CN112953612B - A time-robust maximum ratio combining method and system - Google Patents

Abstract

The invention discloses a maximum ratio combining method and a maximum ratio combining system with time robustness, wherein the method comprises the following steps of: s1, a single-antenna transmitter generates and transmits a transmission signal s (t); s2. Signal x received by ith receiving antenna in multi-antenna receiver _i (t); s3, discrete sampling x after digital-to-analog conversion and matched filtering processing _i (k) (ii) a S4, obtaining an optimized weight vector based on a minimum mean square error criterion

S5, for x _i (k) And carrying out maximum ratio combination with time robustness to obtain an output signal y (k). The invention realizes the improved maximum ratio combination under the condition that timing errors exist among the multiple antennas of the receiver, and effectively solves the problem of non-ideal maximum ratio combination performance caused by time misalignment.

Description

A time-robust maximum ratio combining method and system

technical field

The invention relates to a single-input multiple-output system, in particular to a time-robust maximum-ratio combining method and system.

Background technique

Combining technology is how to use these signals to reduce the influence of fading after receiving multiple independent fading signals. There are mainly selective combining, equal gain combining, square rate combining and maximum ratio combining, among which the maximum ratio combining method has the best performance. The method improves the received signal-to-noise ratio by weighting and summing the different channel attenuations of multi-antenna received signals, thereby providing better bit error rate performance.

Maximum ratio combining requires time alignment of multiple received signals, but in practical applications, due to the limitations of multiple receiving antennas and hardware resolution of different propagation paths, it is almost impossible to achieve perfect time alignment and matched filtering.

Contents of the invention

The purpose of the present invention is to overcome the deficiencies of the prior art, provide a time-robust maximum ratio combining method and system, realize the improved maximum ratio combining in the presence of timing errors, and effectively solve the problem of imperfect time alignment The problem of the deterioration of the output signal-to-noise ratio under the condition is improved, and the output signal-to-noise ratio under the imperfect time alignment is improved, and the maximum ratio combining performance is improved.

The purpose of the present invention is achieved through the following technical solutions: a time-robust maximum ratio merging method, comprising the following steps:

S1. The single-antenna transmitter generates and transmits a transmission signal s(t);

S2. The signal x _i (t) received by the i-th receiving antenna in the multi-antenna receiver;

S3. Discrete sampling x _i (k) processed by digital-to-analog conversion and matched filtering;

S4. Obtain the optimal weight vector based on the minimum mean square error criterion

S5. Perform time-robust maximum ratio combining on x _i (k), i=1, 2, . . . , M, to obtain an output signal y(k).

In the step S1, considering a single-input multiple-output system with M receiving antennas, the transmitted transmission signal s(t); is expressed as:

Wherein, s(k) is the transmitted kth transmission symbol, T is the symbol period, and p(t) is the pulse shaping filter.

In the step S2, after passing through the channel, the signal x _i (t) received by the i-th receiving antenna in the multi-antenna receiver is:

x _i (t) = h _i s(t-τ _i )+n _i (t)

where h _i and τ _i represent the complex channel fading and propagation delay at the i-th receiving antenna, respectively, and n _i (t) is the additive white Gaussian noise at the i-th receiving antenna.

In the step S3, after performing digital-to-analog conversion and matched filter processing at the i-th receiving antenna, discrete sampling is performed, and the discrete sampling result is:

Among them, i=1,2,..,M, x _i (k) represents the sampling result corresponding to the kth transmission symbol received at the i-th antenna, and n _i (k) is the i-th receiving antenna Discrete additive white Gaussian noise corresponding to the kth transmitted symbol.

Said step S4 comprises the following sub-steps:

S401. A two-dimensional tapped delay line model is set at each receiving antenna, and the input end of each two-dimensional tapped delay line model is used to receive the discrete sampling results at the root receiving antenna, and each two-dimensional tapped delay line model The signals output by the output end are combined to obtain the maximum ratio combination result;

