A full-duplex communication multi-stage self-interference suppression and channel equalization integrated method

Abstract

The application discloses a full duplex communication multistage self-interference suppression and channel equalization integrated method, which comprises the following steps: S1, giving the expression of a received signal and a coupled self-interference signal of a receiving end through a RRC filter with a sampling rate of K times a baseband sampling rate; S2, discretely sampling the received signal and a feedback signal at the receiving end; S3, performing minimum mean square error estimation of an expected symbol; S4, estimating the symbol in a multistage iteration mode, and obtaining an optimal coefficient equation of an adaptive filter according to the minimum mean square error estimation; and S5, updating the adaptive filter coefficient through the iteration mode by using an RLS algorithm, and obtaining an estimated value of the expected signal by using the updated coefficient. The application has lower system complexity and lower inter-stage delay, reduces overall quantization noise based on channel estimation and equalization.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of full-duplex wideband wireless communication systems, in particular to a full-duplex communication multi-stage self-interference suppression and channel equalization integrated method. BACKGROUND

[0002] Simultaneous transmit-receive (STR) full-duplex technology has become a potential solution to the bandwidth shortage problem in the next generation (6G) wireless communication system. By transmitting and receiving simultaneously on the same frequency, full-duplex technology almost doubles the network capacity and reduces data transmission delay. At the physical layer, the main challenge of full-duplex communication is the self-interference in the received signal, which reduces the signal-to-interference-and-noise ratio (SINR) and makes the system capacity much lower than expected, i.e., twice that of a half-duplex communication system.

[0003] In full-duplex communication, self-interference suppression techniques can be divided into passive self-interference suppression and active self-interference suppression. Passive self-interference suppression relies on directional antennas, cross-polarization, etc., to increase the loss of self-interference at the receiving end when it propagates. Active self-interference suppression estimates the self-interference channel, reconstructs the self-interference signal in the analog and digital domains, and subtracts it from the received signal.

[0004] In a typical full-duplex system, there is still a 20-45 dB residual self-interference component in the received signal after passive and analog domain active self-interference suppression, which needs to be canceled to the noise floor by digital domain self-interference suppression. Existing multi-stage self-interference suppression techniques treat the desired signal as structured noise to further improve the self-interference suppression capability in the digital domain. By reconstructing the desired signal, a oblique projection estimator of the self-interference signal can be obtained, and after multiple iterations, the system bit error rate approaches the theoretical curve. It is worth noting that this kind of iterative self-interference suppression algorithm does not consider the equalization of the desired signal. This makes the reconstruction of the desired signal in each iteration require a frequency domain or time domain equalizer, and the hardware resources and delay of the system increase linearly with the number of iterations. In addition, the above algorithms all use LS estimation, and there is still room for improvement in the estimation accuracy of each iteration. SUMMARY

[0005] The present application aims to overcome the shortcomings of the prior art and provide a full-duplex communication multi-stage self-interference suppression and channel equalization integrated method, which has lower system complexity and inter-stage delay, reduces the overall quantization noise based on channel estimation and equalization.

[0006] The object of the application is achieved by the following technical solution: a full-duplex communication multi-stage self-interference suppression and channel equalization integrated method, in each stage, the input signal is subtracted from the hard demodulation of the expected symbol of the previous stage as the reference signal of the adaptive filter, the self-interference signal coupled with the receiver and the soft demodulation of the expected symbol are taken as the input signal, the error of the adaptive filter is taken as the input of the nonlinear function tanh, and the output of the tanh function is taken as the MMSE estimation value of the expected symbol of the current stage. In the 0th iteration, the expected symbol is set to all zeros as the initial value.

[0007] Wherein, the initial size of the diagonal loading matrix of the second stage can be set according to the signal-to-noise ratio of the self-interference signal and the expected signal in different environments respectively, so as to achieve the best initial diagonal loading parameter;

[0008] Specifically, the method of the application comprises the following steps:

[0009] S1. For a communication system composed of two full-duplex communication nodes with the same communication system architecture, the two nodes transmit signals and receive signals of the other node at the same frequency point and at the same time; for any node, the received signal and the coupled self-interference signal after passing through a RRC filter with a sampling rate of K times the baseband sampling rate are represented;

[0010] S2. Discretely sampling the received signal and the feedback signal at the receiving end;

[0011] S3. Performing minimum mean square error estimation of the expected symbol, and representing the minimum mean square error estimation of the expected signal in the form of a linear filter combined with a nonlinear function;

[0012] S4. Estimating the symbol in a multi-stage iteration manner, and obtaining the optimal coefficient equation of the adaptive filter according to the minimum mean square error estimation;

[0013] S5. Updating the adaptive filter coefficient by iteration using the RLS algorithm, and obtaining the estimation value of the expected signal using the updated coefficient.

