Signal estimation device, signal estimation method, and computer program

Abstract

A signal estimation device 21 comprises a plurality of signal estimation units 23. Each of the plurality of signal estimation units includes two linear equalizers 232, 233 and one nonlinear converter 234. The plurality of signal estimation units are connected in series in such a manner that an output signal generated by an r-1-th signal estimation unit 23 r -1 is input to an r-th signal estimation unit 23 r following and connected to the r-1-th signal estimation unit. The r-th signal estimation unit uses the two linear equalizers and the non-linear converter to generate an output signal from the output signal generated by the r-1-th signal estimation unit and a plurality of reception signals.

Description

[Technical Field]

[0001] The present invention relates to a signal estimation device, a signal estimation method, and a recording medium capable of estimating multiple transmission signals corresponding to multiple received signals from multiple spatially multiplexed received signals. [Background technology]

[0002] Research is underway on transmission systems that use multicore optical fibers containing multiple cores to transmit multiple spatially multiplexed transmission signals from a transmitting device to a receiving device. In such transmission systems, the receiving device, which receives the multiple spatially multiplexed transmission signals as multiple spatially multiplexed reception signals, is required to perform signal estimation processing (specifically, MIMO (Multi Input Multi Output) equalization processing) to estimate the multiple transmission signals from the multiple reception signals in order to compensate for crosstalk (in other words, interference) that occurs between the multiple cores of the multicore optical fiber.

[0003] One example of signal estimation processing is signal estimation processing using multiple linear equalizers. In this case, the filter coefficients (tap coefficients) of each linear equalizer are optimized to minimize the error between the estimated results of multiple transmission signals obtained by the signal estimation processing and the multiple transmission signals that were actually transmitted. For example, Non-Patent Documents 1 and 2 describe an MMSE (Minimum Mean Square Error) estimation process as an example of signal estimation processing, in which multiple transmission signals are estimated using a linear equalizer whose filter coefficients (tap coefficients) are optimized to minimize the least squares error between the estimated results of multiple transmission signals obtained by the signal estimation processing and the multiple transmission signals that were actually transmitted. [Prior art documents] [Non-patent literature]

[0004] [Non-Patent Document 1] Peter J. Winzer et al., “MIMO capacities and outage probabilities in spatially multiplexed optical transport systems”, Opt. Express, vol. 19, no. 17, pp. 16680-16696, August 2011. [Non-Patent Document 2] K. Shibahara et al., “Advanced MIMO signal processing techniques enabling long-haul dense SDM transmissions”, Journal of Lightwave Technology, vol.36, no.2, pp.336-348, January 2018. [Overview of the project] [Problems that the invention aims to solve]

[0005] While MMSE estimation processing has the advantage of reducing computational costs, it has a technical challenge in that there is room for improvement in the estimation accuracy of multiple transmitted signals.

[0006] Furthermore, similar technical problems may arise not only in transmission systems that transmit multiple signals using multicore optical fibers, but also in transmission systems that transmit multiple signals using radio waves (i.e., wireless communication systems).

[0007] The present invention aims to provide a signal estimation device, a signal estimation method, and a recording medium that can solve the above-mentioned technical problems. As an example, the present invention aims to provide a signal estimation device, a signal estimation method, and a recording medium that can improve the estimation accuracy of multiple transmitted signals. [Means for solving the problem]

[0008] One embodiment of a signal estimation device is a signal estimation device that estimates a plurality of transmission signals corresponding to a plurality of spatially multiplexed reception signals, wherein the signal estimation device comprises a plurality of signal estimation units, each of which comprises two linear equalizers and one nonlinear converter that performs a nonlinear transformation, and the plurality of signal estimation units are connected in series such that the output signal generated by the r-1th signal estimation unit using the two linear equalizers and the nonlinear converter of the r-1th signal estimation unit is input to the rth signal estimation unit connected downstream of the r-1th signal estimation unit, and the rth signal estimation unit uses the two linear equalizers and the nonlinear converter of the r-th signal estimation unit to generate the output signal from the output signal generated by the r-1th signal estimation unit using the two linear equalizers and the nonlinear converter of the r-1th signal estimation unit and the plurality of reception signals.

[0009] One aspect of a signal estimation method is a signal estimation method for estimating a plurality of transmission signals corresponding to a plurality of spatially multiplexed received signals, wherein the signal estimation method includes inputting the plurality of received signals and estimating the plurality of transmission signals from the plurality of received signals using a plurality of signal estimation units connected in series, each of the plurality of signal estimation units comprising two linear equalizers and one nonlinear converter that performs a nonlinear transformation, and the estimation of the plurality of transmission signals is performed i-1 (where i is a variable representing an integer of 2 or more and less than the number of signal estimation units) The process includes inputting the output signal generated by the (i-1)th signal estimation unit using the two linear equalizers and the nonlinear converter provided in the signal estimation unit into the i-th signal estimation unit connected downstream of the (i-1)th signal estimation unit, and generating the output signal to be output by the i-th signal estimation unit from the output signal generated by the (i-1)th signal estimation unit using the two linear equalizers and the nonlinear converter provided in the i-th signal estimation unit and the plurality of received signals.

[0010] One embodiment of a recording medium is a recording medium on which a computer program is recorded that causes a computer to execute a signal estimation method for estimating a plurality of transmission signals corresponding to a plurality of spatially multiplexed received signals, wherein the signal estimation method includes inputting the plurality of received signals and estimating the plurality of transmission signals from the plurality of received signals using a plurality of signal estimation units connected in series, each of the plurality of signal estimation units comprising two linear equalizers and one nonlinear converter that performs a nonlinear transformation, and estimating the plurality of transmission signals is performed by i-1 (where i is 2 or more and the number of signal estimation units) The process includes inputting the output signal generated by the (i-1)th signal estimation unit using the two linear equalizers and the nonlinear converter provided in the (i)th signal estimation unit (a variable representing an integer less than i) to the i)th signal estimation unit connected downstream of the (i)th signal estimation unit, and generating the output signal to be output by the i)th signal estimation unit from the output signal generated by the (i)th signal estimation unit using the two linear equalizers and the nonlinear converter provided in the i)th signal estimation unit and the plurality of received signals. [Effects of the Invention]

[0011] According to the respective embodiments of the signal estimation device, signal estimation method, and recording medium described above, the estimation accuracy of multiple transmitted signals can be improved. [Brief explanation of the drawing]

[0012] [Figure 1] Figure 1 is a block diagram showing the configuration of the transmission system in this embodiment. [Figure 2] Figure 2 is a block diagram showing the configuration of a receiving device that performs MIMO equalization processing. [Figure 3] Figure 3 is a block diagram showing the configuration of a MIMO equalizer. [Figure 4] Figure 4 is a flowchart showing the flow of the MIMO equalization process. [Figure 5] Figure 5 is a block diagram showing the configuration of a nonlinear converter. [Figure 6] Figures 6(a) and 6(b) are graphs showing the relationship between input and output in an activation function, respectively. [Figure 7] Figure 7 is a graph showing the bit error rate of the estimated signal. [Figure 8] Figure 8 is a block diagram showing the configuration of the coefficient update device. [Figure 9] Figure 9 is a block diagram showing the configuration of the coefficient update error propagation unit. [Figure 10] Figure 10 is a flowchart showing the flow of the coefficient update operation. [Figure 11] Figure 11 is a flowchart showing a modified version of the coefficient update operation. [Modes for carrying out the invention]

[0013] Hereinafter, embodiments of the signal estimation device, signal estimation method, and recording medium will be described using a transmission system SYS to which embodiments of the signal estimation device, signal estimation method, and recording medium are applied, with reference to the drawings. However, the present invention is not limited to the embodiments described below.

[0014] <1> Configuration of the transmission systemSYS First, the overall configuration of the transmission system SYS in this embodiment will be described with reference to Figure 1. Figure 1 is a block diagram showing the configuration of the transmission system SYS in this embodiment.

[0015] As shown in Figure 1, the transmission system SYS comprises a transmitter 1 and a receiver 2. Transmitter 1 transmits a MIMO (Multi-Input Multi-Output) transmission signal X, which includes multiple spatially multiplexed transmission signals x, to receiver 2 via a transmission line 3. Receiver 2 receives the MIMO transmission signal X transmitted from transmitter 1 as a MIMO reception signal Y via the transmission line 3. In other words, receiver 2 receives multiple transmission signals x transmitted from transmitter 1 as multiple reception signals y via the transmission line 3. Each transmission signal x may contain multiple signal components and may therefore be referred to as a transmission signal sequence. Similarly, each reception signal y may contain multiple signal components and may therefore be referred to as a reception signal sequence.

