ADAPTIVE EQUALIZER, STEP SIZE DERIVATION METHOD AND PROGRAM

Abstract

This adaptive equalizer comprises an update unit that, on the basis of time-sequential update vectors corresponding to time-sequential adaptive filter inputs and outputs for tracking the polarization state of optical signals received by a coherent optical receiver, updates the step size of a tap coefficient vector for use in controlling the adaptive filter. The update unit updates the step size on the basis of the DC gain of the update vectors. The update unit may update the step size for each component of the update vectors on the basis of the DC gain of each component of the update vectors.

Description

[Technical field]

[0001] The present invention relates to an adaptive equalizer, a step size derivation method, and a program. [Background technology]

[0002] An optical signal has two orthogonal polarization states (x-polarization and y-polarization). In polarization multiplexing used in coherent optical data transmission, separate information symbols are assigned to these two polarization states. Such polarization multiplexing doubles the transmission capacity of optical signals transmitted through optical fibers.

[0003] The polarization state of an optical signal transmitted through an optical fiber is subject to random and unsteady fluctuations over time. For example, in an optical fiber laid in an underground pipe, fluctuations of the order of a few Hz occur in the polarization state of the optical signal. For example, in an optical fiber laid as an overhead wire, fluctuations of the order of a few kHz occur in the polarization state of the optical signal. In particular, in an optical-fiber composite overhead ground wire (OPGW), which is an overhead ground wire that wraps around an optical fiber, fluctuations of the order of MHz occur instantaneously in the polarization state of an optical signal due to the effects of lightning strikes, etc.

[0004] Since the fluctuations in the polarization state need to be compensated for in coherent optical data transmission, the coherent optical receiver uses an adaptive filter to track the fluctuations in the polarization state (see Non-Patent Document 1). [Prior art documents] [Non-patent literature]

[0005] [Non-Patent Document 1] Seb J. Savory, “Digital filters for coherent optical receivers”, Optics Express Vol. 16, Issue 2, pp. 804-817 (2008). Summary of the Invention [Problem to be solved by the invention]

[0006] An optimization algorithm such as the Least Mean Square (LMS) algorithm or the Constant Modulus Algorithm (CMA) is used to control the adaptive filter.

[0007] In the LMS algorithm, the product of the amplitude vector “x” or “y” of the polarization component of the main signal input to an FIR (Finite Impulse Response) filter and the error “e” is repeatedly added to the tap coefficient vector “h” as shown in equation (1).

[0008]

number

[0009] Here, "μ" represents the step size. The step size is a positive real number sufficiently smaller than 1, and is a parameter for controlling the speed at which the polarization state fluctuation is followed. The larger the step size, the better the tracking performance for fast fluctuations in the polarization state. The adaptive filter can track fluctuations in the polarization state of the optical signal in the optical fiber as a transmission line, using a vector of tap coefficients updated according to the step size.

[0010] However, the larger the step size, the more control penalty occurs. In other words, the larger the step size, the more the signal-to-noise ratio (SNR) of the main signal passing through the adaptive filter deteriorates. When the speed of change of the polarization state is constant, the optimal tracking performance can be obtained by setting the tap coefficient vector updated with a step size corresponding to the constant speed of change in the adaptive filter.

[0011] On the other hand, when the speed of change of the polarization state is not constant, the tap coefficients updated with a large step size according to the maximum speed of change of the polarization state are set in the adaptive filter. In this case, the vector of the tap coefficients updated with an unnecessarily large step size is set in the adaptive filter regardless of whether the speed of change of the polarization state is slow or not. This deteriorates the signal-to-noise ratio of the main signal.

[0012] In the optical ground wire, the time period when the polarization state changes very fast is a very limited time period, such as the moment of a lightning strike. In most of the time period, the speed of the polarization state changes is slow. The signal-to-noise ratio of the main signal is degraded in most of the time period because the tap coefficients updated with an unnecessarily large step size are always set in the adaptive filter. In such a case, the power consumption for error correction processing increases. Also, the margin for other degradation factors in coherent optical data transmission is wasted. Thus, when the tracking performance for high-speed fluctuations in the polarization state is improved, the signal-to-noise ratio during low-speed fluctuations in the polarization state may not be improved.

