AFDM underwater acoustic communication channel equalization method based on adaptive decision feedback

Abstract

The invention relates to the field of underwater acoustic communication, in particular to an AFDM underwater acoustic communication channel equalization method based on adaptive decision feedback, aiming at an underwater acoustic channel with long time delay, large Doppler and remarkable time-varying property, an adaptive decision feedback equalizer can timely track the channel change and improve the symbol detection performance by updating the equalizer weight coefficient; the performance of a communication system is improved, error propagation can be reduced, and more reliable underwater information transmission can be realized. As the adaptive decision feedback equalizer belongs to a symbol-level equalization method, the complexity of the adaptive decision feedback equalizer is linearly related to a modulation symbol number N and the size of a filter. Therefore, the calculation complexity of the method is lower than that of other equalization algorithms, and the low calculation complexity better meets the underwater communication requirement with limited calculation resources. According to the method, the transmission performance of underwater acoustic communication is improved, and good balance can be achieved between low complexity and good performance.

Description

Technical Field

[0001] The invention relates to the field of underwater acoustic communication, and in particular to an AFDM underwater acoustic communication channel equalization method based on adaptive decision feedback. Background Art

[0002] Underwater communication technology is a key factor in ensuring the smooth execution of various underwater tasks, and underwater acoustic communication technology is considered to be the only reliable means of long-distance communication in the current marine environment.

[0003] Due to the high complexity of underwater acoustic channels, including propagation loss, multipath effect, Doppler frequency shift and environmental noise, these characteristics have brought a series of challenges and difficulties to the development of underwater acoustic communication technology. In recent years, Orthogonal Frequency Division Multiplexing (OFDM) has been widely used to solve some problems in the communication process, such as reducing or eliminating the inter-code interference caused by multipath effect. OFDM can have good performance in time-invariant frequency selective channels, but in time-varying channels, the performance of OFDM drops sharply. Since the OFDM system requires that the subcarriers must meet the orthogonality, and the frequency offset will destroy the orthogonality between the carriers and generate inter-carrier interference, this leads to the high sensitivity of OFDM to frequency offset. However, Doppler frequency shift is unavoidable in underwater acoustic communication systems, which seriously restricts the development of OFDM in underwater acoustic communication. The proposal and application of OTFS technology effectively solves this problem to a certain extent, but the technology has high complexity. Therefore, a new type of multi-carrier modulation technology, called AFDM, has been recently proposed, which can effectively solve the problem of sharp performance degradation of OFDM in time-varying channels, and has lower complexity than OTFS. The present invention proposes an adaptive decision feedback channel equalization method based on AFDM underwater acoustic communication, which can reduce or eliminate inter-symbol interference, reduce bit error rate, and improve the reliability and accuracy of data transmission. Compared with linear equalization technology, adaptive decision feedback equalization can use a feedforward filter to process the interference of the current symbol, and also eliminate the backward interference caused by the decided symbol through a feedback filter. It has a stronger ability to resist inter-symbol interference, and the adaptive decision feedback equalizer can continuously adjust the filter coefficients according to the real-time received data to better adapt to the dynamic changes of the channel. Compared with the maximum likelihood sequence estimation equalization technology, the adaptive decision feedback equalization technology has a lower computational complexity, and has advantages in convergence speed, and can adapt to channel changes more quickly. Summary of the invention

[0004] The purpose of the present invention is to design a channel equalization method in the field of AFDM underwater acoustic communication based on adaptive decision feedback to improve the transmission performance of underwater acoustic communication. The method can achieve a good balance between lower complexity and better performance.

[0005] The technical solution of the present invention is:

[0006] An AFDM underwater acoustic communication channel equalization method based on adaptive decision feedback comprises the following steps:

[0007] Step 1: Perform AFDM modulation on the transmitted signal at the transmitting end:

[0008] For the information symbol vector x[m] to be transmitted in the discrete affine Fourier domain, an inverse discrete affine Fourier transform is performed to obtain the time domain transmission signal s[n]:

[0009]

[0010] in N represents the number of symbols, c1 and c2 represent the modulation parameters; the time domain transmitted signal is rewritten into a matrix form:

[0011]

[0012] in F is the Fourier transform matrix;

