A method for accurate estimation of fractional delay doppler in a Zak-OTFS system

Abstract

The application discloses a method for accurately estimating fractional delay and Doppler in a Zak-OTFS system, and is an estimation method for the fractional delay and fractional Doppler situation existing due to insufficient delay and Doppler accuracy in an actual scene. The method comprises the following steps: considering the upsampling, pulse shaping and up-conversion and other steps in actual communication, through the signal after upsampling, the interpolation amplification is equivalent to being carried out on the delay axis, and the resolution is improved; the receiving end directly obtains the accurate estimation of the fractional delay and the fractional Doppler by using the signal after the matched filtering and not after the downsampling, and combining the periodicity of the Zak transformation. The application can not only estimate the fractional delay and Doppler, but also directly utilize the signal to obtain the channel information at the receiving end, and compared with the traditional estimation method, the additional algorithm complexity is reduced.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of channel estimation, and particularly relates to a method for accurately estimating fractional delay-Doppler in a Zak-OTFS system. BACKGROUND

[0002] In the traditional method for estimating fractional delay-Doppler, the threshold-based embedded pilot channel estimation has good channel estimation performance only for integer delay and integer Doppler, and for fractional delay and fractional Doppler, although the size of the guard interval can be increased to improve the accuracy of channel estimation, the improved accuracy is limited, and a large amount of grid resources are wasted, reducing the spectral efficiency. Existing methods for estimating fractional delay and fractional Doppler, such as cross-correlation estimation and cooperative estimation, have high complexity and require additional communication overhead. Designing a method for estimating fractional delay-Doppler with good performance and low complexity is a major research problem.

[0003] Therefore, it is necessary to design a method for accurately estimating fractional delay-Doppler in a Zak-OTFS system to solve the above problems. SUMMARY

[0004] The application aims to provide a method for accurately estimating fractional delay-Doppler in a Zak-OTFS system.

[0005] To achieve the above object, the application adopts the following technical scheme, comprising the following steps:

[0006] Step 101: using one-time IDZT transformation at the sending end to generate a signal, and adding a cyclic prefix;

[0007] Step 102: performing up-sampling, pulse shaping and up-conversion processing on the signal, sending the processed signal into a channel, and performing corresponding down-conversion, matched filtering and down-sampling processing at the receiving end;

[0008] Step 103: using the periodicity of Zak transformation to obtain accurate fractional delay and Doppler estimation by averaging and differencing the matched filtered signal.

[0009] As a further improvement of the application, in step 101, the IDZT is as follows:

[0010]

[0011] wherein M and N are the number of grids along the delay domain and the number of grids along the Doppler domain in the delay-Doppler domain grid, respectively,

[0012] n and k are indexes along the delay axis and the Doppler axis in the delay-Doppler grid, respectively, where 0≤n≤M-1, 0≤k≤N-1,

[0013] a constellation modulation signal to be transmitted on the delay-Doppler domain

[0014] x[n+lM] is the time-domain signal after IDZT modulation, x[n+lM]∈C 1×MN , where 0≤n≤M-1, 0≤l≤N-1.

[0015] As a further improvement of the present application, in the step 101, the signal after adding the cyclic prefix is s(t), which is expressed in the vector form of the discrete-time signal as After straightening x[n+lM], L cyclic prefixes are added in front.

[0016] As a further improvement of the present application, in the step 102, the upsampling is specifically: assuming that the number of upsampling points is N sam , the signal s(t) is divided into real and imaginary parts for upsampling, pulse shaping, and quadrature modulation up-conversion to obtain the real transmitted signal s sam (t), which is expressed in the vector form of the discrete-time signal as sam (t) is

[0017] As a further improvement of the present application, in the step 102, the channel is:

[0018] where H is the number of targets, h i , l i and k i respectively represent the complex gain of the i-th target and the coordinates in the delay-Doppler grid,

[0019] is the permutation matrix of the forward cyclic shift,

[0020]

[0021] is a diagonal matrix of (MN+L)·N sam ×(MN+L)·N sam ,

[0022]

[0023] where,

[0024] Consideration of the effect of two-dimensional twisted convolution correction

[0025] where the received signal is the corresponding noise vector at the receiver.

[0026] As a further improvement of the invention, the method for obtaining the accurate fractional delay estimation in step 103 comprises the following steps:

[0027] Step 201: According to the periodicity in the main properties of the discrete Zak transform, Doppler k is periodic with a period of N,

[0028]

[0029] n is quasi-periodic with a period of M, and there is a complex factor

[0030]

[0031] Step 202: Combining the periodicity, quasi-periodicity and IDZT transform of the above two formulas, the IDZT of is obtained, and the signal containing noise and up-sampled through the channel is an N-period extension of a sequence with a period of M·N sam in the time domain, with the same amplitude in each period and the argument satisfying the change of ;

[0032] Step 203: After averaging the amplitudes of N periods, the wave peak in the first period time domain graph of is obtained, the time delay coordinate axis corresponding to the peak value is obtained according to the wave peak, and then divided by the number of sampling points N sam to obtain the fractional delay estimation.

