A high-doppler-resistant orthogonal frequency division doppler multiplex waveform design method

Abstract

The application relates to an anti-high-Doppler orthogonal frequency division Doppler multiplex waveform design method, which comprises the following steps: step 1, digital modulation and OFDDM modulation are performed on data bits to obtain a baseband time domain signal; step 2, the modulated signal reaches a receiver through a time-varying multipath channel, and a frequency-Doppler domain representation of the channel is used to establish a mathematical model between a received signal and a transmitted signal; step 3, OFDDM demodulation is performed on the received signal r(t) by the receiver to obtain a frequency-Doppler domain symbol; and step 4, a frequency-Doppler domain symbol obtained through demodulation is used to extract channel Doppler diversity by using a maximum ratio combining algorithm based on interference cancellation. The superior technical effect of the design method is that the existing OFDM framework can be well compatible, the Doppler extension of the channel can be converted into the degree of freedom of diversity while adapting to the prior art, and the bit error rate performance of OFDM in a high-mobility scene can be greatly improved.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of wireless communication and multicarrier modulation technology, and particularly relates to a waveform design method of high Doppler resistant orthogonal frequency-Doppler division multiplexing (OFDDM). BACKGROUND

[0002] With the development of wireless communication technology, the next generation of wireless systems are expected to support communication services in high mobility scenarios such as high-speed railways, unmanned aerial vehicles, low-orbit satellites, etc. However, the transmission of signals in high mobility scenarios will suffer from non-negligible Doppler shift, which brings great challenges to multicarrier communication systems represented by orthogonal frequency division multiplexing (OFDM). In OFDM, information symbols are carried on parallel subcarriers that are orthogonal to each other, thus having good anti-multipath fading ability and high spectral efficiency. However, when the subcarriers lose orthogonality due to multipath Doppler spread in the propagation environment, severe inter-carrier interference (ICI) will greatly reduce the performance of OFDM. Although the extended subcarrier spacing configuration in 5G NR can alleviate ICI to some extent, it inevitably leads to a decrease in OFDM spectral efficiency and anti-multipath fading ability. Many studies have been devoted to solving this problem, among which Doppler frequency offset estimation and compensation technology is an effective method to eliminate Doppler frequency offset, but the complex Doppler spread in multipath channels is difficult to separate. In addition, techniques such as iterative interference cancellation are also used to suppress ICI, but at the cost of high complexity detection.

[0003] Recently, an increasing number of studies have focused on the design of novel anti-Doppler waveforms. Pulse-shaping orthogonal frequency division multiplexing (PS-OFDM) improves OFDM performance in high-Doppler scenarios by maximizing the signal-to-interference ratio (SIIR) to suppress ICI within the desired region. Filter bank multicarrier (FBMC) has also been shown to achieve superior bit error rate performance compared to OFDM in channels with moderate time dispersion, thanks to the time-frequency localization capability of the prototype filter. Furthermore, a novel two-dimensional modulation technique, Orthogonal Time-Frequency Space (OTFS), uses the Inverse Symplectic Finite Fourier Transform (ISFFT) to convert time-varying multipath channels into quasi-static channels in the Delay-Doppler (DD) domain, demonstrating lower bit error rate performance than OFDM in high-mobility scenarios, and has attracted widespread attention from the academic community. However, due to the additional preprocessing and post-processing modules, OTFS requires a higher implementation complexity than OFDM, which is one of the factors restricting the widespread application of OTFS. Therefore, a new high-Doppler-resistant waveform that achieves an effective compromise between OTFS and OFDM remains to be explored. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention proposes a design method for high-Doppler orthogonal frequency division Doppler multiplexing waveforms.

[0005] The design method described in this invention includes the following steps:

[0006] Step 1: Digitally modulate and OFDDM modulate the data bits to obtain the baseband time-domain signal;

[0007] Step 2: The modulated signal reaches the receiver through the time-varying multipath channel. The frequency-Doppler domain characterization of the channel is used to establish a mathematical model between the received signal and the transmitted signal.

