JP2014072824A - Received signal processing apparatus and received signal processing method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a received signal processing apparatus which is capable of removing influences of code interference of a received signal having a band-limited arbitrary spectrum waveform and maximizing a signal-to-noise ratio and is practical, and a received signal processing method.SOLUTION: The received signal processing apparatus comprises: transfer function determining means for detecting a symbol function represented by a spectrum shape of a symbol constituting a digitized received signal from a spectrum waveform of the received signal and for determining a transfer function represented by a product of an inverse function of the symbol function and a function meeting a Nyquist first reference; and filtering means which shapes the spectrum waveform of the received signal into a waveform meeting the Nyquist first reference on the basis of the transfer function and outputs the shaped waveform.

Description

  The present invention relates to a received signal processing apparatus and a received signal processing method used in the communication field, particularly in the optical fiber communication field.

  Various methods for effectively using a limited frequency band have been proposed in general digital communication apparatuses such as optical fiber communication. A widely used method is to limit the bandwidth of the transmission signal and multiplex the signals with high density in the frequency domain. However, if the bandwidth of the signal is greatly limited, intersymbol interference occurs and the signal The waveform is distorted, and the number of received signal errors increases, which is a problem.

  Nyquist's first standard is known as a condition of a waveform that does not cause intersymbol interference of signals. This criterion is that when the following symbol (1) is satisfied when the symbol rate of the signal is B and the spectrum is S (f), the signal amplitude on the time t-axis is T = 1 except for t = 0. Zero crossing occurs at the interval of / B, and no intersymbol interference occurs. In addition, the right side of following formula (1) should just be a constant, and may be represented with another form.

  As a signal spectrum waveform satisfying the Nyquist first criterion, a raised cosine function represented by the following equation (2) is known.

  In the formula (2), α represents a roll-off coefficient that takes a value of 0 or more and 1 or less, and when α = 0, the spectrum shape of the raised cosine function is rectangular. Note that a filter that uses the raised cosine function expressed by the equation (2) as a transfer function is called a roll-off filter. By making the spectrum of the transmission signal a raised cosine function, Nyquist's first criterion is satisfied for an arbitrary roll-off coefficient α, and intersymbol interference does not occur. The occupied bandwidth of the signal spectrum at this time is B (1 + α), and the closer the α is to 0, the narrower the occupied bandwidth becomes, but the spectrum approaches a rectangle and becomes steep, and the time waveform has a long and oscillating waveform. Occurrence and detection may be difficult.

  In general, the quality of a received signal depends on the waveform distortion of the received signal and the amount of noise added to the received signal, and the receiver is required to have the performance of receiving signals with a minimum number of signal errors. For this reason, various measures are taken in the receiver, such as applying a filter that improves the signal quality by reducing the amount of noise added to the received signal. For example, when the accumulated noise is the largest cause of signal quality deterioration, a filter that suppresses noise power of high frequency components and improves the signal-to-noise ratio is used. A filter that maximizes the signal-to-noise ratio is called a matched filter, and has a transfer function that has the same shape as the received signal spectrum. By using such a filter, the signal-to-noise ratio may be maximized. Shown mathematically.

  As a method for maximizing the signal-to-noise ratio without causing intersymbol interference at the time of reception, the signal spectrum waveform at the time of transmission is a waveform (root) given by the square root of the raised cosine function expressed by the above equation (2). In addition, a method is known in which the transfer function waveform of the matched filter at the time of reception is also a root roll-off waveform. According to this method, the signal-to-noise ratio is maximized because the reception filter satisfies the conditions of the matched filter, and further, the signal spectrum waveform after the output of the matched filter matches the raised cosine function, so intersymbol interference does not occur (above). For example, see Non-Patent Documents 1 and 2).

However, when the signal speed is very high as in an optical communication system, especially when the symbol rate reaches several tens of GHz, it is generally difficult to perform digital-to-analog conversion processing of the signal. It is not realistic to shape the transmission signal waveform into a root roll-off waveform by a digital filter.
Even if the signal waveform can be shaped into a root roll-off waveform at the time of transmission, the root roll-off filter in the receiver does not satisfy the matching filter conditions in a situation where the signal spectrum is shaped in the transmission path. As a result, the signal spectrum waveform after filtering generally collapses from the raised cosine waveform and does not satisfy the Nyquist's first standard, so that intersymbol interference occurs in the received signal. Regarding such a situation, for example, in an optical network, an optical signal is not converted into an electrical signal, and switching or routing processing is performed as it is. As one means for realizing this, a single channel or a plurality of continuous channels on the wavelength axis is used as a wavelength selective switch, with independent wavelengths of wavelength-multiplexed signals as channel units. Switching or routing processing may be performed by separating or synthesizing with a device (see, for example, Non-Patent Documents 3 and 4). At this time, the wavelength selective switch operates as a kind of optical filter, but the transfer characteristic on the wavelength or frequency axis is not an ideal rectangle, but a transfer characteristic represented by a mountain, trapezoid, or super Gaussian function. Therefore, the wavelength component at the end of the signal pass band suffers an unintended large loss. As a result, every time the signal passes through the wavelength selective switch, the spectrum waveform is shaped by receiving a waveform shaping effect (band narrowing by filtering) according to the transfer characteristic of the wavelength selective switch. In addition, since the effect depends on the transmission path in the network, even if the transmission place and the reception place are the same, if the path through which the signal passes is different, a signal having a different waveform is received.

By the way, there is a method in which “Maximum-likelihood sequence estimation / detection (MLSE or MLSD)” (maximum likelihood sequence estimation / determination) is applied to a band-limited signal, and the influence of intersymbol interference is removed at the receiver. It has been proposed (see, for example, non-patent documents 5 to 7).
However, since this method requires a memory for storing data and a lot of calculation processing, it is difficult to apply when high-speed processing such as optical communication is required. However, there is no satisfactory practical signal optimum receiving method that can be applied to the current situation.

