CN109286474B - Underwater acoustic communication adaptive modulation method based on steady-state mean square error - Google Patents

Underwater acoustic communication adaptive modulation method based on steady-state mean square error Download PDF

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CN109286474B
CN109286474B CN201811399364.6A CN201811399364A CN109286474B CN 109286474 B CN109286474 B CN 109286474B CN 201811399364 A CN201811399364 A CN 201811399364A CN 109286474 B CN109286474 B CN 109286474B
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刘志勇
白帆
谭周美
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Harbin Institute of Technology Weihai
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/0001—Systems modifying transmission characteristics according to link quality, e.g. power backoff
    • H04L1/0002—Systems modifying transmission characteristics according to link quality, e.g. power backoff by adapting the transmission rate
    • H04L1/0003—Systems modifying transmission characteristics according to link quality, e.g. power backoff by adapting the transmission rate by switching between different modulation schemes
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Abstract

The invention relates to the technical field of underwater acoustic communication, in particular to an underwater acoustic communication adaptive modulation algorithm based on steady-state mean square error, which is particularly suitable for an actual underwater acoustic communication system and can effectively improve the transmission reliability of the communication system, and is characterized in that a sending end firstly sends a signal to establish a link with a receiving end, processes a received signal to obtain mean square error SMSE and converts the SMSE into SNR; compared with the prior art, the method and the device have the advantages that the state information of the underwater sound channel is not required to be assumed to be known, the adaptive adjustment of the modulation mode is realized based on the output SMSE of the blind equalization, the influence of different underwater sound channels on the detection performance is considered by the index, and the tap length of the blind equalizer can be adaptively adjusted according to the specific underwater sound channel.

Description

Underwater acoustic communication adaptive modulation method based on steady-state mean square error
The technical field is as follows:
the invention relates to the technical field of underwater acoustic communication, in particular to an underwater acoustic communication self-adaptive modulation algorithm based on steady-state mean square error, which is particularly suitable for an actual underwater acoustic communication system, can effectively improve the transmission reliability of the communication system and does not need to assume that channel state information is known.
Background art:
time-space varying multipath and limited bandwidth impose significant limitations on the achievable throughput of a communication system. Rather than adaptive link transmission, to ensure that the system is at an acceptable performance, the system is typically designed for only the worst channel conditions, which results in underutilization of the channel capacity. Particularly, for an underwater acoustic environment, an underwater acoustic channel has a characteristic of narrow bandwidth, and in order to fully utilize limited bandwidth and improve the spectrum utilization rate, research on an adaptive modulation algorithm in underwater acoustic communication is paid attention by researchers at home and abroad.
The existing research on adaptive modulation is mainly focused on terrestrial communication systems, and the research on underwater acoustic environments is limited. Recently, the documents Radosevic A, Ahmed R, Duman T M, et al.adaptive OFDM modulation for underserver access communication [ J ] IEEE Journal of organic Engineering,2014,39(2): 357) 370 propose an adaptive modulation scheme based on channel prediction, which is implemented on the premise that the channel information of the previous time is estimated, and then the channel information of the future is predicted based on the channel information of the previous time, so as to realize the adjustment of the modulation scheme. The documents Wan L, Zhou H, Xu X, et al.adaptive modulation and coding for underserver-based OFDM [ J ]. IEEE Journal of organic Engineering,2015,40(2): 327 and 336 propose an adaptive modulation scheme based on signal-to-noise ratio, which uses the estimated channel state information to calculate the effective signal-to-noise ratio to adjust the modulation mode as a metric. However, both of these adaptive modulation methods need to assume that the Channel State Information (CSI) is known, but due to the complex variability of the underwater acoustic Channel, the CSI is difficult to obtain.
The general architecture of the adaptive modulation system is shown in fig. 1. In operation, first, a transmitter sends a signal to establish a link with a receiver. Then, the receiving end carries out signal-to-noise ratio estimation according to the received signal and feeds back the signal to the transmitter for realizing the self-adaptive selection of the modulation mode.