[0014] The application has the beneficial effects that: the application integrates the equalization module in the self-interference suppression when reconstructing the expected signal, has lower system complexity and lower inter-stage delay, eliminates the decline of the self-interference suppression ability of each stage caused by the quantization error of the equalizer, and reduces the overall quantization noise. BRIEF DESCRIPTION OF DRAWINGS

[0015] Figure 1 It is a schematic diagram of a full-duplex transceiver with multi-stage self-interference suppression and channel equalization integration of expected signal assistance;

[0016] Figure 2A schematic diagram of a multi-stage self-interference suppression and channel equalization integrated module structure assisted by a desired signal;

[0017] Figure 3 A schematic diagram of a multi-stage self-interference suppression and channel equalization integrated module cascade structure;

[0018] Figure 4 A schematic diagram of the relationship between the self-interference suppression capability of each stage and the SNR of the desired signal when the fixed INR is 40 dB;

[0019] Figure 5 A schematic diagram of the relationship between the self-interference suppression capability of each stage and the SNR of the desired signal when the fixed INR is 40 dB and the desired channel is an ISI channel;

[0020] Figure 6 A schematic diagram of the relationship between the bit error rate of each stage and the E b / N0 of the desired signal when the fixed INR is 40 dB;

[0021] Figure 7 A flowchart of the method of the present application. DETAILED DESCRIPTION

[0022] The technical solutions of the present application will be described in further detail below with reference to the accompanying drawings, but the scope of protection of the present application is not limited to the following description.

[0023] As shown in Figure 7 , a full-duplex communication multi-stage self-interference suppression and channel equalization integrated method comprises the following steps:

[0024] S1. For a communication system composed of two full-duplex communication nodes with the same communication system architecture, the two nodes transmit signals and receive signals of the other node at the same frequency point and at the same time; for any node, an expression of the received signal of the receiving end through a RRC filter with a sampling rate of K times the baseband sampling rate and a coupled self-interference signal is given;

[0025] Any full-duplex node described in step S1 comprises a transmitting end, a receiving end, a coupler and a transceiving antenna;

[0026] The transmitting end comprises a QPSK modulation module, a shaping filter, a DAC module, an up-conversion mixer and a power amplifier; the output end of the QPSK modulation module is connected with the coupler through the shaping filter, the DAC module, the up-conversion mixer and the power amplifier in sequence, and the coupler is connected with the transceiving antenna;

[0027] The receiving end comprises a low-noise amplifier, a first ADC module, a second ADC module, a first down-conversion mixer, a second down-conversion mixer, a self-interference suppression filter, an adaptive filtering module and a symbol estimation module;

[0028] The input terminal of the first down-conversion mixer is connected to the output terminal of the power amplifier. The input terminal of the low-noise amplifier is connected to the coupler, and the output terminal of the low-noise amplifier is connected to the second down-conversion mixer. The output terminal of the first down-conversion mixer is connected to the first ADC module, and the output terminal of the second down-conversion mixer is connected to the second ADC module. Both the first and second ADC modules are connected to an adaptive filtering module. The output terminal of the second ADC module is also connected to a self-interference suppression filter. The output terminals of both the adaptive filtering module and the self-interference suppression filter are connected to a symbol estimation module, which outputs the received signal.

[0029] In step S1, for any node, the received signal and coupled self-interference signal after passing through an RRC filter with a sampling rate of K times the baseband sampling rate are given.

[0030] At the receiving end of a full-duplex communication node, there are two input signals: the received signal at the receiving antenna and the coupled self-interference signal.

[0031] Let s be the k-th transmitted symbol sent by a full-duplex communication node. I,k The subscript I represents the interference signal, and the q-th transmitted symbol from another node is denoted as s. D,q The subscript D indicates that the symbol is the desired signal;

[0032] The received signal includes the desired signal containing ISI, the self-interference signal containing ISI, and Gaussian white noise, where ISI represents inter-symbol interference. The received signal is represented as follows:

[0033]

[0034] Where x(t) is the transmitted signal output by the power amplifier after the self-interference signal is passed through the power amplifier. g(t) is the signal pulse waveform, and c0(t) represents the channel impulse response from ADC to PA;

[0035] Let z(t) be the desired signal waveform at another node, where z(t) represents zero-mean Gaussian white noise with variance N0.