[0013] In view of the above circumstances, the present invention aims to provide an adaptive equalizer, a step size derivation method, and a program that can improve the signal-to-noise ratio during slow fluctuations in the polarization state while improving the ability to follow fast fluctuations in the polarization state. [Means for solving the problem]

[0014] One aspect of the present invention is an adaptive equalizer having an update unit that updates a step size of a vector of tap coefficients used to control an adaptive filter, based on a time-series update vector corresponding to a time-series input and output of the adaptive filter that tracks the polarization state of an optical signal received in a coherent optical receiver.

[0015] One aspect of the present invention is a step size derivation method executed by an adaptive equalizer, which includes an update step of updating a step size of a vector of tap coefficients used to control an adaptive filter based on a time-series update vector corresponding to a time-series input and output of the adaptive filter that tracks the polarization state of an optical signal received in a coherent optical receiver.

[0016] One aspect of the present invention is a program for causing a computer to function as the adaptive equalizer described above. Effect of the Invention

[0017] According to the present invention, it is possible to improve the signal-to-noise ratio during slow fluctuations in the polarization state while improving the ability to follow fast fluctuations in the polarization state. [Brief description of the drawings]

[0018] [Figure 1] FIG. 2 is a diagram illustrating an example of the configuration of an adaptive filter in the first embodiment. [Diagram 2] FIG. 4 is a diagram illustrating an example of the configuration of a coefficient updating unit in the first embodiment. [Diagram 3] 5 is a flowchart showing an example of the operation of a coefficient updating unit in the first embodiment. [Figure 4] 5A to 5C are diagrams illustrating an example of improvement in followability to fluctuations in the polarization state in the first embodiment. [Diagram 5] FIG. 11 is a diagram illustrating an example of the configuration of a coefficient updating unit in the second embodiment. [Figure 6] FIG. 2 is a diagram illustrating an example of a hardware configuration of an adaptive filter in each embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0019] DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the present invention will be described in detail with reference to the drawings. (First embodiment) 1 is a diagram showing a configuration example of an adaptive filter 1. The adaptive filter 1 is provided in a coherent optical receiver of an optical communication system. The adaptive filter 1 includes an FIR filter 2-1, an FIR filter 2-2, an FIR filter 2-3, and an FIR filter 2-4 in a butterfly configuration with two input systems and two output systems. The adaptive filter 1 also includes two adders 3, an error derivation unit 4, and a coefficient update unit 5a.

[0020] In the following, the symbol "^" written above a character in a drawing shall be written immediately before the character. For example, the symbol "^" written above a character in a drawing shall be written immediately before the letter "x", such as "^x".

[0021] "x" shown in FIG. 1 represents the amplitude vector of the x polarization component (horizontal polarization component) of the main signal (digital signal) input to the FIR filter 2. "y" represents the amplitude vector of the y polarization component (vertical polarization component) of the main signal (digital signal) input to the FIR filter 2. "^x" represents the amplitude vector of the x polarization component (horizontal polarization component) of the main signal (digital signal) output from the adder 3. "^y" represents the amplitude vector of the y polarization component (vertical polarization component) of the main signal (digital signal) output from the adder 3.

[0022] The FIR filter 2-1 uses the tap coefficients "h xx " to perform finite impulse response filtering on the amplitude vector of the x-polarized component of the primary signal. The FIR filter 2-1 outputs the result of such filtering to the adder 3-1.

[0023] The FIR filter 2-2 uses the tap coefficients "h xy" to perform finite impulse response filtering on the amplitude vector of the y-polarized component of the primary signal. The FIR filter 2-2 outputs the result of such filtering to the adder 3-1.

[0024] The FIR filter 2-3 uses the tap coefficients "h yx " to perform finite impulse response filtering on the amplitude vector of the x-polarized component of the primary signal. The FIR filter 2-3 outputs the result of such filtering to the adder 3-2.

[0025] The FIR filter 2-4 uses the tap coefficients "h yy " to perform finite impulse response filtering on the amplitude vector of the y-polarized component of the primary signal. The FIR filter 2-2 outputs the result of such filtering to the adder 3-2.

[0026] The adder 3-1 adds the result of the filtering by the FIR filter 2-1 and the result of the filtering by the FIR filter 2-2 to output an amplitude vector of the x-polarized component of the main signal (digital signal) from which crosstalk has been removed. The adder 3-2 adds the result of the filtering by the FIR filter 2-3 and the result of the filtering by the FIR filter 2-4 to output an amplitude vector of the y-polarized component of the main signal (digital signal) from which crosstalk has been removed.