[0016] The following explanation describes an example where the number of MIMO transmission signals X and MIMO reception signals Y is D (where D is a variable representing an integer of 2 or greater). In this case, the transmitting device 1 transmits D spatially multiplexed transmission signals x via the transmission path 3. (0) from x (D-1) The MIMO transmission signal X, which includes the D transmission signals x, is transmitted to the receiver 2 via the transmission line 3. The receiver 2 receives the D transmission signals x transmitted from the transmitter 1. (0) from x (D-1) D received signals y, which are spatially multiplexed. (0) from y (D-1) It will be received as such.

[0017] Multiple transmission signals x (0) from x (D-1) To transmit signals, the transmitting device 1 comprises a signal processing device 11 and a storage device 12.

[0018] The signal processing device 11 may include at least one of a CPU (Central Processing Unit), a GPU (Graphic Processing Unit) and an FPGA (Field Programmable Gate Array). The signal processing device 11 may read a computer program. For example, the signal processing device 11 may read a computer program stored in the storage device 12. For example, the signal processing device 11 may read a computer program stored in a computer-readable recording medium using a recording medium reading device not shown in the drawings. The signal processing device 11 may acquire (that is, may download or read) a computer program from a device not shown disposed outside the transmitting device 1 via a communication device not shown. The signal processing device 11 executes the read computer program. As a result, logical functional blocks for executing operations to be performed by the transmitting device 1 are implemented in the signal processing device 11. Specifically, in the signal processing device 11, there are a plurality of transmission signals x (0) to x (D-1) Logical functional blocks for executing transmission operation of transmitting are implemented. That is, the signal processing device 11 can function as a controller for implementing logical functional blocks for executing operations to be performed by the transmitting device 1.

[0019] The storage device 12 can store desired data. For example, the storage device 12 may temporarily store a computer program executed by the signal processing device 11. The storage device 12 may temporarily store data temporarily used by the signal processing device 11 when the signal processing device 11 executes the computer program. The storage device 12 may store data to be stored long-term by the transmitting device 1. Note that the storage device 12 may include at least one of a RAM (Random Access Memory), a ROM (Read Only Memory), a hard disk device, a magneto-optical disk device, an SSD (Solid State Drive) and a disk array device.

[0020] Multiple received signals y (0) from y (D-1) To receive signals, the receiving device 2 includes a signal processing device 21 and a storage device 22.

[0021] The signal processing unit 21 may include at least one of a CPU (Central Processing Unit), a GPU (Graphic Processing Unit), and an FPGA (Field Programmable Gate Array). The signal processing unit 21 may read computer programs. For example, the signal processing unit 21 may read computer programs stored in the storage device 22. For example, the signal processing unit 21 may read computer programs stored on a computer-readable recording medium using a recording medium reader (not shown). The signal processing unit 21 may obtain (i.e., download or read) computer programs from a device (not shown) located outside the receiving device 2 via a communication device (not shown). The signal processing unit 21 executes the read computer program. As a result, logical functional blocks for performing the operations that the receiving device 2 should perform are realized within the signal processing unit 21. Specifically, the signal processing unit 21 contains multiple received signals y (0) from y (D-1) A logical functional block for performing the receiving operation is realized. In other words, the signal processing device 21 can function as a controller for realizing the logical functional block for performing the operation that the receiving device 2 should perform.

[0022] The storage device 22 is capable of storing desired data. For example, the storage device 22 may temporarily store a computer program executed by the signal processing device 21. The storage device 22 may temporarily store data that the signal processing device 21 uses temporarily while it is executing a computer program. The storage device 22 may store data that the receiving device 2 stores long-term. The storage device 22 may include at least one of the following: RAM (Random Access Memory), ROM (Read Only Memory), hard disk drive, magneto-optical disk drive, SSD (Solid State Drive), and disk array device.

[0023] The transmission path 3 may include a wired transmission path implemented by a wired communication cable. For example, the transmission path 3 may include a wired transmission path that includes a multicore optical fiber with multiple cores. In this case, crosstalk (XT) may be permitted between multiple transmission signals x transmitted through the multiple cores. That is, interference between multiple transmission signals x transmitted through the multiple cores may be permitted. In this case, the transmission capacity can be increased compared to when crosstalk is not permitted. Alternatively, the transmission path 3 may include a wireless transmission path implemented by radio waves in addition to or instead of a wired transmission path.

[0024] In the following description, the transmission technique in which the transmitting device 1 transmits a MIMO transmission signal X (i.e., multiple spatially multiplexed transmission signals x) to the receiving device 2 and the receiving device 2 receives a MIMO reception signal Y (i.e., multiple spatially multiplexed reception signals y), whether the transmission path 3 includes a wireless transmission path or does not include a wireless transmission path, is referred to as MIMO transmission technique. In other words, in this embodiment, MIMO transmission technique is not limited to the transmission technique performed when the transmission path 3 includes a wireless transmission path.

[0025] The receiving device 2 receives multiple received signals y (0) from y (D-1) From, multiple transmission signals x(0) from x (D-1) A signal estimation process (in other words, a signal equalization process) that estimates the signal is performed as at least part of the receiving operation. In the following explanation, multiple received signals y (0) from y (D-1) Multiple transmission signals x (0) from x (D-1) The signal estimation process that estimates the signal is called MIMO equalization.

[0026] Specifically, multiple received signals y (0) from y (D-1) and multiple transmission signals x (0) from x (D-1) The relationship between and is expressed by Equation 1. Note that in Equation 1, k is a variable representing an integer between 1 and D-1 (inclusive). In Equation 1, m is a variable representing an integer between 1 and D-1 (inclusive). In Equation 1, h (k、m) This shows the impulse response of each of the D×D transmission paths formed between the transmitter 1 and the receiver 2. In Equation 1, z (k) This represents the white noise component. In equation 1, the symbol "[conv]" is an operator that represents a convolution operation. In the following explanation as well, the symbol "[conv]" will be assumed to represent a convolution operation. Therefore, in the following explanation, "A[conv]B" will represent "the convolution operation of A and B". The receiving device 2 receives multiple received signals y (0) from y (D-1) and multiple transmission signals x (0) from x (D-1) The signal estimation process may be performed assuming that the relationship between the two is expressed by equation 1.

[0027]

number

[0028] The receiving device 2 performs MIMO equalization processing using multiple MIMO equalizers 23 (see Figure 2), as will be described in detail later. The MIMO equalizers 23 may also be referred to as signal equalizers, signal estimators, signal equalization units, or signal estimation units. In this embodiment, the MIMO equalizer 23 comprises two linear equalizers 232 and 233 and one nonlinear converter 234, as will be described in detail later (see Figure 3). In this case, as will be described in detail later, the receiving device 2 processes multiple transmitted signals x (0) from x (D-1) This can improve the estimation accuracy.

[0029] The transmission system SYS is further equipped with a coefficient update device 4. The coefficient update device 4 performs a coefficient update operation to update (in other words, set) the filter coefficients (tap coefficients) g of the linear equalizer 232 and the filter coefficients (tap coefficients) w of the linear equalizer 233. Details of the coefficient update operation will be described later.

[0030] To perform the coefficient update operation, the coefficient update device 4 includes a signal processing device 41 and a storage device 42.

[0031] The signal processing unit 41 may include at least one of a CPU (Central Processing Unit), a GPU (Graphic Processing Unit), and an FPGA (Field Programmable Gate Array). The signal processing unit 41 may read computer programs. For example, the signal processing unit 41 may read computer programs stored in the storage device 42. For example, the signal processing unit 41 may read computer programs stored on a computer-readable recording medium using a recording medium reader (not shown). The signal processing unit 41 may obtain (i.e., download or read) computer programs from a device (not shown) located outside the receiving device 2 via a communication device (not shown). The signal processing unit 41 executes the read computer program. As a result, logical functional blocks for performing the operations that the receiving device 2 should perform are realized within the signal processing unit 41. Specifically, the signal processing unit 41 contains multiple received signals y (0) from y (D-1) A logical functional block for performing the receiving operation is realized. In other words, the signal processing device 41 can function as a controller for realizing the logical functional block for performing the operation that the receiving device 2 should perform.

[0032] The storage device 42 is capable of storing desired data. For example, the storage device 42 may temporarily store a computer program executed by the signal processing device 41. The storage device 42 may temporarily store data that the signal processing device 41 temporarily uses while the signal processing device 41 is executing a computer program. The storage device 42 may store data that the receiving device 2 stores long-term. The storage device 42 may include at least one of the following: RAM (Random Access Memory), ROM (Read Only Memory), hard disk drive, magneto-optical disk drive, SSD (Solid State Drive), and disk array device.

[0033] <2> MIMO equalization process performed by receiver 2 Next, we will explain the MIMO equalization process performed by the receiving device 2.