Each two-dimensional tapped delay line model includes L-1 delays, L-1 adders and L multipliers. In each two-dimensional tapped delay line model, the input of the first delay is connected to To receive the discrete sampling results at the antenna, the output of the first delayer is connected to the input of the second delayer, the output of the second delayer is connected to the input of the third delayer, and so on. The output terminal of the j'th delayer is connected to the input terminal of the j'+1th delayer, j'=1,2,...,L-2; at the same time, the signal at the input terminal of the first delayer passes through the first A multiplier is multiplied by the weight and connected to the first input of the first adder, and the output signal of the first delay is multiplied by the second multiplier and then connected to the first adder. The second input terminal; the output terminal of the first adder is connected to the first input terminal of the second adder, and the output signal of the second delayer is multiplied by the weight by the third multiplier and then connected to the first input terminal The second input of the 2 adders; and so on, the output of the j'th adder is connected to the first input of the j'+1 adder, and the output of the j'+1 delay The signal is multiplied by the weight of the j'+2 multiplier and then connected to the second input of the j'+1 adder, j'=1,2,...,L-2; the L-1 The signal output by each adder is the final output signal of the two-dimensional tapped delay line model;

S402. Set the i-th row and the j-th column of the weight matrix W as w _i,j , i=1,2,...,M, j=1,2,...,L, w _i,j represent the i-th The weight value multiplied by the jth multiplier at the root receiving antenna, and the weight matrix W is a matrix of M×L dimensions;

其中Vec()表示拉直函数，其功能为将矩阵中的每个元素作为一行，从而得到拉直后的向量；Straighten the weight matrix W to get the weight vector of ML×1

Among them, Vec() represents the straightening function, and its function is to treat each element in the matrix as a row, so as to obtain the straightened vector;

S403. Let X(k) represent the input matrix within the sampling period corresponding to the kth transmission symbol, the element of the i-th row and j-th column of X(k) is x _i (k+j), i=1,2,. ., M, j=1, 2,..., L, the input matrix X(k) is a matrix of M×L dimensions;

Straighten the input matrix X(k) to obtain ML×1-dimensional input vector X(k)=Vec(X(k));

S404. Perform maximum ratio combination on the sampling results corresponding to the kth transmission symbol to obtain y(k):

Among them, tr() represents the trace of the matrix;

S405. Obtain the optimal weight vector based on the minimum mean square error criterion

为

的自相关矩阵，且

为

与s(k) 的自相关向量，其中s^*(k)表示s(k)的共轭；E{}表示函数期望；in

for

The autocorrelation matrix of , and

for

The autocorrelation vector with s(k), where s ^* (k) represents the conjugate of s(k); E{} represents the function expectation;

对应的最优权值矩阵表示为：and optimize the weight vector

The corresponding optimal weight matrix is expressed as:

表示最优权值向量

中的第i′个元素，i′＝1,2,...,ML。in

Represents the optimal weight vector

The i′th element in , i′=1,2,...,ML.

Described step S5 comprises:

作为

带入步骤S404中，计算出相应的y(k)，即为最终的最大比合并结果。will optimize the weight vector

as

Entering into step S404, the corresponding y(k) is calculated, which is the final maximum ratio combination result.

A time-robust maximum-ratio merging system comprising:

a single-antenna transmitter for generating and transmitting a transmission signal;

a multi-antenna receiver for signal reception at each antenna;

The discrete sampling module is used to perform digital-to-analog conversion and matched filter processing on the signal received at each antenna, and then perform discrete sampling and discrete sampling results;

The weight vector optimization module obtains the optimal weight vector based on the minimum mean square error criterion;

The maximum ratio merging module is used to perform time-robust maximum ratio merging on discrete sampling results to obtain an output signal.

The maximum ratio combining module includes a two-dimensional tapped delay line model arranged at each receiving antenna, the input end of each two-dimensional tapped delay line model is used to receive the discrete sampling results at the root receiving antenna, and each two The signals output from the output end of the three-dimensional tapped delay line model are combined to obtain the maximum ratio combination result;

Each two-dimensional tapped delay line model includes L-1 delays, L-1 adders and L multipliers. In each two-dimensional tapped delay line model, the input of the first delay is connected to To receive the discrete sampling results at the antenna, the output of the first delayer is connected to the input of the second delayer, the output of the second delayer is connected to the input of the third delayer, and so on. The output terminal of the j'th delayer is connected to the input terminal of the j'+1th delayer, j'=1,2,...,L-2; at the same time, the signal at the input terminal of the first delayer passes through the first A multiplier is multiplied by the weight and connected to the first input of the first adder, and the output signal of the first delay is multiplied by the second multiplier and then connected to the first adder. The second input terminal; the output terminal of the first adder is connected to the first input terminal of the second adder, and the output signal of the second delayer is multiplied by the weight by the third multiplier and then connected to the first input terminal The second input of the 2 adders; and so on, the output of the j'th adder is connected to the first input of the j'+1 adder, and the output of the j'+1 delay The signal is multiplied by the weight of the j'+2 multiplier and then connected to the second input of the j'+1 adder, j'=1,2,...,L-2; the L-1 The signal output by each adder is the final output signal of the two-dimensional tapped delay line model;

The beneficial effects of the present invention are: the present invention realizes the improved maximum ratio combination under the condition of timing error, effectively solves the problem of deterioration of the output signal-to-noise ratio under imperfect time alignment, and improves the performance of the maximum ratio combination.