In addition, a method of receiving a signal by automatically configuring a filter that minimizes an error by using a method called adaptive equalization has been proposed (for example, see Non-Patent Document 1). Specifically, as an example of a technique capable of real-time processing among adaptive equalizers based on least square errors, one symbol is received based on an algorithm called Decision-Directed Last Mean Square (DD-LMS). A method of updating the tap coefficient of the FIR filter each time is often used.
However, in order to apply this method, a large number of received symbols and iterative calculations are required to optimize tap coefficients and filter transfer characteristics, and it takes a relatively long time until the receiver achieves a desired performance. take time. As a result, in the situation where the received signal waveform changes depending on the path as in the case of the optical network described above, iterative calculation processing becomes excessive, and after the path change, significant signal processing is required until the receiver starts optimum operation. Will cause a delay.

J. G. Proakis et al., Digital Communications, McGraw-Hill (2008). Ikuo Oka "Basics of Digital Communication" 1st edition Morikita Publishing, p94-p107, (2009) R. Ramaswami et al., “Routing and wavelength assignment inall-optical networks,” IEEE / ACM Trans. Networking 3, 489-500 (1995). F. Heismann, “Systemrequirements for WSS filter shape incascaded ROADM networks,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2010), paper OThR1. K. Horikoshi et al., “Spectrumnarrowing tolerant 171-Gbit / s PDM-16QAM transmissionover 1200 km using maximum likelihood sequence estimation,” presented at theEur. Conf. Exhib. Opt. Commun., Geneva, Switzerland, Sep. 2011, PaperWe .10.P1.73. J.-X. Cai et al., “20 Tbit / s transmission over 6860 km withsub-Nyquist channel spacing,” J. Lightwave Technol. 30, 651-657 (2012). J. Li et al., “Approaching Nyquist limit in WDM systems by low-complexity receiver-sideduobinary shaping,” J. Lightwave Technol. 30, 1664-1676 (2012)

  An object of the present invention is to solve the above-described problems and achieve the following objects. That is, the present invention eliminates the influence of intersymbol interference of a received signal having an arbitrary spectrum waveform whose band is limited, and at the same time maximizes the signal-to-noise ratio, and provides a practical received signal processing apparatus and received signal processing method. The purpose is to provide.

Means for solving the problems are as follows. That is,
<1> A symbol function represented by a spectrum shape of a symbol constituting the received signal is detected from a digitized spectrum waveform of the received signal, and an inverse function of the symbol function and a function satisfying the first Nyquist criterion Transfer function determining means for determining a transfer function represented by a product, and filtering means for shaping and outputting the spectrum waveform of the received signal into a waveform satisfying the first standard of the Nyquist based on the transfer function, A received signal processing apparatus comprising:
<2> A symbol function represented by a spectrum shape of a symbol constituting the received signal is detected from a digitized spectrum waveform of the received signal, and an inverse function of the symbol function and a function satisfying the first Nyquist criterion Transfer function determining means for determining a transfer function represented by a product, and using the transfer function as an initial condition, a tap coefficient for reducing an error signal in the received signal is repeatedly updated according to detection of a symbol of the received signal And an adaptive equalization means for outputting a filtered signal based on the updated tap coefficient.
<3> The received signal processing according to any one of <1> to <2>, wherein the transfer function determining unit is a unit that repeatedly detects the symbol function over time with respect to a spectrum waveform of the received signal that changes with time. apparatus.
<4> An autocorrelation waveform acquisition unit that obtains an autocorrelation waveform of a spectrum waveform of a received signal, and a main lobe waveform centered around τ = 0 on the time axis τ from the autocorrelation waveform. A main lobe waveform acquiring means for acquiring a symbol function determining means for calculating a square root of a power density spectrum obtained by Fourier transforming the main lobe waveform and determining a function represented by the square root as a symbol function, The received signal processing device according to any one of <1> to <3>.
<5> The received signal processing apparatus according to any one of <1> to <4>, wherein the function that satisfies the Nyquist first criterion is a raised cosine function.
<6> The transfer function determining means includes roll-off coefficient determining means for determining a roll-off coefficient of the raised cosine function within a numerical range including a numerical value that maximizes the signal-to-noise ratio of the received signal, and the roll-off coefficient The received signal processing apparatus according to <5>, wherein a transfer function is determined by:
<7> The received signal processing apparatus according to any one of <1> to <6>, wherein the received signal is an optical signal.
<8> A symbol function represented by a spectrum shape of a symbol constituting the received signal is detected from a digitized spectrum waveform of the received signal, and an inverse function of the symbol function and a function satisfying the first Nyquist criterion A transfer function determining step for determining a transfer function represented by a product, and a filtering step for shaping and outputting the spectrum waveform of the received signal into a waveform satisfying the first standard of the Nyquist based on the transfer function, A received signal processing method comprising:
<9> A symbol function represented by a spectrum shape of a symbol constituting the received signal is detected from the digitized spectrum waveform of the received signal, and an inverse function of the symbol function and a function satisfying the first criterion of Nyquist A transfer function determining step for determining a transfer function represented by a product, and using the transfer function as an initial condition, a tap coefficient for reducing an error signal in the received signal is repeatedly updated according to detection of a symbol of the received signal And an adaptive equalization step of outputting a filter processing signal based on the updated tap coefficient.
<10> The received signal processing method according to <9>, wherein the transfer function determining step is a step of repeatedly detecting a symbol function over time with respect to a spectrum waveform of the received signal that changes with time.
<11> The transfer function determination step includes an autocorrelation waveform acquisition step of acquiring an autocorrelation waveform of the spectrum waveform of the received signal, and only a main lobe waveform centered on τ = 0 on the time axis τ from the autocorrelation waveform. A main lobe waveform acquisition step of acquiring a symbol function, and a symbol function determination step of calculating a square root of a power density spectrum obtained by Fourier transforming the main lobe waveform and determining a function represented by the square root as a symbol function. The received signal processing method according to any one of <9> to <10>.
<12> The received signal processing method according to any one of <8> to <11>, wherein the function that satisfies the Nyquist first criterion is a raised cosine function.
<13> The transfer function determining step includes a roll-off coefficient determining step of determining a roll-off coefficient of the raised cosine function within a numerical range including a numerical value that maximizes the signal-to-noise ratio of the received signal, and the roll-off coefficient The received signal processing method according to <12>, wherein a transfer function is determined by:

  According to the present invention, the above-mentioned problems in the prior art can be solved, and the influence of intersymbol interference of a received signal having an arbitrary band-limited spectrum waveform can be removed and the signal-to-noise ratio can be maximized. Thus, a practical received signal processing apparatus and received signal processing method can be provided.

