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

Signal estimation device, signal estimation method, and recording medium

[0001] The present invention relates to a signal estimation device, a signal estimation method, and a recording medium capable of estimating a plurality of transmitted signals corresponding to a plurality of spatially multiplexed received signals from the plurality of received signals.

[0002] Research is underway into a transmission system that transmits a plurality of spatially multiplexed transmission signals from a transmitter to a receiver using a multi-core optical fiber including a plurality of cores. In such a transmission system, it is desirable that a receiver that receives the plurality of spatially multiplexed transmission signals as a plurality of spatially multiplexed received signals performs signal estimation processing (specifically, MIMO (Multi-Input Multi-Output) equalization processing) that estimates a plurality of transmission signals from the plurality of received signals in order to compensate for crosstalk (in other words, interference) that occurs between the plurality of cores of the multi-core optical fiber.

[0003] An 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 so as to minimize the error between the estimation results of multiple transmission signals obtained by the signal estimation processing and the multiple transmission signals that are actually transmitted. For example, Non-Patent Documents 1 and 2 describe, as an example of signal estimation processing, an MMSE (Minimum Mean Square Error) estimation processing in which multiple transmission signals are estimated using linear equalizers whose filter coefficients (tap coefficients) are optimized so as to minimize the least square error between the estimation results of multiple transmission signals obtained by the signal estimation processing and the multiple transmission signals that are actually transmitted.

[0004] Peter J. Winzer et al. , “MIMO capacities and outage properties in spatially multiplexed optical transport systems”, Opt. Express, vol. 19, no. 17, pp. 16680-16696, August 2011 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

[0005] Although the MMSE estimation process has the advantage of being able to reduce the calculation cost, it has a technical problem in that there is room for improvement in the estimation accuracy of a plurality of transmitted signals.

[0006] It should be noted that similar technical problems may occur not only in transmission systems that transmit multiple transmission signals using multi-core optical fibers, but also in transmission systems that transmit multiple transmission signals using radio waves (i.e., wireless communication systems).

[0007] An object of the present invention is 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, an object of the present invention is to provide a signal estimation device, a signal estimation method, and a recording medium that can improve the estimation accuracy of multiple transmitted signals.

[0008] One aspect of the signal estimation device is a signal estimation device that estimates a plurality of transmitted signals corresponding to a plurality of spatially multiplexed received signals, respectively, from the plurality of received signals, the signal estimation device comprising a plurality of signal estimation units, each of which comprises two linear equalizers and one nonlinear transformer that performs a nonlinear transformation, the plurality of signal estimation units being connected in series such that an output signal generated by the r-1th signal estimation unit using the two linear equalizers and the nonlinear transformer provided in the r-1th (here, r is a variable indicating an integer greater than or equal to 2 and less than the number of signal estimation units) signal estimation unit is input to the rth signal estimation unit connected subsequent to the r-1th signal estimation unit, and the rth signal estimation unit uses the two linear equalizers and the nonlinear transformer provided in the r-1th 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 transformer provided in the r-1th signal estimation unit and the plurality of received signals,

[0009] One aspect of the signal estimation method is a signal estimation method for estimating a plurality of transmission signals corresponding to a plurality of spatially multiplexed reception signals, respectively, from the plurality of reception signals, the signal estimation method including: inputting the plurality of reception signals; and estimating the plurality of transmission signals from the plurality of reception signals using a plurality of signal estimation units connected in series, each of the plurality of signal estimation units including two linear equalizers and one nonlinear transformer that performs nonlinear transformation; and estimating the plurality of transmission signals by an i-1th (where i is a variable indicating an integer equal to or greater than 2 and less than the number of signal estimation units) reception signal. inputting an 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 to an i-th signal estimation unit connected subsequent to the i-1th 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-1th signal estimation unit using the two linear equalizers and the nonlinear converter provided in the i-1th signal estimation unit and the plurality of received signals using the two linear equalizers and the nonlinear converter provided in the i-1th signal estimation unit.

[0010] One aspect of the recording medium is a recording medium having recorded thereon a computer program for causing a computer to execute a signal estimation method for estimating a plurality of transmission signals corresponding to a plurality of spatially multiplexed reception signals from the plurality of reception signals, the signal estimation method including: inputting the plurality of reception signals; and estimating the plurality of transmission signals from the plurality of reception signals using a plurality of signal estimation units connected in series, each of the plurality of signal estimation units including two linear equalizers and one nonlinear transformer for performing a nonlinear transformation; and estimating the plurality of transmission signals by a plurality of signal estimation units including i-1 (where i is 2 or more and is equal to or greater than the number of signal estimation units). inputting an 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 (i-1 being a variable indicating an integer less than 1), to an i-th signal estimation unit connected subsequent to the i-1th 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-1th signal estimation unit using the two linear equalizers and the nonlinear converter provided in the i-1th signal estimation unit and the plurality of received signals, using the two linear equalizers and the nonlinear converter provided in the i-1th signal estimation unit.

[0011] According to each aspect of the above-described signal estimation device, signal estimation method, and recording medium, it is possible to improve the accuracy of estimating a plurality of transmitted signals.

[0012] FIG. 1 is a block diagram showing the configuration of a transmission system in this embodiment. FIG. 2 is a block diagram showing the configuration of a receiving device that performs MIMO equalization processing. FIG. 3 is a block diagram showing the configuration of a MIMO equalizer. FIG. 4 is a flowchart showing the flow of MIMO equalization processing. FIG. 5 is a block diagram showing the configuration of a nonlinear transformer. FIGS. 6(a) and 6(b) are graphs showing the relationship between input and output in an activation function. FIG. 7 is a graph showing the bit error rate of an estimated signal. FIG. 8 is a block diagram showing the configuration of a coefficient updating device. FIG. 9 is a block diagram showing the configuration of a coefficient update error propagation unit. FIG. 10 is a flowchart showing the flow of a coefficient updating operation. FIG. 11 is a flowchart showing the flow of a modified example of the coefficient updating operation.

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

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

[0015] As shown in FIG. 1 , the transmission system SYS includes a transmitter 1 and a receiver 2. The transmitter 1 transmits a MIMO (Multi-Input Multi-Output) transmit signal X including multiple spatially multiplexed transmit signals x to the receiver 2 via a transmission path 3. The receiver 2 receives the MIMO transmit signal X transmitted from the transmitter 1 as a MIMO receive signal Y via the transmission path 3. That is, the receiver 2 receives the multiple transmit signals x transmitted from the transmitter 1 as multiple receive signals y via the transmission path 3. Note that each transmit signal x may include multiple signal components and therefore may be referred to as a transmit signal sequence. Similarly, each receive signal y may include multiple signal components and therefore may be referred to as a receive signal sequence.

[0016] In the following description, an example will be described in which the number of multiplexed MIMO transmission signals X and MIMO reception signals Y is D (where D is a variable indicating an integer equal to or greater than 2). In this case, the transmission device 1 transmits D spatially multiplexed transmission signals x via a transmission path 3. （０） From x （Ｄ－１） The receiver 2 receives the D number of transmission signals x transmitted from the transmitter 1 via a transmission path 3. （０） From x （Ｄ－１） , and the D spatially multiplexed received signals y （０） From y （Ｄ－１） Receive as.

[0017] Multiple transmitted signals x （０） From x （Ｄ－１）In order to transmit the above, the transmitting device 1 includes 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 load a computer program. For example, the signal processing device 11 may load a computer program stored in the storage device 12. For example, the signal processing device 11 may load a computer program stored in a computer-readable storage medium using a storage medium reading device (not shown). The signal processing device 11 may acquire (i.e., download or load) the computer program from a device (not shown) located outside the transmitting device 1 via a communication device (not shown). The signal processing device 11 executes the loaded computer program. As a result, a logical functional block for executing the operation to be performed by the transmitting device 1 is realized within the signal processing device 11. Specifically, a plurality of transmission signals x （０） From x （Ｄ－１） In other words, the signal processing device 11 can function as a controller for realizing the logical function blocks for executing the operations that the transmitting device 1 should perform.

