CN110445525B - Time domain equalization beam forming method under multipath channel - Google Patents
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Abstract
The invention discloses a time domain equalization wave beam forming method under multipath channel, the receiver receives the signal and carries out weighting combination, the shaping weighting combination is carried out in advance, the shaping weighting factors adopt pre-stored shaping weighting factors w1, w2 and … wka, the main wave beam is formed on the useful signal, the data needed by the optimal solution is estimated to be noisy, the synchronization after the weighting combination is favorable for improving the power of the useful signal, the subsequent synchronization correlation can carry out synchronous sliding treatment on a higher SNR, after the synchronization, the channel estimation is obtained according to the training sequence of the channel, the latest wave beam shaping weighting factor is calculated, the combination of the signal is completed, the synchronous position of the signal is redetermined after the combination is completed, and finally, two time domain cross equalization treatment flows based on pilot frequency and data are started, thus the multipath and random noise can be overcome better after the wave beam shaping received by the receiving end is completed.
Description
Technical Field
The invention relates to the field of wireless communication, in particular to a time domain equalization beam forming method under a multipath channel.
Background
The adaptive antenna provides the freedom degree of spatial signal processing for the design of the mobile communication system on the basis of an antenna array, thereby obviously improving the system performance. The method utilizes the directivity of the array antenna wave beam, leads the wave beam to aim at the target direction through self-adaptive wave beam control, automatically tracks the movement of the user target and leads the null to aim at the interference direction. The antenna array directional diagram can be optimized by self-adapting to the change of the radio wave environment, thereby enhancing the effective signal, inhibiting co-channel interference and multiple access interference, remarkably improving the signal-to-interference-and-noise ratio and enhancing the capacity of a communication system.
Fig. 1 is a block diagram of an adaptive array consisting of L array elements. In the figure, the output of array element m is assumed to be continuous baseband χ m (k) Wherein m=1, 2, …, L and takes element 1 as a reference point, and a total of Q sources are assumed to exist, w q (k) The weight vector added to the demodulation of the q-th signal at time k is determined by a criterion such that the quality of the demodulated q-th signal is in a senseAnd the lower is optimal. In optimal beamforming, the weight vector is determined by minimization of the cost function. In general, the smaller this cost function, the better the quality of the array output signal, and therefore the best the adaptive array output signal quality when the cost function is at a minimum.
The cost function has two most common forms, which correspond to two methods widely used in communication systems: in both methods, the least mean square error (MMSE) method and Least Squares (LS) method are performed by finding the appropriate weight vector w q Make output
And d q (k) The difference between is minimized, wherein d q (k) Is an estimate of the desired signal of the qth user obtained at time k.
These two methods are then introduced:
1) MMSE method
MMSE method criteria:
is to make the estimation error y (k) -d q (k) Least mean square (ensemble average) of (a) i.e. cost function takes:
wherein x (k) = [ x ] 0 (k),x 1 (k),......x M-1 (k)] T
The array of the q-th signal of the cost function outputs a mathematical expectation of the square error between the expected form of the signal at time k.
2-7 can be unfolded
The expression (2-8) can be used to obtain:
wherein R is x Is the autocorrelation matrix of the data vector x (k):
R x ＝E{x(k)x H (k)} (2-10)
and rxd is the data vector x (k) and the desired signal q d (k) Is a cross-correlation vector of (2):
r xd ＝E{x(k)d q (k) H } (2-11)
and (3) making:
then it is possible to obtain:
this is the best antenna array weight vector obtained using the MMSE method.
2) LS method
In the MMSE approach, the cost function is defined as the overall average (mean square error) of the square of the error between the array output and the q-th user's expected response; in fact, the actual data vector is always finite long, so the LS method directly defines the cost function as its square of error:
according to the gradient formula:
let the gradient equal zero, obtain:
w q ＝(X H X) -1 X H d q (2-15)
this results in the best weight vector for the beamformer for the q-th user by the least squares method.
Wherein:
X＝[x(1),x(2),....,x(N),] (2-16a)
d q ＝[d q (1),d q (2),....,d q (N)] (2-16b)
where equation a is a data vector and equation b is a desired signal vector.
The core problems of the above MMSE method and LS method are: in beamforming the q-th user, the receiver and transmitter are required to use the expected response of the user. In order to provide this desired response, a training sequence known to both the transmitter and the receiver must be periodically transmitted, which occupies valuable spectral resources of the communication system, a major drawback common to both the MMSE and LS methods.