[0008] Step 3: The receiver performs OFDDM demodulation on the received signal r(t) to obtain the frequency-Doppler domain symbol;

[0009] Step 4: Extract channel Doppler diversity from the frequency-Doppler domain symbols obtained by demodulation using the maximum ratio combining algorithm based on interference cancellation.

[0010] Furthermore, in step 1, the data bits are digitally modulated and OFDDM modulated to obtain the baseband time-domain signal:

[0011] Step 1.1. Set parameters N, M and Q, where N is the number of Doppler bins, M is the number of frequency domain subcarriers, and Q is the size of constellation set. A total of MNlog2Q serial data bit streams are generated by a signal source, and a transmitter maps them to NMconstellation symbols by QAM modulation;

[0012] Step 1.2. Set the symbol time as T and the frequency domain subcarrier interval as Δf. In order to ensure the orthogonality between subcarriers, Δf must satisfy Δf = 1 / T. Therefore, the frequency range of the transmitter is [0, MΔf], and the Doppler range is [0, Δf]. The frequency-Doppler plane is divided by the subcarrier interval Δf and the Doppler interval Δv = 1 / NT to obtain a discrete frequency-Doppler domain grid where m = 0, 1, …, M-1 and k = 0, 1, …, N-1 represent the indexes of subcarriers and Doppler bins, respectively;

[0013] Step 1.3. The input NMconstellation symbols are first placed on the frequency-Doppler domain grid by serial-parallel conversion, denoted as X FD [m, k], the transmitter performs N-point Inverse Discrete Fourier Transform (IDFT) on each row of symbols of the frequency-Doppler domain grid, mapping the frequency-Doppler domain information symbols X FD [m, k] to time-frequency domain samples X FT [m, n], the frequency-Doppler domain and the time-frequency domain are converted by Fourier transform, so the time-frequency domain grid Γ should satisfy Γ = {mΔf, nT}, where m = 0, 1, …, M-1 is the index of frequency, and n = 0, 1, …, N-1 is the index of time slot. This process is described by the following formula (1):

[0014]

[0015] Step 1.4. The samples on the time-frequency domain grid are subjected to Heisenberg transform, and a transmitter pulse shaping function g tx (t) is used to generate a continuous baseband time domain signal s(t). When the transmitter pulse shaping function g tx (t) is a rectangular pulse, the Heisenberg transform degenerates into OFDM modulation. The Heisenberg transform is represented by the following formula (2):

[0016]

[0017] In actual use, the Heisenberg transform process represented by formula (2) is implemented through M-point IDFT, a serial-parallel converter and a digital-to-analog converter. It is similar to OFDM, and the duration is T CPA cyclic prefix will be added at the front of each slot block to combat the inter-symbol interference (ISI) in time domain.

[0018] Further, in step 2, the modulated signal passes through the time-varying multipath channel to the receiver, and a mathematical model between the received signal and the transmitted signal is established using the channel's frequency-Doppler domain representation:

[0019] Step 2.1. Establish the frequency-Doppler domain wireless channel H(v, f); the frequency-Doppler domain channel response of a time-varying multipath channel with P resolvable paths can be expressed by where h p , τ p and v p are the channel complex gain, time delay and Doppler shift of the pth path, respectively; δ(·) is the Dirac delta function.

[0020] Step 2.2. The transmitted time-domain signal s(t) passes through the time-varying multipath channel to the receiving end, and according to the channel frequency-Doppler response, the time-domain expression r(t) of the received signal is calculated by the double integral of the signal spectrum and the channel response, which is described by the following formula (3):

[0021] r(t) = ∫∫H(v, f)S(f)e j2π(v+f)t dvdf+w(t) …… (3),

[0022] where S(f) is the spectrum of the signal s(t), and w(t) is the time-domain additive complex Gaussian noise. Note that the time-domain expression r(t) of the received signal can also be calculated by the time-delay domain, time-frequency domain and time-delay-Doppler domain channel representation and the corresponding form of the transmitted signal, as described in the following formula (4):

[0023]

[0024] where g(t, τ), H(t, f) and h(τ, v) represent the channel responses in the time-delay domain, time-frequency domain and time-delay-Doppler domain, respectively. The channel response in the frequency-Doppler domain presents a series of ridge structures separated from each other, and under the condition that the Doppler resolution is sufficient, any ridge is sufficient to represent the single-path channel response in the corresponding Doppler bin.