It is explanatory drawing explaining the communication system which has a received signal processing apparatus which concerns on 1st Embodiment. It is a block diagram which shows the example of a series of signal processing performed for transfer function G (f) determination. It is a block diagram which shows the example of a series of signal processing performed with a FIR filter. It is a figure which shows the structure of the adaptive equalizer using a DD-LMS algorithm. It is explanatory drawing explaining the outline | summary of an experimental apparatus. It is a figure which shows the transfer function measurement waveform of a 1st optical band pass filter (OBPF1). It is a figure which shows the signal spectrum measurement result of the signal which passed the 1st optical bandpass filter (OBPF1). It is a figure which shows the power density spectrum of a received signal, and the power density spectrum | _SRX (f) | ² of the detected symbol. Is a diagram illustrating the results of calculating the normalized gains g _N for rolloff factor alpha. It is the figure which computed and plotted | G (f) | ² from transfer function G (f). It is a figure which shows the power density spectrum and raised cosine function of the signal output from the filtering means which has G (f) as a transfer function. It is a figure which shows the constellation of the demodulated signal when not receiving signal processing which concerns on this invention is applied. It is a figure which shows the eye pattern of the demodulated signal when not receiving signal processing concerning the present invention is applied. It is a figure which shows the constellation of the signal demodulated after applying the filter with the transfer function G (f) determined by applying the received signal processing which concerns on this invention. It is a figure which shows the eye pattern of the signal demodulated after applying the filter with the transfer function G (f) determined by applying the received signal processing which concerns on this invention. It is a figure which shows the result at the time of not applying the received signal processing which concerns on this invention about a BER characteristic. It is a figure which shows the result at the time of applying the received signal processing which concerns on this invention about a BER characteristic. It is a figure which shows the result of having measured standardization bandwidth (DELTA) and measuring Q value. The initial value c ₀ of the tap coefficients of the FIR filter is a diagram showing the results of measurement of the relative intensity I _k of the error signal contained in the output signal when the received signal processing as 0. Shows a result of measuring the relative intensities I _k of the error signal contained in the output signal when the received signal processing as the inverse Fourier transform value of the transfer the initial value c ₀ of the tap coefficients of the FIR filter function G (f) It is.

(Received signal processing apparatus and received signal processing method)
<First Embodiment>
The received signal processing apparatus according to the first embodiment of the present invention includes a transfer function determining unit, a filtering unit, and other units as necessary.
In addition, the received signal processing method according to the first embodiment of the present invention includes a transfer function determining step, a filtering step, and other means as necessary.

-Transfer function determining means and transfer function determining step-
The transfer function determining means detects a symbol function represented by a spectrum shape of a symbol constituting the received signal from the digitized spectrum waveform of the received signal, and determines an inverse function of the symbol function and a first reference of Nyquist. It is a means for determining a transfer function represented by the product of the function to be satisfied.
In the transfer function determining step, a symbol function represented by a spectrum shape of a symbol constituting the received signal is detected from a digitized spectrum waveform of the received signal, and an inverse function of the symbol function and a first Nyquist function are detected. It is a step of determining a transfer function represented by a product with a function that satisfies a criterion.
By applying the signal processing based on the transfer function determined in the transfer function determining means and step, the output signal is limited even if the received signal is band-limited and has waveform distortion due to intersymbol interference. Since the output waveform is shaped into a waveform that does not generate intersymbol interference, the waveform distortion can be suppressed.

  The function that satisfies the Nyquist's first criterion may be any function as long as this criterion is satisfied, but the raised cosine function represented by the formula (2) is preferable. In addition, when the rectangular filter component obtained by α = 0 in the equation (2) is subtracted from the transfer function and the frequency is set to f for the remaining components, each of the components of f> 0 and f <0. Is a function that is oddly symmetric at f = ± B / 2, the first criterion of the Nyquist is satisfied, and such a function is also included.

The received signal is not particularly limited, and may be a signal having an arbitrary spectrum waveform with a limited band, and a wired or wireless electromagnetic wave signal, particularly an optical signal is preferably exemplified.
The received signal is appropriately digitized before being input to the transfer function determining means.
Further, the modulation format of the received signal is not particularly limited, and various types of modulation signals such as OOK, BPSK, QPSK, and QAM can be targeted.

The configuration of the transfer function determining means is not particularly limited, but from the viewpoint of correctly detecting the symbol function and its inverse function, an autocorrelation waveform acquiring means for acquiring an autocorrelation waveform of the spectrum waveform of the received signal; Main lobe waveform acquisition means for acquiring only the main lobe waveform centered on τ = 0 on the time axis τ from the autocorrelation waveform, and the square root of the power density spectrum obtained by Fourier transforming the main lobe waveform And a symbol function determining unit that determines a function represented by the square root as the symbol function.
Similarly, in the transfer function determination step, an autocorrelation waveform acquisition step of acquiring an autocorrelation waveform of the spectrum waveform of the received signal, and a main function centered on τ = 0 on the time axis τ from the autocorrelation waveform A main lobe waveform acquisition step for acquiring only a lobe waveform, a symbol function determination for calculating a square root of a power density spectrum obtained by Fourier transforming the main lobe waveform, and determining a function represented by the square root as the symbol function It is preferable to have a process.
With such a configuration, it is possible to remove the excessive sidelobe waveform of the autocorrelation function and determine the symbol function only for the main lobe waveform necessary for restoring the spectrum waveform of the received signal. Therefore, it is possible to obtain an output signal of the received signal with higher quality.

When the raised cosine function is used as a function that satisfies the Nyquist's first criterion, the transfer function determining means further includes the raised value within a numerical range including a numerical value that maximizes a signal-to-noise ratio of the received signal. It is preferable to have roll-off coefficient determining means for determining the roll-off coefficient of the cosine function.
Similarly, the transfer function determining step includes a roll-off coefficient determining step for determining the roll-off coefficient of the raised cosine function within a numerical range including a numerical value that maximizes the signal-to-noise ratio of the received signal. It is preferable.
As a specific method for determining the roll-off coefficient, for example, there is a method of calculating the roll-off coefficient so that the noise power of the received signal is minimized.
By having such a roll-off coefficient determination means and a roll-off coefficient determination step, it is possible to determine the optimum value of the roll-off coefficient, and to maximize the signal-to-noise ratio of the received signal. Become.

