Full-duplex self-interference mitigation method and system based on desired signal assistance

CN117040555BActive Publication Date: 2026-08-07UNIV OF ELECTRONICS SCI & TECH OF CHINA
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Patent Information

Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
UNIV OF ELECTRONICS SCI & TECH OF CHINA
Filing Date
2023-08-24
Publication Date
2026-08-07

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Technical Problem

然而,LS与MAP估计都非常消耗计算资源,难以进行实时估计

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Abstract

The application relates to the field of self-interference suppression of wireless communication, in particular to a full-duplex self-interference suppression method and system based on expected signal assistance, which realizes real-time online self-interference suppression. The scheme comprises the following steps: taking the self-interference signal coupled by the receiver as a first reference signal of a filter, taking a received signal as an input signal of the filter, and taking the output signal at the error output end of the filter as an expected signal in a first stage; demodulating the expected signal in the first stage to reconstitute a transmission frame, taking the transmission frame as a second reference signal of the filter, and performing joint adaptive filtering on the second reference signal and the first reference signal, taking the output signal at the error output end of the filter as an expected signal in a second stage; demodulating the expected signal in the second stage to reconstitute a transmission frame, taking the transmission frame as a new second reference signal, and performing joint adaptive filtering on the new second reference signal and the first reference signal again, and repeating the second stage until better self-interference channel performance is obtained. The application is suitable for self-interference suppression.
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Description

Technical Field

[0001] This invention relates to the field of self-interference suppression in wireless communication, and specifically to a full-duplex self-interference suppression method and system based on desired signal assistance. Background Technology

[0002] Simultaneous full-duplex technology has emerged as a potential solution to the bandwidth constraints in next-generation (6G) wireless communication systems. By transmitting and receiving simultaneously on the same frequency, full-duplex technology nearly doubles network capacity and reduces data transmission latency. However, a key challenge in implementing full-duplex wireless communication systems is suppressing high-power co-channel self-interference signals, which are typically orders of magnitude higher than the power of the desired signal to be demodulated in the received signal.

[0003] A primary method for suppressing self-interference signals is to estimate and equalize the self-interference channel parameters. The presence of the desired signal in the received signal degrades the performance of self-interference channel estimation; however, reducing the power of the desired signal reduces its SNR (Signal-Noise Ratio). Existing research demodulates the desired signal and regenerates the communication frame, then jointly performs LS (Least Squares) or MAP (Mean Absolute Percentage Error) estimation with the self-interference signal to achieve better self-interference channel estimation performance. However, both LS and MAP estimations are computationally intensive and difficult to perform in real time. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a full-duplex self-interference suppression method and system based on desired signal assistance, which realizes real-time online self-interference suppression and improves the performance of self-interference channels.

[0005] This invention achieves the above objective by adopting the following technical solution: a full-duplex self-interference suppression method based on desired signal assistance, comprising:

[0006] Self-interference suppression first stage: The self-interference signal coupled by the receiver is used as the first reference signal of the filter, the received signal is used as the input signal of the filter, and the output signal of the filter error output terminal is used as the expected signal of the first stage.

[0007] The desired signal from the first stage is demodulated and reassembled into a transmission frame, which is then used as the second reference signal of the filter and subjected to joint adaptive filtering with the first reference signal. The output signal at the error output terminal of the filter is used as the desired signal for the second stage.

[0008] Self-interference suppression second stage: Demodulate the desired signal from the second stage and reassemble it into a transmission frame. Use this frame as the new second reference signal and perform joint adaptive filtering with the first reference signal again. Repeat the second stage until the self-interference channel performance meets the set requirements.

[0009] Furthermore, the received signal contains the desired multipath signal, the self-interference signal from the multipath, and noise. The received signal is represented as follows:

[0010] r(t) = w x (t)*x(t)+w y (t)*y(t)+z(t), where w x (t) and w y (t) represents the impulse response of the self-interference channel and the desired channel, respectively, y(t) represents the desired signal, z(t) represents the Gaussian distributed white noise signal, x(t) represents the coupled self-interference signal, and r(t) is the received signal.