[0027] The coefficient update unit 5a adaptively controls the tap coefficient vector “h” used in the four FIR filters 2, thereby eliminating crosstalk between the amplitude vector “x” of the x-polarized component input to the FIR filter 2 and the amplitude vector “y” of the y-polarized component input to the FIR filter 2.

[0028] The error derivation unit 4 calculates the difference between the sum of the amplitude vector of the x-polarized component output from the FIR filter 2-1 and the amplitude vector of the y-polarized component output from the FIR filter 2-2 and, for example, a pilot signal (known signal) as error information “e x " to the coefficient update unit 5a.

[0029] The error derivation unit 4 calculates the difference between the sum of the amplitude vector of the y-polarized component output from the FIR filter 2-4 and the amplitude vector of the x-polarized component output from the FIR filter 2-3 and, for example, a pilot signal (known signal) as error information “e y " to the coefficient update unit 5a.

[0030] The coefficient update unit 5a calculates an amplitude vector “x” of the x-polarized component of the primary signal input to the FIR filter 2-1 or the FIR filter 2-3, an amplitude vector “y” of the y-polarized component of the primary signal input to the FIR filter 2-2 or the FIR filter 2-4, and error information “e x ” and the error information of the amplitude vector of the y-polarized component “e y Based on this, the tap coefficient vector “h” used in the four FIR filters 2 is updated.

[0031] The coefficient update unit 5a may optimize the updated tap coefficient vector "h" by executing an optimization algorithm such as the steepest descent method. The steepest descent method executed by the coefficient update unit 5a may be any of the following: a pilot-aided LMS algorithm, a decision-directed LMS algorithm, a constant envelope algorithm, and a multi-modulus algorithm.

[0032] When the pilot-assisted least mean square algorithm is executed, the error derivation unit 4 derives each piece of error information using a pilot signal (known signal). When the decision-directed least mean square algorithm is executed, the error derivation unit 4 derives each piece of error information using a tentative decision.

[0033] When the constant envelope algorithm is executed, the coefficient update unit 5a updates the tap coefficient vector "h" so that the amplitude of the main signal is constant without using phase information of the main signal. When the multi-modulus algorithm is executed, the coefficient update unit 5a updates the tap coefficient vector "h" so that the amplitude of the real part of the amplitude vector and the amplitude of the imaginary part of the amplitude vector are each constant.

[0034] Next, a configuration example of the coefficient update unit 5a will be described. 2 is a diagram showing a configuration example of the coefficient update unit 5a. The coefficient update unit 5a includes four first multiplication units 50, an adaptive equalizer 51a, and four second multiplication units 52. The coefficient update unit 5a also includes four addition units 53 and four delay processing units 54, which are connected to four output systems (h xx ,h yx ,h xy ,h yy ) as a feedback circuit.

[0035] The adaptive equalizer 51a includes a gain derivation unit 510a and an update unit 511. The gain derivation unit 510a includes four averaging units 512, four scale derivation units 513, four absolute value derivation units 514, and three addition units 515. The averaging unit 512 is an FIR filter or an IIR (Infinite Impulse Response) filter. The update unit 511 includes a conversion unit 516 and an averaging unit 517. The averaging unit 517 is an FIR filter or an IIR filter.

[0036] An output terminal of the averaging unit 512-n (n is an integer from 1 to 4) is connected to an input terminal of the scale derivation unit 513-n. An output terminal of the scale derivation unit 513-n is connected to an input terminal of the absolute value derivation unit 514-n.

[0037] In the following, matters common to averaging units 512-1, averaging units 512-2, averaging units 512-3, and averaging units 512-4 will be expressed as "averaging unit 512" with some of the reference numerals omitted.

[0038] In the following, matters common to scale derivation units 513-1, 513-2, 513-3, and 513-4 will be written as "scale derivation unit 513" with some of the reference numerals omitted.

[0039] In the following, matters common to absolute value derivation unit 514-1, absolute value derivation unit 514-2, absolute value derivation unit 514-3, and absolute value derivation unit 514-4 will be expressed as "absolute value derivation unit 514" with some of the reference symbols omitted.