  As the roll-off coefficient determining means and the roll-off coefficient determining step, the transfer function in which the roll-off coefficient is determined in advance is calculated before the filtering process of the filtering means and the filtering step, and this transfer function is calculated. Is preferably implemented as a process for applying the above to the filter process.

  The transfer function determining means and the transfer function determining step are described as off-line processing in the embodiment described later, but as a practical received signal processing, it is preferable to be real-time processing, in this case, The symbol function is applied as means and process for repeatedly detecting the symbol function over time with respect to the spectrum waveform of the received signal that changes with time.

As a specific construction method of the transfer function determining means, there is a construction method using an integrated circuit such as an IC, LSI, FPGA, etc. that is circuitized so as to determine the transfer function.
The transfer function determining step can be executed based on the transfer function determining means.

-Filtering means and filtering step-
The filtering means is means for shaping and outputting the spectral waveform of the received signal into a waveform that satisfies the Nyquist first criterion based on the transfer function.
The filtering step is a step of shaping the spectrum waveform of the received signal into a waveform satisfying the first Nyquist criterion based on the transfer function and outputting the waveform.

An example of the filtering means is a finite impulse response (FIR) filter. The tap coefficient of the FIR filter is determined by inverse Fourier transform of the transfer function G (f).
Further, when the FIR filter is not used, there is a means for multiplying the signal spectrum in the frequency domain by the transfer function G (f) and performing inverse Fourier transform.

As a specific construction method of the filtering means, there is a construction method using an integrated circuit such as an IC, LSI, FPGA or the like circuitized to execute the filtering process.
The filtering step can be executed by the filtering means.

-Other means and other processes-
The received signal processing device may have other means as required. For example, when used in an optical fiber communication system, a conventionally used optical bandpass filter, Means such as an attenuator, an amplifier, an optical spectrum analyzer, and a digital coherent receiver may be included.
Further, the received signal processing method may include other steps as necessary, and may include various signal processing steps using the other means.

Hereinafter, examples of the received signal processing apparatus and the received signal processing method according to the first embodiment of the present invention will be described in more detail.
Fig.1 (a) is explanatory drawing explaining the communication system which has a received signal processing apparatus concerning 1st Embodiment of this invention. From the transmitter 1, information is added to a transmission symbol having a spectrum waveform of S _TX (f), and a signal having a symbol rate of B is transmitted. The signal propagates through a transmission line (channel) whose transfer function is H (f), and is added with additive white Gaussian noise (AWGN), and then received by the received signal processing device 2.
The spectrum waveform S _RX (f) of the symbol at the time of reception is given by S _RX (f) = S _TX (f) H (f) multiplied by the channel transfer function H (f) at the time of transmission.
When the received signal is largely band-limited, intersymbol interference occurs and waveform degradation becomes significant. However, if the received signal processing apparatus 2 can shape the spectrum waveform into a shape that satisfies the Nyquist criterion, the intersymbol interference will occur. Will no longer occur.

Therefore, the filtering means of the received signal processing device 2 performs the filtering process using the transfer function G (f) expressed by the following equation (3). In addition, R _α (f) in the following formula (3) is a raised cosine function whose definition is shown in the formula (2), but any one that satisfies the Nyquist first criterion instead of R _α (f) You may choose a function.

  If such a filtering process is performed, even if the band of the received signal is limited and waveform deterioration due to intersymbol interference occurs, the spectrum waveform after the filter output matches the raised cosine function. The signal has a waveform that does not cause intersymbol interference, and waveform deterioration can be suppressed.

By the way, the raised cosine function has the roll-off coefficient α as a parameter as described above, and the signal-to-noise ratio (S / N ratio) can be maximized by selecting an optimal value of α.
A time waveform r _α (t) of a symbol having the raised cosine function as a spectrum is given by the following equation (4).

From the equation (4), it can be seen that the peak value of the time waveform amplitude of the symbol is obtained at time t = 0 and does not depend on the roll-off coefficient α.
Next, the noise power _PN is calculated from the following equation (5).

In the equation (5), N (f) represents a power density spectrum of noise, and when considering AWGN, N (f) is a constant. Wherein if you choose rolloff factor α such that the value of the noise power P _N which is calculated by the equation (5) is minimized, the signal-to-noise ratio of the signal after passing through the filter of the transfer function G (f) is Maximized.

In order to determine the transfer function G (f) shown in the equation (3), it is necessary to correctly obtain the spectrum waveform S _RX (f) possessed by the symbol of the received signal. However, the desired S _RX (f) cannot be obtained by simply Fourier transforming the received signal time waveform d _RX (t). This is because the signal is modulated by data and added with noise, so that the simple Fourier transform of d _RX (t) has a large noise in the frequency domain. The description will be given later with reference to FIG.

Therefore, here, as a technique for obtaining the reception symbol spectrum waveform S _RX (f) with high quality from the reception signal time waveform d _RX (t), a symbol function acquisition means using the autocorrelation waveform of d _RX (t) is used. suggest.
First, by calculating the inverse Fourier transform of the power density spectrum of the definition formula a _RX (τ) = ∫ _−∞ ^{+ ∞} d _RX ^* (t) d _RX (t + τ) dt or d _RX (t), d _RX ( The autocorrelation waveform a _RX (τ) of t) is obtained.
Next, only the main lobe waveform centered on τ = 0 is extracted on the delay time τ axis. This clipping has an effect of removing the modulation signal and noise component added to d _RX (t). When the autocorrelation waveform thus cut out is subjected to Fourier transform, a power density spectrum | S _RX (f) | ^{2 of} the received symbol is obtained. When the channel transfer function can be written as a real number, the square root | S _RX (f) | of the power density spectrum corresponds to a desired received symbol spectrum waveform (symbol function). For example, if the channel transfer function is a complex number, such as group velocity dispersion or polarization mode dispersion of an optical fiber, but is a known linear function, the existing signal is processed prior to the reception signal processing. By compensating the complex component in advance by the processing method, it is possible to consider only the real number as the spectrum of the received symbol.