[0013] Step 2: Perform AFDM demodulation on the received signal at the receiving end:

[0014] Perform DAFT transformation on the time domain received signal r[n] of a certain channel at the receiving end to obtain the DAFT domain output symbol y[m]:

[0015]

[0016] Rewritten in matrix form:

[0017]

[0018] in w is Gaussian noise; P ≥ 1 is the number of paths in a single channel, h i 、f i and l i are the complex gain, Doppler frequency shift and delay associated with the i-th path respectively, and Π is the forward cyclic shift matrix:

[0019]

[0020] is an N×N diagonal matrix:

[0021]

[0022] Step 3: Equalizing the demodulated received signal by an adaptive decision feedback equalizer, wherein the adaptive decision feedback equalizer comprises a feedforward filter, a decision device and a feedback filter;

[0023] For a demodulated signal y of a certain channel, according to the formula

[0024]

[0025] Get the estimated value after equilibrium Where w is the weight of the feedforward filter, f is the weight of the feedback filter, and d is the estimated value The output after inputting the decision maker, (·) H Represents the Hermitian transform.

[0026] Furthermore, in step 3, the weight w of the feedforward filter and the weight f of the feedback filter are updated by the following formula:

[0027]

[0028] in and represents the updated filter weights, (·) * represents the conjugate transpose, μ w and μ f Represent the step size of the feedforward filter and feedback filter respectively,

[0029] Furthermore, in step 3, the weight w of the feedforward filter is updated by the minimum mean square error method NLMS:

[0030]

[0031] Where δ is a fixed step size.

[0032] Furthermore, in step 3, the weight w of the feedforward filter is updated by the improved proportional normalized minimum mean square error IPNLMS:

[0033]

[0034] Where K[N] is a diagonal matrix:

[0035] K[N]=diag{k0[n],k1[n],…,k M-1 [n]}

[0036] The element calculation formula is:

[0037]

[0038] Where η is a positive constant close to 0, and the parameter λ is a set value between [-1,1];

[0039]

[0040] Furthermore, after AFDM modulation of the transmitted signal, a cyclic prefix is ​​added to the time domain transmitted signal s[n], and the length of the cyclic prefix is ​​greater than or equal to the maximum delay of the channel; then the cyclic prefix is ​​removed after parallel-to-serial conversion and transmission through the time-varying fading underwater acoustic channel to obtain the time domain received signal r[n].

[0041] Beneficial Effects

[0042] (1) For underwater acoustic channels with long delay, large Doppler, and significant time-varying characteristics, the adaptive decision feedback equalizer can track channel changes in a timely manner by updating the equalizer weight coefficients, improve symbol detection performance, improve communication system performance, reduce error propagation, and achieve more reliable underwater information transmission.

[0043] (2) In addition, since the adaptive decision feedback equalizer belongs to the symbol-level equalization method, its complexity is linearly related to the number of modulation symbols N and the filter size. Therefore, its computational complexity is lower than other equalization algorithms, and low computational complexity is more in line with the needs of underwater communications with limited computing resources.

[0044] Additional aspects and advantages of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] The above and / or additional aspects and advantages of the present invention will become apparent and easily understood from the description of the embodiments in conjunction with the following drawings, in which:

[0046] Figure 1 It is the basic structure of AFDM communication system;

[0047] Figure 2 It is an adaptive decision feedback equalizer structure;

[0048] Figure 3 It is a bit error rate performance comparison chart that verifies the effectiveness of the proposed adaptive decision feedback equalizer. DETAILED DESCRIPTION

[0049] Embodiments of the present invention are described in detail below. The embodiments are exemplary and intended to be used to explain the present invention, but should not be construed as limiting the present invention.

[0050] The AFDM underwater acoustic communication channel equalization method based on adaptive decision feedback proposed in this embodiment is based on an underwater acoustic AFDM communication system. Figure 1 shown.

[0051] Step 1: Perform AFDM modulation on the transmitted signal at the transmitting end:

[0052] Let x[m] represent the information symbol vector to be transmitted in the Discrete Affine Fourier Transform (DAFT) domain, and perform an inverse discrete affine Fourier transform on it to obtain the time domain transmission signal s[n]:

[0053]

[0054] in N represents the number of symbols, c1 and c2 represent modulation parameters, which are set according to the delay-Doppler characteristic parameters of the channel; the time domain transmitted signal is rewritten into a matrix form:

[0055]

[0056] in F is the Fourier transform matrix.