[0040] In the following, matters common to addition unit 515-1, addition unit 515-2, and addition unit 515-3 will be expressed as "addition unit 515" with some of the reference numerals omitted.

[0041] The first multiplier 50-1 multiplies the amplitude vector “x” of the x polarization component by error information “e x By multiplying it by , the update vector 'δ' is obtained as shown in equation (2). xx The first multiplier 50-2 similarly derives the update vector "δ yx The first multiplier 50-3 similarly derives the update vector "δ xy The first multiplier 50-4 similarly derives the update vector "δ yy " is derived.

[0042]

number

[0043] Here, the update vectors are the result of dividing the second term on the right hand side of equation (1) by a step size μ. The step size μ is derived based on a measure of the magnitude of each update vector (the DC gain of each update vector).

[0044] When the polarization state is fluctuating at high speed, the tap coefficients (compensation coefficients) need to be updated in a short time, so the scale of the magnitude of the update vector "δ" should be a large value. Therefore, the coefficient update unit 5a increases the step size "μ" according to the scale of the magnitude of the update vector "δ".

[0045] The gain derivation unit 510a derives the DC gain "u" of the update vector "δ" as a measure of the magnitude of the update vector "δ".

[0046] The tap coefficient vector "h" is recursively updated as shown in equation (1). Before each update, the first multiplier 50 updates the update vector "δ=(δ xx , δ xy , δ yx , δ yy The derived update vector "δ" varies significantly due to noise, etc. The coefficient update unit 5a monitors the long-term trend of variation in the update vector "δ" in order to control the step size "μ".

[0047] Therefore, the four averaging units 512 perform averaging processing on each component of the update vector. For example, the four averaging units 512 use a low-pass filter "h LPF By passing each component of the update vector through 〈δ〉, short-term fluctuations in each component of the update vector are removed. The update vector 〈δ〉 averaged over a certain long period of time is expressed as in equation (3).

[0048]

number

[0049] Here, "h LPF " is a tap coefficient of a low pass filter (LPF) of the averaging unit 512. "t" represents time. Note that since the same processing is performed for each update vector, subscripts are omitted in the notation of equation (3).

[0050] The averaged update vector 〈δ〉 = (δ 1 , δ 2 ,…,δ K ) is a complex vector. In contrast, the step size "μ" is a non-negative real number. Therefore, gain derivation unit 510a needs to extract a non-negative real number representing the magnitude of the update vector from update vector "<δ>".

[0051] The four scale derivation units 513 derive the sum of each component of the averaged update vector. The four absolute value derivation units 514 derive the absolute value of the sum of each component of the update vector. The three addition units 515 add the absolute value of the sum of each component for all components of the update vector (xx component, xy component, yx component, yy component).

[0052] That is, the four scale derivation units 513, the four absolute value derivation units 514, and the three addition units 515 derive a parameter "u" that represents the scale of the magnitude of the update vector, as shown in equation (4).

[0053]

number

[0054] Thus, the parameter "u" represents the DC gain of the update vector as a measure of the magnitude of the update vector.

[0055] Note that the measure derivation unit 513 may derive a Euclidean norm or an L2 norm (power) for each component of the update vector, instead of deriving the sum for each component of the update vector.

[0056] The conversion unit 516 converts the parameter "u" into a step size "μ" before averaging by the averaging unit 517. Here, the conversion unit 516 derives the value of the polynomial exemplified on the right side of the equation (5) using the parameter "u". The averaging unit 517 derives the step size "μ" by an averaging process "<>" for the polynomial exemplified on the right side of the equation (5).

[0057]

number

[0058] Here, "μ0" is the minimum step size when the polarization state is stationary (when the value of the parameter "u" is approximately 0). Each of the coefficients such as "α", "β", and "γ" is heuristically optimized. That is, each of the coefficients such as "α", "β", and "γ" is derived by trial and error.

[0059] For example, the relationship between the optimal step size "μ" and the parameter "u" is approximated by a polynomial, so that the polynomial exemplified on the right side of equation (5) is determined.

[0060] For example, the polynomial exemplified on the right side of equation (5) may be determined based on the results of a simulation or experiment based on the relationship between the optimal step size "μ" or parameter "u" and the rate of change of the polarization state.

[0061] Instead of using a polynomial, the conversion unit 516 may convert the parameter "u" into the step size "μ" by using a lookup table in which the relationship between the step size "μ" and the parameter "u" is registered.

