the non-linear quantization in accordance with the degree of skewness indicated in information input from skewness measurement section  301 . Correction coefficient determination section  501  outputs the determined correction coefficients α and β to control section  104 . 
     The quantization control information output from control section  104  includes standard deviation σ, and correction coefficients α and β. 
     Quantization section  502  performs the non-linear quantization on the input signal by use of the quantization control information (σ, α, β) input from control section  104 , and calculates quantization data. To be more specific, quantization section  502  performs the non-linear quantization on the input signal in accordance with cumulative distribution function g(x) expressed by Expression (5) and Expression (2). Expression (5) differs from Expression (1) in that correction coefficients α and β are additionally provided. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Expression 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     5 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     g 
                     ⁡ 
                     
                       ( 
                       x 
                       ) 
                     
                   
                   = 
                   
                     
                       1 
                       2 
                     
                     ⁢ 
                     
                       ( 
                       
                         1 
                         + 
                         
                           erf 
                           ⁡ 
                           
                             ( 
                             
                               
                                 x 
                                 - 
                                 β 
                               
                               
                                 
                                   2 
                                 
                                 ⁢ 
                                 σ 
                                 * 
                                 α 
                               
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     In reception apparatus  600  illustrated in  FIG. 15 , inverse quantization section  601  performs the non-linear inverse quantization on the quantization data input from separation section  202  by use of parameters (σ, α, β) input from control section  203 . That is, inverse quantization section  601  performs a process that is opposite to the non-linear quantization process in quantization section  502  of transmission apparatus  500 . 
     It is to be noted that the quantization control information (σ, α, β) may be notified simultaneously with the quantization data, or preliminarily notified to reception apparatus  600  before the non-linear quantization/inverse quantization. In addition, transmission apparatus  500  may notify the quantization control information (updated σ, α or β) to reception apparatus  600  every time when standard deviation σ, correction coefficient α or correction coefficient β is updated. 
       FIG. 16  is a sequence diagram illustrating an operation of exchanging signals of transmission apparatus  500  and reception apparatus  600 . In  FIG. 16 , the operations identical to those of Embodiment 1 ( FIG. 9 ) and Embodiment 2 ( FIG. 13 ) are denoted with the same reference numerals, and the description thereof will be omitted. To be more specific, at ST 101   b  and  104   b  illustrated in  FIG. 16 , this is different from Embodiment 1 ( FIG. 9 ) and Embodiment 2 ( FIG. 13 ) only in that correction coefficients α and β are notified by use of the field represented by TxSigPath object. That is, correction coefficients α and β are notified to reception apparatus  600  as parameters of TxSigPath object of C&amp;M of ORI. 
     In addition, as with Embodiment 1, transmission apparatus  500  may notify a result (σ′=σ*α) obtained by multiplying standard deviation σ by correction coefficient α to reception apparatus  600  instead of individually notifying standard deviation σ and correction coefficient α at ST 101   b  or ST 104   b  illustrated in  FIG. 16 . In this case, parameter σ′ may be notified by use of the notification field corresponding to standard deviation σ of the existing notification field defined in C&amp;M of ORI. With this configuration, it is unnecessary to newly define the notification field for correction coefficient α. 
     [Way of Setting Correction Coefficients α and β] 
     Next, details of the way of setting correction coefficients α and β used in transmission apparatus  500  and reception apparatus  600  are described. 
     As described in Embodiment 1, correction coefficient determination section  501  sets the value of correction coefficient α such that the value decreases relative to the reference value as the degree of kurtosis of the amplitude distribution of the input signal increases, and that the value increases relative to the reference value as the degree of kurtosis of the amplitude distribution of the input signal decreases (see, for example,  FIG. 4 ). 
     In addition, as described in Embodiment 2, correction coefficient determination section  501  sets the value of correction coefficient β such that the value increases to the positive side as the degree of skewness of the amplitude distribution of the input signal increases to the positive side, and that the value increases to the negative side as the degree of skewness of the amplitude distribution of the input signal increases to the negative side (see, for example,  FIG. 12 ). 
     In this manner, as illustrated in  FIG. 17 , correction coefficient α in accordance with the degree of kurtosis of the amplitude distribution of the input signal is set, and quantization section  502  performs non-linear quantization in which the setting interval of the quantization threshold is adjusted. In addition, as illustrated in  FIG. 17 , correction coefficient β in accordance with the degree of skewness of the amplitude distribution of the input signal is set, and quantization section  502  performs non-linear quantization in which the position of the quantization threshold is adjusted. 
     That is, transmission apparatus  500  appropriately adjusts the interval and the position of the quantization threshold in the non-linear quantization in accordance with the degree of kurtosis and the degree of skewness of the amplitude distribution of the input signal. In this manner, even in the case where the occurrence probability of the input signal varies, non-linear quantization (non-linear inverse quantization) using the quantization threshold in accordance with the amplitude distribution of the input signal is performed, and thus quantization error can be reduced. 
     In the above-mentioned manner, in the present embodiment, transmission apparatus  500  determines correction coefficients α and β in accordance with the degree of kurtosis and the degree of skewness of the amplitude distribution of the IQ signal, and adjusts the interval and the position of the quantization threshold in the non-linear quantization. In this manner, the quantization threshold is appropriately set in accordance with the variation of the amplitude distribution of the IQ signal, and thus the quantization error in the non-linear quantization can be reduced. 
     While the way of adjusting the quantization threshold and the representative value of each quantization zone with correction coefficients α and β has been described above, input signal x and the signal after the inverse quantization may be corrected with correction coefficients α and β. 
     Hereinabove, the embodiments of the present invention have been described. 
     While the embodiments of the present invention is configured with a hardware in the embodiments, the embodiments of the present invention may also be achieved with a software in coordination with a hardware. 
     In addition, typically, the function blocks described in the embodiments are achieved as an integrated circuit, specifically, as an LSI. They may be individually configured as one chip, or may be configured as one chip including a part or whole of them. Depending on the difference in integration density, the LSI may be called an IC, a system LSI, a super LSI, or an ultra LSI. 
     In addition, the integrated circuit may not be configured with an LSI, and may be achieved with a dedicated circuit or a general-purpose processor. It is also possible to utilize an FPGA (Field Programmable Gate Array) which can be programed after manufacturing the LSI, or a reconfigurable processor in which setting or connection of circuit cells in the LSI can be reconfigured. 
     Furthermore, if there is other semiconductor techniques relating to integrated circuits which can replace LSIs, such techniques may be utilized for integration of the function blocks as a matter of course. Application of biotechnologies is highly possible. 
     This application is entitled to and claims the benefit of Japanese Patent Application No. 2015-046053 dated Mar. 9, 2015, the disclosure of which including the specification, drawings and abstract is incorporated herein by reference in its entirety. 
     INDUSTRIAL APPLICABILITY 
     The present invention is suitable for a mobile communication system. 
     REFERENCE SIGNS LIST 
     
         
           10 ,  20 ,  30  Communication system 
           100 ,  300 ,  500  Transmission apparatus 
           101  Standard deviation measurement section 
           102  Kurtosis measurement section 
           103 ,  302 ,  501  Correction coefficient determination section 
           104 ,  203  Control section 
           105 ,  303 ,  502  Quantization section 
           106  Multiplex section 
           107 ,  201  Optical device 
           200 ,  400 ,  600  Reception apparatus 
           202  Separation section 
           204 ,  401 ,  601  Inverse quantization section 
           301  Skewness measurement section