A minimum frequency shift keying demodulation method for underwater acoustic communication based on extended Kalman filter

Abstract

The present invention discloses a method for minimum frequency shift keying (MSK) demodulation of underwater acoustic communication based on an extended Kalman filter, comprising: a transmitting end transmitting an MSK signal including an information sequence and a training sequence; a receiving end receiving the MSK signal transmitted through an underwater acoustic channel, performing channel estimation based on the training sequence, and obtaining a channel impulse response; introducing the channel impulse response into the construction of an observation matrix of the extended Kalman filter, forming a phase tracking model incorporating channel information by modifying the Jacobian matrix, and continuously tracking the phase of the received signal through the phase tracking model to achieve minimum frequency shift keying demodulation. The present invention utilizes the phase continuity characteristic of the MSK signal, fully exploits the correlation between the signal phase and the transmitted code element, performs phase tracking on the received signal at the receiving end, and achieves high-precision demodulation in an underwater acoustic environment. The method has a stronger ability to resist multipath interference, can effectively utilize the channel impulse response, and significantly improves the reliability of underwater acoustic communication.

Description

Technical Field

[0001] The present invention belongs to the technical field of underwater acoustic communication, and in particular relates to an underwater acoustic communication minimum frequency shift keying demodulation method based on extended Kalman filtering. Background Art

[0002] Underwater acoustic communication plays a vital role in fields such as ocean exploration, environmental monitoring, and underwater equipment control. Due to the attenuation and absorption characteristics of underwater acoustic wave transmission, the bandwidth of underwater acoustic communication is severely limited. Minimum Frequency Shift Keying (MSK) signals, as a special continuous phase modulation (CPM) technology, have the characteristics of constant envelope, continuous phase, minimum frequency difference, and strict orthogonality. Compared with traditional modulation signals, they can achieve better bandwidth efficiency. In underwater acoustic communication, modulation and demodulation are key links in realizing underwater information transmission. Reducing the bit error rate by optimizing the modulation and demodulation process is an effective way to improve communication reliability.

[0003] Interference in underwater acoustic channels is also a significant issue. Multipath is a major contributor to channel interference. As sound waves propagate underwater, they are affected by reflection, refraction, and scattering, causing signals to arrive at the receiver along different paths, creating a multipath effect. This multipath interference can lead to severe inter-symbol interference (ISI), further exacerbating channel uncertainty and communication complexity.

[0004] At present, the demodulation method of MSK mainly relies on technologies such as time domain equalization and frequency domain equalization. Although these equalizer-based demodulation methods can provide good performance to a certain extent, their implementation process is relatively complex and the computational overhead is large. In the field of wireless communications, under Gaussian white noise channels, some studies have attempted to introduce extended Kalman filters (EKF) into MSK demodulation. However, the multipath effect in underwater acoustic communication is far more complex than that of traditional wireless channels, which makes the existing MSK demodulation method based on extended Kalman filters show significant limitations in underwater acoustic channels. Therefore, in order to effectively deal with the complex channel characteristics in underwater acoustic communication, an innovative demodulation method is urgently needed that can combine channel information and overcome the interference caused by multipath effects. Summary of the Invention

[0005] The purpose of the present invention is to overcome the defects of the prior art and propose a minimum frequency shift keying demodulation method for underwater acoustic communication based on extended Kalman filtering.

[0006] In view of this, the present invention proposes a minimum frequency shift keying demodulation method for underwater acoustic communication based on extended Kalman filtering, comprising:

[0007] The transmitting end transmits a minimum frequency shift keying modulated signal including an information sequence and a training sequence;

[0008] The receiving end receives the minimum frequency shift keying modulated signal transmitted through the underwater acoustic channel, performs channel estimation based on the training sequence, and obtains the channel impulse response; the channel impulse response is introduced into the construction of the observation matrix of the extended Kalman filter, and a phase tracking model combined with the channel information is formed by modifying the Jacobian matrix. Through the phase tracking model, the phase of the received signal is continuously tracked to achieve minimum frequency shift keying demodulation.

[0009] Preferably, the transmitting end transmits information sequence x a (n) and the training sequence x p (n) minimum frequency shift keying modulation signal x(n); where n represents time n; x[n] is determined by the variable to be tracked and and The column vector of the difference Ω[n] satisfies the following formula:

[0010]

[0011] Where T represents transpose.

[0012] Preferably, the training sequence x p (n) is a sequence known to both the transmitter and the receiver.

