Fractional order time delay and Doppler frequency shift estimation method based on OTFS

Abstract

The invention provides a two-stage fractional order time delay and Doppler frequency shift estimation method based on an orthogonal time frequency space (OTFS). The two-stage fractional order time delay and Doppler frequency shift estimation method based on the OTFS is characterized in that the two-stage fractional order time delay and Doppler frequency shift estimation method based on the OTFS is provided; firstly, integer estimation of time delay and Doppler frequency shift is carried out by using a maximum likelihood estimation method, and the integer range of the time delay and Doppler frequency shift is determined; secondly, the Fibonacci sequence is used for determining the segmentation proportion, and the integer interval is segmented; and then, calculating an inner product of a sending signal subjected to channel influence and a receiving signal, selecting a segmentation point with the maximum inner product to generate a new search area, re-determining the segmentation proportion, and repeating the steps until the maximum iteration frequency is reached. And finally, calculating the distance and the speed of the target by using the obtained time delay and Doppler frequency shift. According to the OTFS modulation-based two-stage fractional order time delay and Doppler frequency shift estimation method designed by the invention, fractional order time delay and Doppler frequency shift can be accurately estimated, and an important theoretical basis is provided for realizing target perception in a communication and induction integrated system.

Description

Technical Field

[0001] The present invention belongs to the parameter estimation method, and specifically relates to a fractional delay and Doppler frequency shift estimation method based on OTFS in an integrated sensing and communications (ISAC) system. Background Art

[0002] With the rapid development of wireless communication technology, the sixth-generation wireless system needs to support emerging location-aware applications such as vehicle-to-everything (V2X), smart home, environmental monitoring, and human-computer interaction. These applications pose more stringent requirements on the communication and sensing performance of today's wireless systems, such as ultra-high data rate, extremely high reliability, ultra-low latency, and high precision. ISAC has been recognized as one of the key scenarios for the next-generation wireless networks (such as beyond 5G and 6G). This technology pursues deep integration between wireless sensing and communication, enabling these two functions to be co-designed to reduce costs, improve hardware, spectrum, and energy efficiency, and obtain mutual performance gains. Through this integration, the communication system can not only transmit data but also effectively sense the surrounding environment, including information such as the distance and speed of the target object. Orthogonal frequency division multiplexing (OFDM) has been widely used in the current ISAC system due to its advantages of high spectral efficiency, robustness against multipath fading, and ease of implementation. However, in a high-dynamic environment, the OFDM technology has significant interference problems in the time-frequency domain, such as performance degradation caused by Doppler frequency shift and delay spread. Orthogonal time frequency space (OTFS) technology uses the delay-Doppler (DD) domain to convert the time-varying multipath channel into an approximately stationary channel, thereby reducing the impact of the double-selective fading of the channel on the signal in a high-dynamic scenario.

[0003] In the ISAC system, the OTFS-based waveform is applied to target sensing. By receiving the echo signal reflected by the target at the transmitter and performing corresponding processing on it, the delay and Doppler frequency shift of the target can be effectively estimated, and then the distance and speed corresponding to the target can be calculated. However, most estimation algorithms assume that the delay and Doppler frequency shift are integer multiples of the delay and Doppler resolution, resulting in a large deviation between the estimated result and the true value, which affects the estimation accuracy of the target distance and speed. Therefore, designing an algorithm that can accurately estimate the fractional delay and fractional Doppler frequency shift can effectively reduce the estimation error of the target distance and speed.

[0004] In summary, this paper designs and implements a fractional delay and Doppler estimation method based on OTFS. At the transmitter, the echo signal reflected by the target is used for two-stage parameter estimation. In the first stage, the integer delay and Doppler frequency shift range of the target are determined through maximum likelihood estimation. In the second stage, the segmentation ratio is determined by generating the Fibonacci sequence and selecting appropriate Fibonacci numbers as ratios, so as to segment the integer interval and estimate the fractional delay and Doppler frequency shift. The proposed parameter estimation method can effectively estimate the fractional delay and Doppler frequency shift, thereby improving the perception accuracy of the target and further enhancing the performance of the ISAC system. Summary of the Invention

[0005] The object of the present invention is to provide a two-stage fractional delay and Doppler frequency shift estimation method based on OTFS in the ISAC system, which can improve the problem of large errors caused by integer estimation and enhance the accuracy of distance and speed estimation of the target.