[0057] After AFDM modulation of the transmitted signal, a cyclic prefix is ​​added to the time domain transmitted signal s[n], and the length of the cyclic prefix is ​​greater than or equal to the maximum delay of the channel; then the cyclic prefix is ​​removed after passing through the time-varying fading underwater acoustic channel, parallel-to-serial conversion and transmission through the underwater acoustic channel to obtain the time domain received signal r[n], which can be expressed as:

[0058]

[0059] Where w[n] is additive Gaussian noise, and s[nl] is the signal of the time domain transmitted signal s[n] after a delay of l. n (l) is the impulse response of a certain channel at time n and time delay l. The present invention uses multiple channels to receive and transmit signals, the number of channels is Q, and the time delay and Doppler shift of each channel are different. Taking one of the channels as an example, the impulse response of the channel at time n and time delay l is:

[0060]

[0061] Where P ≥ 1 is the number of paths in a single channel, δ(·) is the Dirac delta function, and h i 、f i and l i are the complex gain, Doppler shift and delay associated with the i-th path respectively.

[0062] Step 2: Perform AFDM demodulation on the received signal at the receiving end:

[0063] In this embodiment, the receiving end receives signals through 8 channels, and obtains 8 groups of different time domain received signals.

[0064] Perform DAFT transformation on the time domain received signal r[n] of a certain channel at the receiving end to obtain the DAFT domain output symbol y[m]:

[0065]

[0066] Rewritten in matrix form:

[0067]

[0068] in w is Gaussian noise, and since A is a unitary matrix, has the same statistical properties as w; P ≥ 1 is the number of paths in a single channel, h i 、f i and l i are the complex gain, Doppler frequency shift and delay associated with the i-th path respectively, and Π is the forward cyclic shift matrix:

[0069]

[0070] is an N×N diagonal matrix:

[0071]

[0072] When 2Nc1 is an integer and N is an even number,

[0073] Step 3: Equalize the demodulated received signal through an adaptive decision feedback equalizer. The equalizer structure is as follows: Figure 2 As shown, it includes a feedforward filter, a decision device and a feedback filter;

[0074] For a demodulated signal y of a certain channel, according to the formula

[0075]

[0076] Get the estimated value after equilibrium Where w is the weight of the feedforward filter, f is the weight of the feedback filter, and d is the estimated value The output after inputting the decision device, (·) H Represents the Hermitian transform.

[0077] The idea of ​​the LMS adaptive equalization algorithm is to make the mean square of the error value J(n) = E[e 2 [n]] is as small as possible, which is mainly achieved by adjusting the weights of the filters. The weights w of the feedforward filter and the weights f of the feedback filter are updated by the following formula:

[0078]

[0079] in and represents the updated filter weights, (·) * represents the conjugate transpose, μ w and μ f Respectively represent the step sizes of the feedforward filter and the feedback filter. In this embodiment, the adaptive step sizes of the feedforward filter and the feedback filter are 0.2 and 0.05 respectively;

[0080] The Normalized Least Mean Squares (NLMS) method improves the traditional LMS algorithm. Compared with the LMS algorithm, the input signal is normalized. The update formula of the weight w of the feedforward filter is:

[0081]

[0082] Where δ is a fixed step size.

[0083] The Improved Proportionate Normalized Least Mean Squares (IPNLMS) method introduces a diagonal matrix K[N] to improve the performance of the algorithm. The update formula of the weight w of the feedforward filter is:

[0084]

[0085] Where K[N] is a diagonal matrix:

[0086] K[N]=diag{k0[n],k1[n],…,k M-1 [n]}

[0087] The element calculation formula is:

[0088]

[0089] Where η is a positive constant close to 0, and the parameter λ is a set value between [-1, 1]. Generally, λ is 0 or -0.5. In this embodiment, λ is 0;

[0090]

[0091] To verify the performance of the proposed equalization algorithm, a simulation experiment is conducted based on an underwater acoustic AFDM communication system. The simulation experiment sets the number of symbols N = 1024, there are 8 channels, the channels have 6 multipaths, and the maximum Doppler of the channels is about 2Hz. In addition, the channels have obvious time-varying properties.