[0034] <2-1> Configuration of the receiving device 2 (signal processing device 21) First, with reference to Figure 2, the configuration of the receiving device 2 that performs MIMO equalization processing (in particular, the configuration of the signal processing device 21) will be described. Figure 2 is a block diagram showing the logical functional blocks implemented within the signal processing device 21 for performing MIMO equalization processing.

[0035] As shown in Figure 2, the signal processing device 21 is equipped with multiple MIMO equalizers 23 as logical functional blocks for performing MIMO equalization processing. Note that Figure 2 only conceptually (in other words, simply) illustrates the logical functional blocks for performing MIMO equalization processing. That is, the functional blocks shown in Figure 2 do not necessarily have to be implemented in the signal processing device 21 as is; as long as the signal processing device 21 can perform the MIMO equalization processing performed by the functional blocks shown in Figure 2, the configuration of the functional blocks implemented within the signal processing device 21 is not limited to the configuration shown in Figure 2.

[0036] Multiple MIMO equalizers 23 are connected in series (in other words, coupled in series). Specifically, the multiple MIMO equalizers 23 are connected in series such that the output of one MIMO equalizer 23 is input to another MIMO equalizer 23 connected downstream of the first MIMO equalizer 23. The following description will explain an example in which the signal processing device 21 has R (where R is a constant representing an integer of 2 or more) MIMO equalizers 23.

[0037] Furthermore, in the following explanation, the r-th MIMO equalizer 23 out of the R MIMO equalizers 23 (where r is a variable representing an integer between 1 and R) is referred to as MIMO equalizer 23 r This is referred to as the MIMO equalizer 231, MIMO equalizer 232, ..., MIMO equalizer 23 r-1 , MIMO equalizer 23 r,..., MIMO equalizer 23 R-1 , and MIMO equalizer 23 R It also includes R MIMO equalizers 231 to 23 under the condition that the variable r is an integer of 2 or more. R This is MIMO equalizer 23 r-1 The output of MIMO equalizer 23 r-1 MIMO equalizer 23 connected to the subsequent stage r They are connected in series so that they can be input to the device.

[0038] MIMO equalizer 23 r This is a combination of multiple received signals y (i.e., multiple received signals y (0) from y (D-1) ) each corresponds to multiple transmission signals x (that is, multiple transmission signals x (0) from x (D-1) ) is tentatively estimated. Note that in the following explanation, MIMO equalizer 23 r The provisional estimation results of multiple transmitted signals x are given by multiple estimated signals xe r This is what is meant by "MIMO equalizer 23". r Multiple transmitted signals x (0) from x (D-1) The provisional estimation results are given to the estimated signal xe, respectively. r (0) From xe r (D-1) This is what is called. Therefore, MIMO equalizer 23 r From multiple received signals y, multiple estimated signals xe r Generates.

[0039] MIMO equalizer 23 r Furthermore, it generates auxiliary signals s and u. Note that in the following explanation, MIMO equalizer 23 r The auxiliary signals s and u generated by are, respectively, the auxiliary signal s r and auxiliary signal u r This is referred to as the auxiliary signal s. r This involves multiple (specifically, D) auxiliary signals s r (0) from s r (D-1) Includes auxiliary signal ur comprises a plurality of (specifically, D) auxiliary signals u r (0) to u r (D-1) .

[0040] MIMO equalizer 23 r generates a plurality of estimated signals xe from the plurality of received signals y, the auxiliary signals s generated by MIMO equalizer 23 r-1 , the auxiliary signals s generated by MIMO equalizer 23 r-1 and the auxiliary signals u generated by MIMO equalizer 23 r-1 , the auxiliary signals u r-1 , and the auxiliary signals u r and auxiliary signals s r and auxiliary signals u r . For this purpose, MIMO equalizer 23 r-1 outputs the auxiliary signals s r-1 and the auxiliary signals u r-1 to MIMO equalizer 23 r . However, when variable r is 1, there is no MIMO equalizer 230 connected upstream of MIMO equalizer 231, therefore MIMO equalizer 231 uses the plurality of received signals y, auxiliary signals s0 corresponding to initial values of auxiliary signals s (specifically, the plurality of auxiliary signals s0 (0) to s0 (D-1) ) and auxiliary signals u0 corresponding to initial values of auxiliary signals u (specifically, the plurality of auxiliary signals u0 (0) to u0 (D-1) ) to generate a plurality of estimated signals xe1, auxiliary signals s1 and auxiliary signals u1.

[0041] Signal processing device 21 takes the plurality of estimated signals xe generated by the R-th MIMO equalizer 23 R the plurality of estimated signals xe generated by R (0) to xe R (D-1) as the final estimation results of the plurality of transmit signals x respectively corresponding to the plurality of received signals y (0) to y (D-1) the plurality of transmit signals x respectively corresponding to (0) to x (D-1) and outputs them. In other words, signal processing device 21 outputs, as the final estimation results, the plurality of estimated signals xe generated by the R-th MIMO equalizer 23 R the plurality of estimated signals xe generated by R(0) From xe R (D-1) multiple transmission signals x (0) from x (D-1) The final estimation result is multiple estimated signals xe (0) From xe (D-1) Output as follows.

[0042] MIMO equalizer 23 r Configuration (i.e., MIMO equalizers 231 to 23) R An example of the respective configurations is shown in Figure 3. As shown in Figure 3, MIMO equalizer 23 r It comprises a linear equalizer 232, a linear equalizer 233, and a nonlinear transducer 234. Therefore, the MIMO equalizer 23 r This uses two linear equalizers 232 and 233 and one nonlinear converter 234 to process multiple received signals y and an auxiliary signal s r-1 and auxiliary signal u r-1 From there, multiple estimated signals xe r and auxiliary signal s r and auxiliary signal u r It generates and . Furthermore, MIMO equalizer 23 r It comprises adder 231a, adder 231b, adder 231c, adder 231d, and adder 231e.

[0043] <2-2> MIMO Equalization Process Flow Next, with reference to Figures 2 and 3, and also to Figure 4, the MIMO equalization process performed by the receiving device 2 using multiple MIMO equalizers 23 will be explained. Figure 4 is a flowchart showing the flow of the MIMO equalization process.

[0044] As shown in Figure 4, the signal processing device 21 of the receiving device 2 receives multiple received signals y (multiple received signals y (0) from y (D-1) ) is entered (step S21).

[0045] Furthermore, the signal processing device 21 performs initialization processing (step S22). Specifically, the signal processing device 21 initializes the auxiliary signal s0 (multiple auxiliary signals s0(0) from s0 (D-1) Initializes the auxiliary signal u0 (multiple auxiliary signals u0) to zero. Furthermore, the signal processing device 21 initializes the auxiliary signal u0 (multiple auxiliary signals u0) to zero. (0) from u0 (D-1) The signal processing device 21 initializes the variable r to zero.

[0046] Then, MIMO equalizer 23 r The linear equalizer 232 is used to obtain the difference signal v r This generates (step S23). Specifically, the MIMO equalizer 23 r The auxiliary signal s is obtained using adder 231a. r-1 and auxiliary signal u r-1 The difference signal (s) corresponds to the difference between the two. r-1 -u r-1 ) is generated. Then, MIMO equalizer 23 r The linear equalizer 232 is used to calculate the difference signal (s r-1 -u r-1 ) and MIMO equalizer 23 r The filter coefficients g of the linear equalizer 232 provided by r By performing a convolution operation with, the convolution signal d r This generates the auxiliary signal s. In other words, the linear equalizer 232 generates the auxiliary signal s r-1 and auxiliary signal u r-1 As a filtering process using the convolutional signal d r The convolution operation is performed to generate the filter coefficient g. r This consists of D × D filter coefficients g. r (0、0) from g r (D-1、D-1) This is the filter coefficient vector that includes the filter coefficient g. r (0、0) from g r (D-1、D-1) This is updated (set) by the coefficient update device 4, as described later. Convolutional signal d r This consists of D convolutional signals d r (0) from d r (D-1) This includes the MIMO equalizer 23. rThe convolution operation shown in Equation 2 may be performed. In Equation 2, the symbol "←" indicates the operation of substituting the right-hand side into the left-hand side. In the following explanation as well, the symbol "←" indicates the operation of substituting the right-hand side into the left-hand side. Subsequently, MIMO equalizer 23 r This is the convolution signal d output by the linear equalizer 232, using the adder 231b. r And the difference signal v corresponds to the difference between multiple received signals y. r It generates the MIMO equalizer 23. r The convolution signal d is generated using adder 231b. r (k) and the received signal y (k) The difference signal v corresponds to the difference between the two. r (k) The process of generating the signal is repeated while varying the variable k from 0 to D-1, resulting in D difference signals v r (0) from v r (D-1) Difference signal v including r This generates the MIMO equalizer 23. r By performing the operation shown in Equation 3, D difference signals v r (0) from v r (D-1) Difference signal v including r Generates.