In addition to the two best beamforming techniques of MMSE and LS, there are two best beamforming techniques of maximum signal-to-noise ratio (MaxSNR) and Linear Constraint Minimum Variance (LCMV).
The above is based on the calculation of the beamforming factor, and after the calculation of the beamforming factor is completed, the equalization processing needs to be performed on the signals after the combination of multiple antennas, and the subsequent equalization processing plays an important role in the performance of receiving multiple antennas. Subsequent equalization may employ frequency domain equalization or time domain equalization. Since frequency domain equalization requires FFT/IFF processing of the signal, the complexity of the algorithm is increased, and time domain equalization is performed for this purpose. Time domain equalization at this time is required to overcome the multipath and time-varying characteristics of the channel.
In wireless communications, because of the randomness and time-varying nature of mobile fading channels, it is desirable that an equalizer, also known as an adaptive equalizer, must be able to track the time-varying characteristics of the communication channel in real time. The adaptive equalizer can continuously adjust coefficients according to a certain algorithm directly from the transmitted actual digital signals, and can adapt to random changes of channels, so that the equalizer always keeps the optimal working state, and therefore, the adaptive equalizer has better distortion compensation performance.
An adaptive equalizer generally includes two modes of operation, namely a training mode and a tracking mode. First, the transmitter transmits a known fixed-length training sequence so that the equalizer at the receiver can be set correctly. A typical training sequence is a binary pseudo-random sequence signal or a series of pre-specified data bits, followed by the training sequence by the user data to be transmitted. The equalizer at the receiver will evaluate the channel characteristics by a recursive algorithm and modify the filter coefficients to compensate for the channel. In designing the training sequence, it is required that the equalizer obtains the correct filter coefficients through this training sequence even under worst channel conditions. Thus, after receiving the training sequence, the filter coefficient of the equalizer is close to the optimal value; secondly, when receiving data, the adaptive algorithm of the equalizer can track the continuously changing channel, and the adaptive equalizer can continuously change the filtering characteristic
In order to effectively eliminate the intersymbol interference, the equalizer needs to be trained repeatedly periodically. In a digital communication system in which user data is divided into segments and transmitted in corresponding time periods, the equalizer will be modified with the same training sequence each time a new time period is received. The equalizer is typically implemented in the baseband or intermediate frequency portion of the receiver, and the complex representation of the baseband envelope may describe the bandpass signal waveform, so that the channel response, demodulation signal, and adaptation algorithms may be typically emulated and implemented in the baseband portion.
How to better overcome multipath, random noise and time-selective fading by adopting which time domain equalization mode after the receiving end finishes the received wave beam shaping needs a new method.
Disclosure of Invention
The invention aims to provide a time domain equalization beam forming method under a multipath channel so as to solve the problems in the background technology.
In order to achieve the above purpose, the present invention provides the following technical solutions:
a time domain equalization wave beam shaping method under multipath channel, the receiver receives the signal and then carries on weighting combination, the pre-stored shaping weighting factors w1, w2, … wka are adopted as the shaping weighting factors, the main wave beam is formed on the useful signal, the data needed by the best solution is estimated to contain noise, after the weighting combination, the synchronization is carried out, the channel estimation is obtained according to the training sequence of the channel, the latest wave beam shaping weighting factor is calculated, the combination of the signal is completed, after the combination is completed, the synchronous position of the signal is re-determined, finally two time domain cross equalization processing flows based on the pilot frequency and the data are started.
