CN110602016B - Underwater acoustic channel time delay estimation method based on image deconvolution - Google Patents
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Abstract
The invention provides an underwater acoustic channel time delay estimation method based on image deconvolution. Carrying out pilot frequency compensation and fast inverse Fourier transform on the OFDM frequency domain observation signal at a system receiving end to obtain time domain channel response; inputting the time domain channel response as an iteration result of the previous iteration to an accelerated iteration module based on a vector extrapolation method to obtain an accelerated prediction result; inputting the prediction result into a Richardson-Lucy deconvolution module based on fast Fourier transform to obtain an iteration result of the current iteration; and after the iteration is carried out according to the preset iteration times, sending the final iteration result into a post-processing threshold module to screen out the final channel delay estimation result, and solving the frequency domain form of the channel path amplitude and the channel function by utilizing a polynomial basis expansion model. The method obviously improves the time delay estimation precision of the underwater sound OFDM channel, has excellent time delay estimation performance under the condition of Doppler frequency shift, and can be used for realizing high-efficiency and high-precision underwater sound channel estimation.
Description
Technical Field
The invention relates to an underwater acoustic channel time delay estimation method.
Background
In recent years, due to the high bandwidth utilization rate and low complexity of the Orthogonal Frequency Division Multiplexing (OFDM) technology, the OFDM technology is widely applied to underwater acoustic communication systems, and most underwater acoustic OFDM systems in practical application use coherent receivers, which makes the accuracy of channel estimation, especially the accuracy of channel delay estimation, very important.
However, compressed-sensing-based Orthogonal Matching Pursuit (OMP) channel estimation, which is popular due to low computational complexity, has inherent disadvantages that cannot be avoided: in computing the inner product function, there is a large main lobe width problem similar to conventional beamforming. It is feared that the image deconvolution technique (DCV) currently applied to uniform linear array and vector array direction of arrival (DOA) estimation can be used as post-processing of traditional beamforming, so that the main lobe of beamforming becomes narrow and the side lobe becomes low, the width of the main lobe can even be compared with a high-precision DOA estimation algorithm, and the array direction of arrival estimation has a good dual relationship with the OFDM channel delay estimation.
Disclosure of Invention
The invention aims to provide an underwater acoustic channel time delay estimation method based on image deconvolution, which can improve the time delay estimation precision.
The purpose of the invention is realized as follows:
firstly, at a system receiving end, carrying out pilot frequency compensation and fast inverse Fourier transform on an Orthogonal Frequency Division Multiplexing (OFDM) frequency domain observation signal to obtain time domain channel response; inputting the time domain channel response as an iteration result of the previous iteration into an accelerated iteration module based on a vector extrapolation method to obtain an accelerated prediction result; inputting the prediction result into a Richardson-Lucy deconvolution module based on fast Fourier transform to obtain an iteration result of the current iteration; after the above processes are carried out according to the preset iteration times, the final iteration result is sent to a post-processing threshold module to screen out the final channel delay estimation result, and a polynomial basis expansion model is utilized to solve the frequency domain form of the channel path amplitude and the channel function.
Step 1: the initialization is carried out in such a way that,
using the iteration result of the 0 th iteration as the time domain channel response of the receiving end of the underwater sound orthogonal frequency division multiplexing OFDM system, namely
Length of lambdanpλ is an oversampling factor, NpThe number of pilot frequencies in the OFDM system, the iteration index n is 0, the maximum iteration number is R, and the acceleration factor alpha(0)＝α(1)＝α(2)＝0，
Step 2: the process of iteration is carried out in a continuous process,
n is n +1, when n is larger than or equal to R, executing the step 3, otherwise executing the following steps:
(2-1): solving for the acceleration gradient of the nth iteration
Acceleration factor:
t represents a transpose operation;
(2-2): solving the predicted result of the nth iteration
Wherein
Is a direction vector;
(2-3): solving channel time domain channel response h according to prediction result of nth iterationa (n)Estimated value of (a):
(2-4): calculating the ratio between the real value of the channel time domain response and the estimated value of the time domain channel response obtained by the nth iteration:
(2-5): updating the iteration result of the current iteration, namely the distribution function of the multipath channel impulse:
and step 3:
obtaining the distribution function of multipath channel impulse by RL post-processing threshold
Length of lambdanp；
And 4, step 4: according to
Given channel impulse distribution, solving the amplitude corresponding to each multi-path channel impulse by utilizing a polynomial basis expansion model, namely P-BEM
Obtaining the frequency domain form H of the final multipath channel functionest。
The post-processing threshold in the step 3 is constructed based on residual error fitting constraint in a convex set mapping theory, and a specific expression is as follows:
wherein,
is a distribution function of the impulse from the multipath channel
Length of lambdan obtained by discrete samplingpOf the time-domain signal of (a),
is the variance of the noise, gamma is the confidence of the signal PdRelated variable, i.e.