[0047]

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[0048]

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[0049] Then, MIMO equalizer 23 r The linear equalizer 233 is used to estimate the signal xe r This generates (step S24). Specifically, the MIMO equalizer 23 r The linear equalizer 233 is used to obtain the difference signal v r And MIMO Equalizer 23 rThe filter coefficients w of the linear equalizer 233 provided by r By performing a convolution operation with, the convolution signal d' r This generates the difference signal v. r Filtering using (that is, the convolution signal d which is the output of the linear equalizer 232) r (and filtering using multiple received signals y) the convolution signal d' r The convolution operation is performed to generate the filter coefficient w. r This consists of D × D filter coefficients w r (0、0) From lol r (D-1、D-1) This is the filter coefficient vector containing the filter coefficient w. r (0、0) From lol r (D-1、D-1) This is updated (set) by the coefficient update device 4, as described later. Convolutional signal d' r This is D convolutional signals d' r (0) From d' r (D-1) This includes the MIMO equalizer 23. r The convolution operation shown in equation 4 may be performed. After that, the MIMO equalizer 23 r This is the convolution signal d' output by the linear equalizer 232, using the adder 231c. r And the difference signal (s) generated by adder 231a r-1 -u r-1 The signal obtained by adding ) is the estimated signal xe r It is generated as follows: Specifically, MIMO equalizer 23 r The convolution signal d' is generated using adder 231b. r (k) and difference signal (s r-1 (k) -u r-1 (k) The process of adding ) and is repeated while changing the variable k from 0 to D-1, thereby generating multiple estimated signals xe r (0) from xe r (D-1) This generates the MIMO equalizer 23. rBy performing the calculation shown in Equation 5, multiple estimated signals xe r (0) From xe r (D-1) Generates.

[0050]

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[0051]

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[0052] Furthermore, MIMO equalizer 23 r The nonlinear converter 234 is used to convert the auxiliary signal s r This generates (step S24). Specifically, the MIMO equalizer 23 r The MIMO equalizer 23 uses the adder 231d. r Multiple estimated signals xe generated by r And MIMO Equalizer 23 r-1 Auxiliary signal u input from r-1 By adding these together, the summation signal (xe r +u r-1 ) generates. Specifically, MIMO equalizer 23 r The estimated signal xe is then calculated using adder 231d. r (k) and auxiliary signal u r-1 (k) The process of adding and is repeated while changing the variable k from 0 to D-1, thereby generating multiple summation signals (xe r (k) +u r―1 (k) ) is generated. Then, MIMO equalizer 23 r The nonlinear converter 234 is used to add the signal (xe r +u r-1 By performing a nonlinear transformation on the auxiliary signal s r It generates the MIMO equalizer 23. r The nonlinear converter 234 is used to add the signal (xe r (k) +ur-1 (k) By performing a nonlinear transformation on ), the auxiliary signal s r (k) The process of generating the signal is repeated while varying the variable k from 0 to D-1, thereby generating multiple auxiliary signals s r (0) from s r (D-1) ) generates.

[0053] The nonlinear converter 234 performs nonlinear transformation processing using a predetermined activation function. For this reason, the MIMO equalizer 23 r The summing signal (xe r +u r-1 The signal ) is input to the activation function used by the nonlinear converter 234. The activation function is a nonlinear function in which the relationship between the input and output is nonlinear. Subsequently, the output of the activation function is the auxiliary signal s r It is used as such.

[0054] The nonlinear transformation process performed by the nonlinear converter 234 is represented by the mathematical formula shown in Figure 6. The symbol "Π" in formula 6 represents the process. Q The symbol " is an indicator of the output of the activation function. In this case, as shown in Figure 5 which shows the configuration of the nonlinear converter 234, the nonlinear converter 234 may perform nonlinear processing on the real component of the input and nonlinear processing on the imaginary component of the input separately. That is, the nonlinear converter 234 processes the summation signal (xe r +u r-1 The process involves inputting the real components of ) into an activation function and obtaining its output, and the summing signal (xe r +u r-1 The process of inputting the imaginary component of ) into an activation function and obtaining its output may be performed separately.

[0055]

number

[0056] An example of the relationship between input and output in an activation function is shown in Figures 6(a) and 6(b). The relationship between input and output in an activation function may depend on the modulation scheme of the transmitted signal x. In other words, the activation function may depend on the modulation scheme of the transmitted signal x. As an example, Figure 6(a) shows an example of the relationship between input and output in an activation function when the modulation scheme of the transmitted signal x is the QPSK (Quadrature Phase Shift Keying) scheme, in which the transmitted signal x is represented by four points (+1+√(-1), +1-√(-1), -1+√(-1), -1-√(-1)) on the complex plane. Figure 6(b) shows an example of the relationship between the input and output in the activation function when the modulation scheme for the transmitted signal x is the 16QAM (Quadrature Amplitude Modulation) scheme, where the transmitted signal x is represented by 16 points on the complex plane: (+3+3√(-1), +3-3√(-1), -3+3√(-1), -3-3√(-1), +3+√(-1), +3-√(-1), -3-√(-1), -1+3√(-1), -1-3√(-1), 1+√(-1), 1-√(-1), -1+√(-1), -1-√(-1)).

[0057] Again in Figure 4, further, MIMO equalizer 23 r The nonlinear converter 234 is used to obtain the auxiliary signal u r This generates (step S24). Specifically, the MIMO equalizer 23 r The adder 231e is used to add the summation signal (xe) input to the nonlinear converter 234. r +u r-1 ) and the auxiliary signal s output from the nonlinear converter 234 r The difference between this and the auxiliary signal u r It is generated as follows: Specifically, MIMO equalizer 23 r The adder 231e is used to add the signal (xe r (k) +u r―1 (k) ) and auxiliary signals s r (k) The difference is an auxiliary signal u r (k)The process of calculating this is repeated while changing the variable k from 0 to D-1, thereby generating multiple auxiliary signals u r (0) from u r (D-1) This generates the MIMO equalizer 23. r By performing the operation shown in Equation 7, multiple auxiliary signals u r (0) from u r (D-1) Generates.

[0058]

number

[0059] Subsequently, the signal processing device 21 determines whether the variable r is less than the constant R (step S25). If it is determined that the variable r is less than the constant R (step S25: Yes), the signal processing device 21 increments the variable r by 1 (step S26) and then repeats the processes from step S23 to step S25. On the other hand, if it is determined that the variable r is not less than the constant R (step S25: No), the R-th MIMO equalizer 23 R However, multiple estimated signals xe R (0) From xe R (D-1) It is assumed that this is generating the R-th MIMO equalizer 23. R Multiple estimated signals xe generated by R (0) From xe R (D-1) multiple transmission signals x (0) from x (D-1) The final estimation result is multiple estimated signals xe (0) From xe (D-1) Output as follows (step S27).

[0060] <2-3> Technical effects of MIMO equalization treatment As explained above, the receiving device 2 uses multiple MIMO equalizers 23, each comprising two linear equalizers 232 and 233 and one nonlinear converter 234, to process multiple transmission signals x (0) from x (D-1) It estimates the following: In other words, the receiving device 2 uses multiple MIMO equalizers 23, each comprising two linear equalizers 232 and 233 and one nonlinear converter 234, to estimate multiple signals xe (0) From xe (D-1) It generates multiple transmission signals x. (0) from x (D-1) The estimation accuracy (i.e., multiple estimated signals xe) (0) From xe (D-1) The estimation accuracy of the signal can be improved. In other words, the receiving device 2 can use multiple estimated signals xe with fewer errors. (0) From xe (D-1) It can generate [this].

[0061] For example, Figure 7 shows a plurality of estimated signals xe estimated by the receiving device 2 of this embodiment. (0) From xe (D-1) The bit error rate and multiple estimated signals xe estimated by MMSE estimation processing as a comparative example. (0) From xe (D-1) This graph shows the bit error rate on the horizontal axis and the transmission distance on the vertical axis. In the example shown in Figure 7, multiple estimated signals xe estimated by the receiving device 2 of this embodiment are shown. (0) From xe (D-1) The bit error rates shown are the bit error rates when the number R of the MIMO equalizer 23 is 4 and when the number R of the MIMO equalizer 23 is 8. The bit error rates shown in Figure 7 are calculated under conditions where a wired transmission line including a coupled multicore optical fiber with 4 cores is used as the transmission line 3, the multiplexing number D is 8 due to the combination of four cores and polarization multiplexing, the mode-dependent loss (MDL) related to interference (i.e., crosstalk) between multiple cores is 0.1 dB / √(km), and the modal group delay (MGD) is 20 ps / √(km).