[0011] Furthermore, after the transmitted data passes through a power amplifier and an analog-to-digital converter, then:

[0012] The sampling of the self-interference signal and the desired signal are respectively x(n) = [x(n) x(n-1) … x(n-M+1)] T ,y(n)=[y(n) y(n-1)…y(n-L+1)] T M and L are the multipath numbers of the self-interference channel and the desired channel, respectively.

[0013] Furthermore, the method also includes initializing the filter as follows: setting the initial estimates of the self-interference channel and the desired channel... The inverse of the initial autocorrelation matrix is ​​then:

[0014] Among them I M and I L Let δ represent the identity matrix of order M, L. x and δ y This represents the regularization parameters for the self-interference channel and the desired channel.

[0015] Furthermore, in the first stage of self-interference suppression, the acquisition of the desired signal specifically includes:

[0016] Let the reference signal be c(n) = x(n), and the filter error be ξ(n) = ξ x (n), update the filter as follows:

[0017] Let the intermediate parameter π(n) = λ -1 P(n-1)c(n);

[0018] k(n)=π(n) / (1+c H (n)π(n));

[0019]

[0020] Where λ represents the forgetting factor of the adaptive filter, and k(n) represents the gain vector;

[0021] After the update, the filter outputs the desired signal after interference suppression.

[0022] Furthermore, in the second stage of self-interference suppression, the acquisition of the desired signal specifically includes:

[0023] Let the reference signal c(n) = [x T (n) y T (n)] T Filter error ξ(n)=ξ y (n), the estimated value of the channel is in This is the nth estimate of the self-interference channel. This is the nth estimate of the desired channel. The filter is updated as follows:

[0024] π(n)=λ -1 P(n-1)(cn);

[0025] k(n)=π(n) / (1+c H (n)π(n));

[0026]

[0027] After the update, perform the following steps:

[0028]

[0029]

[0030] P(n)=(λ -1 I-λ -1 k(n)c H (n))P(n-1);

[0031] The filter outputs the desired signal after interference suppression.

[0032] A full-duplex self-interference suppression system based on desired signal assistance is used to implement the full-duplex self-interference suppression method based on desired signal assistance described above. The system includes a self-interference suppression signal processing module.

[0033] The self-interference suppression signal processing module is used to, in the first stage of self-interference suppression: use the self-interference signal coupled by the receiver as the first reference signal of the filter, use the received signal as the input signal of the filter, and use the output signal of the filter error output terminal as the desired signal of the first stage.

[0034] The desired signal from the first stage is demodulated and reassembled into a transmission frame, which is then used as the second reference signal of the filter and subjected to joint adaptive filtering with the first reference signal. The output signal at the error output terminal of the filter is used as the desired signal for the second stage.

[0035] In the second stage of self-interference suppression, the desired signal of the second stage is demodulated and reassembled into a transmission frame, which is used as a new second reference signal. This frame is then combined with the first reference signal for joint adaptive filtering. The second stage is repeated until the self-interference channel performance meets the set requirements.

[0036] Furthermore, the received signal contains the desired multipath signal, the self-interference signal from the multipath, and noise. The received signal is represented as follows:

[0037] r(t) = w x (t)*x(t)+w y (t)*y(t)+z(t), where w x (t) and w y (t) represents the impulse response of the self-interference channel and the desired channel, respectively; y(t) represents the desired signal; z(t) represents the Gaussian-distributed white noise signal; x(t) represents the coupled self-interference signal; and r(t) is the received signal.

[0038] After the transmitted data passes through the power amplifier and analog-to-digital converter, then:

[0039] The sampling of the self-interference signal and the desired signal are respectively x(n)=[x(n) x(n-1) … x(n-M+1)]T, x(n)=[x(n) x(n-1) … x(n-M+1)] T M and L are the multipath numbers of the self-interference channel and the desired channel, respectively.

[0040] Furthermore, the self-interference suppression signal processing module is specifically used to, in the first stage of self-interference suppression, let the reference signal c(n) = x(n) and the filter error ξ(n) = ξ x (n), update the filter as follows:

[0041] Let the intermediate parameter π(n) = λ -1 P(n-1)c(n);

[0042] k(n)=π(n) / (1+cH (n)π(n));

[0043]

[0044] Where λ represents the forgetting factor of the adaptive filter, and k(n) represents the gain vector;

[0045] After the update, the filter outputs the desired signal after interference suppression.

