Signal estimation device, signal estimation method, and recording medium

Abstract

A signal estimation device 21 estimates, from a plurality of spatially multiplexed reception signals, a plurality of transmission signals respectively corresponding to the plurality of reception signals. The signal estimation device 21 comprises a signal estimation unit 23 that includes two frequency domain equalizers 231, 232 and one nonlinear converter 233 that carries out nonlinear conversion. The signal estimation device 21 uses the signal estimation unit 23 to carry out a signal estimation operation for R (R being a preset positive integer) times. In an rth (r being a positive integer of R or less) signal estimation operation among the R number of signal estimation operations, the signal estimation device 21 generates, from the plurality of reception signals and an auxiliary signal generated in an (r-1)th signal estimation operation, a plurality of estimated signals that are rth provisional estimation results of the plurality of transmission signals, and an auxiliary signal that is to be used in an (r+1)th signal estimation operation. The signal estimation device 21 uses, as estimation results of the plurality of transmission signals, the plurality of estimated signals generated in the Rth signal estimation operation.

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

[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 a 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 signal estimation unit that includes two frequency domain equalizers and one nonlinear transformer that performs a nonlinear transformation, the signal estimation device performs R (R is a predetermined positive integer) signal estimation operations using the signal estimation unit, the signal estimation device generates, in the r (r is a positive integer not greater than R)-th signal estimation operation of the R signal estimation operations, a plurality of estimated signals that are the r-th provisional estimation results of the plurality of transmitted signals, and the auxiliary signal to be used in the r+1-th signal estimation operation, from the plurality of received signals and an auxiliary signal generated in the r-1-th signal estimation operation, and the signal estimation device sets the plurality of estimated signals generated in the R-th signal estimation operation as estimation results of the plurality of transmitted 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 reception signals, the signal estimation method including: inputting the plurality of reception signals; initializing an auxiliary signal; using the plurality of reception signals and the auxiliary signal, performing two frequency domain equalization processes that convert each of the reception signals and the auxiliary signal into the frequency domain and perform equalization, thereby generating an estimation result for the plurality of transmission signals; and updating the auxiliary signal by nonlinear processing using the auxiliary signal and the estimation result; repeating the steps a predetermined number of times; and using the final estimation result in the predetermined number of repetitions as the estimation result for the plurality of transmission signals.

[0010] One aspect of the recording medium is a recording medium having recorded thereon a computer program that causes 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; initializing an auxiliary signal; using the plurality of reception signals and the auxiliary signal, performing two frequency domain equalization processes that convert each of the reception signals and the auxiliary signal into the frequency domain and perform equalization, thereby generating an estimation result for the plurality of transmission signals; and updating the auxiliary signal by nonlinear processing using the auxiliary signal and the estimation result; repeating the above steps a predetermined number of times; and using the final estimation result in the predetermined number of repetitions as the estimation result for the plurality of transmission signals.

[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 receiving device that performs MIMO equalization processing. FIG. 4 is a block diagram showing the configuration of a MIMO equalizer. FIG. 5 is a flowchart showing the flow of MIMO equalization processing. FIG. 6 is a block diagram showing the configuration of a nonlinear transformer. FIGS. 7(a) and 7(b) are graphs showing the relationship between input and output in an activation function. FIG. 8 is a block diagram showing the configuration of a coefficient update device. FIG. 9 is a flowchart showing the flow of coefficient update operations. FIG. 10 is a block diagram showing the configuration of a coefficient update device. FIG. 11 is a block diagram showing the configuration of a coefficient update device. FIG. 12 is a block diagram showing the configuration of a coefficient update error propagation unit. FIG. 13 is a flowchart showing the flow of coefficient update operations.

[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. <1> Configuration of the transmission system SYS

[0014] 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） The number of multiplexed MIMO transmission signals D ｔ and the number of multiplexed MIMO received signals D ｒ Although the same processing is possible when the number of multiplexes D (= D ｔ =D ｒ Each of the D transmission signals is composed of a pre-set number of quadrature amplitude modulation (QAM) signal points. （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.

[0017] 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.

[0018] 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. （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 .

[0019] 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.

[0020] 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.

[0021] 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.

[0022] 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.

[0023] 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.

[0024] 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

[0025]

[0026] As will be described in detail later, the receiving device 2 performs MIMO equalization processing multiple times using a MIMO equalization unit 23 (see FIGS. 2 and 3). The MIMO equalization unit 23 may also be called a signal equalizer, a signal estimator, a signal equalization section, or a signal estimation section. In particular, in this embodiment, the MIMO equalization unit 23 includes two MIMO equalization processing sections 231 and 232 and one nonlinear converter 233 (see FIG. 4), as will be described in detail later. In this case, the receiving device 2 performs MIMO equalization processing multiple times using a MIMO equalization unit 23 (see FIG. 4), as will be described in detail later. （０）From x （Ｄ－１） This can improve the estimation accuracy.

[0027] The transmission system SYS further includes 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 first MIMO equalization processing unit 231 and the filter coefficients (tap coefficients) W of the second MIMO equalization processing unit 232. Details of the coefficient update operation will be described later. To perform the coefficient update operation, the coefficient update device 4 includes a signal processing device 41 and a storage device 42.

[0028] 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.

[0029] 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 long-term. 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. <2> MIMO Equalization Processing Performed by the Receiving Device 2 Next, the MIMO equalization processing performed by the receiving device 2 will be described. <2-1> Configuration of the Receiving Device 2 (Signal Processing Device 21)

[0030] 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 Figures 2 and 3. Figures 2 and 3 are block diagrams showing logical functional blocks realized in the signal processing device 21 for performing MIMO equalization processing.

[0031] 2, the signal processing device 21a includes one MIMO equalization unit 23 as a logical functional block for performing MIMO equalization processing. The signal processing device 21a is an iterative signal processing device in which one MIMO equalization unit 23 performs signal estimation operations multiple times. The MIMO equalization unit 23 included in the signal processing device 21a is configured so that the output of the MIMO equalization unit 23 is input to the MIMO equalization unit 23.

[0032] 3, the signal processing device 21b may include a plurality of MIMO equalization units 23 as logical functional blocks for performing MIMO equalization processing. The signal processing device 21b is a pipelined signal processing device in which each of the plurality of MIMO equalization units 23 performs one signal estimation operation.

[0033] 2 and 3 merely conceptually (in other words, simply) show logical functional blocks for performing MIMO equalization processing. In other words, the functional blocks shown in Figures 2 and 3 do not need to be implemented as they are in the signal processing device 21. As long as the signal processing device 21 can perform the MIMO equalization processing performed by the functional blocks shown in Figures 2 and 3, the configuration of the functional blocks implemented in the signal processing device 21 is not limited to the configuration shown in Figures 2 and 3.

[0034] 3, the multiple MIMO equalization units 23 included in the signal processing device 21b are connected in series (in other words, coupled in series). Specifically, the multiple MIMO equalization units 23 are connected in series so that the output of one MIMO equalization unit 23 is input to another MIMO equalization unit 23 connected in a subsequent stage of the one MIMO equalization unit 23.

[0035] In the following description, an example will be described in which the signal processing device 21 performs signal estimation operations R times (R is a constant indicating an integer of 2 or more). In this case, the pipelined signal processing device 21b includes R MIMO equalization units 23. The r+1 (r is a variable indicating an integer of 0 or more and R-1 or less)-th MIMO equalization unit 23 among the R MIMO equalization units 23 is designated as the MIMO equalization unit 23. ｒ＋１ In this case, the signal processing device 21 is referred to as a MIMO equalization unit 23. １ , MIMO equalization unit 23 ２ , ..., MIMO equalization unit 23 ｒ－１ , MIMO equalization unit 23 ｒ , ..., MIMO equalization unit 23 Ｒ－１ , and the MIMO equalization unit 23 Ｒ Furthermore, under the condition that the variable r indicates an integer equal to or greater than 2, the R MIMO equalization units 23 １ From 23 Ｒ is the MIMO equalization unit 23 ｒ－１ The output of the MIMO equalization unit 23 ｒ－１ The MIMO equalization unit 23 connected after ｒThe MIMO equalization unit 23 in the signal processing device 21b is connected in series so that the signal is input to the ｒ The MIMO equalization process corresponds to the rth MIMO equalization process among the R MIMO equalization processes performed by the signal processing device 21a.