[0062] As shown in Figure 7, in the comparative example of MMSE estimation processing, the bit error rate exceeds the upper limit at which error correction becomes impossible when the transmission distance is approximately 6200 km. On the other hand, with the receiving device 2 of this embodiment, even when the transmission distance exceeds approximately 6200 km, the bit error rate does not exceed the upper limit at which error correction becomes impossible. In the example shown in Figure 7, with the receiving device 2, when the number R of the MIMO equalizer 23 is 4, the bit error rate does not exceed the upper limit at which error correction becomes impossible until the transmission distance exceeds approximately 8700 km. Similarly, in the example shown in Figure 7, with the receiving device 2, when the number R of the MIMO equalizer 23 is 8, the bit error rate does not exceed the upper limit at which error correction becomes impossible until the transmission distance exceeds approximately 9800 km. Thus, in this embodiment, the receiving device 2 uses multiple estimated signals xe with fewer errors. (0) From xe (D-1) Because it can generate such data, it is possible to extend the transmission distance.

[0063] <3> Coefficient update operation performed by coefficient update device 4 Next, we will explain the coefficient update operation performed by the coefficient update device 4.

[0064] <3-1> Configuration of the coefficient update device 4 (signal processing device 41) First, with reference to Figure 8, the configuration of the coefficient update device 4 that performs the coefficient update operation (in particular, the configuration of the signal processing device 41) will be described. Figure 8 is a block diagram showing the logical functional blocks implemented within the signal processing device 41 for performing the coefficient update operation.

[0065] As shown in Figure 8, the signal processing device 41 is equipped with multiple coefficient update error propagation units 43 as logical functional blocks for performing coefficient update operations. Note that Figure 8 only conceptually (in other words, simply) shows the logical functional blocks for performing coefficient update operations. That is, the functional blocks shown in Figure 8 do not necessarily have to be implemented in the signal processing device 41 as is, and as long as the signal processing device 41 can perform the coefficient update operations performed by the functional blocks shown in Figure 8, the configuration of the functional blocks implemented in the signal processing device 41 is not limited to the configuration shown in Figure 8.

[0066] The number of coefficient update error propagation units 43 in the signal processing device 41 is the same as the number of MIMO equalizers 23 in the signal processing device 21 of the receiving device 2. Therefore, the following description will describe an example in which the signal processing device 41 has R coefficient update error propagation units 43. Specifically, in the following description, the signal processing device 41 has R coefficient update error propagation units 43, which include coefficient update error propagation unit 431, coefficient update error propagation unit 432, ..., coefficient update error propagation unit 43 r-1 , coefficient update error propagation unit 43 r ...Coefficient update error propagation unit 43 R-1 , and coefficient update error propagation unit 43 R Let's explain an example of a feature that includes this.

[0067] Coefficient update error propagation unit 43 r The filter coefficient g r and w r Update (set) the coefficient update error propagation unit 43. r The filter coefficient g r and w r To update (set) the signal d from the receiver 2, r The difference signal v corresponds to the difference between this signal and multiple received signals y. r and auxiliary signal s r-1 The complex conjugate and auxiliary signal u r-1 The difference signal (s) corresponds to the difference between the complex conjugate and the complex conjugate of r-1* -u r-1* ) and estimated signal xe r-1 and auxiliary signal ur-2 The summation signal (xe) corresponds to the sum of the two. r-1 +u r-2 ) and are obtained. In the following explanation, the complex conjugate of signal A will be represented by the symbol signal A*. Coefficient update error propagation unit 43 r is the difference signal v r and difference signal (s r-1* -u r-1* ) and summing signal (xe r-1 +u r-2 Using ), the filter coefficient g r and w r Update (set) it.

[0068] Furthermore, the coefficient update error propagation unit 43 r The filter coefficient g r and w r To update (set) the error signal ∂x r Obtain the error signal ∂x. r This shows the difference (error) between the estimated results of multiple transmission signals x by the receiving device 2 and the multiple transmission signals x actually transmitted by the transmitting device 1. In other words, the error signal ∂x r This shows the difference (error) between the multiple estimated signals xe generated by the receiving device 2 and the multiple transmitted signals x actually transmitted by the transmitting device 1.

[0069] In this embodiment, the error signal ∂x r This is the coefficient update error propagation unit 43 r+1 Therefore, the difference signal v r+1 and difference signal (s r* -u r* ) and summing signal (xe r +u r-1 ) and error signal ∂x r+1 It is generated using the coefficient update error propagation unit 43. r This is the coefficient update error propagation unit 43 r+1 From this, the error signal ∂x r To obtain this, multiple coefficient update error propagation units 43 r+1 The error signal ∂x that is output by r Coefficient update error propagation unit 43 rare connected in series as input to (in other words, coupled in series).

[0070] However, the coefficient update error propagation unit 43 R the error signal ∂x to be acquired by R the coefficient update error propagation unit 43 that generates R+1 does not exist. Therefore, as the error signal ∂x R , the difference (error) between the plurality of estimated signals xe actually generated by the receiving device 2 and the plurality of transmission signals x actually transmitted by the transmitting device 1 may be used.

[0071] An example configuration of the coefficient update error propagation unit 43 r is shown in FIG. 9. As shown in FIG. 9, the coefficient update error propagation unit 43 r comprises an arithmetic unit 431a, an arithmetic unit 431b, an adder 432a, an adder 432b, a coefficient memory 433a, a coefficient memory 433b, a linear arithmetic unit 434, and a non-linear arithmetic unit 435.

[0072] <3-2> Flow of the coefficient update operation Next, together with FIGS. 8 and 9, and with reference to FIG. 10, the coefficient update operation performed by the coefficient updating device 4 using the plurality of coefficient update error propagation units 43 will be described. FIG. 10 is a flowchart showing the flow of the coefficient update operation.

[0073] As shown in FIG. 10, the error signal ∂x is input to the signal processing device 41 of the coefficient updating device 4 R (step S41). The error signal ∂x R comprises D error signals ∂x R (0) to ∂x R (D-1) . The error signal ∂x R (k) is the estimated signal xe actually generated by the receiving device 2 (k) and the transmission signal x actually transmitted by the transmitting device 1 (k) is the difference between.

[0074] Note that, as described above, the error signal ∂x Ris a difference (error) between the plurality of estimated signals xe actually generated by the receiving device 2 and the plurality of transmission signals x actually transmitted by the transmitting device 1. Therefore, in step S41, the plurality of estimated signals xe actually generated by the receiving device 2 and the plurality of transmission signals x actually transmitted by the transmitting device 1 may be input to the signal processing device 41 of the coefficient updating device 4. In this case, the signal processing device 41 obtains the error signal ∂x based on the plurality of estimated signals xe and the plurality of transmission signals x input to the signal processing device 41 R may be generated.

[0075] Further, the signal processing device 41 performs an initialization process (step S42). Specifically, the signal processing device 21 initializes a variable r to a constant R.

[0076] Thereafter, the coefficient update error propagation unit 43 r updates the filter coefficient w r (step S43). Specifically, the coefficient update error propagation unit 43 r updates the filter coefficient w r (k、m) by repeating the updating process while changing each of the variable k and the variable m from 0 to D-1, thereby updating the filter coefficient w, which is a filter coefficient vector including the filter coefficient w from the filter coefficient w r (0、0) to the filter coefficient w r (D-1、D-1) which is a filter coefficient vector including the filter coefficient w r .

[0077] In order to update the filter coefficient w r (k、m) , the coefficient update error propagation unit 43 r uses an arithmetic unit 431a to obtain a difference signal v r (m) performs a convolution operation between the complex conjugate of and the error signal ∂x r (k) . Further, the coefficient update error propagation unit 43 r uses the arithmetic unit 431a to obtain the result of the convolution operation (that is, v r (m)* [conv]∂x r (k)The learning rate η, which is a pre-set real value, is multiplied by the value. Then, the coefficient update error propagation unit 43 r The current filter coefficient w stored in coefficient memory 433a is stored using adder 432a. r (k、m) From this, the output of the arithmetic unit 431a (i.e., η × v) r (m)* [conv]∂x r (k) By subtracting ), the filter coefficient w r (k、m) Update the coefficient update error propagation unit 43. r The filter coefficient w is obtained by performing the operation shown in Equation 8 (including linear operations) using the arithmetic unit 431a and the adder 432a. r (k、m) Update.