Using the symbol function S _RX (f) as the received symbol spectrum waveform thus detected and its inverse function, the transfer function G (f) for a given α can be obtained from the equation (3). .
Then, as described above, the optimum transfer function G (f) is determined by determining the roll-off coefficient α that minimizes the noise output obtained by calculating the equation (5) from the range of 0 ≦ α ≦ 1. ) Can be determined.

In this case, as an example of a method of determining the roll-off factor based on the computation processing of the equation (5), the noise power density spectrum N (f) is set to 1, the noise power P _N, which is calculated by the equation (5) normalized by dividing the total bandwidth of the G (f) (1 + α ) B, from the normalized gain g _N noise AWGN relating to the transfer function G of the following formula (6) (f), the roll-off factor The method of determining is mentioned.

That is, larger than g _N 1 defined by the formula (6), this means that the noise power P _N in a band of the raised cosine function is amplified, g _N such that less than 1 alpha By selecting, the roll-off coefficient that maximizes the signal-to-noise ratio in the output signal can be determined.
An example of a series of signal processing performed for determining the transfer function G (f) described above is shown as a block diagram in FIG.
By repeatedly performing the above processing, even if the spectrum waveform of the received signal changes with time, received signal processing adapted to the waveform change in real time can be performed.

Next, filter processing using the FIR filter is performed. Here, prior to the filter processing of the FIR filter for the received signal, the tap coefficient obtained by inverse Fourier transform of the transfer function G (f) for which the roll-off coefficient has been determined is determined to determine the FIR filter. By inputting in advance, the FIR filter processing can be executed quickly.
An example of a series of signal processing executed by the FIR filter is shown as a block diagram in FIG.

Second Embodiment
The received signal processing apparatus according to the second embodiment of the present invention includes a transfer function determining unit, an adaptive equalizing unit, and other units as necessary.
In addition, the received signal processing method according to the second embodiment of the present invention includes a transfer function determination step, an adaptive equalization step, and other steps as necessary.
Since the transfer function determining means and the transfer function determining step, and the other means and the other steps are the same as those of the received signal processing apparatus and received signal processing method according to the first embodiment of the present invention, Here, the adaptive equalization means and the adaptive equalization step will be described.

-Adaptive equalization means and adaptive equalization process-
The adaptive equalization means uses the transfer function as an initial condition, repeatedly updates a tap coefficient for reducing an error signal in the received signal according to detection of a symbol of the received signal, and sets the updated tap coefficient as the tap coefficient. A means for outputting a filtered signal based thereon.
Further, the adaptive equalization step uses the transfer function as an initial condition, repeatedly updates a tap coefficient for reducing an error signal in the received signal according to detection of a symbol of the received signal, and updates the updated tap. This is a step of outputting a filter processing signal based on the coefficient.
Since adaptive equalization processing requires many received symbols and repeated calculation in order to optimize the tap coefficient of the FIR filter (see Non-Patent Document 1), it is not practical as a received signal processing method at present. is there.
However, by selecting the transfer function determined in the transfer function determination step as an initial condition, iterative calculation processing until the filter characteristic of the FIR filter converges to an optimum value is dramatically reduced, and practical adaptation is achieved. It is possible to provide equalization processing. Further, by using the transfer function G (f) as an initial condition, it is possible to remove the influence of intersymbol interference of the received signal immediately after the operation is started and to maximize the signal-to-noise ratio. .

Examples of the adaptive equalization means include means using a configuration of an adaptive equalizer such as DD-LMS and CMA (Constant-Modulus Algorithm) that are conventionally used. The adaptive equalization step can be executed by the adaptive equalization means.
As a specific construction method of the adaptive equalizer, a construction method using an integrated circuit such as an IC, LSI, FPGA or the like circuitized so as to optimally update the tap coefficient can be cited.
Here, an example of signal processing of the adaptive equalization means using the adaptive equalizer using the DD-LMS algorithm and the adaptive equalization process will be described in detail with reference to the drawings.

FIG. 2 shows a configuration of an adaptive equalizer in which the DD-LMS algorithm is applied to the FIR filter.
The input signal S _n is digital data obtained by discretizing a received signal at a sampling rate m times the symbol rate, and is discrete data at a certain timing n. m is an integer equal to or greater than 1. For example, if four points are sampled per symbol on the time axis, m = 4. Note that the timing is adjusted so that the data when n is an integer multiple of m is the signal data to be demodulated, and at timings other than the integer multiple of m, the signal data at the point of transition between symbols (For example, see the black line in FIGS. 6A and 6C described later). In FIG. 2, a block represented by z ⁻¹ represents a time delay for one sample, and a past input signal for one sample is obtained each time one block is passed. .

The input signal S _n is input to an FIR filter having N + 1 taps (N is an integer greater than or equal to ₀ ). At this time, the tap coefficient _ck is given by an initial value c ₀ and then n Is updated when m is an integral multiple of m, and for the timing n = mk at that time, c _k = [c _{k, 0} c _{k, 1} ... C _{k, N} ] ^T. However, k is an integer greater than or equal to 0 indicating the number of repeated calculation processes, and represents an initial value when k = 0. T represents vector transposition.

The output signal x _n is obtained as a result of the convolution operation of the tap coefficient c _k and the input signal s _n . Specifically, the input signal s _n = [s _n s _n−1. S _n−N ] It is given by the inner product x _n = c _k ^T s _n of the vector signal of ^{T and} the vector signal of the tap coefficient _ck .
Although the tap coefficient _{c k} when n = mk is updated, the output signal _{x mk} at this time, to implement the decision (Decision) for demodulation, placing the determination result with the desired signal _{d k.} As a specific example, in the case of a QPSK signal, when the output signal x _mk is in one of the first quadrant, the second quadrant, the third quadrant, and the fourth quadrant in the complex plane, the determination result is A (1 + i), Let A (-1 + i), A (-1-i), and A (1-i). However, A is an appropriate constant and i is an imaginary unit.
Then, after obtaining the error signal ε _k = d _k −x _mk , the vector signal of the tap coefficient _ck is updated at any time according to the vector arithmetic expression c _{k + 1} = c _k + με _k s ^* _mk . Here, μ is a positive constant called a step size parameter (Step-size parameter).