[0036] The discrete sampling of the received signal after the RRC filter is expressed as follows:

[0037]

[0038] Where M is the self-interference symbol received pulse dispersion length, L is the desired signal symbol received pulse dispersion length, and K is the upsampling factor of the RRC filter;

[0039] Similarly, the discrete-time representation of the coupled self-interference signal after the RRC filter is

[0040]

[0041] where z ref [n] is a zero-mean Gaussian white noise independent of z[n] with variance N1.

[0042] S2. Discretely sampling the received signal and the feedback signal at the receiving end;

[0043] The step S2 includes:

[0044] Let the received vector be

[0045] The self-interference wireless channel vector is The desired signal wireless channel vector is The Gaussian white noise vector is The relationship of the received symbol, the self-interference symbol and the desired signal symbol is

[0046] r = Xh I + Yh D + z,

[0047] where the self-interference signal matrix X = [x[0], x[-1],..., x[-KM+1]], the desired signal matrix Y = [y[0], y[-1],..., y[-KL+1]], the self-interference symbol vector

[0048] The discrete-time model of the feedback signal is

[0049] x ref = Xh0+ z ref ,

[0050] where are the discrete samples of h0(t) and z ref (t), respectively; similar to the noise vector of the received signal, z ref is also a zero-mean Gaussian random variable with covariance matrix N1I.

[0051] S3. Performing a minimum mean square error (MMSE) estimation of the desired symbol, and representing the minimum mean square error estimation of the desired signal in the form of a linear filter combined with a nonlinear function;

[0052] MMSE estimation of the desired symbol. Assuming that the self-interference symbol has a received pulse dispersion length of M and the desired signal symbol has a received pulse dispersion length of L, the set of transmitted symbols related to s D,0 isI = {s I,0 ,…,s I,M-1},S D = {s D,1 ,…,s D,L-1}. According to MMSE (Minimum Mean Square Error) criterion, the expected signal estimation at t=0 is

[0053]

[0054] Let the summation of the latter part of the expression be Since each symbol transmitted by node 1 and node 2 is independent of each other, we have and its expression can be obtained as

[0055]

[0056] where tanh is the hyperbolic tangent function tanh(z) = (e z - e -z ) / (e z + e -z ).

[0057] Assuming that the self-interference suppression is performed at K times the baseband rate, the input of the tanh function needs to be sampled at a symbol rate of 1 / KT = 1 / T'. At the same time, considering that the system starts to transmit symbols after time 0, the estimated symbol is delayed by max(M, L) symbol periods.

[0058] According to the orthogonality of the basis functions of the K-L expansion, when N→∞, the nonlinear function input of

[0059]

[0060] Substitute , and replace the matched filter of the expected channel with an RRC filter The signal after symbol synchronization at the output end of the filter is represented as:

[0061] Since the received pulse dispersion length of the self-interference symbol is generally small, it is not without generality to assume that M < L, i.e., max(M, L) = L. Let r[n] be the output of the received signal after RRC filtering, u I [n] be the output of the feedback signal after RRC filtering, u D [n] be the output of the expected symbol after decision and RRC filtering, w I,n and w D,nThese are the matched filter coefficients for the self-interference signal and the desired signal, respectively. The MMSE estimate of the desired signal can be expressed as a combination of a linear filter and a nonlinear function:

[0062]

[0063] S4. The symbol is estimated using a multi-level iterative method, and the optimal coefficient equation of the adaptive filter is obtained based on the minimum mean square error estimation.

[0064] Since the estimation formula requires prior knowledge of the expected symbol, a multi-level iterative approach is used to estimate the symbol. The MMSE estimation result of the expected signal in the i-th iteration is y. (i) [n], i = 0, 1, ..., represents the result of reconstructing the input using the previous stage's hard demodulation. The substitution, where the estimated value of the desired signal is zero when i = 0:

[0065] To describe the algorithm more concisely, we write the MMSE estimate of the received symbol in a more compact form. Let

[0066]

[0067] The superscript (i) represents the i-th iteration. Then the optimal solution for the i-th level coefficients satisfies...