[0078]

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[0079] Updated filter coefficient w r (k、m) This is stored in the coefficient memory 433a. The MIMO equalizer 23 mentioned above r The linear equalizer 233 that it has contains the filter coefficients w stored in the coefficient memory 433a r (k、m) Filtering is performed using the MIMO equalizer 23. r The linear equalizer 233 that it has contains the filter coefficients w stored in the coefficient memory 433a r (k、m) The obtained filter coefficient w is obtained. r (k、m) Filtering is performed using the following: The filter coefficient w r (k、m) If it has never been updated, the coefficient memory 433a will contain the filter coefficient w. r (k、m) A coefficient representing zero may be stored as the initial value. Alternatively, the coefficient memory 433a may contain the filter coefficient w r (k、m)As initial values, the filter coefficient w r A coefficient that satisfies the condition that the average value is zero may be stored.

[0080] Furthermore, the coefficient update error propagation unit 43 r The filter coefficient g r Update (step S43). Specifically, the coefficient update error propagation unit 43 r The filter coefficient g r (k、m) The process of updating the filter coefficient g is repeated while changing each of the variables k and m from 0 to D-1. r (0、0) From the filter coefficient g r (D-1、D-1) The filter coefficients g are a filter coefficient vector that includes these coefficients. r Update.

[0081] Filter coefficient g r (k、m) To update the coefficient, the coefficient update error propagation unit 43 r The arithmetic unit 431b is used to calculate the filter coefficients w before updating. r (μ、k) The complex conjugate and error signal ∂x r (μ) The first convolution operation to calculate the convolution signal is repeated while changing the variable μ, which represents a variable from 0 to D-1, from 0 to D-1. After that, the coefficient update error propagation unit 43 r The arithmetic unit 431b calculates the sum of the results of the first convolution operation. Then the coefficient update error propagation unit 43 r The arithmetic unit 431b calculates the sum of the results of the first convolution operation and the auxiliary signal s r-1 (m) The complex conjugate and auxiliary signal u r-1 (m) The difference signal (s) corresponds to the difference between the complex conjugate and the complex conjugate of r-1 (m)* -u r-1 (m)* A second convolution operation is performed to calculate the convolution signal with ). Then, the coefficient update error propagation unit 43 rThe arithmetic unit 431b multiplies the result of the second convolution operation by a pre-set real value, the learning rate η. Then the coefficient update error propagation unit 43 r The current filter coefficient g stored in coefficient memory 433a is stored using adder 432b. r (k、m) By subtracting the output of arithmetic unit 431b from this, the filter coefficient g is obtained. r (k、m) Update the coefficient update error propagation unit 43. r The filter coefficient g is obtained by performing the operations shown in Equation 9 (including linear operations) using the arithmetic unit 431b and the adder 432b. r (k、m) Update.

[0082]

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[0083] Updated filter coefficient g r (k、m) This is stored in coefficient memory 433b. MIMO equalizer 23 as described above r The linear equalizer 232 that is equipped with the filter coefficients g stored in the coefficient memory 433b r (k、m) Filtering is performed using the MIMO equalizer 23. r The linear equalizer 232 has filter coefficients g stored in coefficient memory 433a. r (k、m) The obtained filter coefficient g r (k、m) Filtering is performed using the following: Note that the filter coefficient g r (k、m) If it has never been updated, the coefficient memory 433b will contain the filter coefficient g. r (k、m) A coefficient representing zero may be stored as the initial value. Alternatively, the coefficient memory 433b may contain the filter coefficient g. r (k、m) As initial values, the filter coefficient g rA coefficient that satisfies the condition that the average value is zero may be stored.

[0084] Subsequently, the signal processing device 41 determines whether the variable r is greater than 1 (step S44).

[0085] If, as a result of the determination in step S44, the variable r is determined to be greater than 1 (step S44: Yes), then at least the filter coefficient g r-1 and w r-1 It is assumed that the coefficient update error propagation unit 43 has not been updated. Therefore, in this case, the coefficient update error propagation unit 43 r The filter coefficient g r-1 and w r-1 Error signal ∂x used to update r-1 (Step S45) generates the coefficient update error propagation unit 43. r This is the D error signal ∂x r-1 (0) From ∂x r-1 (D-1) Error signal ∂x including ) r-1 This generates the coefficient update error propagation unit 43. r This is the error signal ∂x r-1 (k) The process of generating the error signals ∂x is repeated while varying the variable k from 0 to D-1, thereby generating D error signals ∂x r-1 (0) From ∂x r-1 (D-1) Error signal ∂x including ) r-1 Generates.

[0086] error signal ∂x r-1 (k) To generate, coefficient update error propagation unit 43 r The intermediate signal ∂q is obtained by performing the operation shown in equation 10 (an operation including linear operations) using the linear arithmetic unit 434. (k、m) (Step S45) generates the coefficient update error propagation unit 43. r w is the filter coefficient before the update. r (m、μ) The complex conjugate of and the filter coefficients g before updating r(μ、k) repeats a third convolution operation for calculating a convolution signal with the complex conjugate while varying the variable μ from 0 to D-1. Furthermore, the coefficient update error propagation unit 43 r calculates a sum of results of the third convolution operation. Thereafter, the coefficient update error propagation unit 43 r performs a fourth convolution operation for calculating a convolution signal with a sum of results of the third convolution operation and an error signal ∂x r (m) . As a result, an intermediate signal ∂q is obtained as a result of the fourth convolution operation (k、m) is generated.

[0087] [Math.]]

[0088] Thereafter, the coefficient update error propagation unit 43 r generates an intermediate signal ∂u by performing the operation shown in Formula 11 using the linear operator 434 (k) (step S45). Specifically, the coefficient update error propagation unit 43 r calculates a sum from the intermediate signal ∂q (k、0) to the intermediate signal ∂q (k、D-1) , adds the intermediate signal ∂q to the calculated sum (k、k) , and subtracts the error signal ∂x from the addition result r (k) , thereby generating the intermediate signal ∂u (k) .

[0089] [Math.]]

[0090] Furthermore, the coefficient update error propagation unit 43 r generates an intermediate signal ∂p by performing the operation shown in Formula 12 using the linear operator 434 (k) (step S45). Specifically, the coefficient update error propagation unit 43 r is from the intermediate signal ∂q (k、k) to the intermediate signal ∂u (k)Subtracting twice the result and then doubling the result gives the intermediate signal ∂p (k) Generates.

[0091]

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[0092] Subsequently, the coefficient update error propagation unit 43 r The error signal ∂x is obtained by performing the calculation shown in Equation 13 (nonlinear calculation) using the nonlinear calculator 435. r-1 (k) (Step S45) generates the coefficient update error propagation unit 43. r This is the activation function (Π Q (x) derivative Ψ Q (In other words, dΠ Q (x) / dx) and the estimated signal xe r-1 (k) and auxiliary signal u r-2 (k) The summation signal (xe) corresponds to the sum of the two. r-1 (k) +u r-2 (k) ) is entered. Therefore, the coefficient update error propagation unit 43 r The summing signal (xe r-1 (k) +u r-2 (k) It can be said that a nonlinear process equivalent to the differential process of a nonlinear transformation process using an activation function is performed on ). Subsequently, the coefficient update error propagation unit 43 r The derivative Ψ Q The real part of the output and the intermediate signal ∂p (k) The multiplication is done by multiplying the real part of the derivative Ψ by the imaginary part of the output and the intermediate signal ∂p. (k) The complex number is multiplied by its imaginary part, and the result of the multiplication is added. In formula 13, the symbol "@" is an operator that indicates the addition of the result of multiplying the real part of a complex number by the result of multiplying the imaginary part of a complex number. Therefore, (a+ib)@(c+id) represents ac+ibd (where a, b, c, and d are real numbers, and i represents the imaginary unit). After that, the coefficient update error propagation unit 43r The intermediate signal ∂u is applied to the sum of the multiplication results. (k) By adding ∂x r-1 (k) Generates.

[0093]

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[0094] On the other hand, if it is determined that the variable r is not greater than 1 (step S44: No), the filter coefficients g1 to g R and filter coefficients w1 to w R It is assumed that all of these have been updated. In this case, the signal processing device 41 terminates the coefficient update operation.

[0095] <3-3> Modified Examples of Coefficient Update Operation The coefficient update device 4 may generate filter coefficients g and w that are commonly used by multiple MIMO equalizers 23 by performing a modified version of the coefficient update operation shown in Figure 11. In other words, in this case, the filter coefficient g is generated from MIMO equalizers 231 to 23 R The linear equalizer 232 that each of them possesses uses the common filter coefficient g. (0、0) from g (D-1、D-1) This is the filter coefficient vector that includes . Similarly, the filter coefficients w are obtained from MIMO equalizer 231 to 23 R The linear equalizer 233 that each of them possesses uses the same filter coefficient w (0、0) From lol (D-1、D-1) This is a filter coefficient vector that includes [the specified character].

