Wireless receiving device, method executed by wireless receiving device, and program

Abstract

To provide a device, method, and program that contribute to accurately performing multi-user detection while reducing a computation amount.SOLUTION: A wireless receiving device decomposes a channel matrix defined between transmission antennas of one or more wireless transmitting devices and reception antennas coupled to the wireless receiving device into a left singular matrix U, a singular value matrix Σ, and a right singular matrix V through singular value, generates a diagonal matrix Σ' by using the singular value matrix Σ and an arbitrary diagonal matrix A, generates a replica vector x^ by using a received signal vector y' obtained by applying reception beamforming to the received signal from each of the reception antennas by using the left singular matrix U and a linear filter W generated using the right singular matrix V and the diagonal matrix Σ', and executes a nonlinear signal detection algorithm by using the received signal vector y' and the replica vector x^.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present disclosure relates to a wireless receiving device, and a method and program executed by the wireless receiving device. [Background technology]

[0002] As a method for realizing high-capacity communication, large-scale multi-user multi-input multi-output (MIMO) is known, which performs wireless communication with multiple users using a base station with many antennas. Large-scale multi-user MIMO is also called massive MIMO. Large-scale multi-user MIMO can be used, for example, in the uplink of a multiple access cellular system such as a fifth generation mobile communication (5G) system. A receiver of a large-scale multi-user MIMO needs to perform multi-user detection to separate multi-user signals from a received signal. A 5G base station is composed of a Distributed Unit (DU) and a Central Unit (CU), which are mainly responsible for digital baseband signal processing, and a Radio Unit (RU), which is mainly responsible for Radio Frequency (RF) signal processing for transmitting and receiving wireless signals. Generally, multi-user detection is performed in the DU. At this time, the received signal received in the RU needs to be transmitted to the DU via the fronthaul that connects the RU and the DU. However, in massive multi-user MIMO, wireless signals are received by a large number of antennas, which means that a large number of received signals need to be transmitted via the fronthaul, and this necessitates a wideband fronthaul band connecting the RU and DU.

[0003] A known multi-user detection algorithm is the QR-decomposed Gaussian Belief Propagation (QR-GA-BP) algorithm (see Non-Patent Document 1). The QR-GA-BP algorithm decomposes an N×M (i.e., N rows and M columns) channel matrix defined between M transmitting antennas of one or more wireless transmitting devices and N receiving antennas of a wireless receiving device into an N×M matrix Q and an M-th order upper triangular matrix, in which each column is orthogonal, using QR decomposition. The QR-GA-BP algorithm performs receive beamforming by calculating the matrix product of the Hermitian conjugate of the generated matrix Q and a receive signal vector consisting of the received signals of each antenna, N×1. The QR-GA-BP algorithm then detects the transmitted signal by applying the GaBP (Gaussian Belief Propagation) algorithm to the received signal after receive beamforming. The QR-GA-BP algorithm uses the fact that the channel matrix after receive beamforming is an upper triangular matrix to perform interference removal and belief generation in order of the received signal that contains the fewest transmitted signal components. In the first step, the QR-GA-BP algorithm generates beliefs and replicas using the GaBP algorithm for received signals that contain only one transmitted signal component. In the mth step thereafter, the QR-GA-BP algorithm applies the GaBP algorithm to perform interference removal, belief generation, and replica generation using the (m-1) received signals used in the (m-1)th step, the received signal having m transmitted signal components, and the beliefs and replicas generated in the (m-1)th step. Due to the nature of the upper triangular matrix, the mth received signal contains only the 1st to mth transmitted signal components, so when m is small, the accuracy of the scalar Gaussian approximation according to the central limit theorem deteriorates. Therefore, if the QR-GA-BP algorithm performs belief generation for all received signals simultaneously, accurate beliefs will not be generated. Therefore, the QR-GA-BP algorithm performs detection in order starting from the first received signal without interference, and interference cancellation is performed on the mth transmitted signal component using the first to (m-1)th transmitted signal components that are generated with high accuracy.Therefore, the beliefs and replicas for the m-th transmitted signal component are generated with high accuracy. If completing the above steps for all received signals is considered as one set, the QR-GA-BP algorithm gradually improves the detection accuracy by repeating multiple sets. In addition, by using receive beamforming, the number of received signals transmitted from the RU to the DU via the fronthaul is reduced, thereby reducing the fronthaul bandwidth.

[0004] Another known multi-user detection is K-neighborhood search for zero forcing solution (K-NSF ZF) (see Non-Patent Document 2). K-NSF ZF is a search-type algorithm that generates a replica using a ZF filter, which is a pseudo-inverse matrix of a channel matrix, and uses the generated replica as the initial value of a signal search. K-NSF ZF searches for a candidate vector with the smallest square error between the product of the channel matrix and the candidate vector and the received signal among candidate vectors in which K or less vector elements have changed among vector elements that serve as the initial value of the search. When starting processing from a random initial value, K needs to be set to a very large value in order for K-NSF ZF to search for the optimal signal. Therefore, a huge amount of calculation is required for the search, especially when the number of transmitting antennas is large. On the other hand, K-NSF ZF can start the search from the vicinity of the optimal candidate vector by generating an initial value using ZF, so that the amount of calculation required for the search can be reduced.

[0005] Another known multi-user detection method includes receive beamforming using singular value decomposition, replica generation by ZF, and signal detection by GaBP (see Patent Document 1). The method described in Patent Document 1 has features of both the QR-GA-BP algorithm described in Non-Patent Document 1 and the K-NSF ZF described in Non-Patent Document 2. The QR-GA-BP algorithm described in Non-Patent Document 1 can reduce the fronthaul bandwidth using receive beamforming, but has a problem of long execution time because many iterations are required for multi-user detection. The K-NSF ZF described in Non-Patent Document 2 can reduce the amount of calculation by replicas generated using linear filters, but requires a wide fronthaul bandwidth because the signal received by the receiving antenna is transmitted directly from the RU to the DU. However, the GaBP algorithm described in Patent Document 1 can detect the transmission signal with high accuracy by repeating soft interference removal, belief generation, and soft replica generation. [Prior art documents] [Patent documents]

[0006] [Patent Document 1] JP 2023-037446 A [Non-patent literature]

[0007] [Non-Patent Document 1] S. Tanabe, AD Shigyo, and K. Ishibashi, “Not-so-large MIMO signal detection based on damped QR-decomposed belief propagation,” 2016 International Symposium on Information Theory and Its Applications (ISITA), pp. 463-467, 2016. [Non-Patent Document 2] M. Chaudhary, NK Meena, and RS Kshetrimayum, “Local search based near optimal low complexity detection for large MIMO system,” 2016 IEEE International Conference on Advanced Networks and Telecommunications Systems (ANTS), pp. 1-5, 2016. Summary of the Invention [Problem to be solved by the invention]

[0008] In the method described in Patent Document 1, noise enhancement occurs due to ZF, so it is expected that the accuracy of multiuser detection will be lower than when replicas are generated by Minimum Mean Square Error (MMSE). On the other hand, when replicas are generated using MMSE to improve detection accuracy, the method described in Patent Document 1 cannot be used. Therefore, since an inverse matrix operation is required to generate an MMSE filter, it is expected that the amount of calculation will increase.