[0013] Preferably, performing channel estimation according to the training sequence to obtain a channel impulse response includes:

[0014] Based on the training sequence x p [n], use the least squares method to estimate and obtain the channel estimation result, that is, the channel impulse response for:

[0015]

[0016] Among them, x p is the training sequence transmitted by the transmitter, y p is the training sequence received by the receiver, and H represents the conjugate transpose.

[0017] Preferably, the observation matrix of the extended Kalman filter is:

[0018]

[0019] Among them, x[n] is the state vector of the transmitter, f cis the center frequency, is the tracking variable at time k, t[k] is the time at time k, where nl h +1≤k≤n-1, t[n] is the time at moment n, is the variable tracked at time n, h[nk] is the channel impulse response at time nk, h[0] is the channel impulse response at time 0, l h is the channel length.

[0020] Preferably, the modified Jacobian matrix includes:

[0021] Taking the partial derivative of the observation matrix with respect to the state vector, we get the Jacobian matrix H[n]|:

[0022]

[0023] in, The one-step-ahead estimate of the tracking variable, also called the prior estimate.

[0024] Preferably, the phase tracking model combined with channel information includes:

[0025] Set the initialization condition to

[0026] According to the implementation process of the extended Kalman filter, the prediction equation satisfies the following formula:

[0027]

[0028] in, is the prior estimate of the state vector, P[n|n-1] is the covariance matrix of the prior error, is the covariance of process noise, G is the process noise coefficient, G=[0 1] T , F is the state transfer matrix, expressed as

[0029]

[0030] The observation equation is updated as:

[0031]

[0032] P[n|n]=(IK[n]H[n])P[n|n-1]

[0033] Where K[n] is the Kalman gain, which is used to minimize the estimation error, The covariance of the observation noise P[n|n] is the updated error covariance matrix, is the updated estimate of the state at time n, where The first value of is the estimated phase

[0034] Preferably, the continuous tracking of the phase of the received signal to achieve minimum frequency shift keying demodulation includes:

[0035] In each symbol period, the estimated phase A differential operation is performed and symbol judgment is made based on the average value of the phase change: when the average value of the phase change is greater than 0, it is judged as the symbol "1"; when the average value of the phase change is less than 0, it is judged as the symbol "0", thereby achieving minimum frequency shift keying demodulation.

[0036] Compared with the prior art, the advantages of the present invention are:

[0037] 1. Enhanced anti-interference capability: The present invention uses an extended Kalman filter (EKF) combined with channel information for phase tracking, effectively suppressing the multipath effect and inter-symbol interference in underwater acoustic communications, enabling the system to have stronger anti-interference capability in complex underwater acoustic environments. Compared with traditional methods, the bit error rate is lower at the same signal-to-noise ratio.

[0038] 2. Simplified system design: The present invention does not require the introduction of complex equalizers and can achieve high-precision demodulation only through channel estimation and phase tracking, which simplifies the system hardware and algorithm design and reduces implementation cost and computational complexity. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 This is a system block diagram of the minimum frequency shift keying demodulation method based on extended Kalman filtering of the present invention;

[0040] Figure 2 is a channel impulse response diagram of an embodiment;

[0041] Figure 3 is a phase tracking result diagram of an embodiment;

[0042] Figure 4 3 is a comparison chart of the bit error rate-signal-to-noise ratio simulation performance of the embodiment. DETAILED DESCRIPTION

[0043] To address the high bit error rate (BER) caused by multipath effects in underwater acoustic communications, this paper proposes a minimum shift keying (MSK) demodulation method for underwater acoustic communications based on an extended Kalman filter (EKF). By incorporating channel information into the construction of the EKF model, this method accurately tracks the phase of the received signal, effectively suppressing multipath interference and reducing BER, thereby improving communication reliability.

[0044] The purpose of the present invention is achieved through the following technical solutions, the overall structure of which is as follows: Figure 1As shown. The present invention introduces the channel impulse response into the construction of the observation vector and observation equation of the extended Kalman filter, forming a phase tracking model that combines channel information and can accurately track the phase of the MSK signal under complex multipath channel conditions. By re-deriving the extended Kalman filter, the expression of the Jacobian matrix is ​​corrected, and an EKF demodulation method for MSK in the underwater acoustic channel is constructed. By effectively utilizing the channel information, this method significantly reduces the bit error rate without relying on a complex equalizer, effectively reducing the bit error rate of the system in complex underwater acoustic channels.