[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 that the signal processing device 11 temporarily uses when the signal processing device 11 is executing a computer program. The storage device 12 may store data that the transmitting device 1 stores for a long period of time. 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） In order to receive the signal, the receiving device 2 includes a signal processing device 21 and a storage device 22 .

[0021] The signal processing device 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 device 21 may load a computer program. For example, the signal processing device 21 may load a computer program stored in the storage device 22. For example, the signal processing device 21 may load a computer program stored in a computer-readable storage medium using a storage medium reading device (not shown). The signal processing device 21 may acquire (i.e., download or load) the computer program from a device (not shown) located outside the receiving device 2 via a communication device (not shown). The signal processing device 21 executes the loaded computer program. As a result, a logical functional block for executing the operation to be performed by the receiving device 2 is realized within the signal processing device 21. Specifically, the signal processing device 21 includes a plurality of reception signals y （０） From y （Ｄ－１）In other words, the signal processing device 21 can function as a controller for realizing the logical function blocks for executing the operations that the receiving device 2 should perform.

[0022] The storage device 22 can store 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 temporarily uses when the signal processing device 21 is executing a computer program. The storage device 22 may store data that the receiving device 2 stores for a long period of time. The storage device 22 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.

[0023] The transmission path 3 may include a wired transmission path realized by a wired communication cable. For example, the transmission path 3 may include a wired transmission path including a multi-core optical fiber including multiple cores. In this case, crosstalk (XT) may be allowed between multiple transmission signals x transmitted via the multiple cores. In other words, interference between multiple transmission signals x transmitted via the multiple cores may be allowed. In this case, the transmission capacity can be increased compared to when crosstalk is not allowed. Alternatively, the transmission path 3 may include a wireless transmission path realized by radio waves in addition to or instead of the wired transmission path.

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

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

[0026] Specifically, a plurality of received signals y （０） From y （Ｄ－１） and multiple transmitted signals x （０） From x （Ｄ－１） The relationship between is expressed by Equation 1. In Equation 1, k is a variable indicating an integer greater than or equal to 1 and less than or equal to D-1. In Equation 1, m is a variable indicating an integer greater than or equal to 1 and less than or equal to D-1. （ｋ、ｍ） represents the impulse response of each of the D×D transmission paths formed between the transmitter 1 and the receiver 2. （ｋ） indicates a white noise component. The symbol "[conv]" in Equation 1 is an operator indicating a convolution operation. In the following description, the symbol "[conv]" will also be used to indicate a convolution operation. Therefore, in the following description, "A[conv]B" will indicate "a convolution operation of A and B." The receiving device 2 receives a plurality of received signals y （０） From y （Ｄ－１） and multiple transmitted signals x （０） From x （Ｄ－１）The signal estimation process may be performed on the assumption that the relationship between

[0027]

[0028] As will be described in detail later, the receiving device 2 performs MIMO equalization processing using a plurality of MIMO equalizers 23 (see FIG. 2). The MIMO equalizers 23 may also be referred to as signal equalizers, signal estimators, signal equalization units, or signal estimation units. In particular, in this embodiment, the MIMO equalizers 23 include two linear equalizers 232 and 233 and one nonlinear converter 234 (see FIG. 3), as will be described in detail later. In this case, the receiving device 2 performs MIMO equalization processing using a plurality of transmission signals x （０） From x （Ｄ－１） This can improve the estimation accuracy.

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

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

[0031] The signal processing device 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 device 41 may load a computer program. For example, the signal processing device 41 may load a computer program stored in the storage device 42. For example, the signal processing device 41 may load a computer program stored in a computer-readable storage medium using a storage medium reading device (not shown). The signal processing device 41 may acquire (i.e., download or load) the computer program from a device (not shown) located outside the receiving device 2 via a communication device (not shown). The signal processing device 41 executes the loaded computer program. As a result, a logical functional block for executing the operation to be performed by the receiving device 2 is realized within the signal processing device 41. Specifically, the signal processing device 41 includes a plurality of reception signals y （０） From y （Ｄ－１） In other words, the signal processing device 41 can function as a controller for realizing the logical function blocks for executing the operations that the receiving device 2 should perform.

[0032] The storage device 42 can store 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 when the signal processing device 41 is executing a computer program. The storage device 42 may store data that the receiving device 2 stores for a long period of time. The storage device 42 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.

[0033] <2> MIMO Equalization Process Performed by Receiving Device 2 Next, the MIMO equalization process performed by the receiving device 2 will be described.

[0034] <2-1> Configuration of the Receiving Device 2 (Signal Processing Device 21) First, the configuration of the receiving device 2 that performs MIMO equalization processing (particularly the configuration of the signal processing device 21) will be described with reference to Fig. 2. Fig. 2 is a block diagram showing logical functional blocks realized in the signal processing device 21 for performing MIMO equalization processing.

[0035] As shown in Fig. 2, the signal processing device 21 includes a plurality of MIMO equalizers 23 as logical functional blocks for performing MIMO equalization processing. Note that Fig. 2 merely shows conceptually (in other words, simply) the logical functional blocks for performing MIMO equalization processing. In other words, the functional blocks shown in Fig. 2 do not need to be implemented as they are in the signal processing device 21, and as long as the signal processing device 21 can perform the MIMO equalization processing performed by the functional blocks shown in Fig. 2, the configuration of the functional blocks implemented in the signal processing device 21 is not limited to the configuration shown in Fig. 2.

[0036] The multiple MIMO equalizers 23 are connected in series (in other words, coupled in series). Specifically, the multiple MIMO equalizers 23 are connected in series so that the output of one MIMO equalizer 23 is input to another MIMO equalizer 23 connected in a stage subsequent to the first MIMO equalizer 23. In the following description, an example will be described in which the signal processing device 21 includes R (where R is a constant indicating an integer equal to or greater than 2) MIMO equalizers 23.

[0037] In the following description, the r-th (where r is a variable indicating an integer greater than or equal to 1 and less than or equal to R) MIMO equalizer 23 among the R MIMO equalizers 23 will be referred to as the MIMO equalizer 23 ｒ In this case, the signal processing device 21 is called a MIMO equalizer 23 １ , MIMO equalizer 23 ２ ,..., MIMO equalizer 23 ｒ－１ , MIMO equalizer 23 ｒ ,..., MIMO equalizer 23 Ｒ－１ , and the MIMO equalizer 23Ｒ Furthermore, under the condition that the variable r indicates an integer equal to or greater than 2, R MIMO equalizers 23 １ From 23 Ｒ is the MIMO equalizer 23 ｒ－１ The output of the MIMO equalizer 23 ｒ－１ The MIMO equalizer 23 connected after ｒ are connected in series so that the input is

[0038] MIMO equalizer 23 ｒ is a function of the number of received signals y (i.e., the number of received signals y （０） From y （Ｄ－１） ) corresponding to the plurality of transmission signals x (i.e., the plurality of transmission signals x （０） From x （Ｄ－１） ) is tentatively estimated. In the following description, the MIMO equalizer 23 ｒ The provisional estimation results of the plurality of transmitted signals x are converted into the plurality of estimated signals xe ｒ In other words, in the following description, the MIMO equalizer 23 ｒ Multiple transmitted signals x （０） From x （Ｄ－１） The provisional estimation results of the estimated signal xe ｒ （０） From xe ｒ （Ｄ－１） Therefore, the MIMO equalizer 23 ｒ is a function of deriving a plurality of estimated signals xe from a plurality of received signals y. ｒ Generate.