As a further scheme of the invention: the two time domain cross equalization processing flows based on pilot frequency and data are as follows: each correlation of the received pilot signal and the local pilot signal, obtaining a maximum correlation peak point and correlation peak value Th [ Th, maxpos ] =max (xcorr (rcv_train, loc_train)); xcorr is a correlation processing function, rcv_train is a received pilot signal, loc_train is a local pilot signal, th is the maximum correlation value of the local pilot and the received pilot, th is a complex number, has amplitude and phase, represents the characteristic of the maximum value point of the channel, and maxpos is the peak point position; this value Th will become the initial value of the main path dy=mainpos in the equalization coefficient w, start the training coefficient at the local DATA0, equalize the signal of the local DATA1, and set the initial value of the other position of w to zero value by w (Dy) =conj (Th 0); the local original training sequence LOC_TRAIN and the received pilot sequence RCV_TRAIN are aligned strictly on the time axis before the LMS algorithm is updated iteratively, and the LMS algorithm is processed as follows: y (k) =w rcv_train (k: k+lf-1); e (k) =y (k) -loc_train (k+st), rcv_train is the received pilot signal, loc_train is the local pilot signal, w is the trained equalization coefficient, st is the start position of training, the value of st ensures that two training sequences are synchronous, lf is the length of the equalization coefficient, k is the index of the input signal, before the two training sequences are updated by using the LMS algorithm, the MCMA algorithm is adopted to TRAIN the equalization coefficient w of a certain coefficient, so that the trained coefficient w has certain convergence, then the LMS algorithm is used to update the pilot, thus a more accurate equalization coefficient w can be obtained, and after the pilot sequence is updated, after the useful signal DATA-1 of the section is entered, the updating operation of the MCMA algorithm is continued.
As a further scheme of the invention: the update operation flow of the MCMA algorithm is as follows: (1) Receiving a training sequence RCV_TRAIN1 and a local training sequence LOC_TRAIN sliding correlation to find a peak point maxpos, and determining amplitude phase information TH0 of a maximum path; (2) The amplitude phase information determining the main path position main os of the blind equalization MCMA is TH0: w (mainpos) =th0; (3) If the information of the DATA DATA1 is to be time-domain equalized, the blind equalization MCMA is required to train the time-domain equalization coefficient w from the end of DATA-0; (4) The signal starts DD-LMS coefficient training from DATA-0 training to RCV_TRAIN 1; (5) The DD-LMS coefficient is trained to DATA-1, the equalization coefficient w starts DD-MCMA training, and the original symbol information of DATA-1 is equalized while the coefficient is trained; (6) The new coefficient training and signal equalization process is started from cycle to cycle.
As still further aspects of the invention: the processing flow after the antenna receives the data x transmitted by the space is as follows: the received data stream X is firstly subjected to filtering treatment Y (k) =w X (k: k+Lf-1) with the latest trained w; x is the received signal, this signal X is the traffic DATA delivered or is the received pilot signal rcv_train, Y (k) is the result after equalization of the received signal; if the result is the e (k) which is the result after the equalization of the received pilot signal and the error of the local pilot, if the e (k) is smaller, the better the equalization result is indicated; if the pilot signal is a non-RCV_TRAIN pilot signal, the MCMA blind equalization algorithm is adopted to calculate e (n)
e(n)＝＝y R (k)(R DR -|y R (k)| 2 )+y I (k)(R DI -|y I (k)| 2 )；
The meaning of the above formula: r is R DR Is the statistical real part signal power, R DR The method is characterized in that the method is statistical imaginary signal power, YR (n) and YI (n) are real parts and imaginary parts of results after received signal equalization, the meaning of the formula is that a blind equalization algorithm is adopted to judge the real parts and the imaginary parts respectively, an error coefficient e (n) is obtained through the formula, and the smaller the value is, the more aggregated the signals are, and the more accurate the coefficient of signal training is;
after e (k) is calculated, the unified mode of calculation of the rear forward weighting coefficient weight is as follows:
w=w-mu e (k) '. X (k), w on the left of the formula is the last updated equalization coefficient, w on the right of the formula is the current updated weighting coefficient w, e (n)' is the conjugate of the error signal calculated this time, mu is the update step length, generally take 1/2 Σ, q= [4:10], after filtering the received signal X by w to obtain Y (k), constellation decision is performed on Y (k), if the error between the decided constellation point and the signal without decision is: e2 (K) if the magnitude of e2 (K) is large, this indicates that this point requires a new calculation of the equalization coefficient w: wDD =w+2×u_ldde2' ×x; w is the equalization coefficient updated this time, u_ldd is the update step length of the feedback iteration, 1/2 Σ is taken, q= [5:11], wDD is the coefficient after feedback equalization, and finally w1 and wDD are selected for the next use of w according to the error magnitudes e2 (k) and e (k).
Compared with the prior art, the invention has the beneficial effects that: the invention relates to a time domain equalization wave beam shaping method under multipath channel, a receiver receives signals, carries out weighting combination in advance, carries out shaping weighting combination in advance, adopts pre-stored shaping weighting factors w1, w2 and … wka, forms main wave beams on useful signals, and can better overcome multipath and random noise and time selective fading after receiving end completes wave beam shaping.