[0025] Further, in step 3, the receiver performs OFDM demodulation on the received signal r(t), including the following steps:

[0026] Step 3.1. With the help of the received filter function g rx(t), matched filtering the received time domain signal r(t), which is described by the following equation (5):

[0027]

[0028] Step 3.2. Sampling the matched filtering result with interval t = nT and f = mAf to obtain time-frequency domain sample Y FT [m, n];

[0029] Step 3.3. Applying N-point DFT operation along the time axis to the time- frequency domain sample Y FT [m, n] to map the time-frequency domain signal to the frequency-Doppler domain symbol Y FD [m, k], which is described by the following equation (6):

[0030]

[0031] Further, in step 4, using the maximum ratio combining algorithm based on interference cancellation, the channel Doppler diversity is extracted from the frequency-Doppler domain symbol obtained by demodulation:

[0032] Step 4.1. The frequency-Doppler domain symbol Y FD [m, k] recovered by demodulation is vectorized along the Doppler axis as Each block in Y should include a total of N symbols in all Doppler bins under a subcarrier index, i.e. Similarly, the frequency-Doppler domain symbol sent by the transmitting end is also denoted as Y where

[0033] Step 4.2. According to the input-output relationship of the frequency-Doppler domain, the number of branches for Doppler combining is determined. The frequency-Doppler domain information symbol vector Y of the receiving end after the wireless channel through the modulation and demodulation method described in steps 1-3 satisfies between the symbol vector Y where, is the equivalent channel matrix in the frequency-Doppler domain, which satisfies is the M-dimensional discrete Fourier matrix, (·) H represents the conjugate transpose operation, is the equivalent noise vector in the frequency-Doppler domain, which has a consistent statistical distribution with the time domain noise when the transceiver uses rectangular pulse shaping. The elements in the matrix satisfy the expression form of the following equation (7):

[0034]

[0035] where h p , l p and k p are the channel gain, delay index and Doppler index corresponding to the p-th path, respectively, L CP is the number of sampling points within the CP length, and equation (6) shows that in the frequency-Doppler domain channel matrix, only the matrix is non-zero, which also shows that through the above design of modulation and demodulation, the Doppler spread of the channel is dispersed into at most P Doppler bins, which provides P executable branches to extract Doppler diversity, and also gives the channel matrix sufficient sparsity;

[0036] Step 4.3. The receiver removes the interference from other blocks by reconstructing the received signal using other estimated blocks, so that no more than P data blocks of the received signal after removing the interference are all from the data block to be estimated. Without loss of generality, assuming x k is the data block to be detected, this process is given by equation (8) as follows:

[0037]

[0038] where x represents the data blocks that have been estimated in the current round of the loop, A k′ is the channel matrix from the estimated symbol block x to the received symbol block y , and this step eliminates the interference of other blocks and generates an ideal branch with Doppler index u

[0039] Step 4.4. According to the interference cancellation method in step 4.3., the receiver obtains branches, where is the set of different Doppler indexes in the channel, and the receiver performs maximum ratio combining on the branches to obtain the maximum ratio combining estimate c k of the data block x k in the current loop;

[0040] Step 4.5. The estimate of the data block x k in the current loop is updated as or where represents a hard decision operation, and ω∈[0, 1] is a factor of controlling the convergence speed and the decision accuracy, in a single round of circulation, each data block is updated in turn according to the estimation result of the last round of circulation, and then is used for the next round of update to eliminate the Doppler interference to a greater extent, specifically, a smaller ω will result in higher decision accuracy and iteration times;

[0041] Step 4.6. Steps 4.3. and 4.4. are repeatedly executed, when the loop reaches convergence or the maximum number of loops, the constellation symbol output by the maximum combining ratio is received for constellation demodulation, and a data bit stream is recovered.