[0039] MIMO equalizer 23 ｒ further generates an auxiliary signal s and an auxiliary signal u. ｒ The auxiliary signals s and u generated by ｒ and auxiliary signal u ｒ The auxiliary signal s ｒ is a set of a plurality of (specifically, D) auxiliary signals s ｒ （０） From ｒ （Ｄ－１） The auxiliary signal u ｒ is a set of a plurality of (specifically, D) auxiliary signals u ｒ （０）From U ｒ （Ｄ－１） Includes:

[0040] MIMO equalizer 23 ｒ is a combination of a plurality of received signals y and the MIMO equalizer 23 ｒ－１ The auxiliary signal s generated by ｒ－１ and the MIMO equalizer 23 ｒ－１ The auxiliary signal u generated by ｒ－１ From this, multiple estimated signals xe ｒ and auxiliary signal s ｒ and the auxiliary signal u ｒ Therefore, the MIMO equalizer 23 ｒ－１ is the auxiliary signal s ｒ－１ and auxiliary signal u ｒ－１ and the MIMO equalizer 23 ｒ However, if the variable r is 1, the MIMO equalizer 23 １ The MIMO equalizer 23 connected in front of the ０ Since there is no MIMO equalizer 23 １ is a set of a plurality of received signals y and an auxiliary signal s corresponding to the initial value of the auxiliary signal s. ０ (Specifically, a plurality of auxiliary signals s ０ （０） From ０ （Ｄ－１） ), and an auxiliary signal u corresponding to the initial value of the auxiliary signal u ０ (Specifically, a plurality of auxiliary signals u ０ （０） From U ０ （Ｄ－１） ) and a plurality of estimated signals xe １ and auxiliary signal s １ and the auxiliary signal u １ and generate.

[0041] The signal processing device 21 includes an R-th MIMO equalizer 23 Ｒ A plurality of estimated signals xe generated by Ｒ （０） From xe Ｒ （Ｄ－１） , a plurality of received signals y （０） From y （Ｄ－１） A plurality of transmitted signals x respectively corresponding to （０） From x （Ｄ－１）That is, the signal processing device 21 outputs the R-th MIMO equalizer 23 as the final estimation result. Ｒ A plurality of estimated signals xe generated by Ｒ （０） From xe Ｒ （Ｄ－１） , multiple transmitted signals x （０） From x （Ｄ－１） A plurality of estimated signals xe （０） From xe （Ｄ－１） Output as

[0042] MIMO equalizer 23 ｒ (i.e., the MIMO equalizer 23 １ From 23 Ｒ An example of the configuration of the MIMO equalizer 23 is shown in FIG. ｒ The MIMO equalizer 23 includes a linear equalizer 232, a linear equalizer 233, and a nonlinear converter 234. ｒ is a signal obtained by using two linear equalizers 232 and 233 and one nonlinear transformer 234 to generate a plurality of received signals y and auxiliary signals s ｒ－１ and the auxiliary signal u ｒ－１ From this, multiple estimated signals xe ｒ and auxiliary signal s ｒ and the auxiliary signal u ｒ Furthermore, the MIMO equalizer 23 generates ｒ includes an adder 231a, an adder 231b, an adder 231c, an adder 231d, and an adder 231e.

[0043] 2 and 3, and with reference to Fig. 4, a description will be given of the MIMO equalization process performed by the receiving device 2 using the multiple MIMO equalizers 23. Fig. 4 is a flowchart showing the flow of the MIMO equalization process.

[0044] As shown in FIG. 4, the signal processing device 21 of the receiving device 2 receives a plurality of received signals y (a plurality of received signals y （０） From y （Ｄ－１） ) is input (step S21).

[0045] Furthermore, the signal processing device 21 performs an initialization process (step S22). ０ (multiple auxiliary signals s ０ （０） From ０ （Ｄ－１） ) to zero. Furthermore, the signal processor 21 initializes the auxiliary signal u ０ (multiple auxiliary signals u ０ （０） From U ０ （Ｄ－１） ) to zero. Furthermore, the signal processing device 21 initializes a variable r to 1.

[0046] Then, the MIMO equalizer 23 ｒ is equalized by a linear equalizer 232 to the difference signal v ｒ (Step S23). Specifically, the MIMO equalizer 23 ｒ is added to the auxiliary signal s using the adder 231a. ｒ－１ and auxiliary signal u ｒ－１ A differential signal (s ｒ－１ -u ｒ－１ ) is then generated by the MIMO equalizer 23 ｒ is equalized by a linear equalizer 232 to the difference signal (s ｒ－１ -u ｒ－１ ) and the MIMO equalizer 23 ｒ The filter coefficient g of the linear equalizer 232 ｒ By performing a convolution operation with ｒ That is, the linear equalizer 232 generates the auxiliary signal s ｒ－１ and auxiliary signal u ｒ－１ As a filtering process using ｒ A convolution operation is performed to generate the filter coefficient g ｒ is the D×D filter coefficients g ｒ （０、０） From g ｒ （Ｄ－１、Ｄ－１） is a filter coefficient vector containing the filter coefficients g ｒ （０、０） From g ｒ （Ｄ－１、Ｄ－１） is updated (set) by the coefficient update device 4 as will be described later.ｒ is D convolution signals d ｒ （０） From d ｒ （Ｄ－１） In this case, the MIMO equalizer 23 ｒ may perform the convolution operation shown in Equation 2. The symbol "←" in Equation 2 indicates an operation of substituting the right side into the left side. In the following explanation, the symbol "←" also indicates an operation of substituting the right side into the left side. Then, the MIMO equalizer 23 ｒ is calculated by adding the convolution signal d output by the linear equalizer 232 using the adder 231b. ｒ and a differential signal v corresponding to the difference between the multiple received signals y. ｒ Specifically, the MIMO equalizer 23 generates ｒ is added to the convolution signal d by the adder 231b. ｒ （ｋ） and the received signal y （ｋ） The difference signal v ｒ （ｋ） By repeating the process of generating D differential signals v ｒ （０） From V ｒ （Ｄ－１） The difference signal v ｒ That is, the MIMO equalizer 23 generates ｒ By performing the calculation shown in Equation 3, D differential signals v ｒ （０） From V ｒ （Ｄ－１） The difference signal v ｒ Generate.

[0047]

[0048]

[0049] Then, the MIMO equalizer 23 ｒ is calculated by using a linear equalizer 233 as the estimated signal xe ｒ (Step S24). Specifically, the MIMO equalizer 23 ｒ is equalized by a linear equalizer 233 to the difference signal v ｒ and the MIMO equalizer 23 ｒ The filter coefficients w of the linear equalizer 233ｒ By performing a convolution operation with ｒ That is, the linear equalizer 233 generates the differential signal v ｒ and the convolution signal d ｒ and a plurality of received signals y) to obtain a convoluted signal d' ｒ A convolution operation is performed to generate the filter coefficient w ｒ is the D×D filter coefficients w ｒ （０、０） From lol ｒ （Ｄ－１、Ｄ－１） is a filter coefficient vector containing the filter coefficients w ｒ （０、０） From lol ｒ （Ｄ－１、Ｄ－１） is updated (set) by the coefficient update device 4 as will be described later. ｒ is D convolution signals d' ｒ （０） From d' ｒ （Ｄ－１） In this case, the MIMO equalizer 23 ｒ may perform the convolution operation shown in Equation 4. Then, the MIMO equalizer 23 ｒ is calculated by using an adder 231c as a convolution signal d' output from the linear equalizer 232. ｒ and the difference signal (s ｒ－１ -u ｒ－１ ) is added to the estimated signal xe ｒ Specifically, the MIMO equalizer 23 ｒ is added to the adder 231b to generate the convolution signal d'. ｒ （ｋ） and the differential signal (s ｒ－１ （ｋ） -u ｒ－１ （ｋ） ) is added repeatedly while changing the variable k from 0 to D-1, thereby obtaining a plurality of estimated signals xe ｒ （０） From xe ｒ （Ｄ－１） That is, the MIMO equalizer 23 generates ｒBy performing the calculation shown in Equation 5, a plurality of estimated signals xe ｒ （０） From xe ｒ （Ｄ－１） Generate.