[0045] The specific technical details of the present invention are introduced below:

[0046] (1) Signal transmission and reception

[0047] (1) Signal transmission. MSK modulation signal is a special continuous phase modulation, and its expression can be written as:

[0048]

[0049] where f c is the center frequency, x n is the symbol sent, with a value of ±1, α n is the symbol x n The accumulation can be expressed as:

[0050]

[0051] At the transmitter, the MSK transmission signal x(n) consists of the training sequence x p (n) and information sequence x a (n) composition.

[0052] (2) Signal reception. After passing through the underwater acoustic channel, the underwater acoustic MSK signal at the receiving end can be expressed as:

[0053] y(n)=x(n)*h(n)+w(n) (3)

[0054] Where * represents convolution, x(n), y(n) and w(n) represent the transmitted signal, received signal and additive white Gaussian noise, respectively, and h(n) represents the underwater acoustic channel impulse response.

[0055] (3) Received signal preprocessing. A multi-stage preprocessing operation is performed on the received MSK signal. First, the signal is bandpass filtered to suppress environmental noise and out-of-band interference, ensuring the signal's spectral purity. Furthermore, a Doppler shift compensation algorithm is used to dynamically correct the frequency offset caused by underwater acoustic propagation, thereby enhancing the signal's temporal consistency.

[0056] (2) Construction of state vector and observation vector

[0057] (1) State vector construction: The minimum frequency shift keying transmission signal is constructed into the form required by the extended Kalman filter.

[0058] More specifically, at the transmitter, the state vector x[n] is the state of the system at time n, and the observation vector y[n] is the observation of the system at time n. x[n] is composed of the variables to be tracked. and and The column vector is composed of the difference Ω[n].

[0059]

[0060] (2) Observation vector construction. The received signal y[n] passing through the underwater acoustic channel is constructed as a function of the state vector. When the signal passes through the underwater acoustic channel, it is equivalent to convolving the signal with the channel impulse response. The convolution form of the received signal is written as a summation form to establish the received signal model. The state vector and observation vector can be expressed as:

[0061]

[0062] Where h[n] is the impulse response of the underwater acoustic channel and w[n] is the additive white Gaussian noise.

[0063] (3) Construction of state equation and observation equation

[0064] (1) Construction of state equation. Based on the state vector and the form of Kalman filter, the state equation can be written as:

[0065] x[n]=Fx[n-1]+Gν[n-1] (6)

[0066] The state equation is a linear equation that describes the change relationship of the system state from one moment to the next. The state transition matrix ν[n] is the process noise, which is equal to the difference between Ω[n] and Ω[n-1]. Vector G = [0 1] T .

[0067] (2) Construction of observation equation. The observation equation of the basis observation vector can be written as:

[0068] y[n]=h(x[n])+w[n] (7)

[0069] The observation matrix is:

[0070]

[0071] (4) Jacobian matrix calculation

[0072] (1) Channel estimation. From the measurement matrix obtained in step (3), it can be seen that the observation vector at time n is related to the carrier and the channel. In order to construct the Jacobian matrix required for the extended Kalman filter, channel estimation is required.

[0073] Specifically, based on the training sequence x p [n], estimated using the least squares method, which achieves channel estimation by minimizing the following error function:

[0074]

[0075] The channel estimation result can be expressed as:

[0076]

[0077] where x p is the training sequence transmitted by the transmitter, y p is the training sequence received by the receiver.

[0078] (2) Jacobian matrix calculation. The Jacobian matrix is ​​the partial derivative of the observation function with respect to the state vector, which can be written as:

[0079]

[0080] in is the one-step prediction of the state vector, also called the prior estimate, which contains the variables that need to be tracked.

[0081] (5) Extended Kalman Filter

[0082] (1) Prediction equation. According to the implementation process of the extended Kalman filter, the prediction equation can be written as:

[0083]

[0084] Where P[n|n-1] is the covariance matrix of the prior error, The covariance of process noise describes the statistical characteristics of process noise. G is the process noise coefficient, G = [0 1] T , F is the state transfer matrix, expressed as

[0085]

[0086] (2) Observation equation. According to the implementation process of the extended Kalman filter, the update equation can be written as:

[0087]

[0088] P[n|n]=(IK[n]H[n])P[n|n-1] (16)

[0089] Where K[n] is the Kalman gain, which determines the weighting between the predicted state and the observed value to minimize the estimation error. The covariance of the observation noise describes the statistical characteristics of the observation noise. P[n|n] is the updated error covariance matrix, which describes the uncertainty of the updated state. is the updated estimate of the state at time n, where The first value of is the estimated phase

[0090] (5) Code element judgment.