[0033] As a further improvement of the invention, the method for obtaining the accurate fractional delay estimation in step 103 comprises the following steps:

[0034] Step 301: Utilizing the quasi-periodicity of the discrete Zak transform on the time delay to obtain the accurate estimation of the user Doppler information:

[0035]

[0036] Step 302: Taking the sample of the time delay axis coordinate of a certain wave peak as an example, the arguments of N periods are obtained respectively, and according to the quasi-periodic characteristics, the N arguments satisfy The N arguments are an arithmetic sequence;

[0037] Step 303: Use a differential method to solve the Doppler k, obtain N-1 differences according to the N arguments, average the differences and regard them as tolerance to obtain a Doppler estimate.

[0038] The beneficial effects of the present invention are:

[0039] Compared with the traditional two-step method of estimating parameters in the OTFS system: first a rough estimate and then a fine estimate, the present invention combines practical considerations such as upsampling. At the receiving end, the delay and Doppler information contained in the un-downsampled signal can be utilized. Through the periodicity of the Zak transform, an accurate estimate of the fractional delay-Doppler can be obtained, which greatly reduces the complexity of the traditional estimation algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 This is a flow chart of a method for accurately estimating fractional delay Doppler in a Zak-OTFS system according to the present invention;

[0041] Figure 2 A block diagram of a Zak-OTFS communication system transmission system of the present invention;

[0042] Figure 3 for Figure 1 Flow chart of specific implementation steps of step 103. DETAILED DESCRIPTION

[0043] In order to make the objectives, technical solutions and advantages of the present invention more clear, the present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0044] It should also be noted here that, in order to avoid obscuring the present invention due to unnecessary details, only structures and / or processing steps closely related to the solutions of the present invention are shown in the drawings, while other details that are not closely related to the present invention are omitted.

[0045] like Figure 1 As shown, a method for accurately estimating fractional delay Doppler in a Zak-OTFS system of the present invention comprises the following steps:

[0046] Step 101: Figure 2 As shown, using an IDZT transform at the transmitter to replace the traditional OTFS requires two transforms of ISFFT plus OFDM modulation to generate the signal and add a cyclic prefix; the IDZT is as follows:

[0047]

[0048] M and N are the number of lattices along the delay domain and the number of lattices along the Doppler domain in the delay-Doppler grid, respectively, n and k are the indices along the delay axis and the Doppler axis in the delay-Doppler grid, respectively (where 0≤n≤M-1, 0≤k≤N-1), the constellation modulation signal to be transmitted on the delay-Doppler domain x[n+lM] is the time-domain signal after IDZT modulation x[n+lM]∈C 1×MN (0≤n≤M-1, 0≤l≤N-1).

[0049] Step 102: In combination with the actual transceiver system, consider adding upsampling, pulse shaping and up-conversion after the transmission end, and finally add corresponding down-conversion, matched filtering and downsampling at the receiving end; assume that the number of upsampling points is N sam After upsampling, pulse shaping and quadrature modulation up-conversion, the real transmitted signal is s sam (t), which can be expressed in the form of a vector of discrete-time signals s sam (t) is

[0050] The channel can be expressed as:

[0051] where H is the number of targets, h i , l i and k i represent the complex gain of the i-th target and the coordinates in the delay-Doppler grid, respectively, is the permutation matrix of the forward cyclic shift,

[0052]

[0053] is a diagonal matrix of (MN+L)·N sam ×(MN+L)·N sam ,

[0054]

[0055] where

[0056] Consider the effect of two-dimensional twisted convolution correction

[0057] where the received signal and is the corresponding noise vector at the receiver.

[0058] Step 103: By using the periodicity of Zak transform, the accurate fractional time delay and Doppler estimation can be obtained by averaging and differencing.

[0059] As Figure 3 , step 103 specifically includes the following steps:

[0060] Step 201: According to the periodicity in the main properties of discrete Zak transform, k (Doppler) is periodic with a period of N,

[0061]

[0062] and n (time delay) is quasi-periodic with a period of M, and there is a complex factor

[0063]

[0064] Step 202: Combining the periodicity, quasi-periodicity and IDZT transform of the above two formulas, it can be obtained that the IDZT of and the signal containing noise and up-sampled by the channel is an N-period extension of the sequence with a period of M·N sam in the time domain (time delay domain). And in each period, the amplitude is the same, and the argument satisfies the change of ,

[0065] Step 203: Without considering the argument change, since the amplitude is the same in N periods (in fact, due to the noise in the channel, it is not completely the same, but the numerical value is similar), it is natural to obtain the wave crest in the first period time domain graph of by averaging the amplitudes of N periods. The wave crest is caused by the time delay corresponding to the terminal user. The up-sampling is performed in the time domain, which is equivalent to interpolating and enlarging the time delay axis, improving the resolution. According to the wave crest, the time delay coordinate axis corresponding to the peak value is obtained, and then divided by the sampling point number N sam to obtain the fractional time delay estimation, which is quite accurate compared with the preset time delay of the user terminal.