[0009] One of the objectives that the embodiments of the present disclosure aim to achieve is to provide an apparatus, a method, and a program that contribute to performing multi-user detection with high accuracy while suppressing the amount of calculation. It should be noted that this objective is only one of the objectives that the embodiments disclosed herein aim to achieve. Other objectives or problems and novel features will be apparent from the description of this specification or the accompanying drawings. [Means for solving the problem]

[0010] In a first aspect, a wireless receiving device includes a singular value decomposer, a diagonal matrix corrector, a replica generator, and a nonlinear detector. The singular value decomposer is configured to singular value decompose an N×M channel matrix defined between M transmitting antennas of one or more wireless transmitting devices and N receiving antennas coupled to the wireless receiving device into an N×M left singular matrix U, a singular value matrix Σ that is an M-th order diagonal matrix, and an M×M right singular matrix V. The diagonal matrix corrector is configured to generate a diagonal matrix Σ' by using the singular value matrix Σ and an arbitrary diagonal matrix A. The replica generator is configured to generate a replica vector x̂ by using a received signal vector y' obtained by performing receive beamforming on the received signal of each of the receiving antennas by using the left singular matrix U, and a linear filter W generated by using the right singular matrix V and the diagonal matrix Σ'. The nonlinear detector is configured to execute a nonlinear signal detection algorithm by using the received signal vector y' and the replica vector x̂.

[0011] In a second aspect, a method performed by a wireless receiving device includes: (a) performing singular value decomposition of an N×M channel matrix defined between M transmitting antennas of one or more wireless transmitting devices and N receiving antennas coupled to the wireless receiving device into an N×M left singular matrix U, a singular value matrix Σ that is an M-th order diagonal matrix, and an M×M right singular matrix V; (b) generating a diagonal matrix Σ′ by using the singular value matrix Σ and an arbitrary diagonal matrix A; (c) generating a replica vector x^ using a received signal vector y' obtained by performing receive beamforming on the received signals of each of the receiving antennas using the left singular matrix U, and a linear filter W generated using the right singular matrix V and the diagonal matrix Σ'; (d) performing a nonlinear signal detection algorithm using the received signal vector y' and the replica vector x̂;

[0012] In a third aspect, a program includes instructions (software code) for causing a computer to carry out the method according to the second aspect when the program is loaded into the computer. Effect of the Invention

[0013] According to the above-described aspects, it is possible to provide an apparatus, a method, and a program that contribute to performing multiuser detection with high accuracy while suppressing the amount of calculation. [Brief description of the drawings]

[0014] [Figure 1] FIG. 1 illustrates an example of a wireless receiving device according to an embodiment; [Diagram 2] 5 is a flowchart illustrating an example of an operation of the wireless receiving device according to the embodiment. [Diagram 3] FIG. 1 illustrates an example of a wireless communication system according to an embodiment. [Figure 4] FIG. 2 is a diagram illustrating an example of a system model according to an embodiment. [Diagram 5] FIG. 2 is a diagram illustrating a configuration example of a base station according to an embodiment; [Figure 6] FIG. 2 illustrates an example of a configuration of a processor of a base station according to an embodiment; [Figure 7] FIG. 2 illustrates an example of a configuration of a processor of a base station according to an embodiment; [Figure 8] FIG. 2 is a diagram illustrating a configuration example of a parallel interference cancellation according to an embodiment; [Figure 9] FIG. 2 is a diagram illustrating an example of a configuration of maximum likelihood detection according to an embodiment; [Figure 10] FIG. 1 illustrates an example of a configuration of a belief propagation method according to an embodiment; [Figure 11] 10 is a flowchart illustrating an example of an operation of a base station according to an embodiment. [Figure 12] FIG. 13 illustrates bit error rate performance of a nonlinear detector according to an embodiment. [Figure 13] 1 is a block diagram showing an example of a hardware configuration of an information processing device in which the process of an embodiment is executed; DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0015] In the following, specific embodiments will be described in detail with reference to the drawings. In each drawing, the same or corresponding elements are given the same reference numerals, and duplicated explanations will be omitted as necessary for clarity of explanation. It goes without saying that the text explanations in each embodiment and the drawings referred to for the explanations can also be applied to other embodiments. Furthermore, in this disclosure, unless otherwise specified, when "at least any of" is defined for multiple items, the definition may mean any one item or any multiple items (including all items).

[0016] First embodiment [Configuration Description] Hereinafter, a first embodiment will be described with reference to the drawings. FIG. 1 is a block diagram showing an example of a wireless receiving device. The wireless receiving device R includes a singular value decomposer R1, a diagonal matrix corrector R2, a replica generator R3, and a nonlinear detector R4. The wireless receiving device R is configured as a part of a base station, for example, but the device in which the wireless receiving device R is mounted is not limited to this. Each part (each means) of the wireless receiving device R is controlled by a control unit (controller) not shown. Each part of the wireless receiving device R will be described below.

[0017] The singular value decomposer R1 performs singular value decomposition on an N×M channel matrix defined between M transmitting antennas of one or more wireless transmitting devices and N receiving antennas coupled to the wireless receiving device R into the following three components. The three components are an N×M left singular matrix U, a singular value matrix Σ which is an M-th order diagonal matrix, and an M×M right singular matrix V. Here, the wireless transmitting device is a device that transmits a signal to the wireless receiving device R. In addition, the N receiving antennas may be included in the wireless receiving device R, or may be configured as a device separate from the wireless receiving device R.

[0018] The diagonal matrix corrector R2 is configured to generate a diagonal matrix Σ′ by using a singular value matrix Σ obtained as a result of the singular value decomposition and an arbitrary diagonal matrix A.