[0062] The transform unit 516 may optimize the step size μ by implementing an optimization algorithm, such as a steepest descent algorithm, such as a pilot-assisted least mean square algorithm, a decision-directed least mean square algorithm, a constant envelope criterion algorithm, or a multi-modulus algorithm.

[0063] The second multiplier 52-1 multiplies the step size "μ" and the update vector "δ xx =e x The second multiplier 52-2 multiplies the step size "μ" and the update vector "δ xy =e x The second multiplier 52-3 multiplies the step size "μ" and the update vector "δ xy =e y The second multiplier 52-4 multiplies the step size "μ" and the update vector "δ yy =e y (n)y(n)" is similarly multiplied.

[0064] A feedback circuit including four adders 53 and four delay processors 54 recursively updates the tap coefficient vector “h” by using the multiplication results by the four second multipliers 52 as shown in equation (1). The feedback circuit sets the tap coefficient vector “h” in the four FIR filters 2.

[0065] Next, an example of the operation of the coefficient update unit 5a will be described. 3 is a flowchart showing an example of the operation of the coefficient update unit 5a. The four first multipliers 50 multiply the time-series input (x, y) and output (e x ,e y) to derive a time-series update vector "δ" (step S101). The gain derivation unit 510a derives a DC gain "u" of the update vector based on the time-series update vector "δ" (step S102). The update unit 511 updates the step size "μ" based on the DC gain of the update vector (step S103). The update unit 511 updates the tap coefficient vector "h" based on the updated step size (step S104).

[0066] As described above, the adaptive equalizer 51a controls the adaptive filter 1. The adaptive filter 1 tracks the polarization state of the optical signal received in the coherent optical receiver. The update unit 511 updates the step size "μ" of the tap coefficient vector "h" used to control the adaptive filter 1, based on a time-series update vector "δ" corresponding to the time-series input (x, y) and output (^x, ^y) of the adaptive filter 1. Here, the update unit 511 updates the step size "μ" based on the DC gain of the update vector (a measure of the magnitude of the update vector).

[0067] This makes it possible to improve the signal-to-noise ratio during slow fluctuations in the polarization state while improving the ability to follow fast fluctuations in the polarization state.

[0068] FIG. 4 is a diagram showing an example of improvement in the ability to follow fluctuations in the polarization state (simulation evaluation example). The horizontal axis indicates the polarization rotation frequency [Hz]. The vertical axis indicates the signal-to-noise ratio (SNR) [dB]. In the "conventional method" shown in FIG. 4, each step size "mu" is fixed. The larger the fixed step size "mu", the better the ability to follow fluctuations in the polarization state. However, when the speed of change in the polarization state is slow, the signal-to-noise ratio rapidly decreases.

[0069] In contrast, in the "proposed method" shown in Fig. 4, the step size "Vmu" is variable. The graph of the "proposed method" shown in Fig. 4 is a graph showing the tracking ability of the adaptive filter 1 of the first embodiment. As shown in this graph, the adaptive filter 1 can improve the signal-to-noise ratio during slow fluctuations in the polarization state while improving the tracking performance for fast fluctuations in the polarization state.

[0070] Second embodiment In the second embodiment, four step sizes (μ xx ,μ yx ,μ xy ,μ yy ) is updated, which is the difference from the first embodiment. In the second embodiment, the differences from the first embodiment will be mainly described.

[0071] FIG. 5 is a diagram showing a configuration example of the coefficient update unit 5b. The coefficient update unit 5b includes four first multiplication units 50, an adaptive equalizer 51b, and four second multiplication units 52. The coefficient update unit 5b also includes four addition units 53 and four delay processing units 54, which are connected to four output systems (h xx ,h yx ,h xy ,h yy ) as a feedback circuit.

[0072] The adaptive equalizer 51a includes a gain derivation unit 510a and an updating unit 511. The gain derivation unit 510a includes four averaging units 512, four scale derivation units 513, and four absolute value derivation units 514. The updating unit 511 includes a conversion unit 516 and an averaging unit 517.

[0073] The four scale derivation units 513 and the four absolute value derivation units 514 derive a parameter “u” representing a scale of the magnitude of the update vector for each component of the update vector, as shown in equation (6).