[0066] As Figure 3 , step 103 specifically includes the following steps:

[0067] Step 301: The quasi-periodicity of discrete Zak transform to time delay: to obtain accurate estimation of user Doppler information;

[0068] Step 302: Taking the sample of the time delay axis coordinate of a certain wave crest as an example, the arguments in N periods are obtained respectively. According to the quasi-periodic characteristics, the N arguments should satisfy The N amplitudes are an arithmetic progression;

[0069] Step 303: using a differential method to solve the Doppler k, according to the N amplitudes, N-1 differences are obtained, the differences are averaged to be regarded as a tolerance, and the Doppler k is solved, and the estimation of the Doppler information obtained according to the method is quite accurate.

[0070] In summary, the present application can accurately estimate the fractional time delay and the fractional Doppler; the present application actually considers the up-sampling step in actual communication, combines the periodicity of the Zak transform, and uses the signal before down-sampling at the receiving end to obtain the channel information contained in the signal, that is, the accurate estimation of the fractional time delay and the fractional Doppler is obtained.

[0071] The above embodiments are only used to illustrate the technical solutions of the present application but not limit the present application, and although the present application has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that the technical solutions of the present application can be modified or replaced equivalently without departing from the spirit and scope of the technical solutions of the present application.

Claims

1. A method for accurately estimating fractional delay Doppler in a Zak-OTFS system, characterized in that: The following steps are involved: Step 101: At the transmitting end, an IDZT transform is performed to generate a signal and a cyclic prefix is ​​added. Step 102: performing up-sampling, pulse shaping, and up-conversion processing on the signal, sending the processed signal into a channel, and performing corresponding down-conversion, matched filtering, and down-sampling processing on the receiving end; Step 103: using the periodicity of Zak transform on the matched filtered signal to obtain accurate fractional delay and Doppler estimation by averaging and differencing respectively; In step 101, the IDZT is as follows: ， in, and are the number of grids along the delay domain and the number of grids along the Doppler domain in the delay-Doppler domain grid, and denote the indices along the delay axis and the Doppler axis in the delay-Doppler grid, respectively, where , , is the constellation modulation signal to be transmitted in the delay-Doppler domain , is the time domain signal after IDZT modulation ,in, , ; In step 102, the upsampling is specifically as follows: Assuming the number of upsampling points is , the signal The real part and the imaginary part are up-sampled, pulse-shaped and orthogonal modulated to obtain the actual transmitted signal after up-conversion. , using the vector form of discrete time signal for ; In step 103, the method for obtaining accurate fractional delay estimation includes the following steps: Step 201: Based on the periodicity of the main properties of discrete Zak transform, the Doppler is periodic, with a period of N, ， Delay is quasi-periodic, with a period of , and has a complex factor , ； Step 202: Combining the periodicity, quasi-periodicity and IDZT transformation of the two equations in step 201, we get IDZT, and the signal with channel noise and up-sampled , in the time domain, the period is sequence of The amplitude is the same in each cycle, and the angle satisfies changes; Step 203: Ask After averaging the amplitudes of the cycles, we get The peak in the first cycle of the time domain diagram is obtained according to the peak, and the delay coordinate axis corresponding to the peak value is obtained, and then divided by the number of sampling points , and obtain the fractional delay estimate.

2. The method for accurately estimating fractional delay Doppler in a Zak-OTFS system according to claim 1, wherein: In step 101, the signal after adding the cyclic prefix is , using the vector form of discrete-time signals Expressed as ,Will Add in front after straightening cyclic prefix.

3. The method for accurately estimating fractional delay Doppler in a Zak-OTFS system according to claim 1, wherein: In step 102, the channel is: , Where H is the number of targets, , and Respectively represent The complex gain of each target and its coordinates in the delay-Doppler grid, is the permutation matrix of the forward cyclic shift, ， for The diagonal matrix of ,in, , Considering the effect correction of two-dimensional distorted convolution , Among them, the received signal , is the corresponding noise vector at the receiver.

4. The method for accurately estimating fractional delay Doppler in a Zak-OTFS system according to claim 1, wherein: In step 103, the method for obtaining accurate fractional Doppler estimation includes the following steps: Step 301: Obtain an accurate estimate of the user Doppler information using the quasi-periodicity of the time delay using discrete Zak transform: ； Step 302: Take the sample of the time delay axis coordinate of a certain peak as an example, and obtain its The argument within a period, according to its quasi-periodic characteristics, The angles satisfy , The argument is an arithmetic progression; Step 303: Use the difference method to solve the Doppler , according to the The argument is obtained The differences are averaged and regarded as the tolerance to obtain the Doppler estimation.

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