In the adaptive equalizer having such a configuration, as an initial value c _o to update to determine the tap coefficients c _k, the use of vector value obtained the transfer function G (f) is then inverse Fourier transform , than repeatedly calculating a condition comprising an arbitrary initial value c _o and n = mk, can dramatically reduce the calculation process can be made more practical reception signal processing.

Example 1
As Example 1, the contents of an experiment in which the received signal processing apparatus and method of the present invention are applied to a band-limited signal and the effects confirmed from the experiment will be described.
FIG. 3 shows an outline of the experimental apparatus. As shown in FIG. 3, this experimental system is composed of a transmitter (T _x ) 11, a first optical bandpass filter (OBPF 1) 13, and a received signal processing device 12. Includes a variable optical attenuator (VOA) 14, an erbium-doped fiber amplifier (EDFA) 15, a second optical bandpass filter (OBPF2) 16, an optical spectrum analyzer (OSA) 17, a coherent receiver 18, And an off-line digital signal processor (DSP) 19.

The transmitter (T _x ) 11 generates a QPSK (quaternary phase shift keying) signal having a center wavelength of 1,552.52 nm, a single polarization, and a symbol rate of B = 21.5 [Gbaud]. The QPSK signal is modulated as a data by a pseudo random bit sequence having a length of 2 ¹⁵ −1.
The band of the signal output from the transmitter (T _x ) 11 is limited by passing through an optical bandpass filter (OBPF1) 13 having a variable bandwidth. 4A shows a transfer function measurement waveform of the optical bandpass filter (OBPF1) 13, and FIG. 4B shows a signal spectrum measurement result of a signal that has passed through the optical bandpass filter (OBPF1) 13. However, the dotted line in FIG. 4B is a signal spectrum before passing through the optical bandpass filter (OBPF1) 13.
Here, when the pass band width W of the transfer function in the optical bandpass filter (OBPF1) 13 is defined by the full width at a point where the insertion loss is 0.1 dB smaller than the peak value, the result shown in FIG. Are W = 32.0, 28.0, 22.3, 16.8, 11.3, 8.25, 5.50, 3.50 [GHz] in descending order of bandwidth.
Further, when the passband width W of the optical bandpass filter (OBPF1) 13 is normalized using the signal symbol rate B = 21.5 [Gbaud], and the normalized bandwidth Δ is defined as Δ = W / B. Δ = 1.49, 1.30, 1.03, 0.78, 0.52, 0.38, 0.26, 0.16.

  The signal band-limited by the optical bandpass filter (OBPF1) 13 is input to the reception signal processing device 12. The received signal processing device 12 uses a variable optical attenuator (VOA) 14 and an erbium-doped optical fiber amplifier (EDFA) 15 to set the signal light power and optical signal-to-noise ratio (OSNR) at the time of signal detection to desired values. The value is adjusted and measured by an optical spectrum analyzer (OSA) 17. Note that an optical bandpass filter (OBPF2) having a passband width of 7.5 nm after passing through the erbium-doped optical fiber amplifier (EDFA) 15 is used so that the total optical power including noise does not become too large when receiving light. This filter does not affect the signal quality.

In the received signal processing apparatus and method according to the present invention, the received signal can be processed in real time, but in the received signal processing apparatus and method according to the present embodiment, offline processing is performed.
That is, the signal whose optical power and OSNR are adjusted is received by the coherent receiver 18 and acquired as digital data by the real-time oscilloscope. The obtained digital data is taken into a personal computer as an off-line digital signal processor (DSP) 19 and an off-line digital signal is executed by executing various signal processing programs built on Matlab, which is calculation software that operates in the personal computer. Perform the process.

As the contents of various signal processing, first, sampling rate conversion is performed, and the sampling rate is changed from 80 Gsample / s to 4 times the symbol rate (21.5 Gbaud) (integer multiple may be used here, 4 times is adopted). Convert to 86 GSample / s.
Next, the received signal processing according to the present invention is performed. Specifically, first, the complex amplitude time waveform of the signal is Fourier-transformed to take the square of the absolute value to obtain a power density spectrum. This is subjected to inverse Fourier transform to obtain an autocorrelation waveform, and only the main lobe waveform centered on the time axis τ = 0 is cut out. Next, the extracted autocorrelation waveform is subjected to Fourier transform again to obtain a power density spectrum in the main lobe waveform from which the side lobe waveform is removed, and then the square function is taken to obtain the symbol function S _RX ( f) and its inverse function S _RX ⁻¹ (f) are obtained.
From this, the transfer function G (f) is calculated for an arbitrary roll-off coefficient α using the equation (3), and at the same time, the normalized gain g _N is calculated from the equation (6). The obtained roll-off coefficient α at which the normalized gain g _N becomes the minimum value, that is, the roll-off coefficient α at which the signal-to-noise ratio is maximized is determined, and the spectrum waveform of the transfer function G (f) is determined (transfer) Function determination step). By deriving tap coefficients of the FIR filter such that the transfer function is G (f) from the impulse response obtained by inverse Fourier transform of the transfer function G (f), and calculating the convolution with the signal data, the spectrum is obtained. An output signal filtered so that the waveform is shaped into a raised cosine function R _α (f) is obtained (filtering step).

  After that, the signal clock is extracted and the timing is corrected, the phase error from the local oscillation light used in the coherent receiver 18 is corrected, the bit sequence is restored from the quaternary phase information as the QPSK signal, and finally transmitted. The bit error rate of the received signal is obtained by comparing with a pseudo-random sequence set in the signal. The Q value is obtained from statistical processing of the waveform data.