[0091] In each symbol period, the estimated phase A differential operation is performed, and symbol decision is made based on the average phase change: when the average phase change is greater than 0, it is determined to be a symbol "1"; when the average phase change is less than 0, it is determined to be a symbol "0." This phase-change-based differential decision method achieves high-precision demodulation of MSK signals without relying on complex channel equalizers.

[0092] The technical solution of the present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0093] Example

[0094] like Figure 1 As shown, an embodiment of the present invention proposes a coherent demodulation method for underwater acoustic communication based on an extended Kalman filter. This embodiment uses a shallow water acoustic communication environment as the application background and uses simulation to verify the effectiveness of the present invention. It includes the following steps:

[0095] Step 1: Select the Proakis B channel with a channel impulse response of h = [0.407, 0.815, 0.407] and a signal-to-noise ratio of 0 dB. Using the selected channel, illustrate the application of the present invention in practical underwater acoustic communication. Specifically, the parameters are set as follows: the transmitted signal uses an MSK signal, the symbol rate is set to 50 bps, the duration of the MSK signal is 50 seconds, the number of transmitted symbols is 2500, the training sequence length is 5 seconds, the number of signal symbols is 250, and the transmitted symbol sequence is represented as [1 0 0 1 1 0 0…]. The relationship between the bit signal-to-noise ratio and the signal-to-noise ratio is:

[0096]

[0097] in, is the bit signal-to-noise ratio, R b is the symbol rate, R s is the symbol rate, f s is the sampling frequency.

[0098] Step 2: In order to effectively track and demodulate the MSK signal, its state vector and observation vector need to be established. The state vector x[n] of the MSK signal is composed of the phase The phase difference value Ω[n] is composed, and the observation vector is the received signal y[n].

[0099] The state equation is:

[0100]

[0101] The observation equation is:

[0102] y[n]=h(x[n])+w[n] (19)

[0103] Wherein h represents the mapping relationship between the state vector and the observation vector, which has been derived in the invention content.

[0104] Step 3: At the receiving end of the MSK underwater acoustic communication system, the training sequence is used to perform channel estimation. The training sequence is a sequence known to both the transmitter and receiver. By using the training sequence of the transmitter and receiver to perform channel estimation, the channel impulse response during the communication process can be obtained. The channel impulse response obtained by the least squares channel estimation is The Jacobian matrix is:

[0105]

[0106] Substitute the Jacobian matrix into the update equation of the Kalman filter to complete the construction of the extended Kalman filter model.

[0107] Step 4: Write the prediction equation and update equation according to the process of extended Kalman filter. Use the prediction equation and update equation of extended Kalman filter to track the phase of MSK signal. The initialization condition is The proposed extended Kalman filter model is used to track the phase of the MSK signal. The phase tracking result is relatively accurate. The phase tracking result is differentiated, and the positive and negative values ​​represent the demodulation results. The bit error rate is 0.0210, thus realizing the demodulation of MSK using the extended Kalman filter.

[0108] Furthermore, under the same channel conditions, the bit error rate results of the traditional demodulation method and the bit error rate results of the demodulation method with equalization are calculated. The traditional demodulation method is to first remove the carrier of the signal, and then perform matched filtering and low-pass filtering to judge the obtained baseband symbols, and the bit error rate is 0.3300. The demodulation method with equalization is to demodulate the baseband symbols of the traditional demodulation followed by the NLMS equalizer, and the bit error rate is 0.0450. It can be seen from the demodulation results that the MSK demodulation method based on the extended Kalman filter utilizes the channel information compared to the traditional demodulation method, thereby improving the communication performance. Figure 2 Shown is a graph of the channel impulse response; Figure 3 is the phase tracking result diagram; Figure 4 This is a comparison chart of the simulation performance of bit error rate-signal-to-noise ratio.

[0109] Summary:

[0110] The method of the present invention takes the underwater acoustic channel into consideration in the demodulation method of MSK based on EKF, and constructs a new method for MSK demodulation in underwater acoustic communication. The method utilizes the real-time tracking capability of EKF and the phase continuity of MSK signals, introduces the idea of ​​target tracking in demodulation, and incorporates channel information into the demodulation process, reconstructing the extended Kalman filter model under the underwater acoustic channel. By introducing the channel impulse response into the construction of the EKF model, the model can continuously track the phase of the received signal, significantly reducing the impact of the multipath effect on the demodulation performance. Therefore, a demodulation method proposed by the present invention can effectively reduce the bit error rate without using a complex equalizer, especially showing stronger robustness and reliability in complex underwater acoustic channels.

