CN110784428B - Self-adaptive Doppler compensation method based on Morl-FFT in underwater acoustic communication network - Google Patents

Self-adaptive Doppler compensation method based on Morl-FFT in underwater acoustic communication network Download PDF

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CN110784428B
CN110784428B CN201911063503.2A CN201911063503A CN110784428B CN 110784428 B CN110784428 B CN 110784428B CN 201911063503 A CN201911063503 A CN 201911063503A CN 110784428 B CN110784428 B CN 110784428B
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马雪飞
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Harbin Engineering University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/26—Systems using multi-frequency codes
    • H04L27/2601—Multicarrier modulation systems
    • H04L27/2647—Arrangements specific to the receiver only
    • H04L27/2655—Synchronisation arrangements
    • H04L27/2657—Carrier synchronisation
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B11/00—Transmission systems employing sonic, ultrasonic or infrasonic waves
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B13/00—Transmission systems characterised by the medium used for transmission, not provided for in groups H04B3/00 - H04B11/00
    • H04B13/02—Transmission systems in which the medium consists of the earth or a large mass of water thereon, e.g. earth telegraphy
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/26—Systems using multi-frequency codes
    • H04L27/2601—Multicarrier modulation systems
    • H04L27/2647—Arrangements specific to the receiver only
    • H04L27/2649—Demodulators
    • H04L27/265—Fourier transform demodulators, e.g. fast Fourier transform [FFT] or discrete Fourier transform [DFT] demodulators

Abstract

The invention provides a self-adaptive Doppler compensation method based on Morl-FFT in an underwater acoustic communication network, belonging to the field of underwater acoustic communication. The adaptive Doppler compensation method comprises the following steps: the method comprises the following steps: respectively multiplying OFDM symbols in a received signal by a group of orthogonal wavelet functions; step two: estimating a weighting factor of the carrier by using an adaptive algorithm; step three: the weighted data is demodulated to compensate for doppler. The invention provides a self-adaptive Doppler compensation method based on Morl-FFT in an underwater acoustic communication network, which demodulates OFDM symbols by using a wavelet function and FFT, and determines the optimal combiner weight by adopting a self-adaptive algorithm. Here we use a stochastic gradient algorithm to compute the combiner weights. We propose a detailed experimental analysis of the proposed doppler compensation and array combination method using simulated and experimental data.

Description

Self-adaptive Doppler compensation method based on Morl-FFT in underwater acoustic communication network
Technical Field
The invention relates to a self-adaptive Doppler compensation method based on Morl-FFT (mean-Fourier transform-fast Fourier transform), in particular to a channel estimation, channel equalization and self-adaptive algorithm, belonging to the field of underwater acoustic communication.
Background
In underwater acoustic communications, the underwater acoustic channel is a complex random channel that varies spatially and over time, has limited available bandwidth and suffers from serious drawbacks. Noise characteristics, multipath delays and doppler shifts present significant difficulties to the study and implementation of underwater acoustic communications. Orthogonal Frequency Division Multiplexing (OFDM) technology has been widely used in the field of underwater acoustic communications due to its frequency band advantage, its high utilization rate and strong multipath anti-interference capability. But OFDM frequency offset is very sensitive. The doppler generated when there is relative motion between the transmitting end and the receiving end may cause inter-sub-channel 0 interference. Since the magnitude of the doppler shift is related to the frequency of the signal itself, the magnitude of the frequency shift generated for the sub-channels of different frequencies is different in the OFDM wideband signal. If the data is still extracted according to the original frequency point position, the data will deviate from the orthogonal position to bring serious inter-sub-channel interference. And when the doppler phenomenon is serious, integer times of frequency shift can be caused, so that data cannot be demodulated.
Because the operating frequency is usually low in the underwater sound OFDM system, and because the available bandwidth of the underwater sound channel is narrow, and the sound velocity is much lower than the radio transmission speed, the doppler shift effect on each subcarrier is different, and is more serious than that of the underwater sound OFDM system than that of the radio OFDM system.
Doppler shift due to the complexity of the underwater acoustic channel destroys the orthogonality between OFDM subcarriers, and seriously affects their performance and communication quality. Therefore, how to reduce the influence of doppler shift is a key to improve the quality of OFDM underwater acoustic communication. Researchers have proposed using DFFFT, TFFT and other techniques to compensate for doppler frequency bias.