[0050]

[0051]

[0052] Furthermore, the MIMO equalizer 23 ｒ is converted into an auxiliary signal s using a nonlinear transformer 234. ｒ (Step S24). Specifically, the MIMO equalizer 23 ｒ is added to the MIMO equalizer 23 by using the adder 231d. ｒ A plurality of estimated signals xe generated by ｒ and the MIMO equalizer 23 ｒ－１ Auxiliary signal u input from ｒ－１ By adding the sum signal (xe ｒ +u ｒ－１ Specifically, the MIMO equalizer 23 generates ｒ is calculated by adding the estimated signal xe ｒ （ｋ） and auxiliary signal u ｒ－１ （ｋ） By repeating the process of adding the above while changing the variable k from 0 to D-1, multiple sum signals (xe ｒ （ｋ） +u ｒ―１ （ｋ） ) is then generated by the MIMO equalizer 23 ｒ is converted into the sum signal (xe ｒ +u ｒ－１ ) is subjected to a nonlinear transformation process to obtain the auxiliary signal s ｒ Specifically, the MIMO equalizer 23 generates ｒ is converted into the sum signal (xe ｒ （ｋ） +u ｒ－１ （ｋ） ) is subjected to a nonlinear transformation process to obtain the auxiliary signal s ｒ （ｋ） By repeating the process of generating the auxiliary signals s while changing the variable k from 0 to D-1,ｒ （０） From ｒ （Ｄ－１） ) to generate the

[0053] The nonlinear transformer 234 performs nonlinear transform processing using a predetermined activation function. ｒ is the sum signal (xe ｒ +u ｒ－１ ) is input to an activation function used by the nonlinear transformer 234. The activation function is a nonlinear function that has a nonlinear relationship between the input and the output. The output of the activation function is then used to generate the auxiliary signal s ｒ It is used as.

[0054] The nonlinear conversion process by the nonlinear converter 234 is a process expressed by the equation shown in FIG. 6. The symbol "Π" in equation 6 Ｑ " is a symbol indicating the output of the activation function. In this case, as shown in FIG. 5 showing 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. In other words, the nonlinear converter 234 performs nonlinear processing on the sum signal (xe ｒ +u ｒ－１ ) into the activation function to obtain the output, and ｒ +u ｒ－１ ) into an activation function and obtain its output.

[0055]

[0056] 6(a) and 6(b) show examples of the relationship between input and output in the activation function. The relationship between input and output in the activation function may be determined depending on the modulation method of the transmission signal x. In other words, the activation function may be determined depending on the modulation method of the transmission signal x. As an example, FIG. 6(a) shows an example of the relationship between input and output in the activation function when the modulation method of the transmission signal x is QPSK (Quadrature Phase Shift Keying) method, in which the transmission signal x is represented by four points (+1+√(-1), +1-√(-1), -1+√(-1), -1-√(-1)) on the complex plane. FIG. 6(b) shows an example of the relationship between input and output in the activation function when the modulation method of the transmission signal x is 16QAM (Quadrature Amplitude Modulation) method, in which the transmission 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), -3-√(-1), +1+3√(-1), +1-3√(-1), -1+3√(-1), -1-3√(-1), 1+√(-1), 1-√(-1), -1+√(-1), -1-√(-1)).

[0057] Referring again to FIG. 4, there is further included a MIMO equalizer 23 ｒ is converted into an auxiliary signal u using a nonlinear transformer 234. ｒ (Step S24). Specifically, the MIMO equalizer 23 ｒ is added to the sum signal (xe ｒ +u ｒ－１ ) and the auxiliary signal s output from the nonlinear converter 234 ｒ The difference between the auxiliary signal u ｒ Specifically, the MIMO equalizer 23 ｒ is added to the adder 231e to generate the sum signal (xe ｒ （ｋ） +u ｒ―１ （ｋ） ) and auxiliary signal s ｒ （ｋ） The difference between this and the auxiliary signal u ｒ （ｋ）The process of calculating the auxiliary signals u is repeated while changing the variable k from 0 to D-1. ｒ （０） From U ｒ （Ｄ－１） That is, the MIMO equalizer 23 generates ｒ By performing the calculation shown in Equation 7, a plurality of auxiliary signals u ｒ （０） From U ｒ （Ｄ－１） Generate.

[0058]

[0059] Thereafter, 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 performs the processes from step S23 to step S25 again. On the other hand, if it is determined that the variable r is not less than the constant R (step S25: No), the Rth MIMO equalizer 23 Ｒ is a plurality of estimated signals xe Ｒ （０） From xe Ｒ （Ｄ－１） Therefore, in this case, the signal processing device 21 generates the R-th MIMO equalizer 23 Ｒ A plurality of estimated signals xe generated by Ｒ （０） From xe Ｒ （Ｄ－１） , multiple transmitted signals x （０） From x （Ｄ－１） A plurality of estimated signals xe （０） From xe （Ｄ－１） (step S27).

[0060] <2-3> Technical Effects of MIMO Equalization Processing As described above, the receiving device 2 uses a plurality of MIMO equalizers 23 each including two linear equalizers 232 and 233 and one nonlinear converter 234 to convert a plurality of transmission signals x （０） From x （Ｄ－１）That is, the receiver 2 uses a plurality of MIMO equalizers 23 each including two linear equalizers 232 and 233 and one nonlinear converter 234 to generate a plurality of estimated signals xe （０） From xe （Ｄ－１） Therefore, the receiver 2 generates a plurality of transmission signals x （０） From x （Ｄ－１） (i.e., the accuracy of the estimation of the multiple estimated signals xe （０） From xe （Ｄ－１） In other words, the receiver 2 can improve the estimation accuracy of the multiple estimated signals xe with fewer errors. （０） From xe （Ｄ－１） can be generated.

[0061] For example, FIG. 7 shows a plurality of estimated signals xe estimated by the receiving device 2 of this embodiment. （０） From xe （Ｄ－１） and a plurality of estimated signals xe estimated by the MMSE estimation process as a comparative example. （０） From xe （Ｄ－１） 7 is a graph showing the bit error rate (BER) of the plurality of estimated signals xe estimated by the receiving device 2 of this embodiment on the horizontal axis and the transmission distance on the vertical axis. （０） From xe （Ｄ－１） 7 shows the bit error rate when the number R of the MIMO equalizers 23 is 4 and the bit error rate when the number R of the MIMO equalizers 23 is 8. The bit error rate shown in Fig. 7 is calculated in an environment where a wired transmission line including a coupled multi-core optical fiber with four cores is used as the transmission line 3, the multiplexing number D is 8 by multiplexing combining four cores and polarization multiplexing, the mode dependent loss (MDL) related to interference between multiple cores (i.e., crosstalk) is 0.1 db / √(km), and the modal group delay (MGD) is 20 ps / √(km).

[0062] As shown in FIG. 7 , in the MMSE estimation process as a comparative example, the bit error rate exceeds the upper limit at which error correction is no longer possible when the transmission distance is approximately 6,200 km. On the other hand, according to the receiving device 2 of this embodiment, the bit error rate does not exceed the upper limit at which error correction is no longer possible even when the transmission distance exceeds approximately 6,200 km. In the example shown in FIG. 7 , according to the receiving device 2, when the number R of MIMO equalizers 23 is 4, the bit error rate does not exceed the upper limit at which error correction is no longer possible until the transmission distance exceeds approximately 8,700 km. Similarly, in the example shown in FIG. 7 , according to the receiving device 2, when the number R of MIMO equalizers 23 is 8, the bit error rate does not exceed the upper limit at which error correction is no longer possible until the transmission distance exceeds approximately 9,800 km. In this way, in this embodiment, the receiving device 2 uses a plurality of estimated signals xe with fewer errors. （０） From xe （Ｄ－１） Therefore, it is possible to realize an extension of the transmission distance.

[0063] <3> Coefficient Update Operation Performed by the Coefficient Update Device 4 Next, the coefficient update operation performed by the coefficient update device 4 will be described.