[0068] k = 0, 1, ..., KM + KL - K

[0069] The above system of equations is a Wiener-Hopf equation, from which the optimal coefficients of the i-th stage filter can be obtained. In practice, adaptive filter algorithms are generally used to bring the coefficients close to their optimal values.

[0070] The corresponding post-equilibrium symbol estimate is

[0071]

[0072] S5. Using the RLS algorithm, the adaptive filter coefficients are updated iteratively, and the updated coefficients are used to obtain the estimated value of the desired signal, resulting in an estimated value of the desired signal with smaller error.

[0073] 1. Initialize the initial value P for each iteration. (i) [0]=δ -1 I, w (i) [0] = 0.

[0074] 2. For each iteration i = 0, 1, 2, ..., calculate

[0075]

[0076] w (i) [n] = w (i) [n-1]+k (i) [n]ξ * [n]

[0077] P (i) [n]=λ -1 P (i) [n-1]-λ -1 k (i) [n]u (i)H P[n-1]

[0078] 3. Each level This refers to the MMSE estimation of the desired signal, which can be demodulated after K-fold downsampling.

[0079] 4. Because the expected symbol from the previous stage needs to be hard-demodulated and passed through an RRC filter, the input of each stage... y (i-1) Both [n] and r[n] require a delay of D samples to align with the output of the RRC filter, where D is the group delay of the RRC filter.

[0080] The process iterates continuously from i = 0, 1, 2, ... until the bit error rate of the desired signal meets the system requirements; for example:

[0081] The expected signal estimate y at level i (i) [n], received signal r[n], coupling signal u of self-interference signal I [n], the coefficients are further calculated according to the RLS algorithm to obtain the expected signal estimate y of the (i+1)th level. (i+1) [n], until the bit error rate of the desired signal meets the system requirements.

[0082] In the embodiments of this application, Figures 1-3 The diagrams shown are, respectively, a schematic diagram of a multi-stage self-interference suppression and channel equalization integrated full-duplex transceiver with desired signal assistance, a schematic diagram of the multi-stage self-interference suppression and channel equalization integrated module structure with desired signal assistance, and a schematic diagram of the cascaded structure of the multi-stage self-interference suppression and channel equalization integrated module. Based on these,

[0083] The proposed integrated method for multi-level self-interference suppression and channel equalization is then analyzed and evaluated through simulation. Specific parameter settings are shown in the table below.

[0084] Table 1. Simulation parameter settings for the integrated method of multi-level self-interference suppression and channel equalization

[0085]

[0086] In the integrated method of multi-level self-interference suppression and channel equalization, the input self-interference power is:

[0087]

[0088] Where X(f),C I G(f) and G(f) are the self-interference signal x(t) output by PA and the self-interference wireless channel c, respectively. I (t) and the power spectral density function of the shaped filter impulse response g(t), and U I (f)=X ref (f)G(f) is the output power spectral density of the self-interference feedback signal after passing through the receiver shaping filter.

[0089] Let X be the self-interference signal in the received signal. r (f)=U I (f)-N1G(f), defining each level w I (i) The power spectral density is W I (i) (f) then the residual self-interference power output of each stage filter is

[0090]

[0091] We will use the self-interference suppression ratio (SIRR) to measure the performance of the method. The SIRR is defined as the ratio of the sum of self-interference and additive noise power before and after self-interference suppression. The SIRR for the i-th iteration is:

[0092]

[0093] Appendix Figure 4 With appendix Figure 5 The self-interference suppression capability of each stage in the multi-stage integrated self-interference suppression and channel equalization method under both ISI and non-ISI channels is presented. The interference-to-noise ratio (INR) of the self-interference is fixed at 40 dB in the figures. Improving the signal-to-noise ratio of the desired signal implies a decrease in the interference-to-signal ratio (INR) of the self-interference signal, leading to an increase in the variance of the estimated self-interference channel and consequently a decline in self-interference suppression capability. Multi-stage self-interference suppression can alleviate this phenomenon to some extent; the self-interference capability of this algorithm improves with increasing iteration levels.

[0094] The figure also shows that the algorithm is not significantly affected by ISI after the third iteration, and the self-interference suppression capability of the non-ISI channel and the ISI channel is consistent in the third iteration.

[0095] Appendix Figure 6For fixing INR=40dB, the relationship between the error rate of each stage and the expected signal E b / N0. Without the assistance of the reconstructed expected signal, the error rate decreases slowly with the increase of the expected signal E b / N0, and there is an error rate platform. With the increase of the iteration number, the error rate also decreases obviously.