Drawings
Fig. 1 is a block diagram of an adaptive array consisting of L array elements according to the prior art.
Fig. 2 is a time domain equalization flow chart in the present invention.
Fig. 3 is a cross-over diagram of data and pilot sequences in accordance with the present invention.
Fig. 4 is a flow chart of single carrier time domain cross equalization (LMS-DD-MCMA) in the present invention.
Fig. 5 is a schematic diagram of a decision feedback LMS-MCMA cross equalization selector in accordance with the present invention.
Fig. 6 is a constellation diagram after only MCMA equalization in the present invention
Fig. 7 is a constellation diagram after employing premdma-LMS cross equalization in the present invention.
Fig. 8 is a constellation diagram after MCMA-LMS cross equalization used in the present invention.
Fig. 9 shows the channel equalization coefficients w trained using premdma-LMS in the present invention.
Fig. 10 is a diagram showing the equalization effect after the coefficient w trained by the ZC sequence in the present invention.
Fig. 11 is a graph of equalization effect after m-sequence training of the coefficient w in the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Referring to fig. 1-11, a receiver performs weighted combining after receiving a signal, performs pre-shaped weighted combining, the shaped weighting factors adopt pre-stored shaped weighting factors w1, w2 and … wka, a main beam is formed on a useful signal, and since data required by optimal solution is estimated to be noisy, synchronization after weighted combining is beneficial to improving the power of the useful signal, a subsequent synchronization correlation can perform synchronous sliding processing on a higher SNR, after synchronization, channel estimation is obtained according to a training sequence of the channel, and the channel estimation is used for calculating the latest shaped weighting factor, so that the combination of the signal is completed, the synchronization position of the signal is re-determined after the combination is completed, and finally two time domain cross equalization processing flows based on pilot frequency and data are started, as shown in fig. 2.
Two time domain cross equalization processing flows based on pilot frequency and data are shown in fig. 3, specifically: each correlation of the received pilot signal and the local pilot signal, obtaining a maximum correlation peak point and correlation peak value Th [ Th, maxpos ] =max (xcorr (rcv_train, loc_train)); this value Th will become the initial value of the main path dy=mainpos in the equalization coefficient w, start the training coefficient at the local DATA0, equalize the signal of the local DATA1, and set the initial value of the other position of w to zero value by w (Dy) =conj (Th 0); the local original training sequence LOC_TRAIN and the received pilot sequence RCV_TRAIN are strictly aligned on the time axis before the LMS algorithm iterative update is carried out, when Y (k) =w X (k: k+Lf-1); e (k) =y (k) -loc_train (k+st), the value of st ensures that two training sequences are synchronous, the training of a certain coefficient is performed by adopting the MCMA algorithm before the two training sequences are updated by adopting the LMS algorithm, so that the trained coefficient converges, and after the pilot sequence is updated, the updating operation of the MCMA algorithm is continued after the useful signal DATA-1 in the section is entered.
The update operation flow of the MCMA algorithm is shown in fig. 4, and specifically is as follows: (1) Receiving a training sequence RCV_TRAIN1 and a local training sequence LOC_TRAIN sliding correlation to find a peak point maxpos, and determining amplitude phase information TH0 of a maximum path; (2) The amplitude phase information determining the main path position main os of the blind equalization MCMA is TH0: w (mainpos) =th0; (3) If the information of the DATA DATA1 is to be time-domain equalized, the blind equalization MCMA is required to train the time-domain equalization coefficient w from the end of DATA-0; (4) The signal starts DD-LMS coefficient training from DATA-0 training to RCV_TRAIN 1; (5) The DD-LMS coefficient is trained to DATA-1, the equalization coefficient w starts DD-MCMA training, and the original symbol information of DATA-1 is equalized while the coefficient is trained; (6) The new coefficient training and signal equalization process is started from cycle to cycle.