[0036] The MIMO equalization unit 23 receives a plurality of received signals y (i.e., a plurality 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） In the following description, the provisional estimation results of the multiple transmission signals x by the MIMO equalization unit 23 are referred to as multiple estimated signals xe ｒ In other words, in the following description, the MIMO equalization unit 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） For this reason, the MIMO equalization unit 23 generates a plurality of estimated signals xe from a plurality of received signals y. ｒ Generate.

[0037] The MIMO equalization unit 23 further generates two auxiliary signals, which are internal signals. In the following description, the two auxiliary signals generated by the MIMO equalization unit 23 are referred to as the first auxiliary signal v ｒ and a second auxiliary signal u ｒ The first auxiliary signal v ｒ is a set of multiple (specifically, D) auxiliary signals v ｒ （０） From V ｒ （Ｄ－１） The second auxiliary signal u ｒ is a set of a plurality of (specifically, D) auxiliary signals u ｒ （０） From U ｒ （Ｄ－１） Includes:

[0038] The MIMO equalization unit 23 receives a plurality of received signals y and a first auxiliary signal v generated in the r-th signal estimation operation.ｒ and the second auxiliary signal u generated in the r-th signal estimation operation. ｒ From this, multiple estimated signals xe ｒ＋１ and the first auxiliary signal v ｒ＋１ and a second auxiliary signal u ｒ＋１ To this end, the MIMO equalization unit 23 generates the first auxiliary signal v ｒ and a second auxiliary signal u ｒ However, when the variable r is 0, the signal estimation operation is not performed, and therefore the MIMO equalization unit 23 outputs the plurality of received signals y and the first auxiliary signal v corresponding to the initial value of the first auxiliary signal v. ０ (Specifically, a plurality of first auxiliary signals v ０ （０） From V ０ （Ｄ－１） ) and a second auxiliary signal u corresponding to the initial value of the second auxiliary signal u ０ (Specifically, a plurality of second auxiliary signals u ０ （０） From U ０ （Ｄ－１） ) and a plurality of estimated signals xe １ and the first auxiliary signal v １ and a second auxiliary signal u １ and generate.

[0039] The signal processing device 21 generates a plurality of estimated signals xe generated in the Rth signal estimation operation. Ｒ （０） From xe Ｒ （Ｄ－１） , a plurality of received signals y （０） From y （Ｄ－１） A plurality of transmit signals x respectively corresponding to （０） From x （Ｄ－１） That is, the signal processing device 21 outputs the plurality of estimated signals xe generated in the Rth signal estimation operation as the final estimated results. Ｒ （０） From xe Ｒ （Ｄ－１） , multiple transmitted signals x （０） From x （Ｄ－１） The final estimation results of the plurality of estimated signals xe （０） From xe （Ｄ－１） Output as

[0040] An example of the configuration of the MIMO equalization unit 23 is shown in Fig. 4. As shown in Fig. 4, the MIMO equalization unit 23 includes a first MIMO equalization processing unit 231, a second MIMO equalization processing unit 232, and a nonlinear converter 233. Therefore, the MIMO equalization unit 23 uses the two MIMO equalization processing units 231 and 232 and the one nonlinear converter 233 to generate a plurality of received signals y and a first auxiliary signal v ｒ and a second auxiliary signal u ｒ From this, multiple estimated signals xe ｒ＋１ and the first auxiliary signal v ｒ＋１ and a second auxiliary signal u ｒ＋１ Furthermore, the MIMO equalization unit 23 includes an adder 234 and an adder 235. The first MIMO equalization processing unit 231 includes a discrete Fourier transform device 2311, a multiplier 2312, and an inverse discrete Fourier transform device 2313. The first MIMO equalization processing unit 231 may include a coefficient memory 411M. The second MIMO equalization processing unit 232 includes a discrete Fourier transform device 2321, a multiplier 2322, an adder 2323, and an inverse discrete Fourier transform device 2324. The second MIMO equalization processing unit 232 may include a coefficient memory 412M. <2-2> Flow of MIMO Equalization Processing

[0041] 2 to 4 as well as Fig. 5, a description will be given of the MIMO equalization process performed multiple times by the receiver 2 using the MIMO equalization unit 23. Fig. 5 is a flowchart showing the flow of the MIMO equalization process.

[0042] As shown in FIG. 5, 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).

[0043] Furthermore, the signal processing device 21 performs an initialization process (step S22). Specifically, the signal processing device 21 generates the first auxiliary signal v ０ (a plurality of first auxiliary signals v ０ （０） From V ０ （Ｄ－１）) to zero. Furthermore, the signal processor 21 initializes the second auxiliary signal u ０ (plurality of second auxiliary signals u ０ （０） From U ０ （Ｄ－１） ) to zero. Furthermore, the signal processing device 21 initializes a variable r to 0.

[0044] The MIMO equalization unit 23 uses the first MIMO equalization processing unit 231 to convert the time domain signal y Ｆ Specifically, the MIMO equalization unit 23 generates the first auxiliary signal v using the discrete Fourier transform device 2311 (step S23). ｒ is subjected to discrete Fourier transform to obtain the frequency domain signal F(v ｒ ) is generated. Then, the MIMO equalization unit 23 uses a multiplier 2312 to generate the frequency domain signal F(v ｒ ) and the first filter coefficient G stored in the coefficient memory 411M. （ｌ，ｋ） By multiplying with Ｆ That is, the first MIMO equalization processing unit 231 generates the first auxiliary signal v ｒ－１ As a filtering process using Ｆ A multiplication process is performed to generate the filter coefficient G （ｌ，ｋ） is the D×D filter coefficients G ０、０） From G （Ｄ－１、Ｄ－１） is a filter coefficient vector containing the filter coefficients G （０、０） From G （Ｄ－１、Ｄ－１） is updated (set) by the coefficient update unit 4 as will be described later. The filter coefficient G used in each of the R signal estimation operations （ｌ，ｋ） may be the same. Ｆ is D signals Y Ｆ （０） From Y Ｆ （Ｄ－１） In this case, the MIMO equalization unit 23 may perform the multiplication shown in Equation 2. The symbol "F" in Equation 2 indicates a discrete Fourier transform process. The symbol "←" in Equation 2 indicates an operation of substituting the right side into the left side. In the following description, the symbol "←" also indicates an operation of substituting the right side into the left side.

[0045]

[0046] The symbol "[mult]" in Equation 2 is an operator indicating the multiplication of the components of two sequences. Therefore, A[mult]B represents a sequence obtained by multiplying the components of two sequences A and B. That is, sequence A=A ０ , A １ , A ２ ... and series B = B ０ , B １ , B ２ ..., then series A [mult] B = A ０ B ０ , A １ B １ , A ２ B ２ ... That is, the operation represented by the symbol "[mult]" is an operation similar to the Hadamard product of vectors. In the following description, "[mult]" is also an operator representing a similar operation.

[0047] Then, the MIMO equalization unit 23 uses an inverse discrete Fourier transform device 2313 to convert the signal Y Ｆ is subjected to inverse discrete Fourier transform to obtain the time domain signal y Ｆ In this case, the MIMO equalization unit 23 may perform the calculation shown in Equation 3. －１ " denotes an inverse discrete Fourier transform process.