PdSetting according to the signal-to-noise ratio of the system, wherein P (i) represents that the OFDM signal passes through a channel consisting of only one path with the amplitude of 1 and the time delay of 0, is received by a receiving end through time domain sampling, and has the length of lambda Np。
By looking up a large amount of data, a high-efficiency underwater acoustic channel time delay estimation method related to an image deconvolution technology does not exist at present, so that the time domain channel estimation of a channel is analogized to one-dimensional image deconvolution operation by combining the dual relation in the background technology and using the advantages of the deconvolution method, the channel estimation method based on the image deconvolution technology is provided, the disadvantages of OMP (object model processing) wide main lobe and high side lobe are well avoided, and the time delay estimation precision can be remarkably improved. The image deconvolution method is various, and the deconvolution method based on Bayesian theory and maximum likelihood algorithm, namely Richardson-Lucy iterative algorithm (Richardson-Lucy algorithm), is selected by the invention.
In addition, the underwater acoustic channel estimation by means of the OFDM system has the advantages that the OFDM system does not need to master global frequency domain information, only needs to insert comb-shaped pilot frequency in a frequency domain, and can know the global time domain channel information by partial frequency domain signals; and with the increasing maturity of the deconvolution algorithm, the performance and the calculation complexity of the deconvolution algorithm are further improved, and even if the deconvolution algorithm is applied to a multi-carrier system, the system overhead can be well controlled. In conclusion, the invention introduces the deconvolution theory into the field of underwater acoustic OFDM channel estimation and aims to provide a new direction for high-performance underwater acoustic channel estimation.
The process in step 2 is based on the Richardson-Lucy iterative deconvolution algorithm (RL), and the original Richardson-Lucy iterative method is accelerated by using a Fast Fourier Transform (FFT) and vector extrapolation method, so that the iterative convergence speed is greatly improved, and the efficient channel estimation is realized.
The invention has the beneficial effects that:
1. the invention provides a channel time delay estimation method based on an image deconvolution method aiming at a time domain channel observation signal of a uniform pilot frequency OFDM system, and the method can greatly improve the time delay estimation precision and avoid the wide main lobe problem existing in an OMP channel estimation method.
2. The invention relies on the Richardson-Lucy iterative deconvolution algorithm and combines the Fast Fourier Transform (FFT) and the vector extrapolation method to realize the high-efficiency channel estimation.
3. The method balances the calculation complexity and the time delay estimation precision, can obviously improve the time delay estimation precision on the premise of slightly increasing the calculation complexity, can be used for realizing a high-efficiency and high-precision channel estimation model, and realizes the win-win of energy conservation and high-efficiency operation for an underwater acoustic communication device or system.
Drawings
FIG. 1 is a schematic diagram of the deconvolution of two paths;
FIG. 2 is a model of channel estimation based on an image deconvolution method;
FIG. 3 is an accelerated iteration module based on a vector extrapolation method;
fig. 4 is a richardson-lucy deconvolution module based on a fast fourier transform.
