CN110784428A - 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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CN110784428A
CN110784428A CN201911063503.2A CN201911063503A CN110784428A CN 110784428 A CN110784428 A CN 110784428A CN 201911063503 A CN201911063503 A CN 201911063503A CN 110784428 A CN110784428 A CN 110784428A
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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 and bring serious inter-subchannel 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 acoustic OFDM system, and because the usable bandwidth of the underwater acoustic 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 acoustic OFDM system than that of the radio OFDM system.
Doppler shift due to the complexity of the underwater acoustic channel destroys the orthogonality among the OFDM subcarriers, and seriously affects the performance and communication quality thereof. Therefore, how to reduce the influence of the doppler shift is the key to improve the OFDM underwater acoustic communication quality. 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 BDA0002256873130000021
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 BDA0002256873130000022
wherein S (n) is the multiplied output signal, a (i, j) is the weight, y sFor 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) And (5) when the value is 0, the arithmetic operation process: n 1,2, the 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 an input signal, d (n) is an expected response, μ (n) is a step factor, when d (n) is unknown, the output of the filter represents the expected signal, and the step factor has a value range of:
Figure BDA0002256873130000023
wherein λ maxIs the largest eigenvalue of the autocorrelation matrix of the input signal,
obtaining weight value under the condition of not knowing channel prior information
Figure BDA0002256873130000024
Defining auxiliary variables And using errors in response
Figure 100002_2
Obtaining single weight vector under MMSE criterion
Figure BDA0002256873130000027
Handle of a screwdriver And considered equal, a gradient error is obtained:
Figure BDA00022568731300000210
to prevent noise enhancement and tracking loss, the scale gradient is defined as:
Figure 100002_4
and a random gradient algorithm is adopted to recursively calculate the weight of the combiner:
Figure 100002_3
further, in step three, specifically, the received signal of the mth path is modeled as:
Figure BDA0002256873130000031
after removing the cyclic prefix, the signal passing through the mth path can be represented as:
Figure BDA0002256873130000032
wherein the content of the first and second substances,
Figure BDA0002256873130000033
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 BDA0002256873130000034
according to the maximum likelihood principle, an optimal receiver is established, and the processing result of a receiving end is as follows:
Figure BDA0002256873130000035
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 BDA0002256873130000036
equation (11) can be expressed as:
Figure BDA0002256873130000037
wherein the content of the first and second substances,
Figure BDA0002256873130000038
further, the weight of the combiner corresponding to the k carrier and the k receiving original is expressed by an adaptive algorithm
Figure BDA0002256873130000039
Define the corresponding input vector:
Figure BDA00022568731300000310
the output of the combiner is represented as:
Figure BDA00022568731300000311
the length L of the combiner is larger than or equal to I, when the length L of the combiner is larger than or equal to 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 the length L of the combiner is equal to 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 graph showing a comparison of 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 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 BDA0002256873130000041
where C is a normalization constant at reconstruction, its scale function is absent and is a non-orthogonal decomposition. The OFDM symbols in the received signal are multiplied by a group of orthogonal wavelet functions respectively to obtain the output:
Figure BDA0002256873130000042
wherein S (n) is the multiplied output signal, a (i, j) is the weight, y sFor 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 BDA0002256873130000051
An estimate is made, which is actually performed after channel equalization, usually by adding a filter to complete the channel equalization,
Figure BDA0002256873130000052
the filter that is automatically adjusted according to the received signal is called an adaptive filter, and since the adaptive filter can track and adapt to the dynamic change of the system, so that the adaptive filter can be used for adjusting the tap coefficientTo complete the estimation of the weighting factors.