[0048] The first auxiliary signal v ｒ from the time domain signal y Ｆ The process of generating the first MIMO equalization process is called the first MIMO equalization process.

[0049] Thereafter, the MIMO equalization unit 23 uses the adder 234 to add the time domain signal y Ｆ and a differential signal (y−y Ｆ Specifically, the MIMO equalization unit 23 generates the time domain signal y Ｆ （ｌ） and the received signal y （ｌ）The process of generating a differential signal corresponding to the difference between is repeated while changing the variable l from 0 to D−1, thereby generating D differential signals.

[0050] The MIMO equalization unit 23 uses the second MIMO equalization processing unit 232 to generate the estimated signal xe ｒ＋１ (Step S24). Specifically, the MIMO equalization unit 23 generates a differential signal (y−y Ｆ ) is subjected to a discrete Fourier transform to obtain the signal Y^ ｒ （ｌ） In this case, the MIMO equalization unit 23 may perform the calculation shown in Equation 4. Note that the signal Y^ generated by the calculation shown in Equation 4 ｒ （ｌ） is also used as an input signal to the second filter coefficient update unit 412 shown in FIGS.

[0051]

[0052] The MIMO equalization unit 23 then multiplies the signal Y^ by using a multiplier 2322. ｒ （ｌ） and the first filter coefficient W stored in the coefficient memory 411M. （ｋ，ｌ） By multiplying with Ｆ That is, the first MIMO equalization processing unit 231 generates the differential signal (y−y Ｆ ) (i.e., the time domain signal y Ｆ and a plurality of received signals y) Ｆ A multiplication process is performed to generate the filter coefficient W （ｋ，ｌ） is the D×D filter coefficients W （０、０） From W （Ｄ－１、Ｄ－１） is a filter coefficient vector containing the filter coefficients W （０、０） From W （Ｄ－１、Ｄ－１） is updated (set) by the coefficient update unit 4 as will be described later. The filter coefficient W used in each of the R signal estimation operations is （ｋ，ｌ） may be the same. Ｆ is D signals X Ｆ （０） From XＦ （Ｄ－１） In this case, the MIMO equalization unit 23 may perform the calculation shown in Equation 5.

[0053]

[0054] Then, the MIMO equalization unit 23 uses an adder 2323 to add the signal frequency domain signal F(v ｒ ), and the signal X generated by the multiplier 2322 Ｆ By adding the signal (F(v ｒ ) + X Ｆ The MIMO equalization unit 23 uses an inverse discrete Fourier transform device 2324 to generate a signal (F(v ｒ ) + X Ｆ ) is subjected to inverse discrete Fourier transform to obtain the estimated signal xe ｒ＋１ That is, the MIMO equalization unit 23 performs the calculation shown in Equation 6 to generate a plurality of estimated signals xe ｒ＋１ （０） From xe ｒ＋１ （Ｄ－１） Generate.

[0055]

[0056] Estimated signal xe ｒ＋１ is one of the signals output by the MIMO equalization unit 23, and is a provisional estimation result of the r+1th signal estimation operation. Ｆ , and F(v ｒ ) is input, and the estimated signal xe ｒ＋１ (multiple estimated signals xe ｒ＋１ （０） From xe ｒ＋１ （Ｄ－１） ) is referred to as a second MIMO equalization process.

[0057] Furthermore, the MIMO equalization unit 23 updates the first auxiliary signal v and the second auxiliary signal u using the nonlinear transformer 233 (step S25). Specifically, the MIMO equalization unit 23 updates the first auxiliary signal v and the second auxiliary signal u using the adder 235. ｒ＋１ and the second auxiliary signal u generated in the r-1th signal estimation operation. ｒBy adding the sum signal (xe ｒ＋１ +u ｒ Specifically, the MIMO equalization unit 23 generates the estimated signal xe using the adder 235. ｒ＋１ （ｋ） and the second auxiliary signal u ｒ （ｋ） By repeating the process of adding the above while changing the variable k from 0 to D-1, multiple sum signals (xe ｒ＋１ （ｋ） +u ｒ （ｋ） ) is then generated by the MIMO equalization unit 23 using a nonlinear transformer 233. ｒ＋１ +u ｒ ) is subjected to nonlinear transformation to obtain the intermediate signal s ｒ＋１ Specifically, the MIMO equalization unit 23 generates the sum signal (xe ｒ＋１ （ｋ） +u ｒ （ｋ） ) is subjected to nonlinear transformation to obtain the intermediate signal s ｒ＋１ （ｋ） By repeating the process of generating the intermediate signals s while changing the variable k from 0 to D-1, ｒ＋１ （０） From ｒ＋１ （Ｄ－１） ) to generate the

[0058] The nonlinear transformer 233 performs nonlinear transform processing using a predetermined activation function. ｒ＋１ +u ｒ ) is input to the activation function used by the nonlinear transformer 233. 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 converted into the intermediate signal s ｒ＋１ It is used as.

[0059] The nonlinear conversion process by the nonlinear converter 233 is a process expressed by Equation 7 shown in FIG. Ｑ" is a symbol indicating the output of the activation function. In this case, as shown in FIG. 6 showing the configuration of the nonlinear converter 233, the nonlinear converter 233 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 233 performs nonlinear processing on the sum signal (xe ｒ＋１ +u ｒ ) into the activation function to obtain the output, and ｒ＋１ +u ｒ ) into an activation function and obtain its output.

[0060]

[0061] 7(a) and 7(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 scheme of the transmission signal x. In other words, the activation function may be determined depending on the modulation scheme of the transmission signal x. As an example, FIG. 7(a) shows an example of the relationship between input and output in the activation function when the modulation scheme of the transmission signal x is QPSK (Quadrature Phase Shift Keying), in which the transmission signal x is represented by four points (+1+√(-1), +1-√(-1), -1+√(-1), -1-√(-1)) on the complex plane. FIG. 7(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)).

[0062] Referring again to FIG. 5, the MIMO equalization unit 23 further uses a nonlinear transformer 233 to convert the first auxiliary signal v ｒ＋１ and the second auxiliary signal u ｒ＋１Specifically, the MIMO equalization unit 23 generates a sum signal (xe) input to the nonlinear transformer 233 by multiplying the intermediate signal s output from the nonlinear transformer 233 by two (xe) ｒ＋１ +u ｒ ) is the first auxiliary signal v ｒ＋１ Specifically, the MIMO equalization unit 23 generates the intermediate signal s （ｋ） and the sum signal (xe ｒ＋１ （ｋ） +u ｒ （ｋ） ) is the first auxiliary signal v ｒ＋１ （ｋ） The process of calculating the first auxiliary signal v is repeated while changing the variable k from 0 to D-1. ｒ＋１ （０） From V ｒ＋１ （Ｄ－１） That is, the MIMO equalization unit 23 performs the operation shown in Equation 8 to generate a plurality of first auxiliary signals v ｒ＋１ （０） From V ｒ＋１ （Ｄ－１） Generate.

[0063]

[0064] The MIMO equalization unit 23 also calculates the sum signal (xe ｒ＋１ +u ｒ ) and the intermediate signal s output from the nonlinear converter 233 is used as the second auxiliary signal u ｒ＋１ Specifically, the MIMO equalization unit 23 generates the sum signal (xe ｒ＋１ （ｋ） +u ｒ （ｋ） ) and the intermediate signal s （ｋ） The difference between the first auxiliary signal and the second auxiliary signal is ｒ＋１ （ｋ） The process of calculating the second auxiliary signal u is repeated while changing the variable k from 0 to D-1. ｒ＋１ （０） From U ｒ＋１ （Ｄ－１） That is, the MIMO equalization unit 23 performs the operation shown in Equation 9 to generate a plurality of second auxiliary signals uｒ＋１ （０） From U ｒ＋１ （Ｄ－１） Generate.