[0019] The replica generator R3 is configured to generate a replica vector x^ by using a received signal vector y' and a linear filter W. Here, the received signal vector y' is a signal vector obtained by performing receive beamforming on the received signals of each receiving antenna by using a left singular matrix U obtained as a result of singular value decomposition. In addition, the linear filter W is generated by using a right singular matrix V and a diagonal matrix Σ'. Here, the generation of the received signal vector y' may be performed within the wireless receiving device R or may be performed outside the wireless receiving device R. In addition, the generation of the linear filter W may also be performed within the wireless receiving device R or may be performed outside the wireless receiving device R.

[0020] The nonlinear detector R4 is configured to execute a nonlinear signal detection algorithm using the received signal vector y' and the replica vector x̂. The nonlinear detector R4 may output a result of the executed nonlinear signal detection algorithm.

[0021] [Explanation of operation] FIG. 2 is a flowchart showing an example of a representative process of the wireless receiving device R, and the outline of the process of the wireless receiving device R will be described with reference to this flowchart.

[0022] First, the singular value decomposer R1 performs singular value decomposition on the N×M channel matrix to generate an N×M left singular matrix U, a singular value matrix Σ which is an M-th order diagonal matrix, and an M×M right singular matrix V (step S11). Next, the diagonal matrix corrector R2 generates a diagonal matrix Σ' by using the singular value matrix Σ and an arbitrary diagonal matrix A (step S12).

[0023] The replica generator R3 generates a replica vector x̂ by using the received signal vector y' and the linear filter W (step S13). The nonlinear detector R4 executes a nonlinear signal detection algorithm by using the received signal vector y' and the replica vector x̂ (step S14).

[0024] [Effect description] Next, the effects of this embodiment will be described. The wireless receiving device R according to this embodiment generates a linear filter W by using a right singular matrix V and a diagonal matrix Σ generated by using singular value decomposition. The calculation for generating this linear filter W is a relatively easy calculation such as an inverse matrix calculation of a diagonal matrix or a matrix multiplication of a diagonal matrix and a square matrix. In addition, the calculation result for receiving beamforming is used in the singular value decomposition. Therefore, the amount of calculation required for generation can be suppressed. In addition, by using the generated linear filter W, highly accurate multiuser detection is possible.

[0025] Embodiment 2 Hereinafter, the second embodiment will be described in detail with reference to the drawings. The second embodiment discloses a specific example of the wireless receiving device described in the first embodiment, but the specific example of the wireless receiving device shown in the first embodiment is not limited to the one shown below. Furthermore, the configurations and processes described below are examples and are not limited to these. All or any part of the configurations described in the second embodiment can be appropriately applied to the wireless receiving device described in the first embodiment, and it goes without saying that the drawings shown in the second embodiment can be appropriately applied to the first embodiment.

[0026] [Configuration Description] FIG. 3 shows an example of the configuration of a wireless communication system. Referring to FIG. 3, a base station 1 provides wireless access to a plurality of wireless terminals 2. The base station 1 may be referred to as an access point, a transmission / reception point (TRP), or other names. The base station 1 may be, for example, a gNB of a 5G system, or may be a system including an RU and a DU. The RU may perform RF signal processing and some physical layer or layer 1 (e.g., Low PHY) signal processing. The physical layer signal processing performed by the RU may include, for example, digital beamforming. The DU may perform the remaining physical layer (e.g., High PHY) signal processing and layer 2 signal processing. The RU and the DU are connected via a fronthaul. The fronthaul is also called a mobile fronthaul or a (mobile) fronthaul network. For example, the fronthaul may be a wired fronthaul using one or more optical fibers, or a wireless fronthaul using millimeter wave wireless transmission.

[0027] In some implementations, the wireless communication system may utilize a multi-user MIMO technique for uplink transmission from multiple wireless terminals 2 to the base station 1. In this case, the base station 1 may receive reference signals from the multiple wireless terminals 2, estimate MIMO channels between the multiple wireless terminals 2 and the base station 1 using the received reference signals, and detect transmission signals using data signals received from the multiple wireless terminals 2 and the estimated channels. That is, the base station 1 may perform multi-user detection to separate the multi-user signals of the multiple wireless terminals 2.

[0028] FIG. 4 shows an example of a system model of uplink multi-user MIMO transmission. In FIG. 4, multiple transmitters 20 of multiple wireless terminals 2 communicate with a receiver 10 of a base station 1 via a channel (propagation path) 30. In the example of FIG. 4, each of the M transmitters 20 has one transmit antenna. Alternatively, each transmitter 20 may have two or more transmit antennas. The receiver 10 of the base station 1 has N receive antenna elements (hereinafter, also simply referred to as receive antennas). The total number M of transmit antennas is assumed to be less than or equal to the total number N of receive antennas.

[0029] In the following description, for simplicity, it is assumed that the transmission signal from each wireless terminal 2 (user) is a single carrier transmission, and the propagation path between each wireless terminal 2 and the base station 1 is flat fading. On the other hand, even in a multipath fading environment in which the transmission signal from each user uses Orthogonal Frequency Division Multiplexing (OFDM) or Single Carrier-Frequency Division Multiple Access (SC-FDMA), the transmission path can be regarded as flat fading in each subcarrier unit by inserting a cyclic prefix of an appropriate length into the transmission signal. Therefore, this embodiment may be applied to OFDM and SC-FDMA.

[0030] Assume that a transmission signal modulated by Quadrature Amplitude Modulation (QAM) is transmitted from a total of M transmission antennas of a plurality of wireless terminals 2 and is received at a base station 1 equipped with N reception antennas. In this case, a complex signal model based on an equivalent low-pass expression is expressed by Equation 1:

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[0031] The number of modulation symbols in QAM modulation is Q. For example, Q is 4 for Quadrature Phase Shift Keying (QPSK) and 16 for 16QAM. The amplitude of the modulation symbols is {-c, +c} for the I axis and the Q axis for QPSK and {-3c, -c, +c, +3c} for 16QAM. Here, c is expressed by the following formula 2. E s is the average signal power. The power of the complex noise at each receiving antenna is N 0 Let us assume that.

number

[0032] Fig. 5 shows an example of the configuration of the base station 1. Referring to Fig. 5, the base station 1 includes an RU 11-1 and a DU 11-2. The RU 11-1 includes a Radio Frequency (RF) transceiver 13, a processor 14-1, and a memory 15, and is connected to the antenna array 12. The DU 11-2 includes a processor 14-2, a memory 15, and a network interface 16.