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

[0065] As shown in Fig. 8, the signal processing device 41 includes a plurality of coefficient update error propagation units 43 as logical functional blocks for performing the coefficient update operation. Note that Fig. 8 merely shows a conceptual (in other words, simplified) view of the logical functional blocks for performing the coefficient update operation. In other words, the functional blocks shown in Fig. 8 do not need to be implemented as they are in the signal processing device 41, and the configuration of the functional blocks implemented in the signal processing device 41 is not limited to the configuration shown in Fig. 8 as long as the signal processing device 41 can perform the coefficient update operation performed by the functional blocks shown in Fig. 8.

[0066] The number of coefficient update error propagation units 43 included in the signal processing device 41 is the same as the number of MIMO equalizers 23 included in the signal processing device 21 of the receiving device 2. Therefore, in the following description, an example will be described in which the signal processing device 41 includes R coefficient update error propagation units 43. Specifically, in the following description, it is assumed that the signal processing device 41 includes the coefficient update error propagation units 43 as the R coefficient update error propagation units 43. １ , coefficient update error propagation unit 43 ２ , ..., coefficient update error propagation unit 43 ｒ－１ , coefficient update error propagation unit 43 ｒ , ..., coefficient update error propagation unit 43 Ｒ－１ , and the coefficient update error propagation unit 43 Ｒ An example including the above will be described.

[0067] Coefficient update error propagation unit 43 ｒ is the filter coefficient g ｒ and w ｒ The coefficient update error propagation unit 43 updates (sets) ｒ is the filter coefficient g ｒ and w ｒ In order to update (set), the receiver 2 receives the convolution signal d ｒ and a differential signal v corresponding to the difference between the multiple received signals y ｒ and auxiliary signal s ｒ－１ and the auxiliary signal u ｒ－１ The difference signal (s ｒ－１＊ -u ｒ－１＊ ) and the estimated signal xe ｒ－１ and auxiliary signal u ｒ－２ and the sum signal (xe ｒ－１ +u ｒ－２ ) is obtained. In the following description, the complex conjugate of signal A is represented by the symbol signal A*. Coefficient update error propagation unit 43 ｒ is the differential signal v ｒ and the differential signal (s ｒ－１＊ -u ｒ－１＊ ) and the sum signal (xe ｒ－１ +u ｒ－２ ) and the filter coefficient g ｒ and w ｒ Update (set)

[0068] Furthermore, the coefficient update error propagation unit 43 ｒ is the filter coefficient g ｒ and w ｒ To update (set) the error signal ∂x ｒ The error signal ∂x is obtained. ｒ indicates the difference (error) between the estimation result of the 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 indicates the difference (error) between the plurality of estimated signals xe generated by the receiving device 2 and the plurality of transmitted signals x actually transmitted by the transmitting device 1.

[0069] In this embodiment, the error signal ∂x ｒ is the coefficient update error propagation unit 43 ｒ＋１ By this, the difference signal v ｒ＋１ and the differential signal (s ｒ＊ -u ｒ＊ ) and the sum signal (xe ｒ +u ｒ－１ ) and error signal ∂x ｒ＋１ Therefore, the coefficient update error propagation unit 43 ｒ is the coefficient update error propagation unit 43 ｒ＋１ From the error signal ∂x ｒ To this end, the coefficient update error propagation units 43 obtain the coefficient update error propagation units 43 ｒ＋１ The error signal ∂x output by ｒ is the coefficient update error propagation unit 43 ｒ are connected in series (in other words, coupled in series) so that they are input to

[0070] However, the coefficient update error propagation unit 43 Ｒ The error signal ∂x to be obtained Ｒ a coefficient update error propagation unit 43 that generates Ｒ＋１ Therefore, the error signal ∂x Ｒ As 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] Coefficient update error propagation unit 43 ｒAn example of the configuration of the coefficient update error propagation unit 43 is shown in FIG. ｒ includes an operator 431 a , an operator 431 b , an adder 432 a , an adder 432 b , a coefficient memory 433 a , a coefficient memory 433 b , a linear operator 434 , and a non-linear operator 435 .

[0072] 8 and 9, the coefficient update operation performed by the coefficient update device 4 using the multiple coefficient update error propagation units 43 will be described with reference to Fig. 10. Fig. 10 is a flowchart showing the flow of the coefficient update operation.

[0073] As shown in FIG. 10, the signal processor 41 of the coefficient update device 4 receives the error signal ∂x Ｒ is input (step S41). Ｒ is D error signals ∂x Ｒ （０） From ∂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） This is the difference between.

[0074] As mentioned above, the error signal ∂x Ｒ is a difference (error) between a plurality of estimated signals xe actually generated by the receiving device 2 and a plurality of transmission signals x actually transmitted by the transmitting device 1. Therefore, in step S41, a plurality of estimated signals xe actually generated by the receiving device 2 and a plurality of transmission signals x actually transmitted by the transmitting device 1 may be input to the signal processing device 41 of the coefficient update device 4. In this case, the signal processing device 41 calculates an 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] Furthermore, 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] Then, the coefficient update error propagation unit 43ｒ is the filter coefficient w ｒ (Step S43). Specifically, the coefficient update error propagation unit 43 ｒ is the filter coefficient w ｒ （ｋ、ｍ） The process of updating the filter coefficient w is repeated while changing the variables k and m from 0 to D-1. ｒ （０、０） From the filter coefficient w ｒ （Ｄ－１、Ｄ－１） The filter coefficients w ｒ Update.

[0077] Filter coefficient w ｒ （ｋ、ｍ） a coefficient update error propagation unit 43 to update ｒ is calculated by using the calculator 431a as the differential signal v ｒ （ｍ） and the error signal ∂x ｒ （ｋ） Furthermore, the coefficient update error propagation unit 43 ｒ is calculated by using the calculator 431a as the result of the convolution operation (i.e., v ｒ （ｍ）* [conv] ∂x ｒ （ｋ） ) is multiplied by a learning rate η, which is a real value set in advance. Then, the coefficient update error propagation unit 43 ｒ is calculated by adding the current filter coefficient w stored in the coefficient memory 433a using the adder 432a. ｒ （ｋ、ｍ） From the output of the calculator 431a (i.e., η×v ｒ （ｍ）* [conv] ∂x ｒ （ｋ） ) to obtain the filter coefficient w ｒ （ｋ、ｍ） That is, the coefficient update error propagation unit 43 ｒ is calculated by performing the calculation (including linear calculation) shown in Equation 8 using the calculator 431a and the adder 432a. ｒ （ｋ、ｍ） Update.

[0078]

[0079] Updated filter coefficients w ｒ （ｋ、ｍ） is stored in the coefficient memory 433a. ｒ The linear equalizer 233 provided in the ｒ （ｋ、ｍ） Therefore, the MIMO equalizer 23 ｒ The linear equalizer 233 provided in the ｒ （ｋ、ｍ） and obtain the obtained filter coefficient w ｒ （ｋ、ｍ） The filter coefficient w ｒ （ｋ、ｍ） If the filter coefficient w has never been updated, the coefficient memory 433a stores the filter coefficient w ｒ （ｋ、ｍ） Alternatively, the coefficient memory 433a may store a coefficient indicating zero as the initial value of the filter coefficient w ｒ （ｋ、ｍ） As the initial value of the filter coefficient w ｒ The coefficients may be stored so that the average value of the coefficients satisfies the condition that the coefficients are zero.

[0080] Furthermore, the coefficient update error propagation unit 43 ｒ is the filter coefficient g ｒ (Step S43). Specifically, the coefficient update error propagation unit 43 ｒ is the filter coefficient g ｒ （ｋ、ｍ） The process of updating the filter coefficient g is repeated while changing 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 coefficient vector g ｒ Update.