[0006] A parameter estimation method for integrated communication and sensing of two-stage fractional delay and Doppler frequency shift based on OTFS according to the present invention specifically includes the following steps:

[0007] Step 1: Perform OTFS modulation on the signal. The specific algorithm process is as follows:

[0008] In the ISAC system, NM data information symbols X = [x 1 , x 2 ,..., x NM T are placed in the time delay-Doppler domain signal grid Λ to obtain x[k, l], where there are N rows of data in the Doppler domain and M columns of data in the time delay domain; then, the time delay-Doppler domain signal is transformed into the time-frequency domain grid △ through the inverse symplectic finite Fourier transform, expressed as:

[0009]

[0010] where 0 ≤ n ≤ N - 1, 0 ≤ m ≤ M - 1. The time-frequency domain signal X[n, m] is transformed into the time domain signal s(t) after passing through the Heisenberg transform, expressed as:

[0011]

[0012] where g tx (t) represents the transmitted pulse waveform of the time-frequency modulator. In the time-frequency domain, M and N are equivalently represented as the number of subcarriers and the number of symbols, and T represents the symbol period. The transmitted signal s(t) is reflected by the target and returned to the transmitter. The channel impulse response it experiences is denoted as h(τ, v), and the received signal y(t) is:​

[0013] y(t) = ∫∫h(τ, v)s(t - τ)e j2πv(t-τ) dτdv + n(t)

[0014] where n(t) represents additive white Gaussian noise with a mean of 0 and a variance of σ 2 , and h(τ, v) characterizes the impulse response of the channel to the delay parameter τ and Doppler parameter v of the moving target.

[0015] Step 2: Use maximum likelihood estimation to perform integer estimation of time delay and Doppler shift. The specific algorithm flow is as follows:

[0016] In the ISAC system, assume there are I targets. The transmitter receives the echo signals reflected by the targets, and the transmitted signal is known. Use maximum likelihood estimation to perform integer estimation of time delay and Doppler shift:

[0017]

[0018] where represents the integer time delay index of the i-th target, represents the integer Doppler index of the i-th target, and 1 ≤ i ≤ I. S represents the transmitted signal matrix, and Λ represents the discretized grid in the time delay-Doppler domain Δf represents the frequency interval between adjacent subcarriers, and represent M×M and N×N cyclic shift matrices respectively, which are used to perform shift operations on the transmitted signal matrix S in the time delay-Doppler domain to simulate the influence of the channel on the signal. vec() represents converting a matrix into a vector, and y represents the received signal vector.

[0019] Convert the minimization problem into a maximization problem:

[0020]

[0021] where (·) H represents the transpose, which converts a column vector into a row vector.

[0022] When estimating the parameters of the i-th target, it is necessary to eliminate the interference of the reflected signals from the previous i - 1 targets. For the first estimated target, there is:

[0023]

[0024] When estimating the i-th target, there is:

[0025]

[0026] where

[0027]

[0028] Among them, represents the channel response matrix of the j-th target, where 1 ≤ j ≤ i - 1, and s represents the transmitted signal vector.

[0029] Through integer estimation, the integer range of the time delay can be obtained as The integer range of the Doppler frequency shift is

[0030] Step 3: Generate the Fibonacci sequence and determine the splitting ratio. The specific algorithm process is as follows:

[0031] Generate the Fibonacci sequence, denoted as fibs(n), where n represents the n-th term of the sequence. The 0-th term fibs(0) = 0, the 1-st term fibs(1) = 1, and starting from the 2-nd term, each term is equal to the sum of the previous two terms, that is:

[0032]

[0033] According to the result of Step 2, the interval of the integer time delay is denoted as [a 1 , b 1 , where The interval of the integer Doppler is denoted as [a 2 , b 2 , where Select the Fibonacci number greater than or equal to the larger value of b 1 , b 2 in the Fibonacci sequence, denoted as fibs(c), then the determined splitting ratio is

[0034] Step 4: Divide the integer interval and perform fractional estimation of the time delay and Doppler. The specific algorithm is as follows:

[0035] According to the splitting ratio λ 1 and λ 2 obtained in Step 3, the interval division is as follows:

[0036]

[0037] Then the splitting points of the integer time delay and Doppler frequency shift are (x 1 , y 1 ), (x 1 , y 2 ), (x 2 , y 1 ), (x 2 , y 2 ). Substitute the splitting points into the following formula:

[0038]

[0039] Among them, d ∈ {1, 2}, g ∈ {1, 2}, find the splitting points of time delay and Doppler that maximize f dg and define a new search region, that is:

[0040] If f 11 is the maximum value, the intervals of time delay and Doppler are updated to [a 1 , x 2 and [a 2 , y 2 ;

[0041] If f 12 is the maximum value, the intervals of time delay and Doppler are updated to [a 1 , x 2 and [y 1 , b 2 ;

[0042] If f 21 is the maximum value, the intervals of time delay and Doppler are updated to [x 1 , b 1 and [a 2 , y 2 ;

[0043] If f 22 is the maximum value, the intervals of time delay and Doppler are updated to [x 1 , b 1 and [y 1 , b 2 .

[0044] After obtaining the new intervals of time delay and Doppler shift, repeat steps three and four, that is, reselect the Fibonacci numbers to determine the splitting ratio and search for a new search region until the maximum number of iterations is reached.

[0045] At this time, the and output after reaching the maximum number of iterations are the values of time delay and Doppler shift corresponding to the i-th target, expressed as:

[0046]

[0047] Step five: Calculate the distance and speed of the i-th target according to the values of time delay and Doppler shift obtained in step four The specific algorithm process is as follows:

[0048]

[0049] Among them, c0 is the speed of light, and f c is the carrier frequency.

[0050] Beneficial effects

[0051] First, this method uses the maximum likelihood estimation method to perform integer estimation of time delay and Doppler frequency shift, and determines the integer ranges of time delay and Doppler frequency shift. Secondly, a Fibonacci sequence is generated, and a Fibonacci number greater than or equal to the maximum value in the time delay and Doppler boundaries is selected to determine the segmentation ratio. Then, the obtained segmentation ratio is used to divide the integer interval, the interval division points are substituted into the corresponding matrix of the channel, the inner product of the transmitted signal after being affected by the channel and the received signal is calculated, a new search area is found, and then the segmentation ratio is recalculated, and this is repeated until the maximum number of iterations is reached. Finally, the obtained time delay and Doppler frequency shift are used to calculate the distance and speed of the target.

[0052] The two-stage fractional-order time delay and Doppler frequency shift estimation method based on OTFS modulation designed by the present invention can accurately estimate the fractional-level time delay and Doppler frequency shift. The distance error and speed error of the target calculated therefrom can be small enough to achieve millimeter-level distance estimation accuracy and decimeter-per-second speed estimation accuracy. It can provide a good basis for target perception in the ISAC system. Description of the drawings

[0053] Figure 1 is the algorithm flow chart.

[0054] Figure 2 is the distance estimation error graph of target estimation using this method.

[0055] Figure 3 is the speed estimation error graph of target estimation using this method. Specific implementation

[0056] The purpose of the present invention is to provide a two-stage fractional-order time delay and Doppler frequency shift estimation method based on OTFS in the ISAC system, which can improve the problem of large errors caused by integer estimation and improve the accuracy of distance and speed estimation of the target.

[0057] The integrated communication and sensing parameter estimation method for two-stage fractional-order time delay and Doppler frequency shift based on OTFS described in the present invention specifically includes the following steps:

[0058] Step 1: Perform OTFS modulation on the signal, and the specific algorithm flow is as follows:

[0059] In the ISAC system, NM data information symbols X = [x 1 , x 2 ,..., x NM ​T Place it into the time-delay - Doppler domain signal grid Λ to obtain x[k, l], where There are N rows of data in the Doppler domain and M columns of data in the time-delay domain; then, transform the time-delay - Doppler domain signal to the time-frequency domain grid Δ through the inverse symplectic finite Fourier transform, expressed as:

[0060]

[0061] where 0 ≤ n ≤ N - 1, 0 ≤ m ≤ M - 1. After the time-frequency domain signal X[n, m] undergoes the Heisenberg transform, it becomes the time-domain signal s(t), expressed as:

[0062]

[0063] where g tx (t) represents the transmitted pulse waveform of the time-frequency modulator. In the time-frequency domain, M and N equivalently represent the number of subcarriers and the number of symbols, and T represents the symbol period. The transmitted signal s(t) is reflected by the target and then returns to the transmitter. The channel impulse response it experiences is denoted as h(τ, v), and the received signal y(t) is:

[0064] y(t) = ∫∫h(τ, v)s(t - τ)e j2πv(t-τ) dτdv + n(t)

[0065] where n(t) represents additive white Gaussian noise with an average value of 0 and a variance of σ 2 , and h(τ, v) characterizes the impulse response of the channel to the time-delay parameter τ and Doppler parameter v of the moving target.