The processing flow after the antenna receives the data stream x transmitted by the space is as follows: the received data stream X is firstly subjected to filtering treatment Y (k) =w X (k: k+Lf-1) with the latest trained w; determining that the signal is a data stream X, numberBased on the DATA or rcv_train pilot sequence position, if it is rcv_train pilot sequence, and local pilot to perform LMS algorithm update and calculate error signal e (k) =y (k) -loc_train (k+st), if it is non-rcv_train pilot signal, MCMA blind equalization algorithm is used to calculate e (k) =y R (k)(R DR -|y R (k)| 2 )+y I (k)(R DI -|y I (k)| 2 )；
After e is calculated, the unified mode of calculation of the rear forward weighting coefficient weight is as follows:
w1=w-mu e' ×x, after the previous filtering structure Y (K) is obtained, making a constellation decision, if the decided constellation point and the signal error without decision are large e2 (K), it is indicated that this point needs to be recalculated with w: wDD =w+2×u_ldde2' ×x; finally, w1 and wDD are selected for the next use of w according to the error magnitude.
The following compares the 4 antenna receiving shaping treatment, and finally adopts the comparison of different equalization algorithm performances:
firstly, only MCMA algorithm is adopted, the known training sequence is not utilized to update the coefficient of LMS algorithm, and the demodulated constellation diagram is shown in figure 5.
The constellation diagram after pre-LMS-MCMA cross equalization is adopted, the improvement effect is obvious, and the MCMA-LMS-MCMA algorithm equalization is adopted, namely, a section of blind equalization iteration of signals is performed before the LMS algorithm, as shown in fig. 6.
The constellation diagram after the LMS-MCMA cross equalization is adopted, the improvement effect is obvious, the LMS-MCMA algorithm equalization is adopted, namely, no blind equalization iteration processing is performed in advance before the LMS algorithm, and the performance is slightly reduced, as shown in figure 7.
The MCMA blind equalizer adjusts equalizer tap coefficients according to a random gradient algorithm to minimize an MCMA cost function, and an equalizer tap iteration formula is as follows:
w(n+1)＝w(n)+μe(n)x(n)。
from the above, the basic steps of the mCMA algorithm can be derived:
step 1: initialization of
w(0)＝[0……0 TH 0……0]，R p ＝E{|s(n)| 4 }/E{|s(n)| 2 }，
0<μ<<1，n＝0；
Step 2: updating when n=n+1
y(n)＝x T (n)w(n)；
w(n+1)＝w(n)+μy(n)e(n)x(n)。
It can be seen that the whole update procedure of the tap coefficients in the MCMA algorithm is only related to the statistical properties of the received signal and the transmitted signal, and not to the estimated error signal e (n) =d (n) -y (n), so that the algorithm does not need to transmit a training sequence of a certain length when starting the iteration. This MCMA, in combination with the known pilot signal, can be optimized.
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential characteristics thereof. The present embodiments are, therefore, to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.
Furthermore, it should be understood that although the present disclosure describes embodiments, not every embodiment is provided with a separate embodiment, and that this description is provided for clarity only, and that the disclosure is not limited to the embodiments described in detail below, and that the embodiments described in the examples may be combined as appropriate to form other embodiments that will be apparent to those skilled in the art.
Claims (3)
1. The time domain equalization wave beam shaping method under multipath channel is characterized by that after the signal is received by receiver, it utilizes the weighting combination, and adopts the pre-stored shaping weighting factors w1, w2 and … wka to make the shaping weighting factors undergo the process of advance shaping weighting combination, in which ka is the number of antennas; forming a main beam on a useful signal, carrying out synchronization after weighting and combining the data needed by estimating the optimal solution, obtaining channel estimation according to a training sequence of a channel after synchronization, calculating the latest beamforming weighting factor, finishing the combination of the signal, re-determining the synchronization position of the signal after the combination is finished, and finally starting two time domain cross equalization processing flows based on pilot frequency and data;
the two time domain cross equalization processing flows based on pilot frequency and data are as follows: each correlation of the received pilot signal and the local pilot signal, a maximum correlation peak point and correlation peak value Th,
maxpos ] =max (xcorr (rcv_train, loc_train)); xcorr is a correlation processing function, rcv_train is a received pilot signal, loc_train is a local pilot signal, th is the maximum correlation value of the local pilot and the received pilot, th is a complex number, has amplitude and phase, represents the characteristic of the maximum value point of the channel, and maxpos is the peak point position; this value Th will be the initial value of the main path dy=mainos in the equalization coefficient w, starting the training coefficient at the local DATA0, equalizing the signal of the local DATA1, and using w (Dy) =conj (Th 0), where w (Dy) represents the value of the equalization coefficient at the Dy position; conj (Th 0) represents a conjugate value of the amplitude phase information Th0 of the maximum path; the initial values of the other positions of w are set to zero values; the local pilot signal loc_train is used as an original training sequence and the received pilot signal rcv_train is used as a pilot sequence, and before the LMS algorithm iterative updating is carried out, the time axes are aligned strictly, and the LMS algorithm is processed as follows: y (k) = wDD rcv_train (k: k+lf-1);
e (k) =y (k) -loc_train (k+st), wherein Y (k) is a result after equalization of the received signal, rcv_train is a received pilot signal, loc_train is a local pilot signal, e (k) represents an error between the received training sequence which is spatially filtered and combined by w weighting and the local original training sequence, wDD is a target equalization coefficient, st is a starting position of training, a value of st ensures synchronization of the two training sequences, lf is a length of the equalization coefficient, k is an index of the input signal, a training equalization coefficient of a certain coefficient is performed by adopting an MCMA algorithm before the two training sequences are updated by adopting the LMS algorithm, so that the trained equalization coefficient has certain convergence, then the LMS algorithm is updated by using the pilot to obtain a target equalization coefficient, and after the pilot sequence is updated, updating operation of the MCMA algorithm is continued after the useful signal DATA-1 of the present segment is entered.