In order to confirm the basic operation of the received signal processing apparatus according to the first embodiment, the signal after passing through the first optical bandpass filter (OBPF1) 13 having a normalized bandwidth Δ of 0.26 is The result of applying the received signal processing according to the invention is shown. Note that the OSNR of the signal when receiving the coherent receiver 18 is adjusted to 30 dB.
FIG. 5A is a diagram showing a power density spectrum of a received signal, which is obtained by performing Fourier transform on the complex amplitude of the received optical signal. This power density spectrum is inverse Fourier transformed to derive the autocorrelation waveform of the received signal, and only the main lobe waveform centered on the delay time τ = 0 is cut out and Fourier transformed so as to remove the sidelobe waveform. The square root of symbol power density spectrum, | S _RX (f) | ^2, was detected as shown by the dotted line in FIG. The symbol function S _RX (f) and its inverse function S _RX ⁻¹ (f) were obtained from this dotted line. 5A, the power density spectrum is assumed to include a large noise and has a jagged waveform at the top and bottom, and the desired S _RX ( f) cannot be obtained. Therefore, processing using an autocorrelation waveform is performed.

Using this S _RX (f), the result of calculating the normalized gain g _N by the equation (6) with respect to the roll-off coefficient α in the range of 0 to 1 in the equation (3) is shown in FIG. Shown in b). From this result, it can be seen that 0 <α <0.55 and g _N <1. Since g _N is minimized and the signal-to-noise ratio is maximized when α = 0.23, this value is adopted as the optimum value.

FIG. 5C is a plot of | G (f) | ² calculated from the transfer function G (f) obtained when α = 0.23. The power density spectrum of the signal output from the filtering means having G (f) determined in this way as a transfer function and the raised cosine function (indicated by a dotted line) when α = 0.23 are shown in FIG. ). As can be seen from FIG. 5 (d), both agree well, and suppression of intersymbol interference can be expected as a signal spectrum waveform satisfying the first Nyquist criterion.

When the received signal processing according to the present invention is not applied, the results of the constellation and eye pattern of the demodulated signal are shown in FIGS. 6 (a) and 6 (b), respectively. Intersymbol interference occurs in both the constellation and the eye pattern as a result of the signal band being largely limited by the first optical bandpass filter (OBPF1) 13 having a normalized bandwidth Δ = 0.26. I understand.
On the other hand, similar results of the demodulated signal after applying the received signal processing according to the present invention and applying the filter having the transfer function G (f) determined as described above are shown in FIGS. d) respectively. From this result, it is understood that the intersymbol interference of the received signal is greatly improved by the received signal processing according to the present invention.

Next, the bit error rate (BER) characteristics when the normalized bandwidth Δ of the first optical bandpass filter (OBPF1) 13 and the OSNR of the signal at the time of receiving the light of the coherent receiver 18 are changed according to the present invention. Verify the effect of received signal processing.
Regarding the BER characteristics when the normalized bandwidth is Δ = 1.03, 0.52, 0.38, 0.26, the results when the received signal processing according to the present invention is not applied are respectively shown in FIG. 7 (a) and (b).
As confirmed from FIGS. 7A and 7B, the BER is dramatically improved by applying the received signal processing according to the present invention, and the amount of the improvement is small in the normalized bandwidth Δ. It can be seen that this is the case when the signal is subject to a greater band limitation.
Note that when the standardized bandwidth Δ is large, the BER is improved even though the intersymbol interference does not occur so much. This is because the signal-to-noise ratio has been improved by the processing based on Equation (6).

In order to clarify the relationship between the amount of band limitation on the received signal and the effect of the received signal processing according to the present invention, the OSNR of the signal at the time of receiving light of the coherent receiver 18 is fixed to 13 dB, and the first optical bandpass filter FIG. 8 shows the result of measuring the Q value by changing the normalized bandwidth Δ of (OBPF1) 13.
As can be seen from FIG. 8, in the case where the received signal processing according to the present invention is not applied, the Q value rapidly deteriorates as the normalized bandwidth Δ is reduced, whereas in the case where it is applied, The degree of deterioration is moderate. As a result, it can be seen that by applying the received signal processing according to the present invention, the tolerance of the signal to the band limitation is increased. Actually, compared with the normalized bandwidth Δ = 1.49, the normalized bandwidth Δ when the Q value deteriorates by 1 dB is the normalized bandwidth when the received signal processing according to the present invention is not applied. When the width Δ = 0.51, the standardized bandwidth Δ = 0.31 is applied. Furthermore, when the received signal processing according to the present invention is applied, the improvement amount of the Q value is 0.31 dB when the normalized bandwidth Δ = 1.49, whereas the normalized bandwidth Δ = 0. At 16, it is 3.79 dB.
This means that by applying the received signal processing according to the present invention, the signal can cope with a larger band limitation.

  As described above, it was confirmed that the signal quality can be improved by using the received signal processing apparatus and method according to the present invention when the signal is largely band-limited. The received signal processing apparatus and method can be applied to a general receiver, and the performance of the communication system is improved by using a receiver to which the received signal processing apparatus and method are applied. For example, when considering the case of optical fiber communication, the bandwidth of a signal is more greatly limited at the time of transmission to increase the frequency utilization efficiency, or the path through an optical filter or wavelength selective switch having a narrow pass bandwidth in an optical network A communication system including the above can be realized.

(Example 2)
Next, the contents of the experiment to which the received signal processing according to the second embodiment is applied and the effects confirmed from the experiment will be described.
In the received signal processing apparatus according to the second embodiment, an adaptive equalizer is used instead of the filtering means in the first embodiment. Here, the received signal is processed using the DD-LMS adaptive equalizer shown in FIG. It was decided to perform the process.
Specifically, the transfer function G (f) is determined for the received signal band-limited by the OBPF 1 having an OSNR of 13 dB and a normalized bandwidth Δ of 0.26, as in the first embodiment. in -LMS adaptive equalizer, it was received signal processing using an inverse Fourier transform value of the transfer function G (f) as the initial value c ₀ of the tap coefficients of the FIR filter.
Also, for performance check of the received signal processing apparatus according to the second embodiment, the initial value c ₀ of the tap coefficients of the FIR filter as 0, were subjected to the same reception signal processing.