Detailed Description
The invention is described in more detail below by way of example. A.CP-OFDM system
The OFDM system related by the invention adopts a cyclic prefix mode. Suppose an OFDM symbol block comprises K subcarriers, the transmission symbol on each subcarrier is s (K), and the number of pilot subcarriers is NpThe pilot interval is D. The time length of one OFDM symbol block is T, and the time length of the cyclic prefix is TcpCarrier frequency of fc。
The channel model herein is a multipath channel with L paths, each path having an amplitude and a time delay a, respectively, assuming that the channel remains constant for two symbol durationspAnd τp(p is 1,2, …, L) and assuming that the channel has a doppler compensated residual doppler shift of fd. After sampling and cyclic prefix removing operation, a signal at a receiving end (assuming that the length of the cyclic prefix is greater than the maximum time delay of a channel) is sent to an FFT demodulator, and a frequency domain input-output relational expression in a vector form is obtained as follows:
compensating the frequency domain observed quantity of the pilot frequency position to obtain the following expression:
where l is 0,1,2, …, Np-1. Carrying out inverse Fourier transform on the formula to obtain time domain channel impulse response h (t),
B. channel time delay estimation model based on image deconvolution method
Neglecting the constant coefficient of equation (3), and assuming f in equation (3)dNegligible by the doppler compensation operation, equation (3) can be simplified to convolution form (4):
(4) in the formula, h' (t) is understood as a blurred one-dimensional image, i.e. the response of the OFDM signal to the channel, b (t) can be considered as an unblurred one-dimensional image, and also can be understood as a plurality of impulses distributed on a time domain axis due to the sparsity of a wireless channel, and PSF (t) can be analogized to a Point Spread Function (PSF) in image processing, more precisely, the response of the OFDM system to a single time domain impulse line. The PSF needs to satisfy the shift invariance in the field of image deconvolution (deblurring), and the time shift invariance, PSF (t | τ), in OFDM channel estimationp)＝PSF(t-τp)。
The deconvolution method is various, and a Richardson-Lucy iterative deconvolution algorithm is selected herein. Knowing that A is an unblurred one-dimensional image with a probability P (A) of having a unit pixel at each position ii). B is a blurred one-dimensional image with a probability P (B) of the presence of a unit pixel at each position kk)。P(Bk|Ai) Representing the probability that the pixel at position i in a is spread onto position k in B. The Richardson can be obtained by a Bayesian formula and a total probability formulaOriginal iteration formula of lucy algorithm (r is iteration index):
wherein P is aboutr+1(Ai)、Pr(Ai) Are all the variables to be solved, so the Richardson-Lucy algorithm adopts an iterative method to the true P (A)i) An approximation is made. It should be noted that the richardson-luci algorithm is based on probability theory, and defaults that all variables need to satisfy non-negative constraints, so in order to ensure non-negativity of the iterative process, we use the following approximate form in the analysis and simulation next to
In contrast to formula (7), we compare P (A) abovei)、P(Bk)、P(Bk|Ai) And B in OFDMp(t)、ha(t) and P (t) correspondingly, obtaining a Richardson-Lucy formula based on the OFDM system:
compared with the main lobe, the side lobe of P (t) has negligible influence on the channel delay estimation, so that the non-negativity constraint in the formula (8) does not influence BpThe estimation result of the multipath position in (t) only influences the accuracy of the multipath amplitude. In order to ensure the accuracy of channel estimation, a polynomial basis expansion model method is adopted to solve the path amplitude, and a deconvolution method is only used for judging the multipath delay position.
C. Deconvolution post-processing threshold based on convex set mapping theory
Known haIs from ha(t) time domain samples of length λ NpA column vector of (a) representing a non-negatively constrained noisy channel time domain response vector; bpP representsA non-negative-constrained noiseless channel time-domain response vector, wherein bpIs a length of lambdan derived from B (t) samplespP is a circulant matrix formed by discrete forms P (i) of a point spread function P (t), the sampling intervals of said sampling operations being
In convex set mapping (POCS) channel estimation theory, it will
Defined as residual fit constraints, which reflect the quality of the channel estimate, with an upper error bound
Is the variance of the noise, gamma is the confidence of the signal PdRelated variable, i.e.
erf-1() Representing an inverse error function, PdRelated to the signal-to-noise ratio.
A will nowi＝ha[i]-bpP[i]Not less than 0, in the formula (10), then
Combining with the mean inequality, the formula (11) can be simplified to
From discrete forms of convolution equations
Suppose that
Is provided with
Therefore, the formula (12) can be simplified as follows:
thus, epsilonRLCan be regarded as the average error tolerance of the channel impulse response and the real channel impulse response after being processed by the Richardson-Lucy deconvolution method, and we expect that the confidence coefficient is PdTime, channel estimation result
Satisfies CvI.e. when b is truep[i]When it is 0, if
Less than epsilonRLThen, then
May be considered noise or interference and therefore
And setting 0. The purpose of the threshold is to filter false alarms caused by noise or interference, where e is measuredRLReferred to as the post-processing threshold, and re-expresses equation (13) as:
is greater than εRLIs/are as follows
Regarded as channel impulse response, less than epsilonRLIs/are as follows
Considered as noise or interference, the generation of false alarms is reduced theoretically.