[0042] Compared with the prior art, the design method has the following remarkable beneficial effects:

[0043] 1. The design method can well compatible with the existing OFDM framework, while adapting to the prior art, the Doppler spread of the channel is converted into the degree of freedom of diversity, and the BER performance of OFDM in a high mobility scene is greatly improved.

[0044] 2. Compared with the OTFS modulation method, the design method has lower implementation complexity, and can more directly extract Doppler diversity in a high mobility scene, and obtain similar or even better performance. BRIEF DESCRIPTION OF DRAWINGS

[0045] Figure 1 is a system block diagram of the design method.

[0046] Figure 2 A-2D is a frequency-Doppler domain channel and other common transform domain channel representation diagram used by the design method.

[0047] Figure 3 is a comparison diagram of the bit error performance of the orthogonal frequency division Doppler multiplexing waveform in the design method and the OFDM and OTFS waveforms in the EVA channel model.

[0048] Figure 4 is a comparison diagram of the bit error performance of the orthogonal frequency division Doppler multiplexing waveform in the design method and the OTFS waveform in the synthetic channel model with different path numbers. DETAILED DESCRIPTION

[0049] In order to more clearly understand the above-mentioned purposes, features and advantages of the design method, the specific embodiments of the present application will be described in detail below in conjunction with the drawings and specific embodiments of the present application.

[0050] As Figures 1-4 shown, the design method comprises the following steps:

[0051] Step 1, digital modulation and OFDM modulation are performed on data bits to obtain a baseband time domain signal:

[0052] Step 1.1, parameters N, M and Q are set, wherein N is the number of Doppler bins, M is the number of frequency domain subcarriers, and Q is the size of a constellation set; a total of MNlog2Q data bit streams are generated by a signal source, and the transmitter maps them to NMconstellation symbols by QAM modulation;

[0053] Step 1.2, a symbol time T is set, and a subcarrier interval Δf=1 / T is set to ensure the orthogonality of the subcarriers; the frequency range of the transmitter is [0, MΔf], and the Doppler range is [0, Δf]; the frequency-Doppler plane is divided by a Doppler interval Δv=1 / NT and a subcarrier interval Δf=1 / T to obtain a discrete frequency-Doppler domain grid wherein m=0, 1, …, M-1 and k=0, 1, …, N-1 represent the indexes of the subcarriers and the Doppler bins, respectively;

[0054] Step 1.3, as shown in Figure 1 , the input NMconstellation symbols are first placed on the frequency-Doppler domain grid by serial-parallel conversion, and are denoted as X FD [m, k]; FD The transmitter performs N-point inverse discrete Fourier transform on each row of symbols of the frequency-Doppler domain grid, and maps the information symbols X FT [m, k] of the frequency-Doppler domain to time-frequency domain samples X tx [m, n];

[0055]

[0056] Step 1.4, the samples on the time-frequency domain grid are subjected to a Heisenberg transform, and a continuous baseband time domain signal s(t) is generated by means of a transmitting pulse shaping function g tx (t); when the transmitting pulse shaping function g CP (t) is a rectangular pulse, the Heisenberg transform degenerates into OFDM modulation, and the Heisenberg transform is represented by the following formula (2):

[0057]

[0058] In actual use, the process described in formula (2) is often realized by an M-point IDFT, a serial-parallel converter and a digital-to-analog converter. Similar to OFDM, the duration T CPA cyclic prefix will be added in the front of each slot block to combat ISI in time domain;

[0059] Step 2, the modulated signal passes through the time-varying multipath channel to the receiver, a mathematical model between the received signal and the transmitted signal is established using the channel's frequency-Doppler domain representation;

[0060] Step 2.1. Establish the frequency-Doppler domain wireless channel H(v, f); the frequency-Doppler domain channel response of a time-varying multipath channel with P resolvable paths can be expressed as where h p , τ p and v p are the channel complex gain, time delay and Doppler shift of the pth path, respectively; δ(·) is the Dirac delta function.