A doppler compensation method for waveform fast fourier transform (W-FFT) demodulation is proposed, in which we use a wavelet function and FFT to demodulate OFDM symbols. We employ an adaptive algorithm to determine the optimal combiner weights. Here we use a stochastic gradient algorithm to compute the combiner weights.
Disclosure of Invention
The invention provides a self-adaptive Doppler compensation method based on Morl-FFT in an underwater acoustic communication network, and aims to reduce the influence of Doppler frequency shift of an OFDM underwater acoustic communication system.
The self-adaptive Doppler compensation method based on Morl-FFT in the underwater acoustic communication network comprises the following steps:
the method comprises the following steps: respectively multiplying OFDM symbols in a received signal by a group of orthogonal wavelet functions;
step two: estimating a weighting factor of the carrier by using an adaptive algorithm;
step three: the weighted data is demodulated to compensate for doppler.
Further, in the first step, specifically, the wavelet function is defined as:
Figure GDA0002284834520000021
wherein, C is a normalization constant during reconstruction, and the OFDM symbols in the received signal are multiplied by a set of orthogonal wavelet functions, respectively, to obtain an output:
Figure GDA0002284834520000022
wherein S (n) is the multiplied output signal, a (i, j) is the weight, y s For the received OFDM symbol ψ (i) is the orthogonal wavelet function.
Further, in the second step, specifically, the adaptive algorithm adopts a least mean square algorithm LMS, which is described as:
initialization of initial values of the filter: omega 0 (0) =0, arithmetic operation: n =1,2., error signal: e (n) = d (n) -w H (n-1) u (n), weight coefficient update: w (n) = w (n-1) + μ (n) u (n) e * (n)，
Where u (n) is the input signal, d (n) is the desired response, μ (n) is the step factor, when d (n) is unknown, the desired signal is represented by the output of the filter, and the step factor ranges from:
Figure GDA0002284834520000023
wherein λ max Is the largest eigenvalue of the autocorrelation matrix of the input signal,
obtaining weight value under the condition of not knowing channel prior information
Figure GDA0002284834520000024
Defining auxiliary variables
Figure GDA0002284834520000025
And using errors in response
Figure GDA0002284834520000026
Obtaining single weight vector under MMSE criterion
Figure GDA0002284834520000027
Handle of a screwdriver
Figure GDA0002284834520000028
And
Figure GDA0002284834520000029
considered equal, a gradient error is obtained:
Figure GDA00022848345200000210
to prevent noise enhancement and tracking loss, the scale gradient is defined as:
Figure GDA00022848345200000211
and a random gradient algorithm is adopted to recursively calculate the weight of the combiner:
Figure GDA00022848345200000212
further, in step three, specifically, the received signal of the mth path may be modeled as:
Figure GDA0002284834520000031
after removing the cyclic prefix, the signal passing through the mth path can be represented as:
Figure GDA0002284834520000032
wherein, the first and the second end of the pipe are connected with each other,
Figure GDA0002284834520000033
representing the channel coefficient, w m (t) is the equivalent noise,
demodulating the OFDM symbols using a wavelet function and FFT, the demodulated signal being:
Figure GDA0002284834520000034
according to the maximum likelihood principle, an optimal receiver is established, and the processing result of a receiving end is as follows:
Figure GDA0002284834520000035
approximating equation (10) as a set of smoothly varying channel functions, decomposing the channel coefficients into a set of known functions to compute a channel matched filter, expressed as:
Figure GDA0002284834520000036
equation (11) can be expressed as:
Figure GDA0002284834520000037
wherein the content of the first and second substances,
Figure GDA0002284834520000038
further, the weight of the combiner corresponding to the k carrier and the k receiving original is expressed by an adaptive algorithm
Figure GDA0002284834520000039
Define the corresponding input vector:
Figure GDA00022848345200000310
the output of the combiner is represented as:
Figure GDA00022848345200000311
the length L of the combiner is larger than or equal to I, when I =1, the algorithm in the method is a traditional FFT demodulation structure, a demodulator and an equalizer with the size of L are needed, and when L = I, the algorithm in the method corresponds to a single-tap demodulator.