[0096] Filter coefficient g (0、0) from g (D-1、D-1) To generate the filter coefficient g, the signal processing device 41 uses the least squares method to obtain multiple estimated signals xe, which are the estimation results of multiple transmitted signals x, and multiple received signals y. (0、0) from g (D-1、D-1) (Step S51) generates the following. Specifically, the signal processing device 41 generates the filter coefficient g that satisfies the condition of minimizing the parameter δ shown in Equation 14. (0、0) from g(D-1、D-1) This generates the following. Furthermore, the filter coefficient g satisfies the condition of minimizing the parameter δ shown in equation 14. (0、0) from g (D-1、D-1) The calculation that generates the filter coefficient g is performed in the same way as the method for estimating the impulse response of transmission line 3. (0、0) from g (D-1、D-1) This can be considered equivalent to the operation that generates [the result].

[0097]

number

[0098] Furthermore, the filter coefficient w (0、0) From lol (D-1、D-1) To generate the filter coefficients w, the signal processing device 41 performs a matrix operation using a matrix H whose components are the filter coefficients g and an arbitrarily set parameter γ. (0、0) From lol (D-1、D-1) The signal processing device 41 generates a matrix H whose components are the filter coefficients g. Then, the signal processing device 41 calculates the matrix W by performing the matrix operation shown in equation 15 using matrix H and parameter γ. + The symbol "" represents the Hermitian transpose matrix (i.e., the conjugate transpose matrix). The symbol "I" in equation 15 represents the identity matrix with N rows and N columns. Subsequently, the signal processing device 41 divides the components of matrix W into D × D groups w (k、m) It is then classified into D × D groups w. (k、m) The filter coefficient w (0、0) From lol (D-1、D-1) Output as follows.

[0099]

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[0100] Furthermore, if the coefficient update device 4 generates filter coefficients g and w by performing a modified coefficient update operation, the coefficient update device 4 does not need to be equipped with multiple coefficient update error propagation units 43.

[0101] <4> Note The following additional information is disclosed regarding the embodiments described above. [Note 1] A signal estimation device that estimates multiple transmission signals corresponding to each of the multiple received signals from a plurality of spatially multiplexed received signals, The signal estimation device comprises a plurality of signal estimation units, Each of the multiple signal estimation units comprises two linear equalizers and one nonlinear transformer that performs nonlinear transformations. The plurality of signal estimation units are connected in series such that the output signal generated by the r-1th signal estimation unit using the two linear equalizers and the nonlinear converter provided in the r-1th signal estimation unit is input to the rth signal estimation unit connected downstream of the r-1th signal estimation unit. The r-th signal estimation unit uses the two linear equalizers and the nonlinear converter provided in the r-th signal estimation unit to generate the output signal from the output signal generated by the (r-1)-th signal estimation unit using the two linear equalizers and the nonlinear converter provided in the (r-1)-th signal estimation unit and the plurality of received signals. Signal estimation device. [Note 2] Each of the aforementioned plurality of signal estimation units uses the two linear equalizers and the nonlinear converter to generate a plurality of estimated signals, which are provisional estimation results of the plurality of transmitted signals, and an auxiliary signal as the output signal. The r-th signal estimation unit uses the two linear equalizers and the nonlinear converter provided in the r-th signal estimation unit to generate the plurality of estimated signals and the auxiliary signals as output signals from the auxiliary signal generated by the (r-1)-th signal estimation unit and the plurality of received signals. The multiple estimated signals generated by the R-th signal estimation unit (where R is a constant indicating the number of signal estimation units) among the multiple signal estimation units are used as the multiple transmission signals corresponding to the multiple received signals, respectively. The signal estimation device described in Appendix 1. [Note 3] Each of the aforementioned multiple signal estimation units generates a first auxiliary signal and a second auxiliary signal as auxiliary signals. The first linear equalizer of the two linear equalizers provided in the r-th signal estimation unit performs a first filtering process using the first and second auxiliary signals generated by the (r-1)-th signal estimation unit. The second linear equalizer of the two linear equalizers provided in the r-th signal estimation unit performs a second filtering process using the output of the first linear equalizer provided in the r-th signal estimation unit and the plurality of received signals. The r-th signal estimation unit generates the plurality of estimated signals by adding the difference between the first and second auxiliary signals generated by the (r-1)-th signal estimation unit to the output of the second linear equalizer provided by the r-th signal estimation unit. The nonlinear converter provided in the r-th signal estimation unit generates the sum of the plurality of estimated signals generated by the r-th signal estimation unit and the second auxiliary signal generated by the (r-1)-th signal estimation unit, and inputs the sum of the resulting signal to a predetermined activation function, thereby generating the output of the activation function as the first auxiliary signal. The r-th signal estimation unit generates a first difference signal, which is the difference between the output of the activation function and the input of the activation function, as the second auxiliary signal. The signal estimation device described in Appendix 2. [Note 4] The first linear equalizer in the r-th signal estimation unit performs a convolution operation using the second difference signal, which is the difference between the first and second auxiliary signals generated by the (r-1)-th signal estimation unit, and the first filter coefficient, as the first filtering process. The second linear equalizer in the r-th signal estimation unit performs a convolution operation as the second filtering process, using a third difference signal, which is the difference between the output of the first linear equalizer in the r-th signal estimation unit and the plurality of received signals, and a second filter coefficient. The signal estimation device described in Appendix 3. [Note 5] The first linear equalizer of the two linear equalizers provided in the r-th signal estimation unit performs a first filtering process using the first filter coefficients updated by the coefficient update device. The second linear equalizer of the two linear equalizers provided in the r-th signal estimation unit performs a second filtering process using the second filter coefficients updated by the coefficient update device. A signal estimation device as described in any one of the items 1 to 4 of the appendix. [Note 6] The coefficient update device comprises the same number of coefficient update error propagation units as the number of signal estimation units, Each of the plurality of coefficient update error propagation units updates an error signal which is the difference between the estimated result of the plurality of transmission signals by the signal estimation device and the correct value of the plurality of transmission signals. The r-th coefficient update error propagation unit, which updates the first and second filter coefficients used by the r-th signal estimation unit among the plurality of coefficient update error propagation units, updates the first and second filter coefficients by performing a linear operation which subtracts the result of a convolution operation using the error signal updated by the (r+1)-th coefficient update error propagation unit and the output signal from the first and second filter coefficients before the update. The r-th coefficient update error propagation unit performs a convolution operation using the first and second filter coefficients, and updates the error signal by performing a nonlinear transformation equivalent to the differential processing of the nonlinear transformation performed by the nonlinear converter using the result of the convolution operation. The signal estimation device described in Appendix 5. [Note 7] The coefficient update device updates the first filter coefficient using a method that estimates the impulse response of the transmission path by least squares from the estimation results of the plurality of transmission signals by the signal estimation device and the plurality of reception signals. The coefficient update device generates a second matrix obtained by adding the numerical parameter to the diagonal elements of the product of the first matrix and the conjugate matrix of the first matrix, using a first matrix whose components are the first filter coefficients and a predetermined numerical parameter. The device then updates the second filter coefficients by calculating the components of the product of the inverse matrices of the first matrix and the second matrix as the second filter coefficients. The signal estimation device described in Appendix 5. [Note 8] A signal estimation method for estimating multiple transmission signals corresponding to each of the multiple received signals from a plurality of spatially multiplexed received signals, The aforementioned signal estimation method is: Inputting the aforementioned multiple received signals, Using multiple signal estimation units connected in series, the multiple transmitted signals are estimated from the multiple received signals. Includes, Each of the multiple signal estimation units comprises two linear equalizers and one nonlinear transformer that performs nonlinear transformations. Estimating the aforementioned multiple transmission signals is The output signal generated by the i-1th signal estimation unit using the two linear equalizers and the nonlinear converter provided in the i-1th signal estimation unit (where i is a variable representing an integer greater than or equal to 2 and less than the number of signal estimation units) is input to the ith signal estimation unit connected downstream of the i-1th signal estimation unit. Using the two linear equalizers and the nonlinear converter provided in the i-th signal estimation unit, the output signal to be output by the i-th signal estimation unit is generated from the output signal generated by the i-1 signal estimation unit using the two linear equalizers and the nonlinear converter provided in the i-1 signal estimation unit and the plurality of received signals. A signal estimation method that includes [specific components / methods]. [Note 9] A recording medium on which a computer program is stored causes a computer to execute a signal estimation method for estimating multiple transmission signals corresponding to multiple received signals from multiple spatially multiplexed received signals, The aforementioned signal estimation method is: Inputting the aforementioned multiple received signals, Using multiple signal estimation units connected in series, the multiple transmitted signals are estimated from the multiple received signals. Includes, Each of the multiple signal estimation units comprises two linear equalizers and one nonlinear transformer that performs nonlinear transformations. Estimating the aforementioned multiple transmission signals is The output signal generated by the i-1th signal estimation unit using the two linear equalizers and the nonlinear converter provided in the i-1th signal estimation unit (where i is a variable representing an integer greater than or equal to 2 and less than the number of signal estimation units) is input to the ith signal estimation unit connected downstream of the i-1th signal estimation unit. Using the two linear equalizers and the nonlinear converter provided in the i-th signal estimation unit, the output signal to be output by the i-th signal estimation unit is generated from the output signal generated by the i-1 signal estimation unit using the two linear equalizers and the nonlinear converter provided in the i-1 signal estimation unit and the plurality of received signals. A recording medium that includes this.