[0065]

[0066] The MIMO equalization unit 23 calculates the intermediate signal s output from the nonlinear transformer 233 and the sum signal (xe ｒ＋１ +u ｒ ) is used as the second auxiliary signal u ｒ＋１ Specifically, the MIMO equalization unit 23 generates the intermediate signal s using a nonlinear transformer 233. ｒ （ｋ） and the sum signal (xe ｌ＋１ （ｋ） +u ｌ （ｋ） ) is the auxiliary signal v ｌ＋１ （ｋ） The process of calculating the auxiliary signals v is repeated while changing the variable k from 0 to D-1. ｌ＋１ （０） From V ｌ＋１ （Ｄ－１） That is, the MIMO equalization unit 23 ｒ By performing the operation shown in Equation 9, multiple auxiliary signals v ｌ＋１ （０） From V ｌ＋１ （Ｄ－１） Generate.

[0067] Thereafter, the signal processing device 21 determines whether the variable r+1 is less than the constant R (step S26). If it is determined that the variable r+1 is less than the constant R (step S26: Yes), the signal processing device 21 increments the variable r by 1 (step S27) and then performs the processes from step S23 to step S26 again. On the other hand, if it is determined that the variable r+1 is not less than the constant R (step S26: No), the Rth signal estimation operation is performed using the plurality of estimated signals xe Ｒ （０） From xe Ｒ （Ｄ－１） Therefore, in this case, the signal processing device 21 generates the plurality of estimated signals xe generated by the R-th signal estimation operation.Ｒ （０） From xe Ｒ （Ｄ－１） , multiple transmitted signals x （０） From x （Ｄ－１） The final estimation results of the plurality of estimated signals xe （０） From xe （Ｄ－１） (Step S28). <2-3> Technical Effects of MIMO Equalization Processing

[0068] As described above, the receiver 2 uses the MIMO equalization unit 23, which includes two MIMO equalization processing sections 231 and 232 and one nonlinear converter 233, to repeat signal estimation operations multiple times to generate multiple transmission signals x （０） From x （Ｄ－１） That is, the receiver 2 uses the MIMO equalization unit 23, which includes two MIMO equalization processing sections 231 and 232 and one nonlinear converter 233, to repeat the signal estimation operation multiple times to generate multiple 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.

[0069] In this embodiment, frequency domain equalization using discrete Fourier transform is performed in linear MIMO equalization, thereby reducing the computational cost required for equalization. Compared to performing time domain equalization using convolution instead of frequency domain equalization using discrete Fourier transform, computational cost can be reduced particularly in cases where the impulse response of the transmission path in the MIMO transmission channel is long. <3> Coefficient Update Operation Performed by Coefficient Update Device 4 Next, the coefficient update operation performed by coefficient update device 4 will be described.

[0070] The update of equalizer filter coefficients in MIMO equalization processing can be performed in two ways: a first case in which coefficients are updated using a predetermined specific signal (pilot signal) as the transmission signal, and a second case in which coefficients are updated using a normal data signal as the transmission signal. In the first case, the transmission signal (pilot signal) corresponding to the signal received at the receiving side is known, whereas in the second case, the transmission signal corresponding to the received signal is unknown at the receiving side. The first case is a special training transmission mode performed to optimize parameters within the receiver, such as filter coefficients, while the second case is a normal data transmission mode. The filter coefficient update processing in MIMO equalization processing of this embodiment supports both the update performed in the special training transmission mode and the update performed in the normal data transmission mode. The signal processing device 41 has a first filter coefficient update device 411 and a second filter coefficient update device 412. <3-1> Configuration of the first filter coefficient update device 411

[0071] The configuration of the first filter coefficient updating device 411 that performs the update operation of the first filter coefficients will be described with reference to Fig. 8. Fig. 8 is a block diagram showing logical functional blocks realized in the first filter coefficient updating device 411 for performing the update operation of the first filter coefficients. Fig. 8 shows an example of the configuration of the first filter coefficient updating device 411.

[0072] As shown in FIG. 8 , the configuration of the first filter coefficient updating device 411 is similar to that of the MIMO equalization unit 23 provided in the signal processing device 21. The first filter coefficient updating device 411 includes an update information generating unit 411a and a filter coefficient updating unit 411b. The update information generating unit 411a includes a discrete Fourier transform device 4111, a multiplier 4112, an inverse discrete Fourier transform device 4113, an adder 4114, a discrete Fourier transform device 4115, a converter 4116, and a multiplier 4117. The filter coefficient updating unit 411b includes a weighting unit 4118, an adder 4119, and a coefficient memory 411M that stores first filter coefficients. The first filter coefficient updating device 411 updates the first filter coefficient G based on the transmitted signal x and the received signal y. Note that Figure 8 merely conceptually (in other words, simply) illustrates logical functional blocks for performing the coefficient update operation. In other words, the functional blocks shown in Figure 8 do not need to be implemented as they are in the signal processing device 41, and as long as the signal processing device 41 can perform the coefficient update operation 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. <3-2> Flow of First Filter Coefficient Update Process The first filter coefficient update process will be described with reference to Figure 9. Figure 9 is a flowchart showing the flow of the first filter coefficient update process. As shown in Figure 9, a received signal x and a transmitted signal y are input to the first filter coefficient update device 411 of the signal processing device 41 (step S31).

[0073] In the calculation process of the filter coefficients, in the case of a training transmission mode in which a predetermined pilot signal is used as the transmission signal, the transmission signal x is assumed to be known by the receiving side and is used as the input signal. On the other hand, in the case of a normal data transmission mode other than the training transmission mode, the estimated signal xe generated by the above-mentioned MIMO equalization process is used as the input signal. Ｒ The estimated signal xe generated by the above-mentioned MIMO equalization process is used as the input signal. Ｒ Alternatively, a signal consisting of the QAM signal points closest to the estimated signal xe may be used as the input signal. ＲThe input signal related to the transmission signal is referred to as a transmission signal x, including the case where a signal related to is used as the input signal.

[0074] The first filter coefficient update device 411 uses the update information generation unit 411a to generate update information ΔG （ｌ，ｋ） Specifically, the first filter coefficient updating device 411 performs a discrete Fourier transform on the transmission signal x using a discrete Fourier transform device 4111 to generate a frequency domain signal F(x). Thereafter, the first filter coefficient updating device 411 multiplies the frequency domain signal F(x) by the first filter coefficient G stored in the coefficient memory 411M using a multiplier 4112. （ｌ，ｋ） By multiplying with Ｆ Generates a signal Y Ｆ is D signals Y Ｆ （０） From Y Ｆ （Ｄ－１） That is, the first filter coefficient updating device 411 performs filtering using the transmission signal x to obtain the signal Y Ｆ In this case, the multiplier 4112 may perform the multiplication shown in Equation 10. The process shown in Equation 10 is the same as the first frequency domain equalization process using the first filter coefficient shown in Equation 2.

[0075]

[0076] Then, the first filter coefficient update unit 411 uses the inverse discrete Fourier transform unit 4113 to convert the signal Y Ｆ is subjected to an inverse discrete Fourier transform to obtain the time domain signal F(Y Ｆ ) to generate the time domain signal F －１ (Y Ｆ ) can be considered as a replica of the received signal y. The first filter coefficient update unit 411 uses an adder 4114 to generate the time domain signal F(Y Ｆ ) and the received signal y, the differential signal d is generated. Since the differential signal d is the difference between the replica of the received signal y and the received signal y, the differential signal d can be understood as an error signal. In this case, the first filter coefficient updating device 411 may perform the calculation shown in Equation 11.

[0077]

[0078] Thereafter, the first filter coefficient update unit 411 performs a discrete Fourier transform on the difference signal d using the discrete Fourier transform unit 4115 to generate a discrete Fourier transformed difference signal F(d).