Description of drawings

Fig. 1 is method flowchart of the present invention;

Fig. 2 is a schematic diagram of the system principle of the present invention;

3 is a schematic diagram of a time-robust maximum ratio combining system under a single-input multiple-output system in an embodiment;

Fig. 4 is a schematic diagram of the relationship between the average output signal-to-noise ratio and the timing accuracy in the embodiment;

Fig. 5 is a schematic diagram of the relationship between the average output SNR and the average input SNR in the embodiment.

Detailed ways

The technical solution of the present invention will be further described in detail below in conjunction with the accompanying drawings, but the protection scope of the present invention is not limited to the following description.

As shown in Figure 1, a time-robust maximum ratio combining method includes the following steps:

S1. The single-antenna transmitter generates and transmits a transmission signal s(t);

S2. The signal x _i (t) received by the i-th receiving antenna in the multi-antenna receiver;

S3. Discrete sampling x _i (k) processed by digital-to-analog conversion and matched filtering;

S4. Obtain the optimal weight vector based on the minimum mean square error (MSE) criterion

S5. Perform time-robust maximum ratio combining (MRC) on x _i (k), i=1, 2, . . . , M, to obtain an output signal y(k).

In the step S1, considering a single-input multiple-output (SIMO) system with M receiving antennas, the transmitted transmission signal s(t); is expressed as:

Wherein, s(k) is the transmitted kth transmission symbol, T is the symbol period, and p(t) is the pulse shaping filter.

In the step S2, after passing through the channel, the signal x _i (t) received by the i-th receiving antenna in the multi-antenna receiver is:

x _i (t) = h _i s(t-τ _i )+n _i (t)

where h _i and τ _i denote the complex channel fading and propagation delay at the i-th receiving antenna, respectively, and n _i (t) is the additive white Gaussian noise (AWGN) at the i-th receiving antenna.

In the step S3, after performing digital-to-analog conversion and matched filter processing at the i-th receiving antenna, discrete sampling is performed, and the discrete sampling result is:

Among them, i=1,2,..,M, x _i (k) represents the sampling result corresponding to the kth transmission symbol received at the i-th antenna, and n _i (k) is the i-th receiving antenna Discrete additive white Gaussian noise corresponding to the kth transmitted symbol.

Said step S4 comprises the following sub-steps:

S401. A two-dimensional tapped delay line model is set at each receiving antenna, and the input end of each two-dimensional tapped delay line model is used to receive the discrete sampling results at the root receiving antenna, and each two-dimensional tapped delay line model The signals output by the output end are combined to obtain the maximum ratio combination result;

Each two-dimensional tapped delay line model includes L-1 delays, L-1 adders and L multipliers. In each two-dimensional tapped delay line model, the input of the first delay is connected to To receive the discrete sampling results at the antenna, the output of the first delayer is connected to the input of the second delayer, the output of the second delayer is connected to the input of the third delayer, and so on. The output terminal of the j'th delayer is connected to the input terminal of the j'+1th delayer, j'=1,2,...,L-2; at the same time, the signal at the input terminal of the first delayer passes through the first A multiplier is multiplied by the weight and connected to the first input of the first adder, and the output signal of the first delay is multiplied by the second multiplier and then connected to the first adder. The second input terminal; the output terminal of the first adder is connected to the first input terminal of the second adder, and the output signal of the second delayer is multiplied by the weight value by the third multiplier and then connected to the first input terminal The second input of the 2 adders; and so on, the output of the j'th adder is connected to the first input of the j'+1 adder, and the output of the j'+1 delay The signal is multiplied by the weight of the j'+2 multiplier and then connected to the second input of the j'+1 adder, j'=1,2,...,L-2; the L-1 The signal output by each adder is the final output signal of the two-dimensional tapped delay line model;