The main advantages of the invention are: the invention provides a self-adaptive Doppler compensation method based on Morl-FFT in an underwater acoustic communication network, which demodulates OFDM symbols by using a wavelet function and FFT and determines the optimal combiner weight by adopting a self-adaptive algorithm. Here we use a stochastic gradient algorithm to compute the combiner weights. We propose a detailed experimental analysis of the proposed doppler compensation and array combination method using simulated and experimental data.
Drawings
FIG. 1 is a W-FTT schematic diagram;
FIG. 2 is a schematic diagram of TFFT and W-FFT error rate performance comparison;
FIG. 3 is a diagram comparing MSE performance of W-FFT and TFFT;
fig. 4 is a flowchart of a method of morl-FFT-based adaptive doppler compensation in an underwater acoustic communication network according to the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1 to 4, a morl-FFT-based adaptive doppler compensation method in an underwater acoustic communication network includes the following steps:
the method comprises the following steps: respectively multiplying OFDM symbols in a received signal by a group of orthogonal wavelet functions;
step two: estimating a weighting factor of the carrier wave by using an adaptive algorithm;
step three: the weighted data is demodulated to compensate for doppler.
In this preferred embodiment of this part, in step one, specifically, the Morlet wavelet function is a single-frequency secondary sine function under a gaussian envelope, and the Morlet wavelet function is defined as:
Figure GDA0002284834520000041
where C is a normalization constant at reconstruction, its scale function is absent and is a non-orthogonal decomposition. Multiplying OFDM symbols in the received signal with a group of orthogonal wavelet functions respectively to obtain the output:
Figure GDA0002284834520000042
wherein S (n) is the multiplied output signal, a (i, j) is the weight, y s For the received OFDM symbol ψ (i) is the orthogonal wavelet function.
In the preferred embodiment of this section, in step two, specifically, weighting factors need to be matched at the receiving end
Figure GDA0002284834520000052
An estimate is made, which is actually performed after channel equalization, usually by adding a filter to complete the channel equalization,
Figure GDA0002284834520000053
the tap coefficients corresponding to the tap coefficients of each filter are usually adjusted manually if the information of the channel is known at the receiving end, but for the time-varying underwater acoustic channel, the receiving end needs to automatically adjust the tap coefficients.
Adaptive filters can be divided into finite impulse response filters and infinite impulse response filters, with the difference that their impulse response is finite or infinite. The tap coefficient value of the current moment generated by self-adaptive adjustment is used as the weighted value of signal weighted addition of each delay line, the estimation error is used, the absolute value is obtained through the difference between the result of weighted addition and the expected response of the signal, a self-adaptive algorithm is excited, a new tap coefficient is obtained, and the optimal performance of the filter is achieved through an iterative algorithm. Different adaptive algorithms have different filtering effects, the adaptive algorithm mainly has two modes of an adaptive gradient algorithm and an adaptive Gauss-Newton algorithm, the adaptive gradient algorithm comprises a Least Mean Square (LMS) algorithm and various improved algorithms thereof, and the adaptive Gauss-Newton algorithm comprises a Recursive Least Square (RLS) algorithm and a variant thereof.
The LMS algorithm theory is based on a wiener filter, and is an implementation manner of a descent algorithm, the adopted criterion is a minimum mean square error criterion (MMSE), and the LMS algorithm can be described as:
initialization of initial values of the filter: omega 0 (0) =0, arithmetic operation: n =1,2., error signal: e (n) = d (n) -w H (n-1) u (n), weight coefficient update: w (n) = w (n-1) + μ (n) u (n) e * (n)，
Wherein u (n) is the input signal, d (n) is the expected response, μ (n) is the step size factor, when d (n) is unknown, the expected signal can be represented by the output of the filter, the step size is the key of the LMS algorithm, which determines the convergence speed and steady-state error, and to ensure the convergence of the algorithm, the range of the step size factor is:
Figure GDA0002284834520000051
wherein λ is max Is the largest eigenvalue of the autocorrelation matrix of the input signal,
the LMS algorithm requires that the inputs of the transversal filters are vectors that are statistically independent and uncorrelated with each other, otherwise the convergence rate of the LMS algorithm is greatly reduced, and therefore, the performance of the algorithm can be ensured by eliminating the correlation between the input vectors at each moment.