[0046] Furthermore, the self-interference suppression signal processing module is specifically used to, in the second stage of self-interference suppression, let the reference signal c(n) = [x T (n) y T (n)] T Filter error ξ(n)=ξ y (n), the estimated value of the channel is in This is the nth estimate of the self-interference channel. This is the nth estimate of the desired channel. The filter is updated as follows:

[0047] π(n)=λ -1 P(n-1)c(n);

[0048] k(n)=π(n) / (1+c H (n)π(n));

[0049]

[0050] After the update, perform the following steps:

[0051]

[0052]

[0053] P(n)=(λ -1 I-λ -1 k(n)c H (n))P(n-1);

[0054] The filter outputs the desired signal after interference suppression.

[0055] The beneficial effects of this invention are as follows:

[0056] In this invention, the self-interference signal coupled by the receiver is used as the first reference signal of the filter, the received signal is used as the input signal of the filter, the output signal of the filter error output terminal is used as the expected signal of the first stage, the expected signal of the first stage is demodulated and reassembled into a transmission frame, which is used as the second reference signal of the filter and jointly adaptively filtered with the first reference signal. The output signal of the filter error output terminal is used as the expected signal of the second stage.

[0057] Self-interference suppression second stage: Demodulate the desired signal from the second stage and reassemble it into a transmission frame. Use this frame as the third reference signal for the filter, and perform joint adaptive filtering with the first and second reference signals. Repeating this process can achieve better performance. Attached Figure Description

[0058] Figure 1 This is a flowchart of the full-duplex self-interference suppression method based on desired signal assistance provided in an embodiment of the present invention;

[0059] Figure 2 This is a schematic diagram of a full-duplex OFDM transceiver based on desired signal-assisted adaptive self-interference suppression provided in an embodiment of the present invention;

[0060] Figure 3 This is a schematic diagram of a SIC structure based on desired signal assistance provided in an embodiment of the present invention;

[0061] Figure 4 This refers to the SICR of the first and second stages with different iteration numbers when the INR is fixed at 40dB, as provided in the embodiments of the present invention.

[0062] Figure 5 This refers to the bit error rate of the first and second stages with different iteration numbers when the fixed INR = 40dB is provided in the embodiments of the present invention. Detailed Implementation

[0063] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0064] This invention provides a full-duplex self-interference suppression method based on desired signal assistance, such as... Figure 1 As shown, it includes: Self-interference suppression first stage: The self-interference signal coupled by the receiver is used as the first reference signal of the filter, the received signal is used as the input signal of the filter, and the output signal of the filter error output terminal is used as the desired signal of the first stage.

[0065] The desired signal from the first stage is demodulated and reassembled into a transmission frame. The reassembled transmission frame is used as the second reference signal of the filter and is jointly adaptively filtered with the first reference signal. The output signal of the error output terminal of the filter is used as the desired signal of the second stage.

[0066] Self-interference suppression second stage: After demodulating the expected signal of the second stage, the reconstructed transmission frame is used as the new second reference signal and is jointly adaptively filtered with the first reference signal again. The second stage is repeated until the self-interference channel performance meets the set requirements.

[0067] In one embodiment of the present invention, the initial size of the diagonal loading matrix in the second stage can be set according to the signal-to-noise ratio of the self-interference signal and the desired signal under different environments, so as to achieve the optimal initial diagonal loading parameters.

[0068] like Figure 2 The diagram shows a full-duplex OFDM transceiver based on desired signal-assisted adaptive self-interference suppression provided by this invention. It has two input signals: the received signal r(t) at the receiving antenna and the coupled self-interference signal x(t). The received signal contains the multipath desired signal, the multipath self-interference signal, and noise. The received signal can be expressed as r(t) = w x (t)*x(t)+w y (t)*y(t)+z(t), where w x (t) and w y (t) represents the impulse response of the self-interference channel and the desired channel, respectively, y(t) represents the desired signal, z(t) represents the Gaussian distributed white noise signal, and x(t) represents the coupled self-interference signal.

[0069] After the transmitted data passes through a power amplifier and an ADC (Analog-to-Digital Converter), a sample of the received signal is obtained.