[0081] Filter coefficient g ｒ （ｋ、ｍ） a coefficient update error propagation unit 43 to update ｒis calculated by using the calculator 431b as the filter coefficient w before updating. ｒ （μ、ｋ） and the error signal ∂x ｒ （μ） The first convolution operation for calculating the convolution signal with is repeated while changing the variable μ, which indicates a variable from 0 to D−1, from 0 to D−1. Then, the coefficient update error propagation unit 43 ｒ The coefficient update error propagation unit 43 calculates the sum of the results of the first convolution operation using the calculator 431b. ｒ is calculated by using the calculator 431b by summing the results of the first convolution operation and the auxiliary signal s ｒ－１ （ｍ） and the auxiliary signal u ｒ－１ （ｍ） The difference signal (s ｒ－１ （ｍ）＊ -u ｒ－１ （ｍ）＊ ) and performs a second convolution operation to calculate a convolved signal with the coefficient update error propagation unit 43. ｒ The coefficient update error propagation unit 43 then multiplies the result of the second convolution operation by a learning rate η, which is a real value set in advance, using the calculator 431b. ｒ is calculated by adding the current filter coefficient g stored in the coefficient memory 433a using the adder 432b. ｒ （ｋ、ｍ） By subtracting the output of the calculator 431b from ｒ （ｋ、ｍ） That is, the coefficient update error propagation unit 43 ｒ is calculated by performing the calculation (including linear calculation) shown in Equation 9 using the calculator 431b and the adder 432b. ｒ （ｋ、ｍ） Update.

[0082]

[0083] Updated filter coefficients g ｒ （ｋ、ｍ） is stored in the coefficient memory 433b. ｒThe linear equalizer 232 provided in the ｒ （ｋ、ｍ） Therefore, the MIMO equalizer 23 ｒ The linear equalizer 232 provided in the ｒ （ｋ、ｍ） and obtain the obtained filter coefficient g ｒ （ｋ、ｍ） The filter coefficient g ｒ （ｋ、ｍ） If the filter coefficient g has never been updated, the coefficient memory 433b stores the filter coefficient g ｒ （ｋ、ｍ） Alternatively, the coefficient memory 433b may store a coefficient indicating zero as the initial value of the filter coefficient g ｒ （ｋ、ｍ） As the initial value of the filter coefficient g ｒ The coefficients may be stored so that the average value of the coefficients satisfies the condition that the coefficients are zero.

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

[0085] As a result of the determination in step S44, if it is determined that the variable r is greater than 1 (step S44: Yes), at least the filter coefficient g ｒ－１ and w ｒ－１ Therefore, in this case, the coefficient update error propagation unit 43 ｒ is the filter coefficient g ｒ－１ and w ｒ－１ The error signal ∂x used to update ｒ－１ (Step S45). Specifically, the coefficient update error propagation unit 43 ｒ is D error signals ∂x ｒ－１ （０） From ∂x ｒ－１ （Ｄ－１） ) containing the error signal ∂x ｒ－１ That is, the coefficient update error propagation unit 43 ｒ is the error signal ∂x ｒ－１ （ｋ）By repeating the process of generating the error signal ∂x while changing the variable k from 0 to D-1, D error signals ∂x ｒ－１ （０） From ∂x ｒ－１ （Ｄ－１） ) containing the error signal ∂x ｒ－１ Generate.

[0086] error signal ∂x ｒ－１ （ｋ） a coefficient update error propagation unit 43 to generate ｒ is calculated by the linear calculator 434 using the operation shown in Equation 10 (including linear operation) to obtain the intermediate signal ∂q （ｋ、ｍ） (Step S45). Specifically, the coefficient update error propagation unit 43 ｒ is the filter coefficient before updating w ｒ （ｍ、μ） and the filter coefficient g before updating ｒ （μ、ｋ） The third convolution operation for calculating the convolution signal with the complex conjugate of is repeated while varying the variable μ from 0 to D−1. ｒ calculates the sum of the results of the third convolution operation. Then, the coefficient update error propagation unit 43 ｒ is the sum of the results of the third convolution operation and the error signal ∂x ｒ （ｍ） As a result of the fourth convolution operation, an intermediate signal ∂q （ｋ、ｍ） is generated.

[0087]

[0088] Then, the coefficient update error propagation unit 43 ｒ is calculated by the linear calculator 434 as shown in Equation 11, and the intermediate signal ∂u （ｋ） (Step S45). Specifically, the coefficient update error propagation unit 43 ｒ is the intermediate signal ∂q （ｋ、０） to the intermediate signal ∂q （ｋ、Ｄ－１） The sum up to is calculated, and the intermediate signal ∂q （ｋ、ｋ） and the error signal ∂x is calculated from the sum. ｒ （ｋ）By subtracting the intermediate signal ∂u （ｋ） Generate.

[0089]

[0090] Furthermore, the coefficient update error propagation unit 43 ｒ is calculated by the linear calculator 434 as shown in Equation 12. （ｋ） (Step S45). Specifically, the coefficient update error propagation unit 43 ｒ is the intermediate signal ∂q （ｋ、ｋ） from the intermediate signal ∂u （ｋ） By subtracting twice the value of ∂p （ｋ） Generate.

[0091]

[0092] Then, the coefficient update error propagation unit 43 ｒ is calculated by the nonlinear calculator 435 using the nonlinear calculator 435 to calculate the error signal ∂x ｒ－１ （ｋ） (Step S45). Specifically, the coefficient update error propagation unit 43 ｒ is the activation function (Π Ｑ (x)) derivative Ψ Ｑ (That is, dΠ Ｑ (x) / dx) to the estimated signal xe ｒ－１ （ｋ） and auxiliary signal u ｒ－２ （ｋ） and the sum signal (xe ｒ－１ （ｋ） +u ｒ－２ （ｋ） ) is input to the coefficient update error propagation unit 43. ｒ is the sum signal (xe ｒ－１ （ｋ） +u ｒ－２ （ｋ） ) is subjected to nonlinear processing equivalent to the differential processing of the nonlinear transformation processing using the activation function. ｒ is the derivative Ψ Ｑ The real part of the output and the intermediate signal ∂p （ｋ）and the imaginary part of the output of the derivative Ψ and the intermediate signal ∂p （ｋ） The symbol "@" in Equation 13 is an operator indicating an operation of adding the multiplication result of the real part of a complex number and the multiplication result of the imaginary part of a complex number. Therefore, (a+ib)@(c+id) indicates ac+ibd (where a, b, c, and d each indicate a real number, and i indicates the imaginary unit). Then, the coefficient update error propagation unit 43 ｒ is the intermediate signal ∂u （ｋ） By adding ∂x ｒ－１ （ｋ） Generate.

[0093]

[0094] On the other hand, if it is determined that the variable r is not greater than 1 (step S44: No), the filter coefficient g １ From g Ｒ and the filter coefficient w １ From lol Ｒ In this case, the signal processing device 41 ends the coefficient update operation.

[0095] <3-3> Modification of Coefficient Update Operation The coefficient update device 4 may generate filter coefficients g and w that are used in common by a plurality of MIMO equalizers 23 by performing a modification of the coefficient update operation shown in FIG. １ From 23 Ｒ The filter coefficient g （０、０） From g （Ｄ－１、Ｄ－１） Similarly, the filter coefficients w are the filter coefficient vectors of the MIMO equalizer 23 １ From 23 Ｒ The filter coefficients w （０、０） From lol （Ｄ－１、Ｄ－１） is a filter coefficient vector containing

[0096] Filter coefficient g （０、０） From g （Ｄ－１、Ｄ－１）In order to generate the filter coefficients g, the signal processing device 41 calculates the filter coefficients g from a plurality of estimated signals xe, which are the estimation results of a plurality of transmitted signals x, and a plurality of received signals y, by the least squares method. （０、０） From g （Ｄ－１、Ｄ－１） Specifically, the signal processing device 41 generates a filter coefficient g that satisfies the condition that the parameter δ shown in Equation 14 is minimized (step S51). （０、０） From g （Ｄ－１、Ｄ－１） The filter coefficient g that satisfies the condition of minimizing the parameter δ shown in Equation 14 is generated. （０、０） From g （Ｄ－１、Ｄ－１） The calculation to generate the filter coefficient g is performed in the same manner as the method for estimating the impulse response of the transmission path 3. （０、０） From g （Ｄ－１、Ｄ－１） may be considered equivalent to the operation that produces