The LMS algorithm has the characteristics of low computational complexity, good convergence in an environment where a signal is a stationary signal, unbiased convergence of an expected value to a wiener solution, stability in realizing the algorithm with limited precision, and the like, and is also the algorithm with the best stability and the most wide application in the adaptive algorithm.
Obtaining weight value under the condition of not knowing channel prior information
Figure GDA0002284834520000061
We define auxiliary variables
Figure GDA0002284834520000062
And using errors in response
Figure GDA0002284834520000063
Obtaining single weight vector under MMSE criterion
Figure GDA0002284834520000064
More specifically, the handle
Figure GDA0002284834520000065
And
Figure GDA0002284834520000066
considered equal, a gradient error is obtained:
Figure GDA0002284834520000067
to prevent noise enhancement and tracking loss, the scale gradient is defined as:
Figure GDA0002284834520000068
and a random gradient algorithm is adopted to recursively calculate the weight of the combiner:
Figure GDA0002284834520000069
to further improve stability and prevent error propagation, a thresholding method is employed that keeps the combiner weights constant if the error or gradient exceeds a predetermined level, which prevents abrupt changes in combiner weights that may occur in the event of a decision error.
The update of the error completion weight coefficient can also be calculated by using the output of the current filter if the expected response is unknown, but the estimation can be completed by using the pilot frequency, so the selection of the pilot frequency can also influence the accuracy of the channel equalization and the convergence speed of the algorithm.
In the preferred embodiment of this section, in step three, specifically, the received signal of the mth path is modeled as:
Figure GDA00022848345200000610
after removing the cyclic prefix, the signal passing through the mth path can be represented as:
Figure GDA00022848345200000611
wherein the content of the first and second substances,
Figure GDA00022848345200000612
representing the channel coefficient, w m (t) is the equivalent noise of the noise,
in conventional OFDM systems, the path gain and delay are almost constant over the block duration, i.e. the channel coefficients
Figure GDA0002284834520000071
However, in a fast changing underwater acoustic channel, it is likely that the characteristics of the channel have changed within the duration of the same OFDM symbol, and in this case, if the equalization of all data in one symbol is completed by using the estimation of one channel, a large error occurs, and the channel equalization effect is very poor. Hence, a morl-FFT based demodulation scheme is proposed herein, in which we use a wavelet function and FFT to demodulate OFDM symbols. The traditional FFT demodulation is a typical single frequency analysis technique, and the wavelet analysis is a multi-frequency analysis means, which can characterize the local characteristics of the signal, and the principle is as follows.
In the conventional OFDM demodulation, FFT is performed on a received signal, and the demodulated signal is:
Figure GDA0002284834520000072
according to the Maximum Likelihood (ML) principle, an optimal receiver is established, and the processing result of a receiving end is as follows:
Figure GDA0002284834520000073
due to the correlation of the multipath fading channel, equation (10) can be approximated as a set of smoothly varying channel functions, and the channel coefficients are decomposed into a set of known functions to compute a channel matched filter, expressed as:
Figure GDA0002284834520000074
equation (11) can be expressed as:
Figure GDA0002284834520000075
wherein the content of the first and second substances,
Figure GDA0002284834520000076
in the morl-FFT, a group of wavelet functions are obtained by carrying out translation and expansion transformation on mother wavelets, and then the group of wavelet functions are used for processing OFDM symbols. And removing the cyclic prefix at a receiving end, processing each symbol by using a wavelet function, and then performing equalization according to carriers by using a self-adaptive gradient algorithm to complete Doppler compensation.
In the preferred embodiment of this section, generally, when the channel is not availableWhen known, the channel needs to be estimated first, and then matched filtering and equalization of the channel are realized. However, in the morl-FFT-based demodulation method, two-step linear transformation can be simultaneously performed on the signal, and then a combiner for adaptively determining the weight values can be implemented. That is, we can express the weight of the combiner corresponding to the kth carrier and the kth receiving original through an adaptive algorithm
Figure GDA0002284834520000081
We can define the corresponding input vector:
Figure GDA0002284834520000082
the output of the combiner is represented as:
Figure GDA0002284834520000083
the length L of the combiner is larger than or equal to I, when I =1, the algorithm in the method is a traditional FFT demodulation structure, a demodulator and an equalizer with the size of L are needed, and when L = I, the algorithm in the method corresponds to a single-tap demodulator.