[0074]

number

[0075] In this way, in equation (6), the subscripts "xx", "xy", "yx", and "yy" that represent the components of the update vector are added to the parameter "u". The tap coefficient vector "h" is recursively updated for each component of the update vector as shown in equation (7).

[0076]

number

[0077] In this way, in equation (7), the subscripts "xx", "xy", "yx", and "yy" representing the components of the update vector are attached to the step size "μ".

[0078] As described above, the update unit 511 calculates a time-series update vector “δ=(δ)” according to the time-series input (x, y) and output (^x, ^y) of the adaptive filter 1. xx , δ yx , δ xy , δ yy ) is used to control the adaptive filter 1. xx ,μ yx ,μ xy ,μ yy Here, the update unit 511 updates the step size for each component, μ = (μ xx ,μ yx ,μ xy ,μ yy )"

[0079] This makes it possible to improve the signal-to-noise ratio during slow fluctuations in the polarization state while improving the ability to follow fast fluctuations in the polarization state.

[0080] FIG. 6 is a diagram showing an example of a hardware configuration of the adaptive filter 1 in each embodiment. Some or all of the functional units of the adaptive filter 1 are realized as software by a processor 100 such as a CPU (Central Processing Unit) executing a program stored in a memory 102 having a non-volatile recording medium (non-transient recording medium). The program may be recorded in a computer-readable recording medium. The computer-readable recording medium is, for example, a portable medium such as a flexible disk, a magneto-optical disk, a ROM (Read Only Memory), a CD-ROM (Compact Disc Read Only Memory), or a non-transient recording medium such as a storage device 101 such as a hard disk built into a computer system. Some or all of the functional units of the adaptive filter 1 may be realized using hardware including an electronic circuit (electronic circuit or circuitry) using, for example, a Large Scale Integrated circuit (LSI), an Application Specific Integrated Circuit (ASIC), a Programmable Logic Device (PLD), or a Field Programmable Gate Array (FPGA).

[0081] Although an embodiment of the present invention has been described in detail above with reference to the drawings, the specific configuration is not limited to this embodiment, and designs that do not deviate from the gist of the present invention are also included. [Industrial Applicability]

[0082] The present invention is applicable to optical communication systems and coherent optical receivers. [Explanation of symbols]

[0083] 1...adaptive filter, 2...FIR filter, 3...addition unit, 4...error derivation unit, 5a, 5b...coefficient update unit, 50...first multiplication unit, 51a, 51b...adaptive equalizer, 52...second multiplication unit, 53...addition unit, 54...delay processing unit, 100...processor, 101...storage device, 102...memory, 510a, 510b...gain derivation unit, 511...update unit, 512...averaging unit, 513...scale derivation unit, 514...absolute value derivation unit, 515...addition unit, 516...conversion unit, 517...averaging unit

Claims

1. An update unit that updates a step size of a vector of tap coefficients used to control an adaptive filter based on a time-series update vector corresponding to a time-series input and output of the adaptive filter that tracks the polarization state of an optical signal received in a coherent optical receiver. Equipped with The update unit updates the step size based on a DC gain of the update vector. Adaptive equalizer.

2. 2. The adaptive equalizer according to claim 1, further comprising a gain derivation unit that derives a DC gain of the update vector based on any one of a sum of each component of the update vector, a Euclidean norm of each component of the update vector, and an L2 norm of each component of the update vector.

3. 3. The adaptive equalizer according to claim 1, wherein the update unit updates the step size for each component of the update vector based on a DC gain for each component of the update vector.

4. 1. A step size derivation method implemented by an adaptive equalizer, comprising: an updating step of updating a step size of a vector of tap coefficients used to control an adaptive filter based on a time series of update vectors corresponding to the time series of inputs and outputs of the adaptive filter that tracks the polarization state of the optical signal received in the coherent optical receiver; Including, the updating step includes updating the step size based on a DC gain of the update vector. Step size derivation method.

5. The step size derivation method of claim 4, comprising a gain derivation step of deriving a DC gain of the update vector based on either a sum of each component of the update vector, a Euclidean norm of each component of the update vector, or an L2 norm of each component of the update vector.

6. A step size derivation method as described in claim 4 or claim 5, wherein the update step includes updating the step size for each component of the update vector based on a DC gain for each component of the update vector.

7. A program for causing a computer to function as the adaptive equalizer according to any one of claims 1 to 3.

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