[0079] Each of the plurality of frequency domain signals F(x) is a signal consisting of complex numbers. The first filter coefficient update unit 411 uses a transformer 4116 to convert the complex conjugate F(x) of the frequency domain signal F(x) into a complex conjugate F(x) ＊ In the following description, the complex conjugate of signal A is generated as signal A ＊ This is expressed using the symbol:

[0080] The first filter coefficient update unit 411 uses a multiplier 4117 to calculate the complex conjugate F(x) ＊ and the discrete Fourier transform difference signal F(d), a product (Hadamard product) for each signal component is generated, and the update information ΔG of the first filter coefficient is calculated. （ｌ，ｋ） In this case, the first filter coefficient updating device 411 may perform the calculation shown in Equation 12.

[0081]

[0082] The first filter coefficient updating device 411 uses the filter coefficient updating unit 411b to update the first filter coefficient G （ｌ，ｋ） (step S33). Specifically, the first filter coefficient updating device 411 updates the first filter coefficient G （ｌ，ｋ） The process of updating the first filter coefficient G is repeated while changing the variables k and l from 0 to D−1. （０、０） to the first filter coefficient G （Ｄ－１、Ｄ－１） The first filter coefficient G is updated, which is a filter coefficient vector including:

[0083] The first filter coefficient update device 411 updates the first filter coefficient G so that the difference between the replica of the received signal and the received signal becomes small. The first filter coefficient update device 411 uses a weighter 4118 to update the first filter coefficient ΔG （ｌ，ｋ）Then, the first filter coefficient updating device 411 multiplies the current first filter coefficient G stored in the coefficient memory 411M by a learning rate η, which is a real value set in advance. （ｌ，ｋ） The first filter coefficient G （ｌ，ｋ） The first filter coefficient updating device 411 uses the filter coefficient updating unit 411b to update the first filter coefficient update information ΔG （ｌ，ｋ） The first filter coefficient G （ｌ，ｋ） In other words, the first filter coefficient updating device 411 performs the calculation shown in Equation 13 (calculation including linear calculation) to update the first filter coefficient G （ｌ，ｋ） Update.

[0084] Through the above procedure, the first filter coefficient is updated using the received signal y and the transmitted signal x.

[0085] Updated first filter coefficient G （ｌ，ｋ） are stored in the coefficient memory 411M. The first MIMO equalization processing unit 231 included in the above-described MIMO equalization unit 23 calculates the first filter coefficient G （ｌ，ｋ） Therefore, the first MIMO equalization processing unit 231 included in the MIMO equalization unit 23 performs filtering using the first filter coefficient G stored in the coefficient memory 411M. （ｌ，ｋ） and the obtained first filter coefficient G （ｌ，ｋ） The first filter coefficient G （ｌ，ｋ） If the first filter coefficient G has never been updated, the coefficient memory 411M stores the first filter coefficient G （ｌ，ｋ） A coefficient indicating zero may be stored as the initial value of the second filter coefficient update device 412.

[0086] The configuration of the second filter coefficient updating device 412 that performs the second filter coefficient updating operation will be described with reference to Figures 10 and 11. Figures 10 and 11 are block diagrams showing logical functional blocks realized in the second filter coefficient updating device 412 for performing the second filter coefficient updating operation. Figures 10 and 11 show an example of the configuration of the second filter coefficient updating device 412.

[0087] 10 , the second filter coefficient updating device 412 a includes, as logical functional blocks for performing the second filter coefficient updating process, one error propagation unit 413, a filter coefficient updating section 414, and a multiplier 415. The second filter coefficient updating device 412 a is a repetitive second filter coefficient updating device 412 in which one error propagation unit 413 performs update information generation operations multiple times. The error propagation unit 413 included in the second filter coefficient updating device 412 a is configured so that the output of the error propagation unit 413 is input to the error propagation unit 413.

[0088] 11 , the second filter coefficient updating device 412 b may include a plurality of error propagation units 413, a filter coefficient updating unit 414, and a multiplier 415 as logical functional blocks for performing the second filter coefficient updating operation. Note that FIGS. 10 and 11 merely conceptually (in other words, simply) illustrate logical functional blocks for performing the coefficient updating operation. In other words, the functional blocks shown in FIGS. 10 and 11 do not need to be implemented as they are in the signal processing device 41. As long as the signal processing device 41 can perform the coefficient updating operation performed by the functional blocks shown in FIGS. 10 and 11 , the configuration of the functional blocks implemented in the signal processing device 41 is not limited to the configuration shown in FIGS. 10 and 11 .

[0089] The number of update information generation operations performed by the second filter coefficient updating device 412 is the same as the number of signal estimation operations performed by the signal processing device 21 of the receiving device 2. Therefore, in the following description, an example will be described in which the second filter coefficient updating device 412 performs update information generation operations R times. In this case, the second filter coefficient updating device 412b may include R error propagation units 413.

[0090] The second filter coefficient update device 412 updates (sets) the second filter coefficient W. To update (set) the second filter coefficient W, the second filter coefficient update device 412 receives the signal y Ｆ and a signal Y^ corresponding to the difference between the received signal y ｒ and the estimated signal xe ｒ and the second auxiliary signal u ｒ－１ and the sum signal (xe ｒ +u ｒ－１ ) and get.

[0091] Furthermore, the second filter coefficient update unit 412 updates (sets) the second filter coefficient W by the error signal Δx ｒ The error signal Δx is obtained. ｒ indicates the estimation error of the estimated signal xe estimated by the receiving device 2. ｒ indicates the difference (error) between the estimation result of the multiple transmission signals x by the receiving device 2 and the transmission signal x input to the first filter coefficient update device 411. In other words, the error signal Δx ｒ indicates the difference (error) between the multiple estimated signals xe generated by the receiving device 2 and the transmission signal x input to the first filter coefficient updating device 411. In this case, the second filter coefficient updating device 412 may perform the calculation shown in Equation 14.

[0092] Furthermore, the second filter coefficient updating unit 412 updates (sets) the first filter coefficient G （ｌ，ｋ） Get.

[0093] In this embodiment, the error signal Δx ｒ is calculated by the error propagation unit 413 as the first filter coefficient G and the second filter coefficient W and the sum signal (xe ｒ +u ｒ－１ ) and the error signal Δx ｒ＋１ Therefore, the error propagation unit 413 outputs the error signal Δx ｒ is connected to be input to the error propagation unit 413.

[0094] Fig. 12 shows an example of the configuration of the error propagation unit 413. As shown in Fig. 12, the error propagation unit 413 includes a discrete Fourier transform device 4131, a converter 4132, a multiplier 4133, a converter 4134, a multiplier 4135, an inverse discrete Fourier transform device 4136, and a nonlinear converter 4137. <3-4> Flow of second filter coefficient update operation

[0095] 10 to 12, and with reference to Fig. 13, a description will be given of the coefficient updating operation performed by the second filter coefficient updating device 412 using the error propagation unit 413. Fig. 13 is a flowchart showing the flow of the second filter coefficient updating operation.

[0096] As shown in FIG. 13, the second filter coefficient update unit 412 receives the signal Y^ ｒ and the sum signal (xe ｒ＋１ +u ｒ ) and the error signal Δx Ｒ and the first filter coefficient G （ｌ，ｋ） The error signal Δx is input (step S41). Ｒ is D error signals Δx Ｒ （０） From Δx Ｒ （Ｄ－１） The error signal Δx Ｒ （ｋ） is the estimated signal xe actually generated by the receiving device 2 （ｋ） and the transmission signal x input to the first filter coefficient update device 411 （ｋ） This is the difference between.