The received signals of the modulating signals s (n) after passing through the underwater acoustic channel are as follows:
r(n)＝s(n)*h(n)+v(n) (1)
wherein h (n) is impulse response of the underwater acoustic channel obtained by BELLHOP model, v (n) is additive white Gaussian noise, mean value is zero, and variance is
Figure GDA0002815297350000011
Denotes a convolution operation;
the existing adaptive modulation schemes based on signal-to-noise ratio are as follows: as shown in the system block diagram of the receiving end shown in fig. 2, on one hand, the received signal is sent to the blind equalizer to recover the transmitted modulation information; on one hand, the method is used for estimating the Signal-to-Noise Ratio (SNR) and feeding back the SNR to a sending end for adaptive selection of a modulation mode.
For SNR estimation, after channel estimation is performed based on a Least Square (LS) criterion, SNR calculation is performed according to the channel estimation result. The channel estimation is estimated by a known training sequence, and the basic principle is to estimate the channel impulse response and minimize the error between the estimated channel impulse response and the actual channel impulse response. The received signal is represented by equation (1), and its frequency domain form can be expressed as: r is HS + V (2)
The cost function of the channel estimate is expressed as:
Figure GDA0002815297350000012
the above formula is subjected to partial derivation to obtain:
Figure GDA0002815297350000021
thus, the impulse response function of the channel is derived as:
Figure GDA0002815297350000022
assuming that the transmitted signal energy is normalized, the snr estimate is:
Figure GDA0002815297350000023
after the SNR is estimated, the instantaneous SNR is fed back to the sending end. Assuming that the channel is unchanged during this period, the transmitting end selects the modulation scheme based on the received feedback estimated SNR. Whereas the switching threshold in the adaptive modulation algorithm is of utmost importance. The threshold determination method is obtained based on the maximum system throughput criterion, and the throughput is defined as the information amount which can be correctly transmitted in the system per unit time, and is as follows:
Γ(γ)＝(1-BER(γ))log2(M) (7); it follows that the throughput Γ is a function of the signal-to-noise ratio γ, and M represents the size of the constellation. According to the document [3]The BER approximate formula of the bit error rate and the signal-to-noise ratio under different modulation modes is given in the step (1), and the adaptive modulation algorithm based on the maximized throughput comprises the following steps:
(1) assuming that there are n modulation schemes to be selected in the adaptive modulation scheme, the set thereof can be expressed as m ═ m1,m2,...,mn}；
(2) The throughput curves of n modulation modes will generate n-1 intersection points, the signal-to-noise ratio interval is divided into n sections of intervals, and n-1 throughput curves are calculatedSNR corresponding to the line intersection point is the switching threshold of the modulation mode, and the set s is usedΓ＝{sΓ,1,sΓ,2,...,sΓ,n-1Means that, in order to find the switching threshold of adaptive modulation based on the maximum throughput criterion, the throughputs of two adjacent modulation schemes are made equal, and the intersection point can be solved to obtain the threshold sΓ＝{sΓ,1,sΓ,2,...,sΓ,n-1As shown below:
Γi(γ)＝Γi+1(γ)i＝1,2,...,n-1 (8)
wherein, gamma isiAnd (gamma) represents the throughput of the ith modulation mode selected by the adaptive modulation mode. The following table gives the theoretical thresholds calculated based on the maximize throughput criterion:
table 1 switching threshold statistical table of modulation system
Figure GDA0002815297350000024
(3) Set of threshold values sΓ＝{sΓ,1,sΓ,2,...,sΓ,n-1Dividing the whole SNR interval into n intervals, if the instantaneous SNR fed back by the receiving end is represented by gamma, when gamma is less than sΓ,1、sΓ,j≤γ＜sΓ,j(j is more than or equal to 1 and less than or equal to n-2) or gamma is more than or equal to sΓ,n-1And selecting the modulation mode with the maximum throughput in the corresponding interval.