[0070] The sampling of the self-interference signal and the desired signal are respectively x(n) = [x(n) x(n-1) … x(n-M+1)] T ,y(n)=[y(n) y(n-1)…y(n-L+1)] T M and L are the multipath numbers of the self-interference channel and the desired channel, respectively.

[0071] Before adaptive filtering, the filter is initialized as follows: Set the initial estimates of the self-interference channel and the desired channel... Let the inverse of the initial autocorrelation matrix be...

[0072]

[0073] Among them I M and I L Let δ represent the identity matrix of order M, L. x and δ y The regularization parameters representing the self-interference channel and the desired channel can be set to different values ​​based on the signal-to-noise ratio (SNR) of the self-interference signal and the desired signal, respectively. If the SNR of the self-interference signal is high (greater than 30 dB), δ can be set to a higher value. x <<1, enabling the algorithm to converge quickly; the signal-to-noise ratio of the desired signal is generally low, requiring δ to be set. y A value >1 is used to achieve better global performance. The regularization parameter is a hyperparameter and requires multiple tests based on the actual channel environment to select an optimal value.

[0074] In one embodiment of the present invention, the acquisition of the desired signal in the first stage of self-interference suppression specifically includes:

[0075] Let the reference signal be c(n) = x(n), and the filter error be ξ(n) = ξ x (n), update the filter as follows:

[0076] Let the intermediate parameter π(n) = λ -1 P(n-1)c(n);

[0077] k(n)=π(n) / (1+c H (n)π(n));

[0078]

[0079] Where λ represents the forgetting factor of the adaptive filter, and k(n) represents the gain vector.

[0080] After the update, the filter outputs the desired signal after interference suppression.

[0081] In one embodiment of the present invention, the acquisition of the desired signal in the second stage of self-interference suppression specifically includes:

[0082] Let the reference signal c(n) = [x T (n) y T (n)] T , where y(n) represents the desired signal, (·) T Represents the matrix transpose, filter error ξ(n) = ξ y (n), the estimated value of the channel is in This is the nth estimate of the self-interference channel. This is the nth estimate of the desired channel. The filter is updated as follows:

[0083] π(n)=λ -1 P(n-1)c(n);

[0084] k(n)=π(n) / (1+c H (n)π(n));

[0085]

[0086] After the update, perform the following steps:

[0087]

[0088]

[0089] P(n)=(λ -1 I-λ -1 k(n)c H (n))P(n-1);

[0090] The filter outputs the desired signal after interference suppression.

[0091] The computational complexity of the full-duplex self-interference suppression method based on desired signal assistance in this invention is analyzed below. First, the computational complexity of a single matrix multiplication is calculated. Let the size of matrix A be M×N and the size of matrix B be N×L. Then the computational complexity required for A×B is:

[0092]

[0093] Among them κ mul For multiplication complexity, κ add It has an addition complexity.

[0094] The first stage of the algorithm requires one (M×M)×(M×1) matrix multiplication, one (M×1)×(1×M) vector multiplication, and two (1×M)×(M×1) dot products, therefore requiring a total of 2M. 2 +6M complex multiplications and 2M 2 +6M-1 complex number addition.

[0095] The second stage of the algorithm requires 2(M+L). 2 +6(M+L) complex multiplications and 2(M+L) 2 +6(M+L)-1 complex number additions. However, hardware resources can be reused with the first stage.

[0096] Therefore, this invention has lower computational complexity, from O(M) 3 The value was reduced to O(M) 2), where M represents the order of the filter. It requires fewer computational resources and is more efficient.

[0097] The proposed full-duplex interference suppression method assisted by the desired signal is then analyzed and evaluated through simulation. Specific parameter settings are shown in the table below.

[0098] Table 1. Simulation parameter settings for the FD-NSIC algorithm

[0099]

[0100]

[0101] Table 2. SI Channel Settings

[0102] 0 0 1 -0.9 2 -1.7 3 -2.6 4 -3.5 5 -4.3 6 -5.2 7 -6.1 8 -6.9 9 -7.8 11 -9 14 -11.1 17 -13.7 20 -16.3 24 -19.3 29 -23.2

[0103] like Figure 4 The figure shows the SICR (Self-Interference Cancellation Ratio) for different iteration numbers in the first and second stages when the INR (Interference-Noise Ratio) is fixed at 40 dB, as provided by the present invention.