[0033] The RF transceiver 13 performs analog RF signal processing to communicate with multiple wireless terminals 2. The RF transceiver 13 may include multiple transceivers. The RF transceiver 13 is coupled to the antenna array 12, the processor 14-1 in the RU 11-1, and the processor 14-2 in the DU 11-2. The RF transceiver 13 receives modulation symbol data from the processor 14-1 in the RU 11-1, generates a transmission RF signal, and provides the transmission RF signal to the antenna array 12. The RF transceiver 13 also generates a baseband reception signal based on the reception RF signal received by the antenna array 12, and provides the reception signal to the processor in the DU 11-2 if the reception signal is a reference signal, or to the processor 14-1 in the RU 11-1 if the reception signal is a data signal.

[0034] The processors 14-1 and 14-2 perform digital baseband communication processing (data plane processing) and control plane processing for wireless communication. The processors 14-1 and 14-2 may include multiple processors. For example, the processors 14-1 and 14-2 may include a modem processor (e.g., Central Processing Unit (CPU), Graphics Processing Unit (GPU), or Digital Signal Processor (DSP)) that performs digital baseband signal processing and a protocol stack processor (e.g., Central Processing Unit (CPU) or Micro Processing Unit (MPU)) that performs control plane processing.

[0035] For example, the digital baseband signal processing by the processors 14-1 and 14-2 may include signal processing of the Service Data Adaptation Protocol (SDAP) layer, the Packet Data Convergence Protocol (PDCP) layer, the Radio Link Control (RLC) layer, the Medium Access Control (MAC) layer, and the Physical (PHY) layer. Also, the control plane processing by the processors 14-1 and 14-2 may include processing of Non-Access Stratum (NAS) messages, Radio Resource Control (RRC) messages, Medium Access Control (MAC) Control Elements (CEs), and Downlink Control Information (DCI).

[0036] The network interface 16 is used to communicate with network nodes (e.g., other base stations, a Centralized Unit (CU), and a core network node). The network interface 16 may include, for example, a network interface card (NIC) that complies with the IEEE 802.3 series.

[0037] The memory 15 is composed of a combination of volatile and non-volatile memory. The volatile memory is, for example, Static Random Access Memory (SRAM) or Dynamic RAM (DRAM), or a combination thereof. The non-volatile memory is, for example, Mask Read Only Memory (MROM), Electrically Erasable Programmable ROM (EEPROM), flash memory, or a hard disk drive, or any combination thereof. The memory 15 may include storage located remotely from the processors 14-1 and 14-2. In this case, the processors 14-1 and 14-2 may access the memory 15 via a network interface 16 or other I / O interface.

[0038] The memory 15 may include a computer-readable medium storing one or more software modules (computer programs) including instructions and data for performing at least a part of the processing by the base station 1. In some implementations, the processors 14-1 and 14-2 may be configured to read the software modules from the memory 15 and execute them to perform at least a part of the processing by the base station 1 described in the above-mentioned embodiments.

[0039] According to this embodiment, the processors 14-1 and 14-2 can cause the base station 1 to perform received signal processing for receive beamforming and multi-user detection (MIMO detection). To that end, as shown in Fig. 6, the processor 14-1 in the RU 11-1 can include a beamformer 143, and the processor 14-2 in the DU 11-2 can include a channel estimator 141, a singular value decomposer 142, a diagonal matrix corrector 144, a linear filter generator 145, a replica generator 146, a nonlinear detector 147, and a decision / demodulator 148.

[0040] The channel estimator 141 estimates a MIMO channel based on a reference signal received from the RF transceiver 13. The channel estimator 141 is coupled to the singular value decomposer 142, and supplies an estimated N×M channel matrix H to the singular value decomposer 142. An example of the reference signal here may be, but is not limited to, a sounding reference signal (SRS).

[0041] The singular value decomposer 142 performs singular value decomposition on the channel matrix H received from the channel estimator 141 to generate a left singular matrix U, a singular value matrix Σ, and a right singular matrix V. The singular value decomposer 142 is coupled to the beamformer 143, the diagonal matrix corrector 144, and the linear filter generator 145, and provides the left singular matrix U to the beamformer 143, the singular value matrix Σ to the diagonal matrix corrector 144, and the right singular matrix V to the linear filter generator 145. In addition, as shown in FIG. 7, the singular value decomposer 142 may be coupled to a nonlinear detector 147 to provide the singular value matrix Σ and the right singular matrix V to the nonlinear detector 147.

[0042] For example, as shown in Equation 3, the singular value decomposer 142 performs singular value decomposition of an N×M channel matrix H into a left singular matrix U which is an N×M matrix, a singular value matrix Σ which is an M-th diagonal matrix, and a right singular matrix V which is an M×M matrix. Here, as shown in Equation 4 and Equation 5, the left singular matrix U is a submatrix of a unitary matrix, and the right singular matrix V is a unitary matrix. The column vectors formed by the m-th columns of the left singular matrix U and the right singular matrix V are respectively the m-th diagonal elements σ of the singular value matrix. m The left singular vector u corresponding to m and the right singular vector v m It is.

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[0043] The beamformer 143 performs receive beamforming on a receive signal vector y composed of the receive signals of each receive antenna supplied from the RF transceiver 13. As shown in Equation 6, receive beamforming is performed by setting the Hermitian conjugate of the left singular matrix U received from the singular value decomposer 142 as a receive beamforming weight and calculating the product of the receive signal vector y and the receive beamforming weight. The beamformer 143 is coupled to the replica generator 146 and the nonlinear detector 147, and supplies the receive signal vector y' subjected to receive beamforming via the fronthaul.

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[0044] The diagonal matrix corrector 144 generates a diagonal matrix Σ' using the singular value matrix Σ supplied from the singular value decomposer 142 and an arbitrary diagonal matrix A. The diagonal matrix corrector 144 is coupled to the linear filter generator 145 and supplies the diagonal matrix Σ' to the linear filter generator 145. The diagonal matrix Σ' is generated by adding the diagonal matrix A to the singular value matrix Σ as shown in Equation 7.

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[0045] The linear filter generator 145 generates a linear filter W using the right singular matrix V provided from the singular value decomposer 142 and the diagonal matrix Σ′ provided from the diagonal matrix corrector 144. The linear filter generator 145 is coupled to the replica generator 146 and provides the linear filter W to the replica generator 146. The linear filter W is generated using the product of the right singular matrix V and the inverse matrix of the diagonal matrix Σ′, as shown in Equation 10.