[0066] Step 2: Use maximum likelihood estimation to perform integer estimation of time delay and Doppler frequency shift. The specific algorithm flow is as follows:

[0067] In the ISAC system, assume there are I targets. The transmitter receives the echo signal reflected by the target, and the transmitted signal is known. Use maximum likelihood estimation to perform integer estimation of time delay and Doppler frequency shift:

[0068]

[0069] where represents the integer time-delay index of the i-th target, represents the integer Doppler index of the i-th target, and 1 ≤ i ≤ I, S represents the transmitted signal matrix, Λ represents the discretized grid in the time-delay - Doppler domain Δf represents the frequency interval between adjacent subcarriers, and Denote the cyclic shift matrices of \(M\times M\) and \(N\times N\) respectively, which are used to perform shift operations on the transmitted signal matrix \(S\) in the time-delay Doppler domain to simulate the influence of the channel on the signal. \(vec()\) represents converting a matrix into a vector, and \(y\) represents the received signal vector.

[0070] Convert the minimization problem into a maximization problem:

[0071]

[0072] where, \((\cdot)\) H represents the transpose, which converts a column vector into a row vector.

[0073] When estimating the parameters of the \(i\)-th target, it is necessary to eliminate the interference of the reflected signals from the previous \(i - 1\) targets. For the first estimated target, there is:

[0074]

[0075] When estimating the \(i\)-th target, there is:

[0076]

[0077] where,

[0078]

[0079] where, represents the channel response matrix of the \(j\)-th signal, \(1\leq j\leq i - 1\), and \(s\) represents the transmitted signal vector.

[0080] Through integer estimation, the integer range of the time delay can be obtained as The integer range of the Doppler frequency shift is

[0081] Step 3: Generate the Fibonacci sequence and determine the splitting ratio. The specific algorithm process is as follows:

[0082] Generate the Fibonacci sequence, denoted as \(fibs(n)\), where \(n\) represents the \(n\)-th term of the sequence. The 0-th term \(fibs(0)=0\), the 1-st term \(fibs(1)=1\), and starting from the 2-nd term, each term is equal to the sum of the previous two terms, that is:

[0083]

[0084] According to the result of Step 2, the interval of the integer time delay is denoted as \([a\) 1 ,b\) 1 , where The interval of the integer Doppler is denoted as \([a\) 2 ,b\) 2 , where Select a number greater than or equal to \(b\) in the Fibonacci sequence1 , b 2 For the Fibonacci number of the larger value, denoted as fibs(c), the splitting ratio is determined as

[0085] Step 4: Divide the integer interval and perform fractional estimation of time delay and Doppler. The specific algorithm is as follows:

[0086] According to the splitting ratio λ 1 and λ 2 , the interval division is as follows:

[0087]

[0088] Then the splitting points of the integer time delay and Doppler frequency shift are (x 1 , y 1 ), (x 1 , y 2 ), (x 2 , y 1 ), (x 2 , y 2 ). Substitute the splitting points into the following formula:

[0089]

[0090] where d ∈ {1, 2}, g ∈ {1, 2}, find the splitting points of time delay and Doppler that make f dg the largest, and define a new search area, that is:

[0091] If f 11 is the maximum value, the intervals of time delay and Doppler are updated to [a 1 , x 2 and [a 2 , y 2 ;

[0092] If f 12 is the maximum value, the intervals of time delay and Doppler are updated to [a 1 , x 2 and [y 1 , b 2 ;

[0093] If f 21 is the maximum value, the intervals of time delay and Doppler are updated to [x 1 , b 1 and [a 2 , y 2 ;

[0094] If f 22 is the maximum value, the intervals of time delay and Doppler are updated to [x 1 , b1 [y and 1 , b 2 .

[0095] After obtaining the new time delay and Doppler frequency shift intervals, repeat steps three and four, that is, reselect the Fibonacci numbers to determine the splitting ratio and find a new search interval until the maximum number of iterations is reached.