[0061] Step 2.2. The transmitted time-domain signal s(t) passes through the time-varying multipath channel to the receiving end, according to the channel frequency-Doppler response, the time-domain expression r(t) of the received signal is calculated by double integration of the signal spectrum and the channel response, which is described by the following formula (3):

[0062] r(t) = ∫∫H(v, f)S(f)e j2π(v+f)t dvdf+w(t) …… (3),

[0063] where S(f) is the spectrum of the signal s(t), and w(t) is the time-domain additive complex Gaussian noise. Note that the time-domain expression r(t) of the received signal can also be calculated by the corresponding form of the time-delay domain, time-frequency domain and time-delay-Doppler domain channel representation of the transmitted signal, as described in the following formula (4):

[0064]

[0065] where g(t, τ), H(t, f) and h(τ, v) represent the channel responses in the time-delay domain, time-frequency domain and time-delay-Doppler domain, respectively. As shown in Figure (2), the channel response in the frequency-Doppler domain presents a series of ridge-like structures separated from each other, and under the condition that the Doppler resolution is sufficient, any ridge is sufficient to represent the single-path channel response in the corresponding Doppler bin;

[0066] Step 3, the receiver performs OFDDM demodulation on the received signal r(t), including the following steps:

[0067] Step 3.1. Match filter processing is performed on the received time-domain signal r(t) with the aid of the received filter function g rx (t), which is described by the following formula (5):

[0068]

[0069] Step 3.2. The matched filter result is sampled with interval t = nT and f = mAf to obtain time-frequency domain samples Y FT [m, n];

[0070] Step 3.3. A N-point DFT operation is applied to the time-frequency domain samples Y FT [m, n] along the time axis to map the time-frequency domain signal to a frequency-Doppler domain symbol Y FD [m, k], which is described by the following equation (6):

[0071]

[0072] Step 4. Using the maximum ratio combining algorithm based on interference cancellation, the channel Doppler diversity is extracted from the frequency-Doppler domain symbol obtained by demodulation:

[0073] Step 4.1. The frequency-Doppler domain symbol Y FD [m, k] recovered by demodulation is vectorized along the Doppler axis as Each block in Y wherein Similarly, the frequency-Doppler domain symbol transmitted by the transmitting end is also denoted as Y wherein

[0074] Step 4.2. According to the input-output relationship of the frequency-Doppler domain, the number of branches for Doppler combination is determined. The frequency-Doppler domain information symbol vector Y of the receiving end after the wireless channel through the modulation and demodulation method described in steps 1-3 satisfies wherein wherein is the frequency-Doppler domain noise vector, is the equivalent channel matrix in the frequency-Doppler domain, which satisfies is the M-dimensional discrete Fourier matrix, (·) H denotes the conjugate transpose operation, and the elements in the matrix satisfy the expression form of the following equation (7):

[0075]

[0076] wherein h p , l p and k p represent the channel gain, time delay index and Doppler index corresponding to the pth path, respectively, and LCP This represents the number of sampling points within the CP length. Equation (7) above indicates that in the frequency-Doppler domain channel matrix, only the matrix... The fact that the matrix is ​​non-zero also indicates that, through the above modulation and demodulation design, the Doppler spread of the channel is distributed into at most P Doppler boxes. This characteristic provides P executable branches to extract Doppler diversity, while also giving the channel matrix sufficient sparsity.

[0077] Step 4.3. The receiver reconstructs the received signal using other estimated data blocks to remove interference from other blocks, ensuring that no more than P data blocks of the received signal after interference removal are entirely derived from the data block to be estimated. Without loss of generality, assume x k If the data block to be detected is the current data block, then this process is given by the following equation (8):

[0078]

[0079] in, This represents the data block that has been estimated in the current loop. Assuming that the Doppler interference is fully eliminated, this step generates an ideal branch with a Doppler index of u;

[0080] Step 4.4. Based on the interference cancellation method in Step 4.3, the receiver obtains... One side road, of which, Given a set of different Doppler indices in the channel, the receiver... Each branch performs a maximum ratio merge operation to obtain the data block x in the current loop. k Maximum ratio combined estimate c k ;

[0081] Step 4.5. Current loop data block x k The estimated value will be updated to or in, This indicates a hard decision operation, where ω∈[0,1] is a factor that controls the convergence speed and decision accuracy. In a single loop, each data block is updated sequentially based on the estimation results of the previous loop, and then used for the next update to eliminate Doppler interference to a greater extent. Specifically, a smaller ω leads to higher decision accuracy and fewer iterations.