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[0046] The replica generator 146 performs receive beamforming and applies the linear filter W supplied from the linear filter generator 145 to the received signal vector y′ supplied from the beamformer 143 to generate the following replica vector.

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[0047] The replica generator 146 generates the conditional expectation x^' and the conditional variance Ψ' calculated using the replica vector x^ instead of the replica vector x^ shown in Equation 12. m may be fed to the nonlinear detector 147. In this case, the conditional expectation value x̂′ and the conditional variance value Ψ′ m may be calculated as shown in Equations 13 and 14.

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[0048] Furthermore, when the nonlinear detector 147 executes Vector Approximate Message Passing (VAMP), the replica vector x̂'' and the variance Ψ'' of the replica vector after moment matching may be supplied to the nonlinear detector 147. The replica vector x̂'' and the variance Ψ'' of the replica vector are expressed as the following Equations 15 and 16.

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[0049] As an implementation example, the probability distribution p m (d; x^) is the replica vector x^ with scalar Gaussian approximation (SGA) applied to the components other than the desired signal. m In this case, the variance of the complex Gaussian distribution s m 2 may be an interference noise power obtained by calculation using a linear filter W as shown in Equation 17.

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[0050] Another implementation example is the probability distribution p m (d;x^) may be a probability distribution shown in Equation 18, in which vector Gaussian approximation (VGA) is performed on components other than the desired signal contained in the replica vector x^.

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[0051] The nonlinear detector 147 executes a nonlinear signal detection algorithm using the replica vector x^ supplied from the replica generator 146 for the received signal vector y' after receive beamforming supplied from the beamformer 143. The nonlinear detector 147 may further use the singular value matrix Σ and right singular matrix V supplied from the singular value decomposer 142 and the linear filter W supplied from the linear filter generator 145 in the nonlinear signal detection algorithm. The nonlinear detector 147 is coupled to the decision / demodulator 148, and supplies the detected signal vector of Equation 20 detected by the nonlinear signal detection algorithm to the decision / demodulator 148.

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[0052] In one implementation, the detected signal vector x− is detected using parallel interference cancellation, where the nonlinear detector 147 includes an interference canceller 41 and a transmitted signal detector 42 as shown in FIG.

[0053] The interference canceller 41 generates the vector shown in Equation 21 by canceling interference signals other than the m-th transmission signal component from the received signal vector y′ that has been subjected to receive beamforming.

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[0054] The transmitted signal detector 42 detects the interference-removed received signal vector y′. m and the m-th detected signal x- m The transmitted signal is detected as the m-th column vector h′ of the channel matrix subjected to receive beamforming, as shown in Equation 25. m and the Hermitian conjugate of the interference-removed received signal vector y~' m It is expressed as the product of and.

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[0055] In another implementation, the detected signal vector x is detected using maximum likelihood detection. In maximum likelihood detection, the candidate signal vector x that has the smallest squared error e is selected as shown in Equation 26. cand is detected as the detection signal vector x-.

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[0056] The candidate generator 51 generates a vector obtained by changing the vector element of the replica vector x^ supplied from the replica generator by up to K bits, and generates the candidate signal vector x cand The candidate generator 51 is coupled to a transmitted signal detector 52 and supplies the transmitted signal detector 52 with a candidate signal vector x cand Here, when the modulation method is QPSK, there are four possible values ​​for the vector elements: -c-cj, -c+cj, c-cj, and c+cj. For example, when the vector element of the replica vector is c+cj, compared with c+cj, -c+cj and c-cj are vector elements in which a 1-bit change has occurred, and -c-cj is a vector element in which a 2-bit change has occurred. The candidate generator 51 can sum up the number of changed bits in all vector elements to find the change from the replica vector. When K is 1, 2M candidate signal vectors are generated.

[0057] The transmitted signal detector 52 calculates the squared error e for all the candidate signal vectors in the set X supplied from the candidate generator 51, as shown in Equation 27, and selects the candidate signal vector x with the smallest squared error e. cand Determine.

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[0058] In another implementation, the detection signal vector x- is detected using belief propagation, which is an iterative algorithm including a soft interference remover 61, a belief generator 62, and a soft replica generator 63, as shown in FIG.

[0059] The soft interference canceller 61 uses the soft replica generated in the previous iteration step to cancel interference signal components from the received signal vector y' subjected to receive beamforming. The soft interference canceller 61 is coupled to the belief generator 62, and supplies the received signal from which interference has been cancelled to the belief generator 62. Here, in the first iteration step, the soft interference canceller 61 cancels interference using the replica vector x^ generated by the replica generator 146. The soft interference canceller 61 performs the first interference cancellation using the replica vector x^, and therefore can perform interference cancellation with high accuracy even in the first interference cancellation.

[0060] The belief generator 62 generates a belief, which is transmission signal information, from the interference-removed received signal supplied from the soft interference canceller 61. The belief generator 62 is coupled to the soft replica generator 63, and supplies the belief to the soft replica generator 63.

[0061] The soft replica generator 63 generates a soft replica by using the beliefs shared by the belief generator 62. The soft replica generator 63 is coupled to the soft interference canceller 61, and supplies a soft replica to the soft interference canceller 61. The soft replica generator 63 generates the soft replica by combining the beliefs supplied from the belief generator 62 for each transmitting antenna.

[0062] When the belief propagation algorithm is GAMP, the residual interference signal component and noise component of the received signal from which interference has been removed are approximated by scalar Gaussian approximation (SGA) using the central limit theorem. Therefore, the base station 1 can perform multi-user detection with a reduced amount of calculation.

[0063] Furthermore, when the belief propagation algorithm is VAMP, the nonlinear detector 147 performs multi-user detection by applying the singular value matrix Σ, the right singular matrix V, and the replica vector x̂ to the received signal vector y′ to execute a nonlinear signal detection algorithm. At this time, the singular value matrix Σ and the right singular matrix V may be supplied from the singular value decomposer 142. By using the singular value matrix Σ and the right singular matrix V generated by the singular value decomposer 142 in the calculation, the nonlinear detector 147 does not need to perform additional singular value decomposition, and the amount of calculation of the base station 1 as a whole can be reduced.

[0064] The soft interference canceller 61 in the VAMP uses the right singular matrix V and the soft replica vector x generated by the soft replica generator 63 as shown in Equation 28. BA to generate a signal vector y{tilde over (y)} after interference cancellation. The soft interference canceller 61 supplies the signal vector y{tilde over (y)} after interference cancellation to a belief generator 62.