As can be seen from the above, in the conventional SNR-based adaptive modulation scheme, the modulation scheme is selected by using the signal-to-noise ratio as an index, and the estimation of the signal-to-noise ratio depends on the estimation of the underwater acoustic channel. In fact, due to the complex variability of the underwater acoustic channel, the channel state information is difficult to estimate and obtain, so that the signal-to-noise ratio estimation is difficult to implement, and therefore the traditional adaptive modulation scheme based on the signal-to-noise ratio is not suitable for the actual underwater acoustic communication system.
The invention content is as follows:
aiming at the defects and shortcomings in the prior art, the invention provides the underwater acoustic communication adaptive modulation algorithm based on the steady-state mean square error, which is more suitable for an actual underwater acoustic communication system, realizes adaptive modulation based on the output SMSE of a blind equalizer, converts the SMSE into a signal-to-noise ratio to select a modulation mode, does not need channel estimation, and obtains the state information of an underwater acoustic channel.
The invention can be achieved by the following measures:
a underwater acoustic communication self-adaptive modulation algorithm based on steady-state mean square error is characterized in that a sending end firstly sends a signal to establish a link with a receiving end, and the received signal is processed to obtain mean square error SMSE and converted into SNR; then, feeding back to the sending end to perform adaptive selection of a modulation mode, wherein a received signal vector entering the blind equalizer is represented by the following formula:
uf(n)＝[r(n),...,r(n+L-1)] (10)
the output of the signal vector after blind equalization is:
Figure GDA0002815297350000031
wherein, the tap weight vector and the tap coefficient update are respectively:
wf(n)＝[c(0),c(1),...,c(L-1),]T (12)
Figure GDA0002815297350000032
wherein the error signal is:
e(n)＝efR(n)+jefI(n) (14)
wherein the real part e of the error signalfR(n) and imaginary part efIThe specific calculation formula of (n) is as follows:
Figure GDA0002815297350000033
Figure GDA0002815297350000034
blind equalization employs a Multi-Modulus Algorithm (MMA), where the constant Modulus R is constant2Real part R of2RWith the imaginary part R2IRespectively, as follows:
Figure GDA0002815297350000035
Figure GDA0002815297350000041
calculating SMSE from the output error signal e (n) of the blind equalization, which can be given by:
Figure GDA0002815297350000042
the SNR can be calculated by:
Figure GDA0002815297350000043
then, on the basis of the result of the formula (19), the estimated SNR is corrected by using a data fitting algorithm, so that the modulation mode can be better selected, and the specific steps are as follows:
(1) using a polynomial curve fitting method, for a given two sets of data: the actual SNR and the estimated SNR are respectively represented by gammas＝[γs,1,γs,2,...,γs,m]And gammag＝[γg,1,γg,2,...,γg,m]Expressing, constructing an n (n ≦ m) degree polynomial expressed as follows:
Figure GDA0002815297350000044
to make the estimated signal-to-noise ratio closer to the actual signal-to-noise ratio, the sum of the squared data errors at the same location is minimized as shown in the following equation:
Figure GDA0002815297350000045
thus, the problem translates into the solution I (a)0,a1,...,an) The minimum problem of (a) is expressed as follows:
Figure GDA0002815297350000046
namely, it is
Figure GDA0002815297350000047
In matrix form, can be represented as:
Figure GDA0002815297350000048
as known from mathematical knowledge, the formula (25) has only a unique solution, and the unique solution is an nth-order polynomial pn(γg) Coefficient A ═ a0,a1,...,an]And the coefficient array A can be obtained by solving the equation set (25) by a principal component elimination method in mathematics.
(2) Obtaining a polynomial coefficient A ═ a through the step (1)0,a1,...,an]Then, a polynomial fitting relation between the actual SNR and the estimated SNR is obtained and substituted into the solved polynomial relation
Figure GDA0002815297350000051
After obtaining the curve fit, the improved SMSE versus SNR relationship is as follows:
Figure GDA0002815297350000052
wherein, S ═ SMSE1,SMSE2,...,SMSEn](i ═ 1,2,. cndot., n), and (0 < SMSE)i≤1)。
After the relation between the SMSE and the SNR is obtained through data fitting, the adaptive modulation algorithm is realized according to the maximum throughput criterion, and the steps are the same as the conventional adaptive modulation processing flow based on the SNR, which is not repeated.