[0096] At this time, the and output after reaching the maximum number of iterations are the values of the time delay and Doppler frequency shift corresponding to the i-th target, denoted as:

[0097]

[0098] Step five: According to the values of the time delay and Doppler frequency shift obtained in step four calculate the distance and speed of the i-th target. The specific algorithm flow is as follows:

[0099]

[0100] where c 0 is the speed of light and f c is the carrier frequency.

Claims

1. A two-stage fractional-order time delay and Doppler frequency shift synaesthesia integrated parameter estimation method based on OTFS, comprising the following steps: Step 1: OTFS modulate the signal, and the transmitted signal is reflected by the target and then returns to the transmitting end; Step 2: Use maximum likelihood estimation to perform integer estimation of delay and Doppler shift. Assuming there are I targets, when estimating the parameters of the i-th target, 1≤i≤I, it is necessary to eliminate the interference from the first i-1 targets. Through integer estimation, the integer range of the delay can be obtained as The integer range of Doppler frequency shift is Step 3: Generate the Fibonacci sequence, denoted as fibs(n); According to the integer range of delay and Doppler frequency shift obtained in step 2, select the appropriate Fibonacci number, denoted as fibs(c), and determine the segmentation ratio: Step 4: Split the integer interval and bring the interval split points into the channel response matrix Calculate the inner product of the transmitted signal after being affected by the channel and the received signal |(Γ i (τ i ,ν i )s) H y ni | 2 , select the segmentation point that maximizes the inner product to generate a new search range, and reselect the Fibonacci number to generate a new segmentation ratio, and repeat this process until the maximum number of iterations is reached; at this point, the fractional level of delay and Doppler shift is output. Step 5: Take the fractional delay and Doppler shift values ​​obtained in step 4 Calculate the distance and speed of the target.

2. According to the two-stage fractional-order delay and Doppler shift synaesthesia integrated parameter estimation method based on OTFS in claim 1, the steps three and four use the Fibonacci sequence to determine the segmentation ratio of the interval, bring the segmentation point into the channel response matrix, calculate the inner product of the transmitted signal after the channel influence and the received signal, select the segmentation point with the largest inner product to generate a new search area, then redetermine the segmentation ratio, repeat the above process until the maximum number of iterations is reached, including the following steps: Generate the Fibonacci sequence, denoted as fibs(n), where n represents the nth term of the sequence, the 0th term fibs(0) = 0, the 1st term fibs(1) = 1, and starting from the 2nd term, each term is equal to the sum of the previous two terms, that is: According to the result of integer estimation, the interval of integer delay is recorded as [a1,b1], where The integer Doppler interval is denoted as [a2,b2], where represents the integer delay index of the i-th target, represents the integer Doppler index of the i-th target, M represents the number of subcarriers, N represents the number of symbols, T represents the symbol period, and Δf represents the frequency interval between adjacent subcarriers; select the Fibonacci number greater than or equal to the larger value of b1 and b2 in the Fibonacci sequence, denoted as fibs(c), and determine the segmentation ratio as Split the integer interval to perform fractional estimation of delay and Doppler. According to the obtained split ratios λ1 and λ2, the interval division is: Then the division points of integer delay and Doppler frequency shift are (x1, y1), (x1, y2), (x2, y1), (x2, y2). Substituting the division points into the following formula: in, Among them, d∈{1,2},g∈{1,2}; (·) H represents transpose, converting a column vector into a row vector; represents the channel response matrix of the jth target, s represents the transmitted signal vector, y represents the received signal vector, and y ni It means removing the interference of the first i-1 signals on the i-th signal; Find the value such that f dg The maximum delay and Doppler split point defines a new search area, namely: If f 11 is the maximum value, the delay and Doppler intervals are updated to [a1,x2] and [a2,y2]; If f 12 is the maximum value, the delay and Doppler intervals are updated to [a1,x2] and [y1,b2]; If f 21 is the maximum value, the delay and Doppler intervals are updated to [x1,b1] and [a2,y2]; If f 22 is the maximum value, the delay and Doppler intervals are updated to [x1,b1] and [y1,b2]; After obtaining the new time delay and Doppler frequency shift interval, repeat the above process, that is, reselect the Fibonacci number to determine the segmentation ratio and find a new search interval until the maximum number of iterations is reached; At this point, the output after reaching the maximum number of iterations is and That is, the value of the time delay and Doppler frequency shift corresponding to the i-th target, expressed as:

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