[0102] The present invention may be modified as appropriate, insofar as it does not contradict the gist or idea of ​​the invention as can be inferred from the claims and the specification as a whole, and communication systems, transmitting devices, receiving devices, transmitting methods, receiving methods, and computer programs involving such modifications are also included in the technical concept of the present invention. [Explanation of Symbols]

[0103] 1. Transmitter 11 Signal Processing Device 122 Signal Synthesis Unit 123 Phase shift section 125 Feedback signal receiving unit 126 Phase update section 2. Receiving device 21 Signal Processing Equipment 222 MIMO Equalization Processing Unit 224 Communication status detection unit 225 Phase control information generation unit 226 Feedback signal generation unit SYS Wireless Communication System

Claims

1. A signal estimation device that estimates multiple transmission signals corresponding to each of the multiple received signals from a plurality of spatially multiplexed received signals, The signal estimation device comprises a plurality of signal estimation units, Each of the multiple signal estimation units comprises two linear equalizers and one nonlinear transformer that performs nonlinear transformations. The plurality of signal estimation units are connected in series such that the output signal generated by the (r-1)th signal estimation unit using the two linear equalizers and the nonlinear converter provided in the (r-1)th signal estimation unit is input to the (r)th signal estimation unit connected downstream of the (r-1)th signal estimation unit. The (r)th signal estimation unit uses the two linear equalizers and the nonlinear converter provided in the (r)th signal estimation unit to generate the output signal generated by the (r-1)th signal estimation unit using the two linear equalizers and the nonlinear converter provided in the (r-1)th signal estimation unit, and the plurality of received signals, to generate the output signal. Signal estimation device.

2. Each of the aforementioned plurality of signal estimation units uses the two linear equalizers and the nonlinear converter. The output signal is a plurality of estimated signals which are provisional estimation results of the plurality of transmission signals. , generates auxiliary signals, The r-th signal estimation unit uses the two linear equalizers and the nonlinear converter provided in the r-th signal estimation unit to generate the plurality of estimated signals and the auxiliary signals as output signals from the auxiliary signal generated by the (r-1)-th signal estimation unit and the plurality of received signals. The multiple estimated signals generated by the R-th signal estimation unit (where R is a constant indicating the number of signal estimation units) among the multiple signal estimation units are used as the multiple transmission signals corresponding to the multiple received signals, respectively. The signal estimation device according to claim 1.

3. Each of the aforementioned multiple signal estimation units generates a first auxiliary signal and a second auxiliary signal as auxiliary signals. The first linear equalizer of the two linear equalizers provided in the r-th signal estimation unit performs a first filtering process using the first and second auxiliary signals generated by the (r-1)th signal estimation unit. The second linear equalizer of the two linear equalizers provided in the r-th signal estimation unit performs a second filtering process using the output of the first linear equalizer provided in the r-th signal estimation unit and the plurality of received signals. The r-th signal estimation unit generates the plurality of estimated signals by adding the difference between the first and second auxiliary signals generated by the (r-1)-th signal estimation unit to the output of the second linear equalizer provided in the r-th signal estimation unit. The nonlinear converter provided in the r-th signal estimation unit generates the first auxiliary signal by inputting the summation signal, which is generated by adding the plurality of estimated signals generated by the r-th signal estimation unit and the second auxiliary signal generated by the (r-1)-th signal estimation unit, into a predetermined activation function, thereby generating the output of the activation function as the first auxiliary signal. The r-th signal estimation unit generates a first difference signal, which is the difference between the output of the activation function and the input of the activation function, as the second auxiliary signal. The signal estimation device according to claim 2.

4. The first linear equalizer in the r-th signal estimation unit performs a convolution operation using the second difference signal, which is the difference between the first and second auxiliary signals generated by the (r-1)-th signal estimation unit, and the first filter coefficient, as the first filtering process. The second linear equalizer in the r-th signal estimation unit performs a convolution operation as the second filtering process, using a third difference signal, which is the difference between the output of the first linear equalizer in the r-th signal estimation unit and the plurality of received signals, and a second filter coefficient. The signal estimation device according to claim 3.

5. The first linear equalizer of the two linear equalizers provided in the r-th signal estimation unit performs a first filtering process using a first filter coefficient updated by the coefficient update device, and the second linear equalizer of the two linear equalizers provided in the r-th signal estimation unit performs a second filtering process using a second filter coefficient updated by the coefficient update device. The signal estimation device according to claim 1 or 2.

6. The coefficient update device comprises the same number of coefficient update error propagation units as the number of signal estimation units, Each of the plurality of coefficient update error propagation units updates an error signal which is the difference between the estimated result of the plurality of transmission signals by the signal estimation device and the correct value of the plurality of transmission signals. The r-th coefficient update error propagation unit, which updates the first and second filter coefficients used by the r-th signal estimation unit among the plurality of coefficient update error propagation units, performs a linear operation by subtracting the result of a convolution operation using the error signal updated by the r+1-th coefficient update error propagation unit and the output signal from the first and second filter coefficients before the update, thereby Update the first and second filter coefficients, The r-th coefficient update error propagation unit performs a convolution operation using the first and second filter coefficients, and updates the error signal by performing a nonlinear transformation equivalent to the differential processing of the nonlinear transformation performed by the nonlinear converter using the result of the convolution operation. The signal estimation device according to claim 5.

7. The coefficient update device updates the first filter coefficient using a method that estimates the impulse response of the transmission path by least squares from the estimation results of the plurality of transmission signals by the signal estimation device and the plurality of reception signals. The coefficient update device generates a second matrix obtained by adding the numerical parameter to the diagonal elements of the product of the first matrix and the conjugate matrix of the first matrix, using a first matrix whose components are the first filter coefficients and predetermined numerical parameters. The device then updates the second filter coefficients by calculating the components of the product of the inverse matrices of the first matrix and the second matrix as the second filter coefficients. The signal estimation device according to claim 5.

8. A signal estimation method for estimating multiple transmission signals corresponding to each of the multiple received signals from a plurality of spatially multiplexed received signals, The signal estimation method described above is: Inputting the aforementioned multiple received signals, Using multiple signal estimation units connected in series, the multiple transmitted signals are estimated from the multiple received signals. Includes, Each of the multiple signal estimation units comprises two linear equalizers and one nonlinear transformer that performs nonlinear transformations. Estimating the aforementioned multiple transmission signals is The output signal generated by the i-1th signal estimation unit using the two linear equalizers and the nonlinear converter provided in the i-1th signal estimation unit (where i is a variable representing an integer of 2 or more and less than or equal to the number of signal estimation units) is input to the ith signal estimation unit connected downstream of the i-1th signal estimation unit. Using the two linear equalizers and the nonlinear converter provided in the i-th signal estimation unit, the i-th signal estimation unit generates the output signal to be output by the i-th signal estimation unit from the output signal generated by the i-1 signal estimation unit using the two linear equalizers and the nonlinear converter provided in the i-1 signal estimation unit and the plurality of received signals. A signal estimation method that includes [specific components / methods].

9. A computer program that causes a computer to execute a signal estimation method for estimating multiple transmission signals corresponding to multiple received signals from multiple spatially multiplexed received signals, The signal estimation method described above is: Inputting the aforementioned multiple received signals, Using multiple signal estimation units connected in series, the multiple transmitted signals are estimated from the multiple received signals. Includes, Each of the multiple signal estimation units comprises two linear equalizers and one nonlinear transformer that performs nonlinear transformations. Estimating the aforementioned multiple transmission signals is The output signal generated by the i-1th signal estimation unit using the two linear equalizers and the nonlinear converter provided in the i-1th signal estimation unit (where i is a variable representing an integer of 2 or more and less than or equal to the number of signal estimation units) is input to the ith signal estimation unit connected downstream of the i-1th signal estimation unit. Using the two linear equalizers and the nonlinear converter provided in the i-th signal estimation unit, the i-th signal estimation unit generates the output signal to be output by the i-th signal estimation unit from the output signal generated by the i-1 signal estimation unit using the two linear equalizers and the nonlinear converter provided in the i-1 signal estimation unit and the plurality of received signals. A computer program that includes this.

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