[0104]

[0105] Figure 4 In the first stage, the SICR decreases rapidly with increasing SNR (Signal to Noise Ratio). This is because in the first stage, the desired signal is considered additional noise, leading to an increase in self-interference channel estimation error with increasing SNR. However, the SIC performance improves in the second stage, where the reconstructed desired signal serves as an auxiliary reference signal for SI estimation. Specifically, in the second iteration of the second stage, only a small increase in SICR is observed when the SNR is <20, indicating that one iteration of the second stage is sufficient in practice, reducing signal demodulation delay. The SIC structure is as follows: Figure 3 As shown.

[0106] like Figure 5 The figure shows the bit error rate (BER) of the first and second stages with different iteration numbers when the INR is fixed at 40 dB, according to an embodiment of the present invention. The figure shows that when only the first stage is used for self-interference suppression, the BER decreases slowly as the desired signal-to-noise ratio increases, reaching 5 × 10⁻⁶. -3 There are frequent bit error rate plateaus in the vicinity. However, after the expected signal reconstructed in the second stage participates in self-interference suppression, the bit error rate decreases significantly compared to the first stage.

[0107] The above description is merely a preferred embodiment of the present invention. It should be understood that the present invention is not limited to the forms disclosed herein and should not be construed as excluding other embodiments. It can be used in various other combinations, modifications, and environments, and can be altered within the scope of the concept described herein through the above teachings or related technologies or knowledge. Modifications and variations made by those skilled in the art that do not depart from the spirit and scope of the present invention should be within the protection scope of the appended claims.

Claims

1. A full-duplex self-interference suppression method based on desired signal assistance, characterized in that, include: Self-interference suppression first stage: The self-interference signal coupled by the receiver is used as the first reference signal of the filter, the received signal is used as the input signal of the filter, and the output signal of the filter error output terminal is used as the expected signal of the first stage. The desired signal from the first stage is demodulated and reassembled into a transmission frame, which is used as the second reference signal of the filter and jointly adaptively filtered with the first reference signal. The output signal of the error output terminal of the filter is used as the desired signal of the second stage. The second stage of self-interference suppression: After demodulating the expected signal of the second stage, the transmitted frame is reconstructed and used as the new second reference signal. It is then jointly adaptively filtered with the first reference signal again. The output signal of the error output terminal of the filter in this stage is used as the expected signal of the next stage. This stage operation is repeated. That is, in each iteration, the expected signal output from the current stage is demodulated and reconstructed as the new second reference signal and jointly adaptively filtered with the first reference signal until the self-interference channel performance reaches the set requirements.

2. The full-duplex self-interference suppression method based on desired signal assistance according to claim 1, characterized in that, The received signal contains the desired multipath signal, the self-interference signal from the multipath, and noise. The received signal is represented as: ,in and These represent the impulse responses of the self-interference channel and the desired channel, respectively. Represents the desired signal. White noise signal representing Gaussian distribution, This represents the self-interference signal of the coupling. To receive signals.

3. The full-duplex self-interference suppression method based on desired signal assistance according to claim 2, characterized in that, After the transmitted data passes through a power amplifier and an analog-to-digital converter, the sampled received signal is as follows: The sampling of the self-interference signal and the desired signal are respectively , M and L are the multipath numbers of the self-interference channel and the desired channel, respectively.

4. The full-duplex self-interference suppression method based on desired signal assistance according to claim 3, characterized in that, The method also includes initializing the filter as follows: setting the initial estimates of the self-interference channel and the desired channel... , Then the inverse of the initial autocorrelation matrix is: ,in and This represents the identity matrix of order M and L. and This represents the regularization parameters for the self-interference channel and the desired channel.

5. The full-duplex self-interference suppression method based on desired signal assistance according to claim 3, characterized in that, In the first stage of self-interference suppression, the acquisition of the desired signal specifically includes: Let the reference signal Filter error The filter is updated as follows: Let intermediate parameters ; ; ; in The forgetting factor represents the adaptive filter. Represents the gain vector. It is the inverse of the autocorrelation matrix of the previous time step. This is the (n-1)th estimate of the self-interference channel. Indicates reference signal The conjugate transpose of; After the update, the filter outputs the desired signal after interference suppression. .