[0097] The second filter coefficient update unit 412 uses a multiplier 415 to generate the signal Q （ｋ，ｍ） The second filter coefficient update device 412 uses the multiplier 415 to multiply the current second filter coefficient W stored in the coefficient memory 412M by the first filter coefficient G, thereby generating D×D signals Q （ｋ，ｍ） The second filter coefficient update unit 412 performs the operation shown in Equation 15 to generate the signal Q （ｋ，ｍ） Generate.

[0098] Furthermore, the second filter coefficient update unit 412 performs an initialization process (step S43). Specifically, the signal processing unit 21 initializes a variable r to a constant R-1.

[0099] The second filter coefficient update device 412 uses the error propagation unit 413 to generate update information ΔW ｒ （ｋ，ｌ） Specifically, the second filter coefficient update unit 412 generates the error signal Δx using the discrete Fourier transform unit 4131. ｒ＋１ is subjected to discrete Fourier transform to obtain the frequency domain signal F(Δx ｒ＋１ The first filter coefficient update unit 411 uses a multiplier 4112 to generate a signal Y^ ｒ The complex conjugate Y^ of ｒ ＊ Then, the first filter coefficient update unit 411 uses the inverse discrete Fourier transform unit 4113 to generate the complex conjugate Y^ ｒ ＊ and the frequency domain signal F(Δx ｒ＋１ ) to obtain the update information ΔW of the second filter coefficient. ｒ （ｋ，ｌ） The update information ΔW of the second filter coefficient is generated. ｒ （ｋ，ｌ） The second filter coefficient update unit 412 may perform the multiplication shown in Equation 16.

[0100] Update information ΔW of the second filter coefficient ｒ （ｋ，ｌ） are input to the filter coefficient update unit 414.

[0101] The second filter coefficient update device 412 determines whether the variable r is greater than 0 (step S45). Note that in the Rth operation of the error propagation unit 413, it is not necessary to generate D error signals Δx (described later). Therefore, the update information ΔW of the second filter coefficient is ｒ （ｋ，ｌ） A determination step is provided after the generation step.

[0102] If it is determined that the variable r is not greater than 0 (step S45: No), the second filter coefficient updating device 412 updates the second filter coefficient W （ｋ、ｌ） (step S46). Specifically, the second filter coefficient updating device 412 updates the second filter coefficient W （ｋ、ｌ） The process of updating the second filter coefficient W is repeated while changing the variables k and l from 0 to D−1. （０、０） to the second filter coefficient W （Ｄ－１、Ｄ－１） The second filter coefficient W is updated as a filter coefficient vector including:

[0103] The second filter coefficient update device 412 updates the second filter coefficient W so that the difference between the input signal x (the transmitted signal x or the signal related to the estimated signal xe) and the estimated signal xe (the output signal of the second frequency domain equalizer in the Rth signal estimation operation) becomes small. The second filter coefficient update device 412 updates the second filter coefficient W using the weighter 4141. ｒ （ｋ，ｌ） , the learning rate η ｒ The second filter coefficient update device 412 uses a weighter 4141 to calculate update information ΔW ｒ （ｋ，ｌ） Then, the second filter coefficient update unit 412 uses an adder 4142 to calculate a weighted average of the current second filter coefficient W stored in the coefficient memory 412M. （ｋ、ｍ） From the output of the adder 4142 (i.e., Ση ｒ ×ΔW ｒ （ｋ，ｌ） ) to obtain the second filter coefficient W （ｋ、ｍ） The second filter coefficient updating device 412 updates the second filter coefficient update information ΔW ｒ （ｋ，ｌ） The second filter coefficient W （ｋ、ｌ）In other words, the second filter coefficient updating device 412 performs the calculation shown in Equation 17 (a calculation including a linear calculation) using the weighter 4141 and the adder 4142 to update the second filter coefficient W （ｋ、ｍ） Update.

[0104]

[0105] Updated second filter coefficient W （ｋ、ｌ） is stored in the coefficient memory 412M. The second MIMO equalization processing section 232 included in the above-described MIMO equalization unit 23 calculates the second filter coefficient W （ｋ、ｌ） Therefore, the second MIMO equalization processing section 232 included in the MIMO equalization unit 23 performs filtering using the second filter coefficient W stored in the coefficient memory 412M. （ｋ、ｌ） and the obtained second filter coefficient W （ｋ、ｌ） The filter processing is performed using the second filter coefficient W （ｋ、ｌ） If the second filter coefficient W has never been updated, the coefficient memory 412M stores the second filter coefficient W （ｋ、ｌ） A coefficient indicating zero may be stored as the initial value of .

[0106] As a result of the determination in step S45, if it is determined that the variable r is greater than 0 (step S45: Yes), at least the update information ΔW of the second filter coefficient is ｒ Therefore, in this case, the error propagation unit 413 does not generate the update information ΔW ｒ The error signal Δx used to generate ｒ Specifically, the error propagation unit 413 generates D error signals Δx ｒ （０） From Δx ｒ （Ｄ－１） ) the error signal Δx ｒ That is, the error propagation unit 413 generates the error signal Δx ｒ （ｋ） By repeating the process of generating the error signal Δx while changing the variable k from 0 to D−1, D error signals Δx ｒ （０）From Δx ｒ （Ｄ－１） ) the error signal Δx ｒ Generate.

[0107] error signal Δx ｒ （ｋ） To generate the intermediate signal q （ｋ、ｍ） Specifically, the converter 4134 generates the signal Q （ｋ，ｍ） The error propagation unit 413 uses a multiplier 4135 to generate the complex conjugate of Q （ｋ，ｍ）＊ and the frequency domain signal F(Δx ｒ＋１ The error propagation unit 413 performs an inverse discrete Fourier transform on the result of the multiplication by the multiplier 4135 using an inverse discrete Fourier transform device 4136. As a result, D×D intermediate signals q （ｋ、ｍ） is generated.

[0108]

[0109] Thereafter, the error propagation unit 413 performs the calculation shown in Equation 19 to obtain the intermediate signal Δu （ｋ） Specifically, the error propagation unit 413 generates 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 Δx is calculated from the result of the addition. ｒ＋１ （ｋ） By subtracting the intermediate signal Δu （ｋ） Generate.

[0110]

[0111] Furthermore, the error propagation unit 413 performs the calculation shown in Equation 20 to obtain the intermediate signal p （ｋ） Specifically, the error propagation unit 413 generates the intermediate signal q （ｋ、ｋ） to the intermediate signal Δu （ｋ） By subtracting twice the value of p and doubling the result of the subtraction, the intermediate signal p （ｋ） Generate.

[0112]

[0113] Thereafter, the error propagation unit 413 uses the nonlinear converter 4137 to perform the calculation (nonlinear calculation) shown in Equation 21 to obtain the error signal Δx ｒ （ｋ） (step S45). Specifically, the error propagation unit 413 generates the above-mentioned activation function (Π Ｑ (x)) derivative Ψ Ｑ (That is, dΠ Ｑ (x) / dx) to the estimated signal xe ｒ （ｋ） and the second auxiliary signal u ｒ－１ （ｋ） and the sum signal (xe ｒ （ｋ） +u ｒ－１ （ｋ） ) is input to the error propagation unit 413. ｒ （ｋ） +u ｒ－１ （ｋ） ) is subjected to nonlinear processing equivalent to the differentiation of the nonlinear transformation processing using the activation function. 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） and the imaginary part of the complex number, and then adds up the multiplication results. Note that the symbol "@" in Equation 21 is an operator indicating an operation of adding up the multiplication results of the real parts of the complex numbers and the multiplication results of the imaginary parts of the complex numbers. Therefore, (a+ib)@(c+id) indicates ac+ibd (note that a, b, c, and d each indicate a real number, and i indicates the imaginary unit). Thereafter, the error propagation unit 413 propagates the intermediate signal Δu （ｋ） By adding Δx ｒ （ｋ） Generate.