D. Channel time delay estimation model based on accelerated deconvolution method
The construction process is shown in fig. 2, and the specific steps are as follows:
step 1: initialization: the iteration result of the 0 th iteration is the time domain channel response of the receiving end of the underwater sound OFDM system, namely
(length of. lamda.N)pλ is an oversampling factor, NpIs the number of pilots in the OFDM system), the iteration index n is 0, and the maximum number of iterations is R. Acceleration factor alpha(0)＝α(1)＝α(2)＝0，
Step 2: iteration: n is n +1, when n is larger than or equal to R, executing the step 3, otherwise executing the following steps:
(2-1): solving for the acceleration gradient of the nth iteration
Acceleration factor:
t represents a transpose operation;
(2-2): solving the predicted result of the nth iteration
Wherein
Is a direction vector.
(2-3): solving channel time domain channel response h according to prediction result of nth iterationa (n)Estimated value of (a):
(2-4): calculating the ratio between the real value of the channel time domain response and the estimated value of the time domain channel response obtained by the nth iteration:
(2-5): update the iteration result of the current iteration, i.e. the distribution function of the multipath channel impulse (channel taps):
and step 3:
obtaining the distribution function of multipath channel impulse by post-processing threshold
Length of lambdanp。
And 4, step 4: according to
Given channel impulse distribution, solving the amplitude corresponding to each multipath channel impulse by utilizing a polynomial basis expansion model (P-BEM)
And gives the frequency domain form H of the final multipath channel functionest。
The above steps and flows are only for illustrating the technical idea of the present invention, and are not intended to limit the present invention, and any modification and improvement made on the technical scheme, technical idea, introduction method proposed by the present invention are within the protection scope of the present invention.
Claims (1)
1. An underwater acoustic channel time delay estimation method based on image deconvolution is characterized by comprising the following steps:
step 1: initializing, taking the iteration result of the 0 th iteration as the underwater sound orthogonal frequency division multiplexingI.e. the time domain channel response at the receiving end of the OFDM system, i.e.
Length of lambdanpλ is an oversampling factor, NpThe number of pilot frequencies in the OFDM system, the iteration index n is 0, the maximum iteration number is R, and the acceleration factor alpha(0)＝α(1)＝α(2)＝0，
Wherein
Representing a Fourier transform, P (i) representing a received signal obtained by time-domain sampling at a receiving end of an OFDM signal through a channel consisting of only one path with amplitude of 1 and time delay of 0, and the length of the received signal is also lambdanp；
Step 2: iteration, n is equal to n +1, when n is larger than or equal to R, executing the step 3, otherwise executing the following steps:
(2-1): solving for the acceleration gradient of the nth iteration
Acceleration factor:
t represents a transpose operation;
(2-2): solving the predicted result of the nth iteration
Wherein
Is a direction vector;
(2-3): solving channel time domain channel response h according to prediction result of nth iterationa (n)Estimated value of (a):
(2-4): calculating the ratio between the real value of the channel time domain response and the estimated value of the time domain channel response obtained by the nth iteration:
(2-5): updating the iteration result of the current iteration, namely the distribution function of the multipath channel impulse:
and step 3:
obtaining the distribution function of multipath channel impulse by RL post-processing threshold
Length of lambdanp；
The post-processing threshold is constructed based on residual error fitting constraint in a convex set mapping theory, and a specific expression is as follows:
wherein,
is a distribution function of the impulse from the multipath channel
Length of lambdan obtained by discrete samplingpOf the time-domain signal of (a),
is the variance of the noise, gamma is the confidence of the signal PdRelated variable, i.e.
PdSetting according to the signal-to-noise ratio of the system;
and 4, step 4: according to
Given channel impulse distribution, solving the amplitude corresponding to each multi-path channel impulse by utilizing a polynomial basis expansion model, namely P-BEM
Obtaining the frequency domain form H of the final multipath channel functionest。
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