[0082] Step 4.6. Repeat steps 4.3 and 4.4. When the loop reaches convergence or the maximum number of loops, receive the constellation symbols output with the maximum combining ratio, perform constellation demodulation, and restore the data bit stream.

[0083] The following, in conjunction with the description of the drawings, further verifies the superior technical effects of the design method described in the present application, and performs Monte Carlo simulation on the bit error rate performance of the OFDDM system to evaluate the performance of the scheme under different frame sizes, UE moving speed, channel path number, signal-to-noise ratio and the like. As shown in Figure 3 , the bit error rate performances of different waveform technologies under different UE moving speeds are compared. In the Monte Carlo simulation, the channel model adopts the 3GPP extended vehicle A (EVA) channel, and the delay parameters are 0, 30, 150, 310, 370, 710, 1090, 1730, 2510 ns; the relative power of tap attenuation is -0.0, -1.5, -1.4, -3.6, -0.6, -9.1, -7.0, -12.0, -16.9 dB, the carrier frequency is 27.5 GHz, the subcarrier spacing is 15 kHz, the frame size is MxN = 64x16, and the modulation mode is 4QAM; in the comparison, the OFDM adopts the classical frequency domain single tap equalization, and the OTFS and OFDDM adopt the maximum ratio combining detection in the delay-Doppler domain and the frequency-Doppler domain respectively. As can be seen from Figure 3 , the BER curve generally decreases with the increase of the signal-to-noise ratio, wherein the error rate of OFDM in the scene of terminal maximum moving speed of 30km / h is much higher than that of OTFS and OFDDM, which is due to the non-negligible Doppler spread in the millimeter wave frequency band. In the scene of terminal maximum moving speed of 120km / h, the error rate performance of OFDDM is close to and exceeds that of OTFS, because as the speed increases, the number of resolvable Doppler taps in the channel also increases, which provides higher Doppler diversity gain. When the terminal maximum moving speed exceeds 240km / h, each multipath of the EVA channel can be resolved into different Doppler boxes, and at this time the bit error performance of OFDDM-MRC is 2dB lower than that of OTFS-MRC which performs delay combining. In order to study the influence of multipath effect on different modulation schemes, in the simulation of Figure 4 , a time-frequency doubly selective synthetic multipath channel is adopted in the design method described in the present application, although the time-frequency doubly selective synthetic multipath channel model may not exist in any actual scene, but it is a common means to study the performance of the receiver. Specifically, the maximum delay spread of the time-frequency doubly selective synthetic multipath channel is set to τ max =2510ns, the maximum moving speed of the UE is V UE =120km / h, the channel path number P is changed so that each path equally divides the channel power, and the envelope obeys the Rayleigh distribution; and the delay τ p and the Doppler shift v p of the pth path respectively obey (0, τ max) and (-v max , v max ) of the uniform distribution. The simulation results show that the BER performance of both OFDDM and OTFS is improved as the number of paths increases. In addition, OTFS can extract the double diversity from both delay and Doppler, and thus achieves a more significant BER reduction than OFDDM. However, it is noted that in high mobility scenarios, the Doppler diversity plays a more critical role in the reduction of BER. When the channel only has sparse multipath components, the Doppler diversity makes OFDDM achieve a more significant performance gain than OTFS, and this gain is further improved as N increases.

[0084] The above disclosed is only a preferred embodiment of the present application, obviously cannot be with the specific embodiments provided by the present application to limit the protection scope of the present application, in the premise of not departing from the concept and scope of the present application, according to the various changes and improvements made by the present application still belong to the protection scope covered by the claims of the present application.