[0096] The error rates of different iterations of stage one and stage two are shown in the figure. When only the first stage is used for self-interference suppression, the error rate decreases slowly with the increase of the expected signal signal-to-noise ratio, and there is an error rate platform when it reaches a certain value. After the second stage of the reconstructed expected signal is used for self-interference suppression, the error rate decreases obviously compared with the first stage.

[0097] The above is the preferred embodiment of the present application, and it should be understood that the present application is not limited to the form disclosed herein, and should not be considered as excluding other embodiments, but can be used in other combinations, modifications and environments, and can be modified within the scope of the concept described herein by the above teaching or related technical or knowledge. Any modification and change made by the person skilled in the art without departing from the spirit and scope of the present application shall be within the protection scope of the claims of the present application.

Claims

1. A method for integrating multi-level self-interference suppression and channel equalization in full-duplex communication, characterized in that: Includes the following steps: S1. For a communication system consisting of two full-duplex communication nodes with identical communication system architecture, the two nodes transmit signals and receive signals from the other node at the same frequency and time. For any node, give the representation of the received signal and the coupled self-interference signal after passing through an RRC filter with a sampling rate of K times the baseband sampling rate at the receiving end. S2. Discretely sample the received signal and the feedback signal at the receiving end; Step S2 includes: Let the received vector Self-interference wireless channel vector Desired signal wireless channel vector Gaussian white noise vector The relationship between the received symbol, the self-interference symbol, and the desired signal symbol is as follows: r=Xh I +Yh D +z, Where the self-interference signal matrix X = [x[0],x[-1],...,x[-KM+1]], The desired signal matrix Y = [y[0], y[-1], ..., y[-KL+1]], and the self-interference symbol vector The discrete-time model of the feedback signal is expressed as follows: x ref =Xh0+z ref , in h0(t) and z are respectively ref Discrete sampling of (t); similar to the noise vector of the received signal, z ref It is also a Gaussian random variable with zero mean and covariance matrix N1I; S3. Perform minimum mean square error estimation of the desired symbol, and express the minimum mean square error estimation of the desired signal as a combination of a linear filter and a nonlinear function; Step S3 includes: Assuming the self-interference symbol received pulse dispersion length is M, and the desired signal symbol received pulse dispersion length is L, then the desired signal s at time t=0... D,0 The relevant set of transmitted symbols is S I ={s I,0 ,…,s I,M-1 },S D ={s D,1 ,…,s D,L-1 According to the MMSE criterion, the expected signal at t=0 is estimated as follows: Let the summation of the second half of the expression be denoted as... Its expression is: in tanh is the hyperbolic tangent function: tanh(z)=(e z -e -z ) / (e z +e -z ); Assuming self-interference suppression is performed at K times the baseband rate, the input of the tanh function needs to be sampled at a symbol rate of 1 / KT = 1 / T′; considering that the system starts transmitting symbols after time 0, the symbol delay will be estimated as max(M,L) symbol periods. Assume M < L, that is, max(M, L) = L. Let r[n] be the output of the received signal passing through the RRC filter, and u I [n] be the output of the feedback signal passing through the RRC filter, and u D [n] be the output of the expected symbol after decision passing through the RRC filter large, and w I,n and w D,n be the matched filter coefficients of the self-interference signal and the desired signal respectively; Express the MMSE estimate of the desired signal in the form of the combination of a linear filter and a non-linear function: Where MMSE refers to the minimum mean square error estimate; S4. The symbol is estimated using a multi-level iterative method, and the optimal coefficient equation of the adaptive filter is obtained based on the minimum mean square error estimation. S5. Using the RLS algorithm, the coefficients of the adaptive filter are updated iteratively, and the updated coefficients are used to obtain the estimated value of the desired signal.