[0114] The second filter coefficient updating device 412 decrements the variable r by 1 (step S48), and then returns to step S44. <3-5> Technical Effects of the Coefficient Update Process

[0115] In this embodiment, the same filter coefficients are used in each iteration of the signal estimation operation, so that the computational cost required for optimizing the filter coefficients of the linear MIMO equalizer can be reduced, for example, compared to when different filter coefficients are required for each iteration of the signal estimation operation.

[0116] Furthermore, according to the MIMO equalization method of this embodiment, it is possible to calculate optimal filter coefficients with a training transmission amount that is approximately the same as the training transmission amount required for MMSE equalization processing. <4> Supplementary Note The following supplementary note is further disclosed regarding the embodiment described above. [Supplementary Note 1] A signal estimation device that estimates a plurality of transmitted signals respectively corresponding to a plurality of spatially multiplexed received signals from the plurality of received signals, the signal estimation device comprising: a signal estimation unit that includes two frequency domain equalizers and one nonlinear transformer that performs a nonlinear transformation; the signal estimation device performs R (R is a predetermined positive integer) signal estimation operations using the signal estimation unit; the signal estimation device generates, in an r (r is a positive integer not greater than R)-th signal estimation operation of the R signal estimation operations, a plurality of estimated signals that are the r-th tentative estimation results of the plurality of transmitted signals, and the auxiliary signal to be used in the r+1-th signal estimation operation, from the plurality of received signals and an auxiliary signal generated in the r-1-th signal estimation operation; and the signal estimation device uses the plurality of estimated signals generated in the R-th signal estimation operation as estimation results of the plurality of transmitted signals. [Supplementary Note 2] The signal estimation device according to Supplementary Note 1, wherein each of the two frequency domain equalizers comprises a discrete Fourier transform device, a multiplier, and an inverse discrete Fourier transform device. [Supplementary Note 3] The signal estimation unit generates a first auxiliary signal and a second auxiliary signal as the auxiliary signals, generates the plurality of estimated signals in the r-th signal estimation operation from the plurality of received signals and the first auxiliary signal generated in the r-1th signal estimation operation, and updates the first auxiliary signal and the second auxiliary signal from the plurality of estimated signals generated in the r-1th signal estimation operation using the nonlinear transformer, thereby generating the first auxiliary signal and the second auxiliary signal to be used in the r+1th signal estimation operation.[Supplementary Note 4] The signal estimation device according to Supplementary Note 1, wherein a first frequency domain equalizer of the two frequency domain equalizers included in the signal estimation unit performs first equalization processing using first filter coefficients updated by a first filter coefficient updating device, and the first filter coefficient updating device uses the frequency domain equalizer to generate replicas of the plurality of received signals from input signals related to the plurality of transmitted signals, generates update information for the first filter coefficients from differences between the replicas and the plurality of received signals and the input signals, and updates the first filter coefficients by subtracting the update information for the first filter coefficients from the first filter coefficients, and the input signals are the plurality of transmitted signals or signals related to estimation results of the plurality of transmitted signals. [Supplementary Note 5] The second frequency domain equalizer of the two frequency domain equalizers included in the signal estimation unit performs a second equalization process using second filter coefficients updated by a second filter coefficient updating device, the second filter coefficient updating device including an error propagation unit and a coefficient updating unit, the error propagation unit: generates update information for the second filter coefficients using an error signal, which is a difference between the input signal and estimation results of the plurality of transmission signals by the signal estimation device, the auxiliary signal, and the first filter coefficient, and performs an update information generation operation R times, the update information generation operation including updating the error signal; in the r-th update information generation operation of the R update information generation operations, generates r-th update information for the second filter coefficients from the error signal and the auxiliary signal updated in the r-1-th update information generation operation; and updates the error signal used in the r+1-th update information generation operation from the error signal, the auxiliary signal, and the first filter coefficient updated in the r-1-th update information generation operation by nonlinear processing; the coefficient update unit updates the second filter coefficient by subtracting an amount based on each of the R pieces of update information for the second filter coefficients generated by the R update information generation operations from the second filter coefficient.[Supplementary Note 6] The signal estimation device according to Supplementary Note 5, wherein a first discrete Fourier transform device included in the first frequency domain equalizer performs a discrete Fourier transform on the first auxiliary signal; a first multiplier included in the first frequency domain equalizer performs a first multiplication process using the first filter coefficient and a processing result of the first discrete Fourier transform device; a first inverse discrete Fourier transform device included in the first frequency domain equalizer performs an inverse discrete Fourier transform on a result of the first multiplication process; a second discrete Fourier transform device included in the second frequency domain equalizer performs a discrete Fourier transform on a difference between an output of the first frequency domain equalizer and the plurality of received signals; a second multiplier included in the second frequency domain equalizer performs a second multiplication process using the second filter coefficient and a processing result of the second discrete Fourier transform device; and a second inverse discrete Fourier transform device included in the second frequency domain equalizer performs an inverse discrete Fourier transform on a result of the second multiplication process. [Supplementary Note 7] A signal estimation method for estimating a plurality of transmission signals respectively corresponding to a plurality of spatially multiplexed reception signals, the signal estimation method comprising: inputting the plurality of reception signals; initializing an auxiliary signal; using the plurality of reception signals and the auxiliary signal, performing two frequency domain equalization processes that convert each of the reception signals and the auxiliary signal into a frequency domain and perform equalization, thereby generating an estimation result for the plurality of transmission signals, and updating the auxiliary signal by nonlinear processing using the auxiliary signal and the estimation result, a predetermined number of times; and using the final estimation result in the predetermined number of repetitions as an estimation result for the plurality of transmission signals.[Supplementary Note 8] The signal estimation method according to Supplementary Note 7, wherein a first frequency domain equalization process of the two frequency domain equalization processes performs first equalization using first filter coefficients updated by a first filter coefficient updating method, and the first filter coefficient updating method includes: inputting an input signal related to the plurality of transmission signals and the plurality of reception signals; generating replicas of the plurality of reception signals by frequency domain equalization using the input signal; generating update information for the first filter coefficients using a difference between the replica and the plurality of reception signals and the input signal; and updating the first filter coefficients by subtracting the update information for the first filter coefficients from the first filter coefficients, and the input signal is a signal related to the plurality of transmission signals or estimation results of the plurality of transmission signals. [Supplementary Note 9] The signal estimation method according to Supplementary Note 8, wherein the second frequency domain equalization process of the two frequency domain equalization processes performs second equalization using second filter coefficients updated by a second filter coefficient updating method, and the second filter coefficient updating method includes: inputting estimation error information of the signal estimation method, the auxiliary signal updated by the signal estimation method, and the first filter coefficients; generating update information for the second filter coefficients from the estimation error information and the auxiliary signal, and updating the estimation error information by nonlinear processing using the estimation error information, the auxiliary signal, and the first filter coefficients; and updating the second filter coefficients by subtracting an amount based on the update information for the second filter coefficients generated by the predetermined number of repetitions from the second filter coefficients.[Supplementary Note 10] A recording medium having recorded thereon 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 signal estimation method comprising: inputting the plurality of received signals; initializing an auxiliary signal; using the plurality of received signals and the auxiliary signal, performing two frequency domain equalization processes that convert each of the received signals and the auxiliary signal into the frequency domain and perform equalization, thereby generating an estimation result for the plurality of transmitted signals, and updating the auxiliary signal by nonlinear processing using the auxiliary signal and the estimation result, a predetermined number of times; and using the final estimation result in the predetermined number of repetitions as the estimation result for the plurality of transmitted signals.

[0117] 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 a signal estimation device, a signal estimation method, and a recording medium that involve such modifications are also included in the technical idea of ​​the present invention.