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[0065] The belief generator 62 receives the signal vector y~ after interference cancellation received from the soft interference canceller 61, the right singular matrix V, and the variance Ψ of the soft replica vectors generated by the soft replica generator 63. BA Using the above, the belief vector x ABand the variance of beliefs Ψ AB The belief generator 62 generates a belief vector x AB and the variance of beliefs Ψ AB supplies.

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[0066] The soft replica generator 63 receives the belief vector x AB and the variance of beliefs Ψ AB Using and, we create the soft replica vector x as shown below. BA and soft replica distribution Ψ BA The soft replica generator 63 generates a soft replica vector x BA and soft replica distribution Ψ BA supplies.

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[0067] [Explanation of operation] 11 shows an example of the operation of the base station 1. In step 71, the processor 14-2 (eg, the channel estimator 141) in the DU 11-2 receives a reference signal received by the antenna via the RF transceiver 13.

[0068] In step 72, the processor 14-2 (e.g., the singular value decomposer 142) in the DU 11-2 performs singular value decomposition of the estimated N×M channel matrix H into an N×M left singular matrix U, a singular value matrix Σ which is an M-th diagonal matrix, and an M×M right singular matrix V.

[0069] In step 73, the processor 14-1 (e.g., the beamformer 143) in the RU 11-1 receives the data signal received by the antenna via the RF transceiver 13, and performs receive beamforming using the generated left singular matrix U. The processor 14-1 transmits the beamformed signal to the processor 14-2 (e.g., the replica generator 146 and the nonlinear detector 147) in the DU 11-2.

[0070] In step 74, the processor 14-2 (eg, the diagonal matrix corrector 144) in the DU 11-2 adds an arbitrary diagonal matrix A to the singular value matrix Σ supplied from the singular value decomposer 142 to generate a diagonal matrix Σ'.

[0071] In step 75, the processor 14-2 (e.g., the linear filter generator 145) in the DU 11-2 generates a linear filter W by calculating the product of the right singular matrix V provided from the singular value decomposer 142 and the inverse of the diagonal matrix Σ' shared from the diagonal matrix corrector 144.

[0072] In step 76, the processor 14-2 (e.g., replica generator 146) in DU 11-2 multiplies the linear filter W provided from the linear filter generator 145 by the received signal vector y' after receive beamforming provided from the beamformer 143 to generate a replica vector x^.

[0073] In step 77, the processor 14-2 (e.g., nonlinear detector 147) in the DU 11-2 executes a nonlinear signal detection algorithm using the replica vector x^ provided by the replica generator 146 for the received signal vector y' provided by the beamformer 143. The received signal vector y' is a vector subjected to receive beamforming. The processor 14-2 thus generates a detected signal vector x-. Thereafter, the processor 14-2 (e.g., decision / demodulator 148) in the DU 11-2 decodes the transmitted signals of all M users based on the detected signal vector x-.

[0074] [Effect description] Next, the effects of this embodiment will be described. The base station 1 according to the present embodiment performs receive beamforming using the above-mentioned left singular matrix U, thereby reducing the number of received signals transmitted by the fronthaul and reducing the required fronthaul bandwidth. In addition, the base station 1 can generate a linear filter (e.g., MMSE or RZF) with high detection accuracy and suppressed noise enhancement with a low amount of calculations using a singular value matrix and a right singular matrix generated using singular value decomposition. The base station 1 can perform highly accurate multi-user detection by utilizing a replica generated using a linear filter in a nonlinear signal detection algorithm. In this calculation, only the matrix product of a diagonal matrix and a square matrix is ​​performed, so that the base station 1 can generate a linear filter with a small amount of calculations. In addition, the matrix product of a diagonal matrix and a square matrix is ​​calculated only by the product of the diagonal elements of the diagonal matrix and the matrix elements of the square matrix.

[0075] FIG. 12 is a graph showing a comparison of bit error rate (BER) performance in the following cases. The plotted line graphs (1) to (3) shown in FIG. 12 are graphs relating to the simulation results for a multi-user MIMO configuration where M is the number of terminals and N is the number of receiving antennas, and (N, M) = (64, 24). Note that the number of GAMP iterations is 1, the modulation method is QPSK, and the error correction code is an LDPC code with a coding rate of approximately 0.6. Graphs (1) to (3) in FIG. 12 respectively show the following: (1): BER performance when GAMP is executed using replica vectors generated using an MMSE filter after receive beamforming using a left singular matrix according to this embodiment (2): BER performance when performing MMSE without receive beamforming (3): BER performance when GAMP is executed using replica vectors generated by a ZF filter after receive beamforming using a left singular matrix, as described in Patent Document 1.

[0076] 12 are comparative examples for graph (1). With reference to graphs (1) to (3), the method of the present embodiment shown in (1) has a BER of 10 -3 It can be seen that an improvement of about 2 dB or more is observed.

[0077] The present disclosure is not limited to the above embodiment, and can be modified as appropriate without departing from the spirit of the present disclosure. For example, in the belief propagation method, the adjustable parameters included in the algorithm do not have to be obtained by learning. Furthermore, the coefficient α may be derived by any method.

[0078] The singular value decomposer 142 may be included in the processor 14-1 in the RU 11-1, instead of in the processor 14-2 in the DU 11-2. In this case, the singular value decomposer 142 supplies the generated left singular matrix U to the beamformer 143 in the RU 11-1. The singular value decomposer 142 also supplies the generated singular value matrix Σ to the diagonal matrix corrector 144 in the DU 11-2, and supplies the generated right singular matrix V to the linear filter generator 145 in the DU 11-2.

[0079] In the above-described embodiment, an example has been described in which a base station performs processing on a signal received wirelessly. However, the processing described in the embodiment can also be performed in any wireless receiving device other than a base station.

[0080] In the above-mentioned embodiment, this disclosure has been described as a hardware configuration, but this disclosure is not limited to this. This disclosure can also be realized by making a processor in a computer execute a computer program to perform the processing (steps) of the base station described in the above-mentioned embodiment.

[0081] 13 is a block diagram showing a hardware configuration example of an information processing device for executing the processes of the above-described embodiment. Referring to FIG. 13, the information processing device 90 is a device constituting the base station 1, and includes a signal processing circuit 91, a processor 92, and a memory 93.