The invention further provides variable tap length adaptive modulation based on SMSE, wherein a receiving end structure adopts a piecewise linear filter structure, and a blind equalizer updates the length of a tap coefficient vector by comparing Accumulated mean square errors (ASE) under different lengths, feeds back the length to a sending end for carrying out adaptive selection of a modulation mode to estimate SNR, and also obtains the estimated SNR based on the output SMSE of variable tap length blind equalization;
where l is represented as the tap length of the segmented FIR filter used in the current algorithm, and the tap weight vector of the blind equalizer is wv(n)＝[c(0),c(1),...,c(l-1),]TWith u (n) ═ r (0),.., r (l-1)]Representing the signal vector, w (n +1) at the next time instant is given according to the principle of the stochastic gradient descent method, as shown in the following equation:
Figure GDA0002815297350000053
Figure GDA0002815297350000054
the ASE used for tap length adjustment can be derived from:
Figure GDA0002815297350000055
wherein l represents the number of segments contained in the current tap vector, the length of each segment is p, beta is less than or equal to 1, and e is a forgetting factor in the algorithmvl(n) is the error of the current segment;
evl(n)＝yvl,R(n)(|yvl,R(n)|2-R2R)+jyvl,I(n)(|yvl,I(n)|2-R2I) (30)
wherein the constant modulus R in the blind equalizer2See expressions (17) and (18);
as shown by the formula (29), the segment l can be obtained
Figure GDA0002815297350000056
For obtaining stage l-1 in the same way
Figure GDA0002815297350000057
Figure GDA0002815297350000061
If it is
Figure GDA0002815297350000062
It is shown that increasing the tap length improves the performance of the blind equalization. In the next iteration, the algorithm will increase the tap length of the blind equalization, since the filter tap weight vector w (n) in the blind equalization is initialized to the minimum value of the desired value of the cost function only if the center tap of the non-zero value is initialized, i.e., to w (0) ([ 0.. 0., 0,1, 0.. 0., 0.](ii) a To ensure the weight of the center tap is the greatest, in the algorithm update of adding p taps, the weight tap vector wv(n) spread to both sides as shown in the following formula:
Figure GDA0002815297350000063
accordingly, the signal vector uv(n) is:
uv(n)＝[r(n),...,r(n+l+p-1)] (33)
if it is
Figure GDA0002815297350000064
It is indicated that increasing the tap length will decrease the performance of blind equalization, and in the next iteration the algorithm will decrease the tap length of blind equalization, with its tap weight vector wv(n) and a signal vector uv(n) respectively represent the following:
Figure GDA0002815297350000065
uv(n)＝[r(n),...,r(n+l-p-1)] (35)
parameter alpha participating in tap updating in variable tap blind equalization algorithmupAnd alphadownThe following relationship should be satisfied:
Figure GDA0002815297350000066
wherein alpha isupAnd alphadownThe closer the value of (d), the more frequently the tap length changes; and fitting the SMSE obtained by the blind equalization of the variable tap length to obtain a corrected estimated SNR, feeding the corrected estimated SNR back to a transmitting end, and realizing the self-adaptive adjustment of the modulation mode based on the maximum system throughput criterion.
The invention provides an adaptive modulation algorithm taking a blind equalization output Steady-State Mean Square Error (SMSE) as an index, the algorithm does not need to assume that the state information of a hydroacoustic channel is known, the adaptive adjustment of a modulation mode is realized based on the output SMSE of the blind equalization, the index considers the influence of different hydroacoustic channels on the detection performance, and the tap length of the blind equalizer can be adaptively adjusted according to the specific hydroacoustic channel.
Description of the drawings:
fig. 1 is a general block diagram of adaptive modulation.
Fig. 2 is a block diagram of an adaptive modulation receiving end based on SNR.
Fig. 3 is a block diagram of a receiver structure of the SMSE-based fixed tap length adaptive modulation in the present invention.
Fig. 4 is a block diagram of a receiver structure of the SMSE-based variable tap length adaptive modulation.