[0118] REFERENCE SIGNS LIST 1 Transmitter 11 Signal processing device 2 Receiving device 21, 21a, 21b Signal processing device 23 MIMO equalization unit 231 First MIMO equalization processing unit 2311 Discrete Fourier transform device 2312 Multiplier 2313 Inverse discrete Fourier transform device 232 Second MIMO equalization processing unit 2321 Discrete Fourier transform device 2322 Multiplier 2323 Adder 2324 Inverse discrete Fourier transform device 233 Nonlinear transformer 234 Adder 235 Adder 4 Coefficient update device 41 Signal processing device 411 First filter coefficient update device 411M Coefficient memory 411a Update information generation unit 411b Filter coefficient update unit 4111 Discrete Fourier transform device 4112 Multiplier 4113 Inverse discrete Fourier transform device 4114 Adder 4115 Discrete Fourier transform device 4116 Converter 4117 Multiplier 4118 Weighting device 4119 Adder 412, 412a, 412b Second filter coefficient update device 412M Coefficient memory 413 Error propagation unit 4131 Discrete Fourier transform device 4132 Converter 4133 Multiplier 4134 Converter

Claims

1. A signal estimation device that estimates a plurality of transmitted signals respectively corresponding to a plurality of spatially multiplexed received signals, the signal estimation device comprising a signal estimation unit having two frequency domain equalizers and one nonlinear transformer that performs a nonlinear transformation, the signal estimation device performs R (R is a preset positive integer) signal estimation operations using the signal estimation unit, the signal estimation device generates, in the r (r is a positive integer not greater than R)-th signal estimation operation of the R signal estimation operations, a plurality of estimated signals that are the rth tentative estimation results of the plurality of transmitted signals, and the auxiliary signal used in the r+1th signal estimation operation, from the plurality of received signals and an auxiliary signal generated in the r-1th signal estimation operation, and the signal estimation device sets the plurality of estimated signals generated in the Rth signal estimation operation as estimation results of the plurality of transmitted signals.

2. The signal estimation device according to claim 1, wherein each of said two frequency domain equalizers comprises a discrete Fourier transform device, a multiplier, and an inverse discrete Fourier transform device.

3. The signal estimation device according to claim 1, wherein the signal estimation unit: generates a first auxiliary signal and a second auxiliary signal as the auxiliary signal; generates the multiple estimated signals in the r-th signal estimation operation from the multiple received signals and the first auxiliary signal generated in the r-1th signal estimation operation; and uses the nonlinear converter to update the first auxiliary signal and the second auxiliary signal from the multiple estimated signals generated in the r-th signal estimation operation and the second auxiliary signal generated in the r-1th signal estimation operation, to generate the first auxiliary signal and the second auxiliary signal to be used in the r+1th signal estimation operation.

4. The signal estimation device according to claim 1, wherein a first frequency domain equalizer of the two frequency domain equalizers provided in the signal estimation unit performs a first equalization process using a first filter coefficient updated by a first filter coefficient updating device, and the first filter coefficient updating device uses a frequency domain equalizer to generate replicas of the multiple received signals from an input signal related to the multiple transmitted signals, generates update information for the first filter coefficient from a difference between the replica and the multiple received signals and the input signal, and updates the first filter coefficient by subtracting the update information for the first filter coefficient from the first filter coefficient. The input signal is the multiple transmitted signals or a signal related to an estimation result of the multiple transmitted signals.

5. A second frequency domain equalizer of the two frequency domain equalizers provided in the signal estimation unit performs a second equalization process using a second filter coefficient updated by a second filter coefficient updating device, the second filter coefficient updating device comprising an error propagation unit and a coefficient updating unit, the error propagation unit: performs an update information generating operation R times, including generating update information for the second filter coefficient using an error signal, which is a difference between an estimation result of the plurality of transmission signals by the signal estimation device and the input signal, the auxiliary signal, and the first filter coefficient, and updating the error signal; in the r-th update information generating operation in the R update information generating operations, generates an r-th update information for the second filter coefficient from the error signal and the auxiliary signal updated in the r-1-th update information generating operation; and updates the error signal used in the r+1-th update information generating operation from the error signal, the auxiliary signal, and the first filter coefficient updated in the r-1-th update information generating operation by nonlinear processing; 5. The signal estimation device according to claim 4, wherein the coefficient update unit updates the second filter coefficient by subtracting an amount based on each of the R pieces of update information for the second filter coefficient generated by the R update information generation operations from the second filter coefficient.

6. The signal estimation device according to claim 5, wherein a first discrete Fourier transform device included in the first frequency domain equalizer performs a discrete Fourier transform on the first auxiliary signal, a first multiplier included in the first frequency domain equalizer performs a first multiplication process using the first filter coefficient and a processing result of the first discrete Fourier transform device, a first inverse discrete Fourier transform device included in the first frequency domain equalizer performs an inverse discrete Fourier transform on a result of the first multiplication process, a second discrete Fourier transform device included in the second frequency domain equalizer performs a discrete Fourier transform on a difference between an output of the first frequency domain equalizer and the multiple received signals, a second multiplier included in the second frequency domain equalizer performs a second multiplication process using the second filter coefficient and a processing result of the second discrete Fourier transform device, and a second inverse discrete Fourier transform device included in the second frequency domain equalizer performs an inverse discrete Fourier transform on a result of the second multiplication process.

7. A signal estimation method for estimating a plurality of transmission signals respectively corresponding to a plurality of spatially multiplexed received signals from the plurality of received signals, the signal estimation method comprising: repeating a predetermined number of the steps of: inputting the plurality of received signals; initializing an auxiliary signal; using the plurality of received signals and the auxiliary signal, performing two frequency domain equalization processes for converting each of the signals into the frequency domain and equalizing them, to generate estimation results for the plurality of transmission signals, and updating the auxiliary signal by nonlinear processing using the auxiliary signal and the estimation results; and setting the final estimation result in the predetermined number of repetitions as the estimation result for the plurality of transmission signals.

8. A signal estimation method according to claim 7, wherein a first frequency domain equalization process of the two frequency domain equalization processes performs a first equalization process using a first filter coefficient updated by a first filter coefficient updating method, the first filter coefficient updating method including: inputting an input signal related to the plurality of transmitted signals and the plurality of received signals; generating a replica of the plurality of received signals by frequency domain equalization process using the input signal; generating update information for the first filter coefficient using a difference between the replica and the plurality of received signals and the input signal; and updating the first filter coefficient by subtracting the update information for the first filter coefficient from the first filter coefficient, and the input signal is a signal related to the plurality of transmitted signals or an estimation result of the plurality of transmitted signals.

9. A signal estimation method according to claim 8, wherein a second frequency domain equalization process of the two frequency domain equalization processes performs a second equalization process using second filter coefficients updated by a second filter coefficient updating method, and the second filter coefficient updating method includes: inputting estimated error information of the signal estimation method, the auxiliary signal updated by the signal estimation method, and the first filter coefficients; generating update information for the second filter coefficients from the estimated error information and the auxiliary signal, and updating the estimated error information by nonlinear processing using the estimated error information, the auxiliary signal, and the first filter coefficients; repeating the above steps a predetermined number of times; and updating the second filter coefficients by subtracting an amount based on the update information for the second filter coefficients generated by the predetermined number of repetitions from the second filter coefficients.

10. 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 respectively corresponding to a plurality of spatially multiplexed reception signals, the signal estimation method including: inputting the plurality of reception signals; initializing an auxiliary signal; using the plurality of reception signals and the auxiliary signal, generating an estimation result for the plurality of transmission signals by two frequency domain equalization processes that convert each of the plurality of reception signals and the auxiliary signal into the frequency domain and perform equalization, and updating the auxiliary signal by nonlinear processing using the auxiliary signal and the estimation result, a predetermined number of times; and setting the final estimation result in the predetermined number of repetitions as the estimation result for the plurality of transmission signals.

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