S402. Set the i-th row and j-th column of the weight matrix W as w _i,j , i=1,2,...,M, j=1,2,...,L, w _i,j represent the i-th The weight value multiplied by the jth multiplier at the root receiving antenna, and the weight matrix W is a matrix of M×L dimensions;

其中Vec()表示拉直函数，其功能为将矩阵中的每个元素作为一行，从而得到拉直后的向量；Straighten the weight matrix W to get the weight vector of ML×1

Among them, Vec() represents the straightening function, and its function is to treat each element in the matrix as a row, so as to obtain the straightened vector;

S403. Let X(k) represent the input matrix within the sampling period corresponding to the kth transmission symbol, the element of the i-th row and j-th column of X(k) is x _i (k+j), i=1,2,. .,M,j=1,2,...,L, the input matrix X(k) is a matrix of M×L dimensions;

Straighten the input matrix X(k) to obtain ML×1-dimensional input vector X(k)=Vec(X(k));

S404. Perform maximum ratio combination on the sampling results corresponding to the kth transmission symbol to obtain y(k):

Among them, tr() represents the trace of the matrix;

S405. Obtain the optimal weight vector based on the minimum mean square error criterion

为

的自相关矩阵，且

为

与s(k) 的自相关向量，其中s^*(k)表示s(k)的共轭；E{}表示函数期望；in

for

The autocorrelation matrix of , and

for

The autocorrelation vector with s(k), where s ^* (k) represents the conjugate of s(k); E{} represents the function expectation;

对应的最优权值矩阵表示为：and optimize the weight vector

The corresponding optimal weight matrix is expressed as:

表示最优权值向量

中的第i′个元素，i′＝1,2,...,ML。in

Represents the optimal weight vector

The i′th element in , i′=1,2,...,ML.

Described step S5 comprises:

作为

带入步骤S404中，计算出相应的y(k)，即为最终的最大比合并结果。will optimize the weight vector

as

Entering into step S404, the corresponding y(k) is calculated, which is the final maximum ratio combination result.

As shown in Figure 2, a time-robust maximum-ratio combining system includes:

a single-antenna transmitter for generating and transmitting a transmission signal;

a multi-antenna receiver for signal reception at each antenna;

The discrete sampling module is used to perform digital-to-analog conversion and matched filter processing on the signal received at each antenna, and then perform discrete sampling and discrete sampling results;

The weight vector optimization module obtains the optimal weight vector based on the minimum mean square error criterion;

The maximum ratio merging module is used to perform time-robust maximum ratio merging on discrete sampling results to obtain an output signal.

The maximum ratio combining module includes a two-dimensional tapped delay line model arranged at each receiving antenna, the input end of each two-dimensional tapped delay line model is used to receive the discrete sampling results at the root receiving antenna, and each two The signals output from the output end of the three-dimensional tapped delay line model are combined to obtain the maximum ratio combination result;

Each two-dimensional tapped delay line model includes L-1 delays, L-1 adders and L multipliers. In each two-dimensional tapped delay line model, the input of the first delay is connected to To receive the discrete sampling results at the antenna, the output of the first delayer is connected to the input of the second delayer, the output of the second delayer is connected to the input of the third delayer, and so on. The output terminal of the j'th delayer is connected to the input terminal of the j'+1th delayer, j'=1,2,...,L-2; at the same time, the signal at the input terminal of the first delayer passes through the first A multiplier is multiplied by the weight and connected to the first input of the first adder, and the output signal of the first delay is multiplied by the second multiplier and then connected to the first adder. The second input terminal; the output terminal of the first adder is connected to the first input terminal of the second adder, and the output signal of the second delayer is multiplied by the weight by the third multiplier and then connected to the first input terminal The second input of the 2 adders; and so on, the output of the j'th adder is connected to the first input of the j'+1 adder, and the output of the j'+1 delay The signal is multiplied by the weight of the j'+2 multiplier and then connected to the second input of the j'+1 adder, j'=1,2,...,L-2; the L-1 The signal output by each adder is the final output signal of the two-dimensional tapped delay line model;

In the embodiment of the present application, taking the quadrature phase shift keying (QPSK) signal as a communication transmitter and transmitting it on a Rayleigh fading channel as an example, the time robust maximum ratio combining system under the single-input multiple-output system is as follows As shown in Figure 3, the communication transmitter radiates out through the antenna, and the multiple antennas of the receiver receive the signals separately and combine them using the time-robust maximum ratio combining method.