Claims

1. A method for designing an anti-high Doppler orthogonal frequency division Doppler multiplexing waveform, characterized in that, The design method comprises: Step 1, digitally modulating and OFDDM modulating data bits to obtain a baseband time domain signal: Step 1.1, setting parameters N, M and Q, wherein N is the number of Doppler boxes, M is the number of frequency domain subcarriers, and Q is the size of a constellation set; a total of MNlog2Q serial data bit streams are generated by a signal source, and the transmitter maps the serial data bit streams to NM constellation symbols through QAM modulation; Step 1.

2. Set the symbol time as T, the frequency domain subcarrier interval as Δf, and in order to ensure the orthogonality between subcarriers, Δf = 1 / T needs to be met, thus the frequency range of the transmitter is [0, MΔf], the Doppler range is [0, Δf], the frequency-Doppler plane is divided by the subcarrier interval Δf and the Doppler interval Δv = 1 / NT to obtain a discrete frequency-Doppler domain grid wherein m = 0, 1, …, M-1 and k = 0, 1, …, N-1 respectively represent the indexes of subcarriers and Doppler bins; Step 1.

3. The input N M constellation symbols are first placed on a frequency-Doppler domain grid, denoted as X FD [m, k], the transmitter performs an N-point inverse discrete Fourier transform on each row of the frequency-Doppler domain grid of information symbols X FD [m, k] to map the frequency-Doppler domain information symbols X FT [m, n], the conversion between the frequency-Doppler domain and the time-frequency domain is established by Fourier transform, so the time-frequency domain grid Γ should satisfy Γ = {mΔf, nT}, where m = 0, 1, …, M - 1 is the index of frequency, n = 0, 1, …, N - 1 is the index of time slot, and this process is described by the following equation (1): Step 1.

4. Apply the Heisenberg transform to the samples on the time- frequency domain grid, with the help of the transmit pulse shaping function g tx (t) is a rectangular pulse, the Heisenberg transform is reduced to OFDM modulation, which is represented by the following equation (2): tx (t) is a rectangular pulse, the Heisenberg transform is reduced to OFDM modulation, which is represented by the following equation (2): In practical use, the process of the Heisenberg transformation represented by formula (2) is implemented through an M-point IDFT, a parallel-serial converter and a digital-to-analog converter, and the duration is T CP A cyclic prefix will be added at the front of each slot block to counter the inter-symbol interference ISI in the time domain. Step 2, the modulated signal passes through a time-varying multipath channel to reach a receiver, and a mathematical model between a received signal and a transmitted signal is established by using a frequency-Doppler domain representation of the channel: Step 2.

1. Establish the frequency-Doppler domain wireless channel H(v, f); the frequency-Doppler domain channel response of a time-varying multipath channel with P resolvable paths can be expressed by where h p ,τ p and v p are the channel complex gain, time delay and Doppler shift of the pth path, respectively; δ(·) is the Dirac delta function. p ,τ p and v p are the channel complex gain, time delay and Doppler shift of the pth path, respectively; δ(·) is the Dirac delta function. Step 2.2, the transmitted time domain signal s(t) passes through a time-varying multipath channel to reach a receiving end, and according to the channel frequency-Doppler response, a time domain expression r(t) of the received signal is calculated through a double integral of a signal spectrum and a channel response, which is described by the following formula (3): r(t) = ∫∫ H(v, f) S(f) e j2π(v+f)t dvdf+ w(t)... (3), Wherein S(f) is the frequency spectrum of the signal s(t), w(t) is a time domain additive complex Gaussian noise, and the time domain expression r(t) of the received signal can also be calculated through a corresponding form of a time-delay domain, a time-frequency domain and a time-delay-Doppler domain channel representation of the transmitted signal, as described by the following formula (4): Wherein g(t, τ), H(t, f) and h(τ, v) represent the channel responses in the time-delay domain, the time-frequency domain and the time-delay-Doppler domain respectively, the channel response in the frequency-Doppler domain presents a series of ridge-shaped structures separated from each other, and in the case of sufficient Doppler resolution, any ridge is sufficient to represent a single-path channel response in the corresponding Doppler box; Step 3, the receiver performs OFDDM demodulation on the received signal r(t) to obtain a frequency-Doppler domain symbol; Step 4, using a maximum ratio combining algorithm based on interference cancellation, the frequency-Doppler domain symbol obtained through demodulation is used to extract channel Doppler diversity: Step 4.