[0082] The signal processing circuit 91 is a circuit for processing signals in accordance with the control of the processor 92. Note that the signal processing circuit 91 may include a communication circuit for receiving a signal from a transmitting device.

[0083] The processor 92 is connected (coupled) to the memory 93, and performs the processing of the device described in the above embodiment by reading and executing software (computer programs) from the memory 93. The processor 92 corresponds to at least one of the processors 14-1 and 14-2 in the above embodiment. Examples of the processor 92 include a CPU (Central Processing Unit), an MPU (Micro Processing Unit), an FPGA (Field-Programmable Gate Array), a DSP (Demand-Side Platform), and an ASIC (Application Specific Integrated Circuit). As the processor 92, one processor may be used, or multiple processors may be used in cooperation with each other.

[0084] The memory 93 is composed of a volatile memory, a non-volatile memory, or a combination thereof. The volatile memory may be, for example, a RAM (Random Access Memory) such as a DRAM (Dynamic Random Access Memory) or a SRAM (Static Random Access Memory). The non-volatile memory may be, for example, a ROM (Read Only Memory) such as a PROM (Programmable Random Only Memory) or an EPROM (Erasable Programmable Read Only Memory), a flash memory, or an SSD (Solid State Drive). As the memory 93, one memory may be used, or multiple memories may be used in cooperation with each other.

[0085] The memory 93 is used to store one or more instructions. Here, the one or more instructions are stored in the memory 93 as a group of software modules. The processor 92 can perform the processes described in the above-mentioned embodiments by reading and executing the group of software modules from the memory 93.

[0086] The memory 93 may include a memory built into the processor 92 in addition to a memory provided outside the processor 92. The memory 93 may also include a storage device disposed away from the processors constituting the processor 92. In this case, the processor 92 can access the memory 93 via an I / O (Input / Output) interface.

[0087] As described above, one or more processors included in each device in the above-mentioned embodiments execute one or more programs including a set of instructions for causing a computer to execute the algorithm described using the drawings. By performing this processing, the information processing described in each embodiment can be realized.

[0088] The program includes a set of instructions (or software code) that, when loaded into a computer, causes the computer to perform one or more functions described in the embodiments. The program may be stored in a non-transitory computer-readable medium or a tangible storage medium. By way of example and not limitation, the computer-readable medium or tangible storage medium includes random-access memory (RAM), read-only memory (ROM), flash memory, solid-state drive (SSD) or other memory technology, CD-ROM, digital versatile disk (DVD), Blu-ray® disk or other optical disk storage, magnetic cassette, magnetic tape, magnetic disk storage or other magnetic storage device. The program may be transmitted on a transitory computer-readable medium or communication medium. By way of example and not limitation, the transitory computer-readable medium or communication medium includes electrical, optical, acoustic, or other forms of propagated signals.

[0089] The above-mentioned embodiment is merely an example of the application of the technical idea obtained by the inventor of the present invention. In other words, the technical idea is not limited to the above-mentioned embodiment, and various modifications are possible.

[0090] For example, some or all of the above-described embodiments may be described as, but are not limited to, the following supplementary notes. (Appendix 1) A wireless receiving device, a singular value decomposer configured to perform singular value decomposition of an N×M channel matrix defined between M transmitting antennas of one or more wireless transmitting devices and N receiving antennas coupled to the wireless receiving device into an N×M left singular matrix U, a singular value matrix Σ that is an M-th diagonal matrix, and an M×M right singular matrix V; a diagonal matrix corrector configured to generate a diagonal matrix Σ′ by using the singular value matrix Σ and an arbitrary diagonal matrix A; a replica generator configured to generate a replica vector x^ by using a received signal vector y' obtained by performing receive beamforming on the received signals of each of the receive antennas by using the left singular matrix U, and a linear filter W generated by using the right singular matrix V and the diagonal matrix Σ'; a non-linear detector configured to perform a non-linear signal detection algorithm using the received signal vector y′ and the replica vector x̂. Radio receiving device. (Appendix 2) the diagonal matrix corrector generates the diagonal matrix A by multiplying an inverse matrix of the singular value matrix Σ by a positive real number α, and generates the diagonal matrix Σ' by adding the generated diagonal matrix A to the singular value matrix Σ; 2. A wireless receiving device as described in claim 1. (Appendix 3) The diagonal matrix corrector generates the diagonal matrix Σ′ by setting a ratio of noise power per one of the receiving antennas to a transmission power per one of the transmitting antennas as the positive real number α. 3. A wireless receiving device as described in claim 2. (Appendix 4) The replica generator generates the replica vector x^ by calculating a conditional expectation of a modulation symbol obtained using a conditional probability that is a condition on the product of the linear filter W and the received signal vector y'. 4. A wireless receiving device according to claim 1. (Appendix 5) a linear filter generator that generates the linear filter W by calculating a product of the right singular matrix V and the diagonal matrix Σ′. 5. A wireless receiving device according to claim 1. (Appendix 6) the nonlinear detector executes one of a parallel interference cancellation algorithm, a maximum likelihood detection algorithm, and a belief propagation algorithm as the nonlinear signal detection algorithm; 6. A wireless receiving device according to claim 1. (Appendix 7) The nonlinear detector executes, as the nonlinear signal detection algorithm, any one of Gaussian belief propagation, generalized approximation message propagation, expectation propagation, and vector approximation message propagation as the belief propagation algorithm. 7. A wireless receiving device as described in claim 6. (Appendix 8) The nonlinear detector executes the nonlinear signal detection algorithm on the received signal vector y' using the singular value matrix Σ, the right singular matrix V, and the replica vector x̂. 8. A wireless receiving device according to claim 1. (Appendix 9) the nonlinear detector executes a vector approximation message propagation algorithm as the nonlinear signal detection algorithm; 9. The wireless receiving device according to claim 8. (Appendix 10) and a beamformer configured to generate the received signal vector y′ by calculating a product of a Hermitian conjugate of the left singular matrix U generated by the singular value decomposer and a received signal vector y configured from received signals of each of the receive antennas. 10. A wireless receiving device according to any one of claims 1 to 9. (Appendix 11) The wireless receiving device includes a Radio Unit (RU) and a Distributed Unit (DU) connected via a fronthaul; the beamformer is included in the RU; the diagonal matrix corrector, the replica generator, and the nonlinear detector are included in the DU; The singular value decomposer is included in either the RU or the DU. 11. The wireless receiving device according to claim 10. (Appendix 12) A method performed by a wireless receiving device, comprising: singular value decomposition of an N×M channel matrix defined between M transmitting antennas of one or more wireless transmitting devices and N receiving antennas coupled to the wireless receiving device into an N×M left singular matrix U, a singular value matrix Σ that is an M-th order diagonal matrix, and an M×M right singular matrix V; A diagonal matrix Σ′ is generated by using the singular value matrix Σ and an arbitrary diagonal matrix A; A replica vector x^ is generated by using a received signal vector y' obtained by performing receive beamforming on the received signals of each of the receiving antennas using the left singular matrix U, and a linear filter W generated by using the right singular matrix V and the diagonal matrix Σ'; performing a nonlinear signal detection algorithm using the received signal vector y' and the replica vector x^; method. (Appendix 13) A program for causing a computer to execute a method for a wireless receiving device, the method comprising: singular value decomposition of an N×M channel matrix defined between M transmitting antennas of one or more wireless transmitting devices and N receiving antennas coupled to the wireless receiving device into an N×M left singular matrix U, a singular value matrix Σ that is an M-th order diagonal matrix, and an M×M right singular matrix V; A diagonal matrix Σ′ is generated by using the singular value matrix Σ and an arbitrary diagonal matrix A; A replica vector x^ is generated by using a received signal vector y' obtained by performing receive beamforming on the received signals of each of the receiving antennas using the left singular matrix U, and a linear filter W generated by using the right singular matrix V and the diagonal matrix Σ'; performing a nonlinear signal detection algorithm using the received signal vector y' and the replica vector x^; program. [Explanation of symbols]