6. The full-duplex self-interference suppression method based on desired signal assistance according to claim 3, characterized in that, In the second stage of self-interference suppression, the acquisition of the desired signal specifically includes: Let the reference signal Filter error The estimated value of the channel is ,in This is the nth estimate of the self-interference channel. This is the nth estimate of the desired channel. The filter is updated as follows: ; ; ; After the update, perform the following procedure: ; ; ; The filter outputs the desired signal after interference suppression. ; in The forgetting factor represents the adaptive filter. Represents the gain vector. This represents the conjugate transpose of the gain vector. It is the inverse of the autocorrelation matrix of the previous time step. This is the (n-1)th estimate of the self-interference channel. This is the (n-1)th estimate of the desired channel. Let T be the inverse of the autocorrelation matrix at the current time step, and let T denote the matrix transpose. Indicates intermediate parameters. Indicates reference signal The conjugate transpose of .

7. A full-duplex self-interference suppression system based on desired signal assistance, used to implement the full-duplex self-interference suppression method based on desired signal assistance as described in any one of claims 1-6, characterized in that, The system includes a self-interference suppression signal processing module; The self-interference suppression signal processing module is used to, in the first stage of self-interference suppression: use the self-interference signal coupled by the receiver as the first reference signal of the filter, the received signal as the input signal of the filter, and the output signal of the filter error output terminal as the desired signal of the first stage; demodulate the desired signal of the first stage and reassemble it into a transmission frame, use it as the second reference signal of the filter, and perform joint adaptive filtering with the first reference signal, and use the output signal of the filter error output terminal as the desired signal of the second stage. In the second stage of self-interference suppression, the desired signal of the second stage is demodulated and reconstructed into a transmission frame, which is used as a new second reference signal. This frame is then used in conjunction with the first reference signal for joint adaptive filtering. The output signal of the error output terminal of the filter in this stage is used as the desired signal for the next stage. This stage operation is repeated. In other words, in each iteration, the desired signal output from the current stage is demodulated and reconstructed as a new second reference signal, which is then used in conjunction with the first reference signal for joint adaptive filtering until the self-interference channel performance meets the set requirements.

8. The full-duplex self-interference suppression system based on desired signal assistance according to claim 7, characterized in that, The received signal contains the desired multipath signal, the self-interference signal from the multipath, and noise. The received signal is represented as: ,in and These represent the impulse responses of the self-interference channel and the desired channel, respectively. Represents the desired signal. White noise signal representing Gaussian distribution, This represents the self-interference signal of the coupling. To receive signals; After the transmitted data passes through the power amplifier and analog-to-digital converter, the sampled received signal is as follows: The sampling of the self-interference signal and the desired signal are respectively , M and L are the multipath numbers of the self-interference channel and the desired channel, respectively.

9. The full-duplex self-interference suppression system based on desired signal assistance according to claim 8, characterized in that, The self-interference suppression signal processing module is specifically used to, in the first stage of self-interference suppression, set the reference signal... Filter error The filter is updated as follows: Let intermediate parameters ; ; ; in The forgetting factor represents the adaptive filter. Represents the gain vector. It is the inverse of the autocorrelation matrix of the previous time step. This is the (n-1)th estimate of the self-interference channel. Indicates reference signal The conjugate transpose of; After the update, the filter outputs the desired signal after interference suppression. .

10. The full-duplex self-interference suppression system based on desired signal assistance according to claim 8, characterized in that, The self-interference suppression signal processing module is specifically used to, in the second stage of self-interference suppression, make the reference signal Filter error The estimated value of the channel is ,in This is the nth estimate of the self-interference channel. This is the nth estimate of the desired channel. The filter is updated as follows: ; ; ; After the update, perform the following procedure: ; ; ; The filter outputs the desired signal after interference suppression. ; in The forgetting factor represents the adaptive filter. Represents the gain vector. This represents the conjugate transpose of the gain vector. It is the inverse of the autocorrelation matrix of the previous time step. This is the (n-1)th estimate of the self-interference channel. This is the (n-1)th estimate of the desired channel. Let T be the inverse of the autocorrelation matrix at the current time step, and let T denote the matrix transpose. Indicates intermediate parameters. Indicates reference signal The conjugate transpose of .

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