1. Recover the frequency-Doppler domain symbols Y from the demodulation FD [m, k] is vectorized along the Doppler axis as Each block in Y should include a total of N symbols in all Doppler bins under one subcarrier index, i.e. where, k = 0, 1, …, N - 1, the frequency-Doppler domain symbols sent by the transmitting end are also denoted as where k = 0, 1, …, N - 1; Step 4.

2. Determine the number of branches to be combined in Doppler domain according to the input-output relationship in frequency-Doppler domain, the frequency-Doppler domain information symbol vector at the receiving end after passing through the wireless channel is determined by the modulation and demodulation method described in steps 1-3 and the symbol vector at the transmitting end satisfies wherein, is the equivalent channel matrix in frequency-Doppler domain, satisfying is the M-dimensional discrete Fourier matrix, (·) H represents the conjugate transpose operation, is the equivalent noise vector in frequency-Doppler domain, when the transceiver adopts rectangular pulse shaping, it has a consistent statistical distribution with the noise in time domain, the elements in matrix satisfy the expression form of the following formula (7): where h p , l p and k p denote the channel gain, delay index and Doppler index corresponding to the p-th path, respectively, L CP denotes the number of sampling points within the CP length, and equation (6) indicates that in the frequency-Doppler domain channel matrix, only the matrix is non-zero, and the Doppler spread of the channel is spread into at most P Doppler bins, which provides P executable branches to extract Doppler diversity, and also gives the channel matrix sufficient sparsity. Step 4.

3. The receiver reconstructs the received signal by using other estimated data blocks to remove the interference from other blocks, so that no more than P data blocks of the interference-removed received signal are completely from the data block to be estimated, let x k be the data block to be detected, then this process is given by the following equation (8): wherein, denotes the data block that has been estimated in the current round of the loop, A k′ is the channel matrix from the estimated symbol block to the received symbol block In the assumption that the Doppler interference is sufficiently cancelled, this step eliminates the interference of other blocks and generates an ideal branch with Doppler index u Step 4.

4. According to the interference cancellation method in step 4.3., the receiver obtains branches, where is the set of different Doppler indices in the channel, the receiver performs maximum ratio combining operation on these branches to obtain the maximum ratio combining estimate value c k of the data block x k under the current cycle; Step 4.

5. The estimated value of the data block x of the current cycle will be updated as k or wherein, represents a hard decision operation, ω ∈ [0, 1] is a factor controlling the convergence speed and the decision accuracy, in a single round of cycle, each data block is updated in turn according to the estimation result of the last round of cycle, and then used for the next round of update to eliminate the Doppler interference to a greater extent. Specifically, a smaller ω will result in higher decision accuracy and iteration times.​ Step 4.6, steps 4.3 and 4.4 are repeatedly executed, when the loop reaches convergence or the maximum number of loops, the constellation symbol output by the maximum combining ratio is constellation demodulated to recover the data bit stream.

2. The design method according to claim 1, characterized in that, In step 3, the receiver performs OFDDM demodulation on the received signal r(t) to obtain a frequency-Doppler domain symbol, comprising: Step 3.

1. Matched filtering of the received time domain signal r(t) by means of a receive filter function g(t) rx (t), the received time domain signal r(t) is matched filtered, which is described by the following equation (5): Step 3.

2. The matched filter result is sampled at intervals t = nT and f = mAf to obtain time-frequency domain samples Y FT [m,n]; Step 3.

3. On time-frequency domain samples Y FT [m,n] applies an N-point DFT operation along the time axis, mapping the time- frequency domain signal into the frequency-Doppler domain symbol Y FD [m,k], which is described by the following equation (6):

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