Fig. 5 is a graph of estimated SNR versus actual SNR for BPSK modulation in a simulated embodiment of the invention.
Fig. 6 is a graph of the estimated SNR versus the actual SNR under 4QAM modulation in a simulated embodiment of the present invention.
Fig. 7 is a graph of estimated SNR versus actual SNR under 8QAM modulation in a simulated embodiment of the present invention.
Fig. 8 is a graph of estimated SNR versus actual SNR for 16QAM modulation in a simulated embodiment of the present invention.
Fig. 9 is a graph of throughput for different modulation schemes based on fixed tap length of SNR in a simulated embodiment of the present invention.
Fig. 10 is a graph of throughput for different modulation schemes based on SNR for varying tap lengths in a simulated embodiment of the present invention.
Fig. 11 is a graph of throughput for different modulation schemes based on the fixed tap length of SMSE in a simulated embodiment of the present invention.
Fig. 12 is a graph of throughput for different modulation schemes based on SMSE's varying tap lengths in a simulated embodiment of the invention.
Fig. 13 is a graph of throughput comparison for SNR-based adaptive modulation schemes in a simulated embodiment of the present invention.
The specific implementation mode is as follows:
the invention is further explained by combining the attached drawings and simulation experiments.
The system simulation parameters are set as follows: assuming that the length of the transmitted information sequence is 1000 bits, the carrier frequency is 12kHz, the underwater acoustic channel is obtained by adopting a BELLHOP model, the transmitting end and the receiving end are both positioned at 10m deep positions below the sea surface, the sea wave is 0.6m high, and the distance between the transmitting end and the receiving end is 100 m. The modulation modes are BPSK, 4QAM, 8QAM and 16 QAM.
The SNR estimate based on the SMSE fit to the data is as follows: the effectiveness of the SNR estimation based on SMSE is first verified and the corrected estimate, the uncorrected estimate, and the actual SNR are compared. When the modulation scheme is BPSK, the simulation result is shown in fig. 5, and this result verifies that the relationship between SMSE and SNR in equation (20) is correct, and that selection of the adjustment scheme can be achieved by estimating SNR using SMSE, but due to the non-ideality of blind equalization, there is an error between the output SMSE and the theoretical optimum value. As can be seen from fig. 5, the relationship between the SNR estimation value obtained by the polynomial curve fitting method and the actual SNR is more approximate, and the relationship after the curve fitting is as follows:
Figure GDA0002815297350000071
wherein S is SMSE value in the adaptive modulation system, gammagTo estimate the SNR value.
When the modulation scheme is 4QAM, the relationship curve between the estimated SNR and the actual SNR is as shown in fig. 6, and the curve fitting relationship between the estimated SNR and the actual SNR is as follows:
Figure GDA0002815297350000072
when the modulation scheme is 8QAM, the relationship curve between the estimated SNR and the actual SNR is as shown in fig. 7, and the curve fitting relationship between the estimated SNR and the actual SNR is as follows:
Figure GDA0002815297350000073
when the modulation scheme is 16QAM, the relationship curve between the estimated SNR and the actual SNR is as shown in fig. 8, and the curve fitting relationship between the estimated SNR and the actual SNR is as follows:
Figure GDA0002815297350000081
as can be seen from fig. 5 to 8, the results are similar, and the fitted estimated SNR equalization approaches the actual SNR, so that a scheme for implementing a modulation scheme based on SMSE is feasible.
The simulation results of the throughput curves under different modulations are compared, wherein fig. 9-10 show the simulation results of the throughput curves under different modulation modes based on the SNR in the prior art.
Fig. 11-12 show simulation results of throughput curves based on SMSE under different modulation modes.
As can be seen from the throughput curves of the different adaptive modulation schemes described above, the intersection point of the throughput curve with adaptive modulation based on fixed taps is smaller than the intersection point of the throughput curve with adaptive modulation based on variable tap lengths. This is because when adaptive modulation adopts a variable-tap blind equalization algorithm, better SMSE performance can be obtained, thereby improving output SNR and improving throughput performance of the system.