[0091] R Radio receiving device R1 Singular Value Decomposer R2 diagonal matrix corrector R3 Replica Generator R4 Nonlinear Detector 1 base station 2. Wireless terminals 10 Receiver 11-1 Radio Unit (RU) 11-2 Distributed Unit (DU) 12 Antenna Array 13 RF Transceiver Processor in 14-1 RU 14-2 Processor in DU 15 Memory 16 Network Interfaces 141 Channel Estimator 142 Singular Value Decomposer 143 Beamformer 144 Diagonal Matrix Corrector 145 Linear Filter Generator 146 Replica Generator 147 Nonlinear Detectors 148 Decision / Demodulator 20 Transmitter 30 channels (transmission path) 41 Interference Canceller 42 Transmitted signal detector 51 Candidate generator 52 Transmitted signal detector 61 Soft Interference Canceller 62 Belief Generator 63 Soft Replica Generator

Claims

1. A wireless receiving device, a singular value decomposer configured to perform singular value decomposition of an N×M channel matrix defined between M transmitting antennas of one or more wireless transmitting devices and N receiving antennas coupled to the wireless receiving device into an N×M left singular matrix U, a singular value matrix Σ that is an M-th diagonal matrix, and an M×M right singular matrix V; a diagonal matrix corrector configured to generate a diagonal matrix Σ′ by using the singular value matrix Σ and an arbitrary diagonal matrix A; a replica generator configured to generate a replica vector x^ by using a received signal vector y' obtained by performing receive beamforming on the received signals of each of the receive antennas by using the left singular matrix U, and a linear filter W generated by using the right singular matrix V and the diagonal matrix Σ'; a non-linear detector configured to perform a non-linear signal detection algorithm using the received signal vector y′ and the replica vector x̂. Radio receiving device.

2. the diagonal matrix corrector generates the diagonal matrix A by multiplying an inverse matrix of the singular value matrix Σ by a positive real number α, and generates the diagonal matrix Σ' by adding the generated diagonal matrix A to the singular value matrix Σ; 2. The wireless receiving device according to claim 1.

3. The diagonal matrix corrector generates the diagonal matrix Σ′ by setting a ratio of noise power per one of the receiving antennas to a transmission power per one of the transmitting antennas as the positive real number α.

3. The wireless receiving device according to claim 2.

4. The replica generator generates the replica vector x^ by calculating a conditional expectation of a modulation symbol obtained using a conditional probability that is a condition on the product of the linear filter W and the received signal vector y'.

4. The radio receiving device according to claim 1.

5. a linear filter generator that generates the linear filter W by calculating a product of the right singular matrix V and the diagonal matrix Σ′.

4. The radio receiving device according to claim 1.

6. the nonlinear detector executes one of a parallel interference cancellation algorithm, a maximum likelihood detection algorithm, and a belief propagation algorithm as the nonlinear signal detection algorithm; 4. The radio receiving device according to claim 1.

7. The nonlinear detector executes, as the nonlinear signal detection algorithm, any one of Gaussian belief propagation, generalized approximation message propagation, expectation propagation, and vector approximation message propagation as the belief propagation algorithm.

7. The wireless receiving device according to claim 6.

8. the nonlinear detector executes the nonlinear signal detection algorithm on the received signal vector y' using the singular value matrix Σ, the right singular matrix V, and the replica vector x̂; 4. The radio receiving device according to claim 1.

9. A method performed by a wireless receiving device, comprising: singular value decomposition of an N×M channel matrix defined between M transmitting antennas of one or more wireless transmitting devices and N receiving antennas coupled to the wireless receiving device into an N×M left singular matrix U, a singular value matrix Σ that is an M-th diagonal matrix, and an M×M right singular matrix V; A diagonal matrix Σ′ is generated by using the singular value matrix Σ and an arbitrary diagonal matrix A; A replica vector x^ is generated by using a received signal vector y' obtained by performing receive beamforming on the received signals of each of the receiving antennas using the left singular matrix U, and a linear filter W generated by using the right singular matrix V and the diagonal matrix Σ'; performing a nonlinear signal detection algorithm using the received signal vector y' and the replica vector x^; method.

10. A program for causing a computer to execute a method for a wireless receiving device, the method comprising: singular value decomposition of an N×M channel matrix defined between M transmitting antennas of one or more wireless transmitting devices and N receiving antennas coupled to the wireless receiving device into an N×M left singular matrix U, a singular value matrix Σ that is an M-th diagonal matrix, and an M×M right singular matrix V; A diagonal matrix Σ′ is generated by using the singular value matrix Σ and an arbitrary diagonal matrix A; A replica vector x^ is generated by using a received signal vector y' obtained by performing receive beamforming on the received signals of each of the receiving antennas using the left singular matrix U, and a linear filter W generated by using the right singular matrix V and the diagonal matrix Σ'; performing a nonlinear signal detection algorithm using the received signal vector y' and the replica vector x^; program.

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