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 algorithm (LMS) and various improved algorithms thereof, and the adaptive Gauss-Newton algorithm comprises a recursive least square algorithm (RLS) 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) And (5) when the value is 0, the arithmetic operation process: n 1,2, the 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 an input signal, d (n) is an expected response, μ (n) is a step size factor, when d (n) is unknown, the output of the filter can be used to represent the expected signal, 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 BDA0002256873130000053
wherein λ maxIs 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 BDA0002256873130000061
We define auxiliary variables
Figure 6
And using errors in response Obtaining single weight vector under MMSE criterion More specifically, the handle
Figure BDA0002256873130000065
And
Figure BDA0002256873130000066
considered equal, a gradient error is obtained:
Figure BDA0002256873130000067
to prevent noise enhancement and tracking loss, the scale gradient is defined as:
Figure 7
and a random gradient algorithm is adopted to recursively calculate the weight of the combiner:
Figure 8
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 BDA00022568731300000610
after removing the cyclic prefix, the signal passing through the mth path can be represented as:
Figure BDA00022568731300000611
wherein the content of the first and second substances,
Figure BDA00022568731300000612
representing the channel coefficient, w m(t) is the equivalent noise,
in conventional OFDM systems, the path gain and delay are almost constant over the block duration, i.e. the channel coefficients
Figure BDA0002256873130000071
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. Therefore, a morl-FFT based demodulation scheme is proposed herein, in which we use waveletsThe function and FFT to demodulate the OFDM symbol. 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 BDA0002256873130000072
according to the Maximum Likelihood (ML) principle, an optimal receiver is established, and the processing result of a receiving end is as follows:
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:
equation (11) can be expressed as:
Figure BDA0002256873130000075
wherein the content of the first and second substances,
in the morl-FFT, a group of wavelet functions are obtained by performing translation and scaling transformation on a mother wavelet, and then OFDM symbols are processed by using the group of wavelet functions, so that the processed data has smaller correlation, the method has great effect on reducing inter-carrier interference, and has higher convergence rate in a subsequent gradient algorithm and a self-adaptive algorithm. 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 unknown, we need to estimate the channel first and then perform matched filtering and equalization of the channel. 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 RE-GDA0002284834520000081
We can define the corresponding input vector:
Figure BDA0002256873130000082
the output of the combiner is represented as:
Figure BDA0002256873130000083
the length L of the combiner is larger than or equal to I, when the length L of the combiner is larger than or equal to 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 the length L of the combiner is equal to I, the algorithm in the method corresponds to a single-tap demodulator.

Claims (5)

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 to compensate for doppler.
2. The morl-FFT-based adaptive doppler compensation method in an underwater acoustic communication network according to claim 1, wherein in the first step, specifically, the wavelet function is defined as:
Figure FDA0002256873120000011
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 FDA0002256873120000012
wherein S (n) is the multiplied output signal, a (i, j) is the weight, y sFor the received OFDM symbol ψ (i) is the orthogonal wavelet function.
3. 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) And (5) when the value is 0, the arithmetic operation process: n 1,2, the 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 an input signal, d (n) is an expected response, μ (n) is a step factor, when d (n) is unknown, the output of the filter represents the expected signal, and the step factor has a value range of:
Figure FDA0002256873120000013
wherein λ maxIs the largest eigenvalue of the autocorrelation matrix of the input signal,
obtaining weight value under the condition of not knowing channel prior information
Figure FDA0002256873120000014
Defining auxiliary variables
Figure 1
And using errors in response
Figure 2
Obtaining single weight vector under MMSE criterion
Figure FDA0002256873120000017
Handle of a screwdriver And
Figure FDA0002256873120000019
considered equal, a gradient error is obtained:
Figure FDA0002256873120000021
to prevent noise enhancement and tracking loss, the scale gradient is defined as:
Figure 3
and a random gradient algorithm is adopted to recursively calculate the weight of the combiner:
。
4. the method of claim 1, wherein in step three, specifically, the received signal of the mth path is modeled as:
after removing the cyclic prefix, the signal passing through the mth path can be represented as:
Figure FDA0002256873120000025
wherein the content of the first and second substances,
Figure FDA0002256873120000026
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 FDA0002256873120000027
according to the maximum likelihood principle, an optimal receiver is established, and the processing result of a receiving end is as follows:
Figure FDA0002256873120000028
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:
equation (11) can be expressed as:
Figure FDA00022568731200000210
wherein the content of the first and second substances,
Figure FDA00022568731200000211
5. the morl-FFT-based adaptive Doppler compensation method in the underwater acoustic communication network as claimed in claim 4, wherein a group corresponding to a k-th carrier and a k-th receiving element is represented by an adaptive algorithmWeights of combiners
Figure FDA0002256873120000031
Define the corresponding input vector:
Figure FDA0002256873120000032
the output of the combiner is represented as:
Figure FDA0002256873120000033
the length L of the combiner is larger than or equal to I, when the length L of the combiner is larger than or equal to 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 the length L of the combiner is equal to I, the algorithm in the method corresponds to a single-tap demodulator.
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