Claims (4)

1. The self-adaptive Doppler compensation method based on Morl-FFT in the underwater acoustic communication network is characterized by comprising the following steps:
the method comprises the following steps: respectively multiplying OFDM symbols in a received signal by a group of orthogonal wavelet functions;
step two: estimating a weighting factor of the carrier by using an adaptive algorithm;
step three: the weighted data is demodulated, doppler compensated,
in the first step, specifically, the wavelet function is defined as:
Figure FDA0003734116140000011
wherein, C is a normalization constant during reconstruction, and the OFDM symbols in the received signal are multiplied by a set of orthogonal wavelet functions, respectively, to obtain an output:
Figure FDA0003734116140000012
wherein S (n) is the multiplied output signal, a (i, j) is the weight, y s For the received OFDM symbol ψ (i) is the orthogonal wavelet function.
2. The morl-FFT-based adaptive doppler compensation method in an underwater acoustic communication network according to claim 1, wherein in the second step, specifically, the adaptive algorithm employs a least mean square algorithm LMS, which is described as:
initialization of initial values of the filter: omega 0 (0) =0, arithmetic operation: n =1,2., error signal: e (n) = d (n) -w H (n-1) u (n), weight coefficient update: w (n) = w (n-1) + μ (n) u (n) e * (n)，
Where u (n) is the input signal, d (n) is the desired response, μ (n) is the step factor, when d (n) is unknown, the desired signal is represented by the output of the filter, and the step factor ranges from:
Figure FDA0003734116140000013
wherein λ max Is the largest eigenvalue of the autocorrelation matrix of the input signal,
obtaining weight value under the condition of not knowing channel prior information
Figure FDA0003734116140000014
Defining auxiliary variables
Figure FDA0003734116140000015
And using responsesError of the measurement
Figure FDA0003734116140000016
Obtaining single weight under MMSE criterion
Figure FDA0003734116140000017
When handle
Figure FDA0003734116140000018
And
Figure FDA0003734116140000019
considered equal, a gradient error is obtained:
Figure FDA00037341161400000110
to prevent noise enhancement and tracking loss, the proportional gradient is defined as:
Figure FDA0003734116140000021
and a random gradient algorithm is adopted to recursively calculate the weight of the combiner:
Figure FDA0003734116140000022
3. the method for adaptive doppler compensation based on morl-FFT in an underwater acoustic communication network as claimed in claim 1, wherein in step three, specifically, the received signal of the mth path is modeled as:
Figure FDA0003734116140000023
after removing the cyclic prefix, the signal passing through the mth path can be represented as:
Figure FDA0003734116140000024
wherein the content of the first and second substances,
Figure FDA0003734116140000025
representing the channel coefficient, w m (t) is the equivalent noise,
demodulating the OFDM symbols using a wavelet function and FFT, the demodulated signal being:
Figure FDA0003734116140000026
according to the maximum likelihood principle, an optimal receiver is established, and the processing result of a receiving end is as follows:
Figure FDA0003734116140000027
approximating equation (10) as a set of smoothly varying channel functions, and decomposing the channel coefficients into a set of known functions to compute a channel matched filter, expressed as:
Figure FDA0003734116140000028
equation (11) can be expressed as:
Figure FDA0003734116140000029
wherein the content of the first and second substances,
Figure FDA00037341161400000210
4. according to claimThe morl-FFT-based adaptive Doppler compensation method in the underwater acoustic communication network as claimed in claim 3, wherein the channel reconstruction coefficient of the kth carrier signal received by the mth receiving hydrophone is expressed by an adaptive algorithm
Figure FDA00037341161400000211
Define the corresponding input vector:
Figure FDA0003734116140000031
the output of the combiner is represented as:
Figure FDA0003734116140000032
the length L of the combiner is larger than or equal to I, when I =1, the algorithm in the method is a traditional FFT demodulation structure, a demodulator and an equalizer with the size of L are needed, and when L = I, the algorithm in the method corresponds to a single-tap demodulator.
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