2. The integrated method for multi-level self-interference suppression and channel equalization in full-duplex communication according to claim 1, characterized in that: Each full-duplex node mentioned in step S1 includes a transmitter, a receiver, a coupler, and a transceiver antenna; The transmitting end includes a QPSK modulation module, a shaping filter, a DAC module, an up-conversion mixer, and a power amplifier; the output of the QPSK modulation module is connected to a coupler in sequence through the shaping filter, the DAC module, the up-conversion mixer, and the power amplifier, and the coupler is connected to the transceiver antenna; The receiving end includes a low-noise amplifier, a first ADC module, a second ADC module, a first down-conversion mixer, a second down-conversion mixer, a self-interference suppression filter, an adaptive filtering module, and a symbol estimation module. The input terminal of the first down-conversion mixer is connected to the output terminal of the power amplifier. The input terminal of the low-noise amplifier is connected to the coupler, and the output terminal of the low-noise amplifier is connected to the second down-conversion mixer. The output terminal of the first down-conversion mixer is connected to the first ADC module, and the output terminal of the second down-conversion mixer is connected to the second ADC module. Both the first and second ADC modules are connected to an adaptive filtering module. The output terminal of the second ADC module is also connected to a self-interference suppression filter. The output terminals of both the adaptive filtering module and the self-interference suppression filter are connected to a symbol estimation module, which outputs the received signal.

3. The integrated method for multi-level self-interference suppression and channel equalization in full-duplex communication according to claim 2, characterized in that: The full-duplex node also includes a local oscillator module, which provides local oscillator signals for the upconversion mixer, the first downconversion mixer, and the second downconversion mixer.

4. The integrated method for multi-level self-interference suppression and channel equalization in full-duplex communication according to claim 1, characterized in that: In step S1, for any node, the received signal and coupled self-interference signal after passing through an RRC filter with a sampling rate of K times the baseband sampling rate are given. At the receiving end of a full-duplex communication node, there are two input signals: the received signal at the receiving antenna and the coupled self-interference signal. Let s be the k-th transmitted symbol sent by a full-duplex communication node. I,k The subscript I represents the interference signal, and the q-th transmitted symbol from another node is denoted as s. D,q The subscript D indicates that the symbol is the desired signal; The received signal includes the desired signal containing ISI, the self-interference signal containing ISI, and Gaussian white noise, where ISI represents inter-symbol interference. The received signal is represented as follows: Where x(t) is the transmitted signal output by the power amplifier after the self-interference signal is passed through the power amplifier. g(t) is the signal pulse waveform, and c0(t) represents the channel impulse response from ADC to PA; Let z(t) be the desired signal waveform at another node, where z(t) represents zero-mean Gaussian white noise with variance N0. The discrete sampling of the received signal after the RRC filter is expressed as follows: Where M is the self-interference symbol received pulse dispersion length, L is the desired signal symbol received pulse dispersion length, and K is the upsampling factor of the RRC filter; Similarly, the discrete sampling representation of the coupled self-interference signal after the RRC filter is as follows: Where z ref [n] is zero-mean Gaussian white noise independent of z[n], with a variance of N1.

5. The integrated method for multi-level self-interference suppression and channel equalization in full-duplex communication according to claim 1, characterized in that: Step S4 includes: The expected signal MMSE estimation result of the i-th iteration is y. (i) [n], i = 0, 1, ..., represents the result of reconstructing the input using the previous stage's hard demodulation. Instead, the hard-demodulated symbols are passed through an RRC filter and upsampled by a factor of K, where the estimated value of the desired signal is zero when i = 0: y (0) =0; where MMSE refers to the minimum mean square error estimate; To write the MMSE estimate of the received symbol in a more compact form, define u I [n]=[x[n] x[n-1] … x[n-(KM-1)]] T Let the superscript i represent the i-th iteration, then the optimal solution of the i-th level coefficients satisfies The above system of equations is a Wiener-Hopf equation, i.e., the optimal coefficient equation for an adaptive filter; the optimal coefficients of the i-th stage filter can then be derived from this equation.

6. The integrated method for multi-level self-interference suppression and channel equalization in full-duplex communication according to claim 1, characterized in that: Step S5 includes: S501. Initialize the initial value P for each iteration. (i) [0]=δ -1 I, w (i) [0] = 0; S502. For each iteration i = 0, 1, 2, ..., calculate w (i) [n]=w (i) [n−1]+k (i) [n]ξ * [n] P (i) [n]=λ -1 P (i) [n−1]−λ -1 k (i) [n]u (i)H P[n−1] S503. Each level The desired MMSE estimation of the signal can be demodulated after K-fold downsampling; S504. Because the expected symbol from the previous stage needs to be hard-demodulated and passed through an RRC filter, the input u of each stage... I [n],y (i-1) Both [n] and r[n] are delayed by D samples to align with the output of the RRC filter, where D is the group delay of the RRC filter.

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