2. The method for time domain equalization beamforming under a multipath channel according to claim 1, wherein the updating operation flow of the MCMA algorithm is as follows:
receiving a training sequence rcv_train1 and a local training sequence loc_train sliding correlation to find a peak point maxpos, and determining amplitude phase information Th0 of a maximum path;
the amplitude phase information determining the main path position main os of the blind equalization MCMA is TH0: w (mainpos) =th0; where w (mainpos) represents the equalization coefficient value of the mainpos position;
if the information of the DATA DATA1 is to be time-domain equalized, the blind equalization MCMA is required to train the time-domain equalization coefficients from the end of DATA-0; the signal starts DD-LMS coefficient training from DATA-0 training to RCV_TRAIN 1;
the DD-LMS coefficient is trained to DATA-1, the equalization coefficient w starts DD-MCMA training, and the original symbol information of DATA-1 is equalized while the coefficient is trained.
3. The method for time domain equalization beamforming under multipath channel as claimed in claim 2, wherein the processing flow after the antenna receives the data transmitted from the space is as follows: the received signal is firstly subjected to filtering treatment Y (k) = wDD X (k: k+lf-1) with the latest trained target equalization coefficient; where wDD is the target equalization coefficient; x is the received signal; the received signal is the transmitted traffic DATA or the received pilot signal rcv_train, Y (k) being the result after equalization of the received signal; if the received signal is rcv_train pilot sequence, carrying out LMS algorithm updating and calculating e (k) with the local pilot, if e (k) is smaller, indicating that the equalization result is better;if the received signal is a non-rcv_train pilot signal, e (k) =y is calculated by using MCMA blind equalization algorithm R (k)(R DR -|y R (k)| 2 )+y I (k)(R DI -|y I (k)| 2 ) The method comprises the steps of carrying out a first treatment on the surface of the Wherein R is DR Is the statistical real part signal power, R DI Is the statistical imaginary signal power, y R (k) Representing the real part, y, of the result after equalization of the received signal I (k) An imaginary part representing a result after equalizing the received signal;
after e (k) is calculated, the unified mode of calculation of the rear forward weighting coefficient weight is as follows:
W (n) ＝w (n+1) -mu*e(k)'*X(k)，w (n) is the last updated equalization coefficient, w (n+1) Is the equalization coefficient updated this time, e (k)' is the conjugate of the error signal calculated this time, mu is the update step length, mu takes on the value 1/2≡Q, Q= [4:10]]X (k) is a signal received at time k; after filtering the received signal X to obtain Y (k), performing constellation diagram decision on Y (k), if the error between the decided constellation diagram point and the signal without decision is: e2 (K), the signal Y (K) after equalization is decided to be Y1 (K), the error between Y (K) and Y1 (K) is e2 (K) =y (K) -Y1 (K), if the magnitude of e2 (K) is large, it is indicated that this point needs to be calculated again as the target equalization coefficient: wDD =w (n+1) +2*u_ldd*e2(k)*X；w (n+1) Is the equalization coefficient updated this time, u_ldd is the update step length of the feedback iteration, and 1/2≡Q is taken, Q= [5:11]]wDD is the target equalization coefficient, and finally w is based on the error magnitudes e2 (k) and e (k) (n) And wDD for the next use of w.
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