[0092] Figure 3 The bit error rate performance of the decision feedback equalizer based on NLMS and IPNLMS adaptive update algorithms is compared with the bit error rate performance of zero-forcing equalization. Figure 3 It can be seen that compared with the NLMS-based decision feedback equalizer, the IPNLMS algorithm is used as an adaptive algorithm, and its performance has been greatly improved due to its effective use of the sparsity of the underwater acoustic channel. The bit error rate performance of the zero-forcing equalization is much worse than that of the adaptive decision feedback equalizer using the IPNLMS update algorithm. The adaptive decision feedback equalization can use the decision information of past symbols to eliminate inter-symbol interference, and the noise suppression effect is usually better than the zero-forcing equalization, especially when there is severe fading and noise in the channel. The adaptive decision feedback equalization technology is more adaptable to the dynamic changes of the channel, can quickly track the time-varying characteristics of the channel, adjust parameters in time, and adapt to changes in channel conditions, thereby maintaining a good equalization effect.

[0093] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations on the present invention. A person skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention without departing from the principles and intent of the present invention.

Claims

1. An AFDM underwater acoustic communication channel equalization method based on adaptive decision feedback, characterized in that: The following steps are involved: Step 1: Perform AFDM modulation on the transmitted signal at the transmitting end: For the information symbol vector x[m] to be transmitted in the discrete affine Fourier domain, an inverse discrete affine Fourier transform is performed to obtain the time domain transmission signal s[n]: in N represents the number of symbols, c1 and c2 represent the modulation parameters; the time domain transmitted signal is rewritten into a matrix form: in F is the Fourier transform matrix; Step 2: Perform AFDM demodulation on the received signal at the receiving end: Perform DAFT transformation on the time domain received signal r[n] of a certain channel at the receiving end to obtain the DAFT domain output symbol y[m]: Rewritten in matrix form: in w is Gaussian noise; P ≥ 1 is the number of paths in a single channel, h i 、f i and l i are the complex gain, Doppler frequency shift and delay associated with the i-th path respectively, and Π is the forward cyclic shift matrix: is an N×N diagonal matrix: Step 3: Equalizing the demodulated received signal by an adaptive decision feedback equalizer, wherein the adaptive decision feedback equalizer comprises a feedforward filter, a decision device and a feedback filter; For a demodulated signal y of a certain channel, according to the formula Get the estimated value after equilibrium Where w is the weight of the feedforward filter, f is the weight of the feedback filter, and d is the estimated value The output after inputting the decision device, (·) H Represents the Hermitian transform.

2. The AFDM underwater acoustic communication channel equalization method based on adaptive decision feedback as claimed in claim 1, characterized in that: In step 3, the weight w of the feedforward filter and the weight f of the feedback filter are updated by the following formula: in and represents the updated filter weights, (·) * represents the conjugate transpose, μ w and μ f Represent the step size of the feedforward filter and feedback filter respectively, 3. The AFDM underwater acoustic communication channel equalization method based on adaptive decision feedback as claimed in claim 2, characterized in that: In step 3, the weight w of the feedforward filter is updated by the minimum mean square error method NLMS: Where δ is a fixed step size.

4. The AFDM underwater acoustic communication channel equalization method based on adaptive decision feedback as claimed in claim 2, characterized in that: In step 3, the weight w of the feedforward filter is updated by the improved proportional normalized minimum mean square error IPNLMS: Where K[N] is a diagonal matrix: K[N]=diag{k0[n],k1[n],…,k M-1 [n]} The element calculation formula is: Where η is a positive constant close to 0, and the parameter λ is a set value between [-1,1]; 5. The AFDM underwater acoustic communication channel equalization method based on adaptive decision feedback as claimed in claim 1, characterized in that: After AFDM modulation of the transmitted signal, a cyclic prefix is ​​added to the time domain transmitted signal s[n], and the length of the cyclic prefix is ​​greater than or equal to the maximum delay of the channel; then the cyclic prefix is ​​removed after passing through the time-varying fading underwater acoustic channel, parallel-to-serial conversion and transmission through the underwater acoustic channel to obtain the time domain received signal r[n].

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