The following compares the throughput of different adaptive modulation schemes:
fig. 13 shows a comparison of throughput curves for two adaptive modulation schemes under the maximize throughput criterion. As can be seen from fig. 13, regardless of whether adaptive modulation is implemented based on SNR or based on SMSE, when the receiving end uses variable tap length blind equalization, the throughput of the system is improved. This is because the variable tap length blind equalization detection can achieve better error rate performance. This shows that the adaptive modulation algorithm based on the variable tap length is more suitable for the complicated and varied underwater sound channel. Furthermore, as can be seen from fig. 13, under the same blind equalization precondition, the adaptive modulation scheme based on SMSE proposed by the present invention can obtain throughput performance close to that of the adaptive modulation scheme based on SNR. However, the scheme provided by the invention does not need to estimate the underwater acoustic channel, and is more suitable for the actual underwater acoustic communication system.
In summary, the invention provides a steady-state mean square error-based underwater acoustic communication adaptive modulation algorithm, and the scheme is based on output SMSE estimation SNR of blind equalization, realizes adaptive selection of a modulation mode based on a maximum system throughput criterion, and does not need underwater acoustic channel state information estimation in the traditional method. In addition, a variable tap length blind equalization detection algorithm is provided, which is used for improving the error rate performance of the system and further improving the throughput index of the system. The simulation result verifies the effectiveness of the algorithm for realizing the adaptive modulation and the blind equalization detection with the variable tap length based on the SMSE. Simulation results also verify that the adaptive modulation algorithm can obtain system throughput performance similar to that of the traditional method, but the scheme is more suitable for realizing the actual underwater acoustic communication system.

Claims (2)

1. A underwater acoustic communication adaptive modulation method based on steady state mean square error is characterized in that a sending end firstly sends a signal to establish a link with a receiving end, processes a received signal to obtain mean square error SMSE and converts the SMSE into SNR; then the receiving end feeds back to the sending end to perform adaptive selection of a modulation mode, wherein a received signal vector entering the blind equalizer is represented as the following formula:
uf(n)＝[r(n),...,r(n+L-1)] (10)
the output of the signal vector after blind equalization is:
Figure FDA0002815297340000011
wherein, the tap weight vector and the tap coefficient update are respectively:
wf(n)＝[c(0),c(1),...,c(L-1),]T (12)
Figure FDA0002815297340000012
wherein the error signal is:
e(n)＝efR(n)+jefI(n) (14)
wherein the real part e of the error signalfR(n) and imaginary part efIThe specific calculation formula of (n) is as follows:
Figure FDA0002815297340000013
Figure FDA0002815297340000014
blind equalization employs a Multi-Modulus Algorithm (MMA), where the constant Modulus R is constant2Real part R of2RWith the imaginary part R2IRespectively, as follows:
Figure FDA0002815297340000015
Figure FDA0002815297340000016
calculating SMSE from the output error signal e (n) of the blind equalization, which can be given by:
Figure FDA0002815297340000017
the SNR can be calculated by:
Figure FDA0002815297340000018
then, on the basis of the result of the formula (20), the estimated SNR is corrected by using a data fitting algorithm, so that the modulation mode can be better selected, and the specific steps are as follows:
step (1) adopts a polynomial curve fitting method, and for given two groups of data: the actual SNR and the estimated SNR are respectively represented by gammas＝[γs,1,γs,2,...,γs,m]And gammag＝[γg,1,γg,2,...,γg,m]Expressing, constructing an n (n ≦ m) degree polynomial expressed as follows:
Figure FDA0002815297340000021
to make the estimated signal-to-noise ratio closer to the actual signal-to-noise ratio, the sum of the squared data errors at the same location is minimized as shown in the following equation:
Figure FDA0002815297340000022
thus, the problem translates into the solution I (a)0,a1,...,an) The minimum problem of (a) is expressed as follows:
Figure FDA0002815297340000023
namely, it is
Figure FDA0002815297340000024
In matrix form, can be represented as:
Figure FDA0002815297340000025
as known from mathematical knowledge, the formula (25) has only a unique solution, and the unique solution is an nth-order polynomial pn(γg) Coefficient A ═ a0,a1,...,an]And the coefficient array A can be obtained by solving an equation set (25) by a principal component elimination method in mathematics; step (2) obtains a polynomial coefficient a ═ a through step (1)0,a1,...,an]Then, a polynomial fitting relation between the actual SNR and the estimated SNR is obtained and substituted into the solved polynomial relation
Figure FDA0002815297340000026
After obtaining the curve fit, the improved SMSE versus SNR relationship is as follows:
Figure FDA0002815297340000031
wherein, S ═ SMSE1,SMSE2,...,SMSEn](i ═ 1,2,. cndot., n), and (0 < SMSE)i≤1)；
After the relation between the SMSE and the SNR is obtained through data fitting, the adaptive modulation algorithm is realized according to the maximum throughput criterion.