The parameters are set as follows:

Figure 4 shows the relationship between the timing accuracy and the average output SNR after the time-robust maximum ratio combining method under different tap numbers of the tapped delay line (TDL) model. When the timing accuracy is 0.5, compared with the traditional maximum ratio combining (L=1) method, the proposed time-robust maximum ratio combining (L=7) method improves the average output SNR from the original 7.7 dB increased to 9dB.

Figure 5 shows the relationship between the average output SNR and the average input SNR for different tap numbers and timing precision. The average output SNR increases with the increase of the average input SNR. For larger input SNR, the time-robust maximum ratio combining method proposed in this paper improves the performance more obviously. For example, when the timing accuracy is 0.5 and the number of taps of the tapped delay line model is 5, this scheme improves 0.5dB compared with the traditional maximum ratio combining method when the average input SNR is -10dB. When it is 10dB, it improves 3dB compared with the traditional maximum ratio combining method.

Here, the present invention has been described in detail through specific implementation examples. The description of the above embodiments is provided in order to enable those skilled in the art to make or apply the present invention. Various modifications of these embodiments are easy for those skilled in the art understand. The invention is not limited to these examples, or to certain aspects thereof. The scope of the present invention is specified by the appended claims.

The above description shows and describes a preferred embodiment of the present invention, but as mentioned above, it should be understood that the present invention is not limited to the form disclosed herein, and should not be regarded as excluding other embodiments, but can be used in various Various other combinations, modifications, and environments can be made within the scope of the inventive concept described herein, by the above teachings or by skill or knowledge in the relevant field. However, changes and changes made by those skilled in the art do not depart from the spirit and scope of the present invention, and should all be within the protection scope of the appended claims of the present invention.

Claims (6)

1. A time-robust maximum ratio merging method, characterized in that: comprises the following steps: S1. The single-antenna transmitter generates and transmits a transmission signal s(t); S2. The signal x _i (t) received by the i-th receiving antenna in the multi-antenna receiver; S3. Discrete sampling x _i (k) processed by digital-to-analog conversion and matched filtering; S4. Obtain the optimal weight vector based on the minimum mean square error criterion

Said step S4 comprises the following sub-steps: S401. A two-dimensional tapped delay line model is set at each receiving antenna, and the input end of each two-dimensional tapped delay line model is used to receive the discrete sampling results at the root receiving antenna, and each two-dimensional tapped delay line model The signals output by the output end are combined to obtain the maximum ratio combination result; Each two-dimensional tapped delay line model includes L-1 delays, L-1 adders and L multipliers. In each two-dimensional tapped delay line model, the input of the first delay is connected to To receive the discrete sampling results at the antenna, the output of the first delayer is connected to the input of the second delayer, the output of the second delayer is connected to the input of the third delayer, and so on. The output terminal of the j'th delayer is connected to the input terminal of the j'+1th delayer, j'=1,2,...,L-2; at the same time, the signal at the input terminal of the first delayer passes through the first A multiplier is multiplied by the weight and connected to the first input of the first adder, and the output signal of the first delay is multiplied by the second multiplier and then connected to the first adder. The second input terminal; the output terminal of the first adder is connected to the first input terminal of the second adder, and the output signal of the second delayer is multiplied by the weight value by the third multiplier and then connected to the first input terminal The second input of the 2 adders; and so on, the output of the j'th adder is connected to the first input of the j'+1 adder, and the output of the j'+1 delay The signal is multiplied by the weight of the j'+2 multiplier and then connected to the second input of the j'+1 adder, j'=1,2,...,L-2; the L-1 The signal output by each adder is the final output signal of the two-dimensional tapped delay line model; S402. Let the i-th row and j-th column of the weight matrix W be w _i,j , i=1,2,...,M, j=1,2,...,L, w _i,j represent the The weight value multiplied by the jth multiplier at the i receiving antenna, the weight matrix W is a matrix of M×L dimensions; Straighten the weight matrix W to get the weight vector of ML×1

Among them, Vec() represents the straightening function, and its function is to treat each element in the matrix as a row, so as to obtain the straightened vector; S403. Let X(k) represent the input matrix within the sampling period corresponding to the kth transmission symbol, the element of the i-th row and j-th column of X(k) is x _i (k+j), i=1,2,. ..,M,j=1,2,...,L, the input matrix X(k) is a matrix of M×L dimensions; Straighten the input matrix X(k) to obtain ML×1-dimensional input vector X(k)=Vec(X(k)); S404. Perform maximum ratio combination on the sampling results corresponding to the kth transmission symbol to obtain y(k):