FIG. 9 shows the result of measuring the relative strength I _k = | ε _k / d _k | ² of the error signal included in the output signal when the received signal processing is performed with the initial value c ₀ of the tap coefficient of the FIR filter set to 0. Shown in a).
In addition, the result of measuring the relative intensity I _k of the error signal included in the output signal when the received signal processing is performed using the initial value c ₀ of the tap coefficient of the FIR filter as the inverse Fourier transform value of the transfer function G (f). As shown in FIG.
Note that the measurement was performed by measuring how the relative intensity I _k of the error signal changes with respect to the number of FIR filter iterations k = n / m. Regarding the measurement result, if I _k converges to a constant value, it can be considered that the transfer characteristic of the filter has converged to the optimum value.

As it confirmed from figure 9 (a), in the case of performing the reception signal processing the initial value c ₀ of the tap coefficients of the FIR filter as 0, through the repetitive calculation process more than 8,000 times, the FIR filter The filter characteristics have converged to the optimum value.
On the other hand, as can be seen from FIG. 9B, when the received signal processing is performed using the initial value c ₀ of the tap coefficient of the FIR filter as the inverse Fourier transform value of the transfer function G (f), it is only 1,000. It can be seen that the filter characteristic of the FIR filter has converged to the optimum value after repeated calculation processing about once. Further, a is obtained small value I _k immediately after starting the reception operation, without waiting for the optimization of the transfer function, it is possible to immediately use as a receiver.
Therefore, according to the present invention, even when an adaptive equalizer is used, it is possible to eliminate the influence of intersymbol interference of a received signal, maximize the signal-to-noise ratio, and enable high-speed processing. A typical received signal processing apparatus.

  The received signal processing apparatus and method according to the present invention can be practically used for signal processing that remarkably improves the quality of received signals, and therefore can be suitably used in the communication field, particularly the optical fiber communication field.

DESCRIPTION OF SYMBOLS 1,11 Transmitter 2,12 Received signal processing apparatus 13 1st optical band pass filter (OBPF1)
14 Variable optical attenuator (VOA)
15 Erbium-doped fiber amplifier (EDFA)
16 Second optical bandpass filter (OBPF2)
17 Optical Spectrum Analyzer (OSA)
18 Coherent receiver 19 Digital signal processor (DSP)

Claims (13)

A symbol function represented by a spectrum shape of a symbol constituting the received signal is detected from the digitized spectrum waveform of the received signal, and expressed by a product of an inverse function of the symbol function and a function satisfying the Nyquist first criterion. Transfer function determining means for determining a transfer function to be performed;
Filtering means for shaping and outputting the spectrum waveform of the received signal into a waveform satisfying the first standard of the Nyquist based on the transfer function;
A received signal processing apparatus comprising: A symbol function represented by a spectrum shape of a symbol constituting the received signal is detected from the digitized spectrum waveform of the received signal, and expressed by a product of an inverse function of the symbol function and a function satisfying the Nyquist first criterion. Transfer function determining means for determining a transfer function to be performed;
Using the transfer function as an initial condition, a tap coefficient for reducing an error signal in the received signal is repeatedly updated according to detection of a symbol of the received signal, and a filtered signal based on the updated tap coefficient is output. Adaptive equalization means;
A received signal processing apparatus comprising:   3. The received signal processing apparatus according to claim 1, wherein the transfer function determining means is means for repeatedly detecting the symbol function over time with respect to a spectrum waveform of the received signal that changes with time.   The transfer function determining means acquires autocorrelation waveform acquiring means for acquiring the autocorrelation waveform of the spectrum waveform of the received signal, and acquires only the main lobe waveform centered on τ = 0 on the time axis τ from the autocorrelation waveform. A main lobe waveform acquisition unit; and a symbol function determination unit that calculates a square root of a power density spectrum obtained by Fourier transforming the main lobe waveform and determines a function represented by the square root as a symbol function. The received signal processing apparatus according to any one of 1 to 3.   5. The received signal processing apparatus according to claim 1, wherein the function that satisfies the Nyquist first criterion is a raised cosine function.   The transfer function determining means has roll-off coefficient determining means for determining a roll-off coefficient of the raised cosine function within a numerical range including a numerical value that maximizes the signal-to-noise ratio of the received signal, and the transfer function is determined by the roll-off coefficient. The received signal processing apparatus according to claim 5, wherein:   The received signal processing apparatus according to claim 1, wherein the received signal is an optical signal. A symbol function represented by a spectrum shape of a symbol constituting the received signal is detected from the digitized spectrum waveform of the received signal, and expressed by a product of an inverse function of the symbol function and a function satisfying the Nyquist first criterion. A transfer function determining step for determining a transfer function to be performed;
A filtering step of shaping and outputting the spectral waveform of the received signal into a waveform that satisfies the Nyquist first criterion based on the transfer function;
A received signal processing method. A symbol function represented by a spectrum shape of a symbol constituting the received signal is detected from the digitized spectrum waveform of the received signal, and expressed by a product of an inverse function of the symbol function and a function satisfying the Nyquist first criterion. A transfer function determining step for determining a transfer function to be performed;
Using the transfer function as an initial condition, a tap coefficient for reducing an error signal in the received signal is repeatedly updated according to detection of a symbol of the received signal, and a filtered signal based on the updated tap coefficient is output. An adaptive equalization process;
A received signal processing method.   10. The received signal processing method according to claim 9, wherein the transfer function determining step is a step of repeatedly detecting a symbol function over time with respect to a spectrum waveform of the received signal that changes with time.   The transfer function determining step acquires an autocorrelation waveform acquisition step of acquiring the autocorrelation waveform of the spectrum waveform of the received signal, and acquires only the main lobe waveform centering on τ = 0 on the time axis τ from the autocorrelation waveform. A main lobe waveform acquisition step, and a symbol function determination step of calculating a square root of a power density spectrum obtained by Fourier transforming the main lobe waveform and determining a function represented by the square root as a symbol function. The received signal processing method according to any one of 9 to 10.   The received signal processing method according to claim 8, wherein the function that satisfies the Nyquist first criterion is a raised cosine function.   The transfer function determining step includes a roll-off coefficient determining step for determining a roll-off coefficient of the raised cosine function within a numerical range including a numerical value that maximizes the signal-to-noise ratio of the received signal, and the transfer function is determined by the roll-off coefficient. The received signal processing method according to claim 12, wherein: is determined.