2. The underwater acoustic communication adaptive modulation method based on the steady-state mean square error is characterized in that adaptive modulation of variable tap length based on SMSE is provided, a receiving end structure adopts a piecewise linear filter structure, a blind equalizer updates the length of a tap coefficient vector by comparing accumulated mean square errors under different lengths, and feeds back the length to an estimated SNR (signal to noise ratio) used for carrying out adaptive selection of a modulation mode at a sending end, and the estimated SNR is also obtained based on the output SMSE of the variable tap length blind equalization;
where l is represented as the tap length of the segmented FIR filter used in the current algorithm, and the tap weight vector of the blind equalizer is wv(n)＝[c(0),c(1),...,c(l-1),]TWith u (n) ═ r (0),.., r (l-1)]Representing the signal vector, w (n +1) at the next time instant is given according to the principle of the stochastic gradient descent method, as shown in the following equation:
Figure FDA0002815297340000032
Figure FDA0002815297340000033
the ASE used for tap length adjustment can be derived from:
Figure FDA0002815297340000034
wherein l represents the number of segments contained in the current tap vector, the length of each segment is p, beta is less than or equal to 1, and e is a forgetting factor in the algorithmvl(n) is the error of the current segment;
evl(n)＝yvl,R(n)(|yvl,R(n)|2-R2R)+jyvl,I(n)(|yvl,I(n)|2-R2I) (30)
wherein the constant modulus R in the blind equalizer2See expressions (17) and (18);
expressed by formula (29), giving segment I
Figure FDA0002815297340000035
For obtaining stage l-1 in the same way
Figure FDA0002815297340000036
Figure FDA0002815297340000037
If it is
Figure FDA0002815297340000038
It is shown that increasing the tap length improves the performance of the blind equalization, and in the next iteration, the algorithm will increase the tap length of the blind equalization, and since the filter tap weight vector w (n) in the blind equalization is initialized to the minimum value of the expected value of the cost function only if the center tap of the non-zero value is initialized, that is, to w (0) ([ 0., 0,1, 0., 0)](ii) a To ensure the weight of the center tap is the greatest, in the algorithm update of adding p taps, the weight tap vector wv(n) spread to both sides as shown in the following formula:
Figure FDA0002815297340000041
accordingly, the signal vector uv(n) is:
uv(n)＝[r(n),...,r(n+l+p-1)] (33)
if it is
Figure FDA0002815297340000042
It is shown that increasing the tap length reduces the performance of the blind equalization and in the next iteration the algorithmThe tap length of the blind equalization will be reduced by the tap weight vector wv(n) and a signal vector uv(n) respectively represent the following:
Figure FDA0002815297340000043
uv(n)＝[r(n),...,r(n+l-p-1)] (35)
parameter alpha participating in tap updating in variable tap blind equalization algorithmupAnd alphadownThe following relationship should be satisfied:
Figure FDA0002815297340000044
wherein alpha isupAnd alphadownThe closer the value of (d), the more frequently the tap length changes; and fitting the SMSE obtained by the blind equalization of the variable tap length to obtain a corrected estimated SNR, feeding the corrected estimated SNR back to a transmitting end, and realizing the self-adaptive adjustment of the modulation mode based on the maximum system throughput criterion.
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