Among them, tr() represents the trace of the matrix; x _i (k) represents the sampling result corresponding to the k-th transmission symbol received at the i-th antenna; S405. Obtain the optimal weight vector based on the minimum mean square error criterion

in

for

The autocorrelation matrix of , and

for

The autocorrelation vector with s(k), where s ^* (k) represents the conjugate of s(k), and s(k) is the kth transmission symbol sent; E{} represents the function expectation; and optimize the weight vector

The corresponding optimal weight matrix is expressed as:

in

Represents the optimal weight vector

The i′th element in , i′=1,2,...,ML; S5. Perform time-robust maximum ratio combining on x _i (k) to obtain an output signal y(k); Described step S5 comprises: will optimize the weight vector

as

Entering into step S404, the corresponding y(k) is calculated, which is the final maximum ratio combination result. 2. A kind of time-robust maximum ratio combining method according to claim 1, characterized in that: in the step S1, considering a single-input multiple-output system with M receiving antennas, the transmitted transmission signal s(t), expressed as:

Wherein, s(k) is the transmitted kth transmission symbol, T is the symbol period, and p(t) is the pulse shaping filter. 3. A kind of time-robust maximum ratio combining method according to claim 2, characterized in that: in said step S2, after setting through the channel, the i-th receiving antenna in the multi-antenna receiver receives The signal x _i (t) is: x _i (t) = h _i s(t-τ _i )+n _i (t) where h _i and τ _i represent the complex channel fading and propagation delay at the i-th receiving antenna, respectively, and n _i (t) is the additive white Gaussian noise at the i-th receiving antenna. 4. a kind of maximum ratio combining method with time robustness according to claim 3 is characterized in that: in described step S3, after carrying out digital-to-analog conversion and matched filter processing at the i-th receiving antenna place, then Perform discrete sampling, the result of discrete sampling is:

Among them, i=1,2,...,M, x _i (k) represents the sampling result corresponding to the kth transmission symbol received at the i-th antenna, and n _i (k) is the i-th receiving antenna The discrete additive white Gaussian noise corresponding to the kth transmitted symbol at . 5. A maximum ratio merging system with time robustness, adopting the method described in any one of claims 1-4, characterized in that: comprising: a single-antenna transmitter for generating and transmitting a transmission signal; a multi-antenna receiver for signal reception at each antenna; The discrete sampling module is used to perform digital-to-analog conversion and matched filter processing on the signal received at each antenna, and then perform discrete sampling and discrete sampling results; The weight vector optimization module obtains the optimal weight vector based on the minimum mean square error criterion; The maximum ratio merging module is used to perform time-robust maximum ratio merging on discrete sampling results to obtain an output signal. 6. A kind of time-robust maximum ratio combining system according to claim 5, characterized in that: said maximum ratio combining module includes a two-dimensional tapped delay line model arranged at each receiving antenna , the input end of each two-dimensional tapped delay line model is used to receive the discrete sampling result at the receiving antenna, and the signals output by the output ends of each two-dimensional tapped delay line model are combined to obtain the maximum ratio combination result; Each two-dimensional tapped delay line model includes L-1 delays, L-1 adders and L multipliers. In each two-dimensional tapped delay line model, the input of the first delay is connected to To receive the discrete sampling results at the antenna, the output of the first delayer is connected to the input of the second delayer, the output of the second delayer is connected to the input of the third delayer, and so on. The output terminal of the j'th delayer is connected to the input terminal of the j'+1th delayer, j'=1,2,...,L-2; at the same time, the signal at the input terminal of the first delayer passes through the first A multiplier is multiplied by the weight and connected to the first input of the first adder, and the output signal of the first delay is multiplied by the second multiplier and then connected to the first adder. The second input terminal; the output terminal of the first adder is connected to the first input terminal of the second adder, and the output signal of the second delayer is multiplied by the weight value by the third multiplier and then connected to the first input terminal The second input of the 2 adders; and so on, the output of the j'th adder is connected to the first input of the j'+1 adder, and the output of the j'+1 delay The signal is multiplied by the weight of the j'+2 multiplier and then connected to the second input of the j'+1 adder, j'=1,2,...,L-2; the L-1 The signal output by each adder is the output signal of the two-dimensional tapped delay line model.

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