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

Abstract

The present invention relates to the field of underwater acoustic communications, and specifically to an AFDM underwater acoustic communication channel equalization method based on adaptive decision feedback. For underwater acoustic channels with long delays, large Doppler, and significant time-varying properties, the adaptive decision feedback equalizer can track channel changes in a timely manner by updating the equalizer weight coefficient, thereby improving symbol detection performance, improving communication system performance, reducing error propagation, and achieving more reliable underwater information transmission. Since the adaptive decision feedback equalizer belongs to a symbol-level equalization method, its complexity is linearly related to the number of modulation symbols N and the filter size. Therefore, its computational complexity will be lower than other equalization algorithms, and low computational complexity is more in line with the needs of underwater communications with limited computing resources. The present invention improves the transmission performance of underwater acoustic communications and can achieve a good balance between lower complexity and better performance.

Description

Technical Field

[0001] The present 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 effects, Doppler 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-symbol interference caused by multipath effects. OFDM can have good performance in time-invariant frequency-selective channels, but its performance drops sharply in time-varying channels. Since OFDM systems require that subcarriers must be orthogonal, frequency offsets will destroy the orthogonality between carriers and generate inter-carrier interference, which makes OFDM highly sensitive to frequency offsets. However, Doppler shift is unavoidable in underwater acoustic communication systems, which seriously restricts the development of OFDM in underwater acoustic communications. The proposal and application of OTFS technology has effectively solved 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 stronger anti-inter-symbol interference capability, 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 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. This method can achieve a good balance between low complexity and good performance.

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

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

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

[0008] For the information symbol vector x[m] to be transmitted in the discrete affine Fourier domain, perform an inverse discrete affine Fourier transform on it 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 as follows:

[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 signal r[n] received at the receiving end in a certain channel 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 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 through an adaptive decision feedback equalizer, wherein the adaptive decision feedback equalizer includes a feedforward filter, a decision detector, and a feedback filter;

[0023] For the 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 least mean square error method NLMS:

[0030]

[0031] where δ is a fixed step size.

[0032] Furthermore, in step 3, the weights w of the feedforward filter are 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, after passing through a time-varying fading underwater acoustic channel, the cyclic prefix is ​​removed after parallel-to-serial conversion and transmission through the 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 variation, the adaptive decision feedback equalizer can track channel changes in a timely manner by updating the equalizer weight coefficient, 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 is a 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 that of other equalization algorithms, and low computational complexity is more suitable for underwater communication with limited computing resources.

[0044] Additional aspects and advantages of the present invention will be set forth in part in the description which follows and, in part, will be obvious from the description which follows, or may be learned by 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 readily understood from the following description of the embodiments with reference to the accompanying 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 comparison chart of bit error rate performance to verify the effectiveness of the proposed adaptive decision feedback equalizer. DETAILED DESCRIPTION

[0049] The following describes in detail embodiments of the present invention. The embodiments are exemplary and intended to explain the present invention, but are not to 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 the underwater acoustic AFDM communication system, as shown in the attached Figure 1 shown.

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

[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 the 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 as follows:

[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 cyclic prefix length is greater than or equal to the maximum delay of the channel. After passing through the time-varying fading underwater acoustic channel, the cyclic prefix is ​​removed after 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 channel at time n and time delay 1. 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 1 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 signal r[n] received at the receiving end in a certain channel to obtain the DAFT domain output symbol y[m]:

[0065]

[0066] Rewritten in matrix form:

[0067]

[0068] in w is Gaussian noise, since A is a unitary matrix, and w have the same statistical properties; P≥1 is the number of paths in a single channel, h i 、f i and l i are the complex gain, Doppler 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 maker and a feedback filter;

[0074] For the 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 maker, (·) 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 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 algorithm performance. 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 was conducted based on an underwater acoustic AFDM communication system. The simulation set the symbol number N to 1024, with eight channels, six multipath paths, and a maximum Doppler of approximately 2 Hz. Furthermore, the channels exhibit significant time-varying characteristics.

[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 As can be seen, compared to the NLMS-based decision feedback equalizer, the IPNLMS algorithm, as an adaptive algorithm, significantly improves performance due to its effective utilization of the sparsity of the underwater acoustic channel. However, the bit error rate performance of the adaptive decision feedback equalizer using zero-forcing equalization is significantly worse than that of the IPNLMS update algorithm. Adaptive decision feedback equalization can utilize decision information from past symbols to eliminate inter-symbol interference, and is generally more effective at suppressing noise than zero-forcing equalization, especially in the presence of severe fading and noise. Adaptive decision feedback equalization technology is more adaptable to dynamic channel changes, quickly tracking the time-varying characteristics of the channel and adjusting parameters in a timely manner to adapt to changing channel conditions, thereby maintaining a good equalization effect.

[0093] Although the embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative 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 purpose 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 transmitter: For the information symbol vector x[m] that needs to be transmitted in the discrete affine Fourier domain, perform an inverse discrete affine Fourier transform on it to obtain the time domain transmission signal : in , N represents the number of symbols, and Represents the modulation parameters; rewrite the time domain transmitted signal into matrix form: in , is the Fourier transform matrix; Step 2: Perform AFDM demodulation on the received signal at the receiving end: For the receiving end receiving the signal in the time domain of a certain channel Perform DAFT transformation to obtain DAFT domain output symbols : Rewritten in matrix form: in , , is Gaussian noise; , is the number of paths in a single channel, 、 and are the complex gain, Doppler shift and delay associated with the i-th path, is the forward cyclic shift matrix: , is an N×N diagonal matrix: Step 3: Equalizing the demodulated received signal through an adaptive decision feedback equalizer, wherein the adaptive decision feedback equalizer includes a feedforward filter, a decision detector, and a feedback filter; For the demodulated signal 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 Output after inputting the decision maker.

2. The AFDM underwater acoustic communication channel equalization method based on adaptive decision feedback according to 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 using the following formula: in represents the updated feedforward filter weights, represents the updated feedback filter weights, and 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 least mean square error method NLMS: in represents the updated feedforward filter weights, and 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: in represents the updated feedforward filter weights, δ is a fixed step size, is a diagonal matrix: The element calculation formula is: In the formula is a positive constant close to 0, the parameter for The set value between 。 5. The AFDM underwater acoustic communication channel equalization method based on adaptive decision feedback according to claim 1, characterized in that: After AFDM modulation of the transmitted signal, the signal is sent in the time domain Add a cyclic prefix, the length of which is greater than or equal to the maximum delay of the channel; then pass through the time-varying fading underwater acoustic channel, after parallel-to-serial conversion and transmission through the underwater acoustic channel, remove the cyclic prefix and obtain the time domain received signal .

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