[0111] Finally, it should be noted that the above embodiments are intended only to illustrate the technical solutions of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions to the technical solutions of the present invention do not depart from the spirit and scope of the technical solutions of the present invention and are intended to be encompassed by the claims of the present invention.

Claims

1. A minimum frequency shift keying demodulation method for underwater acoustic communication based on extended Kalman filtering, comprising: The transmitting end transmits a minimum frequency shift keying modulated signal including an information sequence and a training sequence; The receiving end receives the minimum frequency shift keying modulated signal transmitted through the underwater acoustic channel, performs channel estimation based on the training sequence, and obtains the channel impulse response; the channel impulse response is introduced into the construction of the observation matrix of the extended Kalman filter, and a phase tracking model combined with the channel information is formed by modifying the Jacobian matrix. Through the phase tracking model, the phase of the received signal is continuously tracked to achieve minimum frequency shift keying demodulation.

2. The method for minimum frequency shift keying demodulation of underwater acoustic communication based on extended Kalman filtering according to claim 1 is characterized in that: The transmitting end transmits information sequence x a [n] and training sequence x p [n] minimum frequency shift keying modulation signal x[n]; where n represents time n; x[n] is determined by the variable to be tracked and and The column vector of the difference Ω[n] satisfies the following formula: Where T represents transpose.

3. The method for minimum frequency shift keying demodulation of underwater acoustic communication based on extended Kalman filtering according to claim 2 is characterized in that: The training sequence x p [n] is a sequence known to both the transmitter and the receiver.

4. The method for minimum frequency shift keying demodulation of underwater acoustic communication based on extended Kalman filtering according to claim 3 is characterized in that: The performing channel estimation according to the training sequence to obtain a channel impulse response includes: Based on the training sequence x p [n], use the least squares method to estimate and obtain the channel estimation result, that is, the channel impulse response for: Among them, x p is the training sequence transmitted by the transmitter, y p is the training sequence received by the receiver, and H represents the conjugate transpose.

5. The method for underwater acoustic communication minimum frequency shift keying demodulation based on extended Kalman filtering according to claim 4 is characterized in that: The observation matrix of the extended Kalman filter is: Among them, x[n] is the state vector of the transmitter, f c is the center frequency, is the tracking variable at time k, t[k] is the time at time k, where nl h +1≤k≤n-1, t[n] is the time at moment n, is the variable tracked at time n, h[nk] is the channel impulse response at time nk, h[0] is the channel impulse response at time 0, l h is the channel length.

6. The method for minimum frequency shift keying demodulation of underwater acoustic communication based on extended Kalman filtering according to claim 5 is characterized in that: The modified Jacobian matrix includes: Taking the partial derivative of the observation matrix with respect to the state vector, we get the Jacobian matrix H[n]|: in, The one-step-ahead estimate of the tracking variable, also called the prior estimate.

7. The method for minimum frequency shift keying demodulation of underwater acoustic communication based on extended Kalman filtering according to claim 6 is characterized in that: The phase tracking model combined with channel information includes: Set the initialization condition to According to the implementation process of the extended Kalman filter, the prediction equation satisfies the following formula: in, is the prior estimate of the state vector, P[n|n-1] is the covariance matrix of the prior error, is the covariance of process noise, G is the process noise coefficient, G = [01] T , F is the state transfer matrix, expressed as The observation equation is updated as: P[n|n]=(IK[n]H[n])P[n|n-1] Where K[n] is the Kalman gain, which is used to minimize the estimation error, The covariance of the observation noise P[n|n] is the updated error covariance matrix, is the updated estimate of the state at time n, where The first value of is the estimated phase y[n] is the received signal through the underwater acoustic channel.

8. The method for minimum frequency shift keying demodulation of underwater acoustic communication based on extended Kalman filtering according to claim 7 is characterized in that: The continuous tracking of the phase of the received signal to achieve minimum frequency shift keying demodulation includes: In each symbol period, the estimated phase A differential operation is performed to determine the symbol based on the average value of the phase change: when the average value of the phase change is greater than 0, it is determined to be a symbol "1"; when the average value of the phase change is less than 0, it is determined to be a symbol "0", thereby achieving minimum frequency shift keying demodulation.

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