[0097]

[0098] Furthermore, the filter coefficient w （０、０） From lol （Ｄ－１、Ｄ－１） In order to generate the filter coefficient w, the signal processing device 41 performs a matrix operation using a matrix H having the filter coefficient g as an element and a parameter γ that can be set arbitrarily. （０、０） From lol （Ｄ－１、Ｄ－１） (Step S52). Specifically, the signal processing device 41 generates a matrix H having filter coefficients g as components. Thereafter, the signal processing device 41 calculates a matrix W by performing a matrix operation shown in Equation 15 using the matrix H and a parameter γ. The symbol " ＋ " denotes a Hermitian transpose matrix (i.e., a conjugate transpose matrix). The symbol "I" in Equation 15 denotes an identity matrix with N rows and N columns. Thereafter, the signal processing device 41 divides the elements of the matrix W into D x D groups w （ｋ、ｍ） Then, the signal processing device 41 classifies the signals into D×D groups w （ｋ、ｍ） , the filter coefficient w （０、０） From lol （Ｄ－１、Ｄ－１） Output as

[0099]

[0100] It should be noted that if the coefficient updating device 4 generates the filter coefficients g and w by performing a modified coefficient updating operation, the coefficient updating device 4 does not need to include a plurality of coefficient update error propagation units 43 .

[0101] <4> Supplementary Notes The following supplementary notes are further disclosed regarding the above-described embodiment. [Supplementary Note 1] A signal estimation device that estimates a plurality of transmission signals respectively corresponding to a plurality of spatially multiplexed reception signals from the plurality of reception signals, the signal estimation device comprising a plurality of signal estimation units, each of the plurality of signal estimation units comprising two linear equalizers and one nonlinear transformer that performs nonlinear transformation, the plurality of signal estimation units being connected in series such that an output signal generated by an r-1th signal estimation unit (here, r is a variable indicating an integer greater than or equal to 2 and less than the number of signal estimation units) using the two linear equalizers and the nonlinear transformer provided in the r-1th signal estimation unit is input to an rth signal estimation unit connected subsequent to the r-1th signal estimation unit, and the rth signal estimation unit uses the two linear equalizers and the nonlinear transformer provided in the r-1th signal estimation unit to generate the output signal from the plurality of reception signals and the output signal generated by the r-1th signal estimation unit using the two linear equalizers and the nonlinear transformer provided in the r-1th signal estimation unit. [Supplementary Note 2] The signal estimation device according to Supplementary Note 1, wherein each of the plurality of signal estimation units uses the two linear equalizers and the nonlinear transformer to generate, as the output signals, a plurality of estimation signals which are provisional estimation results of the plurality of transmission signals, and an auxiliary signal; the r-th signal estimation unit uses the two linear equalizers and the nonlinear transformer included in the r-th signal estimation unit to generate, as the output signals, the plurality of estimation signals and the auxiliary signal from the auxiliary signal generated by the r-1-th signal estimation unit and the plurality of received signals; and the plurality of estimation signals generated by an R-th signal estimation unit (where R is a constant indicating the number of signal estimation units) among the plurality of signal estimation units are used as the plurality of transmission signals respectively corresponding to the plurality of received signals.[Supplementary Note 3] Each of the plurality of signal estimation units generates a first auxiliary signal and a second auxiliary signal as the auxiliary signal; a first linear equalizer of the two linear equalizers included 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; a second linear equalizer of the two linear equalizers included in the r-th signal estimation unit performs a second filtering process using an output of the first linear equalizer included in the r-th signal estimation unit and the plurality of received signals; and the r-th signal estimation unit generates the plurality of estimated signals by adding a difference between the first and second auxiliary signals generated by the r-1-th signal estimation unit to an output of the second linear equalizer included in the r-th signal estimation unit. The nonlinear transformer included in the r-th signal estimation unit generates an output of the activation function as the first auxiliary signal by inputting an added signal 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 to a predetermined activation function, and the r-th signal estimation unit generates a first difference signal, which is a difference between the output of the activation function and the input of the activation function, as the second auxiliary signal. [Supplementary Note 4] The signal estimation device according to Supplementary Note 3, wherein the first linear equalizer included in the r-th signal estimation unit performs, as the first filter processing, a convolution operation using a second difference signal which is a difference between the first and second auxiliary signals generated by the r-1-th signal estimation unit and a first filter coefficient, and the second linear equalizer included in the r-th signal estimation unit performs, as the second filter processing, a convolution operation using a third difference signal which is a difference between an output of the first linear equalizer included in the r-th signal estimation unit and the plurality of received signals and a second filter coefficient.[Supplementary Note 5] The signal estimation device according to any one of Supplementary Notes 1 to 4, wherein a first linear equalizer of the two linear equalizers included in the r-th signal estimation unit performs a first filtering process using first filter coefficients updated by a coefficient updating device, and a second linear equalizer of the two linear equalizers included in the r-th signal estimation unit performs a second filtering process using second filter coefficients updated by the coefficient updating device. [Supplementary Note 6] The signal estimation device according to Supplementary Note 5, wherein the coefficient updating device includes a plurality of coefficient update error propagation units, the number of which is the same as the plurality of signal estimation units, and each of the plurality of coefficient update error propagation units updates an error signal that is a difference between an estimation result of the plurality of transmission signals by the signal estimation device and a correct value of the plurality of transmission signals, and an r-th coefficient update error propagation unit that updates 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 of subtracting a result of a convolution operation using the error signal updated by the r+1-th coefficient update error propagation unit that updates the first and second filter coefficients used by the r+1-th signal estimation unit among the plurality of coefficient update error propagation units and the output signal, and 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 using a result of the convolution operation to perform a nonlinear transformation that is equivalent to a differentiation process of the nonlinear transformation performed by the nonlinear transformer. [Supplementary Note 7] The signal estimation device according to Supplementary Note 5, wherein the coefficient updating device updates the first filter coefficients using a method of estimating an impulse response of a transmission channel by a least squares method from the estimation results of the plurality of transmission signals by the signal estimation device and the plurality of received signals, and the coefficient updating device generates a second matrix obtained by adding the numerical parameters to diagonal elements of a product matrix of the first matrix and a conjugate arrangement matrix of the first matrix, from a first matrix having the first filter coefficients as elements, and the numerical parameters, and updates the second filter coefficients by calculating elements of the product matrix of the first matrix and an inverse matrix of the second matrix as the second filter coefficients.[Supplementary Note 8] A signal estimation method for estimating a plurality of transmission signals corresponding to a plurality of spatially multiplexed reception signals, respectively, from the plurality of reception signals, the signal estimation method comprising: inputting the plurality of reception signals; and estimating the plurality of transmission signals from the plurality of reception 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 transformer that performs nonlinear transformation, and estimating the plurality of transmission signals comprises inputting an output signal generated by an i-1th signal estimation unit (where i is a variable indicating an integer equal to or greater than 2 and less than the number of signal estimation units) using the two linear equalizers and the nonlinear transformer provided in the i-1th signal estimation unit to an i-th signal estimation unit connected subsequent to the i-1th signal estimation unit; generating the output signal output by the i-th signal estimation unit from the output signal generated by the i-1-th signal estimation unit and the plurality of received signals using the two linear equalizers and the nonlinear converter provided in the i-th signal estimation unit, and[Supplementary Note 9] A recording medium having recorded thereon a computer program for causing a computer to execute a signal estimation method for estimating a plurality of transmission signals corresponding to a plurality of spatially multiplexed reception signals, respectively, from the plurality of reception signals, the signal estimation method comprising: inputting the plurality of reception signals; and estimating the plurality of transmission signals from the plurality of reception 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 transformer that performs nonlinear transformation, and estimating the plurality of transmission signals comprises inputting an output signal generated by the i-1th signal estimation unit using the two linear equalizers and the nonlinear transformer provided in the i-1th (note that i is a variable indicating an integer equal to or greater than 2 and less than the number of signal estimation units) signal estimation unit to an i-th signal estimation unit connected subsequent to the i-1th signal estimation unit; generating the output signal output by the i-th signal estimation unit from the output signal generated by the i-1-th signal estimation unit and the plurality of received signals using the two linear equalizers and the nonlinear converter provided in the i-th signal estimation unit, and

[0102] The present invention can be modified as appropriate within the scope that does not contradict the gist or idea of ​​the invention that can be read from the claims and the entire specification, and communication systems, transmitting devices, receiving devices, transmitting methods, receiving methods, and computer programs that involve such modifications are also included in the technical idea of ​​the present invention.

[0103] REFERENCE SIGNS LIST 1 Transmitter 11 Signal Processing Device 122 Signal Combining Unit 123 Phase Shift Unit 125 Feedback Signal Receiving Unit 126 Phase Update Unit 2 Receiving Device 21 Signal Processing Device 222 MIMO Equalization Processing Unit 224 Communication State Detection Unit 225 Phase Control Information Generator 226 Feedback Signal Generator SYS Wireless Communication System

Claims

1. A signal estimation device that estimates a plurality of transmitted signals corresponding to a plurality of spatially multiplexed received signals, the signal estimation device comprising: the signal estimation device includes a plurality of signal estimation units; each of the plurality of signal estimators includes two linear equalizers and one nonlinear transformer that performs a nonlinear transformation; the plurality of signal estimation units are connected in series such that an output signal generated by an r-1-th signal estimation unit using the two linear equalizers and the nonlinear converter included in the r-1-th signal estimation unit (where r is a variable indicating an integer equal to or greater than 2 and equal to or less than the number of signal estimation units) is input to an r-th signal estimation unit connected subsequent to the r-1-th signal estimation unit; The r-th signal estimation unit generates the output signal from the output signal generated by the r-1-th signal estimation unit and the plurality of received signals using the two linear equalizers and the nonlinear converter included in the r-th signal estimation unit and the two linear equalizers and the nonlinear converter included in the r-1-th signal estimation unit. Signal estimator.

2. each of the plurality of signal estimating units generates, as the output signals, a plurality of estimated signals which are provisional estimation results of the plurality of transmitted signals and an auxiliary signal using the two linear equalizers and the nonlinear transformer; the r-th signal estimation unit generates, as the output signals, the plurality of estimated signals and the auxiliary signal from the auxiliary signal generated by the r-1-th signal estimation unit and the plurality of received signals, using the two linear equalizers and the nonlinear transformer included in the r-th signal estimation unit; The plurality of estimated signals generated by an Rth (where R is a constant indicating the number of signal estimation units) signal estimation unit among the plurality of signal estimation units are used as the plurality of transmitted signals corresponding to the plurality of received signals, respectively.

2. A signal estimation device according to claim 1.

3. each of the plurality of signal estimators generates a first auxiliary signal and a second auxiliary signal as the auxiliary signal; a first linear equalizer of the two linear equalizers included 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; a second linear equalizer of the two linear equalizers included in the r-th signal estimation unit performs a second filtering process using an output of the first linear equalizer included 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 a difference between the first and second auxiliary signals generated by the r-1-th signal estimation unit to an output of the second linear equalizer included in the r-th signal estimation unit; the nonlinear converter included in the r-th signal estimation unit adds the plurality of estimation signals generated by the r-th signal estimation unit and the second auxiliary signal generated by the r-1-th signal estimation unit to generate an addition signal, and inputs the addition signal to a predetermined activation function to generate an output of the activation function as the first auxiliary signal; The r-th signal estimation unit generates a first difference signal, which is a difference between an output of the activation function and an input of the activation function, as the second auxiliary signal.

3. A signal estimation device according to claim 2.

4. the first linear equalizer included in the r-th signal estimation unit performs, as the first filtering process, a convolution operation using a second difference signal, which is a difference between the first and second auxiliary signals generated by the r-1-th signal estimation unit, and a first filter coefficient; The second linear equalizer included in the r-th signal estimation unit performs a convolution operation using a third difference signal, which is a difference between an output of the first linear equalizer included in the r-th signal estimation unit and the plurality of received signals, and a second filter coefficient as the second filter processing.

4. A signal estimation device according to claim 3.

5. a first linear equalizer of the two linear equalizers included in the r-th signal estimation unit performs a first filtering process using a first filter coefficient updated by a coefficient updating device; The second linear equalizer of the two linear equalizers included in the r-th signal estimation unit performs a second filtering process using second filter coefficients updated by the coefficient updating device.

3. A signal estimation device according to claim 1 or 2.

6. the coefficient update device includes a plurality of coefficient update error propagation units, the number of which is the same as the number of the plurality of signal estimating units; each of the plurality of coefficient update error propagation units updates an error signal that is a difference between the estimation results of the plurality of transmission signals by the signal estimation device and correct values ​​of the plurality of transmission signals; an r-th coefficient update error propagation unit among the plurality of coefficient update error propagation units, which updates the first and second filter coefficients used by the r-th signal estimation unit, updates the first and second filter coefficients by performing a linear operation of subtracting a result of a convolution operation using the output signal and an error signal updated by the r+1-th coefficient update error propagation unit among the plurality of coefficient update error propagation units, which updates the first and second filter coefficients used by the r+1-th signal estimation unit, from the first and second filter coefficients before updating; 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 corresponding to a differentiation process of the nonlinear transformation performed by the nonlinear transformer using a result of the convolution operation.

6. A signal estimation device according to claim 5.

7. the coefficient update device updates the first filter coefficients using a method of estimating an impulse response of a transmission path by a least squares method from the estimation results of the plurality of transmission signals by the signal estimation device and the plurality of received signals; The coefficient updating device generates a second matrix obtained by adding the numerical parameters to diagonal elements of a product matrix of the first matrix and a conjugate arrangement matrix of the first matrix, from a first matrix having elements of the first filter coefficients and a predetermined numerical parameter, and updates the second filter coefficients by calculating elements of the product matrix of the first matrix and an inverse matrix of the second matrix as the second filter coefficients.

6. A signal estimation device according to claim 5.

8. A signal estimation method for estimating a plurality of transmitted signals corresponding to a plurality of spatially multiplexed received signals, the method comprising: The signal estimation method includes: inputting the plurality of received signals; estimating the plurality of transmitted signals from the plurality of received signals using a plurality of signal estimators connected in series; Including, each of the plurality of signal estimators includes two linear equalizers and one nonlinear transformer that performs a nonlinear transformation; estimating the plurality of transmitted signals inputting an output signal generated by the i-1-th signal estimation unit using the two linear equalizers and the nonlinear converter included in the i-1-th signal estimation unit (where i is a variable indicating an integer equal to or greater than 2 and less than the number of signal estimation units), to an i-th signal estimation unit connected subsequent to the i-1-th signal estimation unit; generating an 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 and the plurality of received signals using the two linear equalizers and the nonlinear converter provided in the i-th signal estimation unit, and A signal estimation method comprising:

9. A computer program that causes a computer to execute a signal estimation method for estimating a plurality of transmitted signals corresponding to a plurality of spatially multiplexed received signals, the computer program comprising: The signal estimation method includes: inputting the plurality of received signals; estimating the plurality of transmitted signals from the plurality of received signals using a plurality of signal estimators connected in series; Including, each of the plurality of signal estimators includes two linear equalizers and one nonlinear transformer that performs a nonlinear transformation; estimating the plurality of transmitted signals inputting an output signal generated by the i-1-th signal estimation unit using the two linear equalizers and the nonlinear converter included in the i-1-th signal estimation unit (where i is a variable indicating an integer equal to or greater than 2 and less than the number of signal estimation units), to an i-th signal estimation unit connected subsequent to the i-1-th signal estimation unit; generating an 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 and the plurality of received signals using the two linear equalizers and the nonlinear converter provided in the i-th signal estimation unit, and A computer program comprising: