Inter-Doppler interference suppression method based on Gaussian learning factor particle swarm optimization

Abstract

The invention discloses an inter-Doppler interference suppression method based on a Gaussian learning factor particle swarm algorithm. The inter-Doppler interference suppression method comprises the following steps that pilot frequency and data symbols are coded to a resource grid of a two-dimensional time delay Doppler domain through orthogonal time-frequency space modulation; on a transmitter, mapping data on a time delay Doppler domain grid to a time-frequency domain through inverse symplectic finite Fourier transform to obtain a time-frequency domain signal; performing Hisenberg transformation on the time-frequency domain signal to obtain a time domain sending signal; obtaining a time domain receiving signal after the time domain sending signal passes through a wireless channel; performing Doppler compensation processing on the time domain receiving signal by using Doppler frequency shift to obtain a signal after Doppler compensation; then performing matched filtering on the signal after Doppler compensation and a received pulse, and sampling to obtain a matched filter output signal; and the matched filter output signal is subjected to the Sextile Fourier transform to obtain a time delay Doppler receiving signal. The method can realize suppression of inter-Doppler interference to a certain extent.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technology, and in particular to a method for suppressing inter-Doppler interference (IDI) generated by smaller data frames in orthogonal time frequency space (OTFS) modulation. Background Art

[0002] In the scenario of Internet of Vehicles, due to the serious Doppler effect caused by the relative motion between the transmitter, receiver and scatterers, the orthogonal subcarriers of Orthogonal Frequency Division Multiplexing (OFDM) widely used in 4G and 5G communication systems are no longer orthogonal, resulting in a direct collapse of its performance. In 2017, Hadani et al. proposed a new two-dimensional modulation technology - Orthogonal Time-Frequency Space Modulation. OTFS introduces the concept of Delay Doppler-domain (DD). OTFS converts data symbols from the time-frequency domain to the Delay Doppler domain through the Symplectic Finite Fourier Transform (SFFT). At this time, the channel is also converted from a complex time-varying multipath channel in the time-frequency domain to a Delay Doppler channel characterized by a limited number of reflectors. The Delay Doppler domain channel has the characteristics of sparseness and time-invariance. Compared with the OFDM system, the system's anti-Doppler effect performance is improved.

[0003] However, in the scenario of higher speed and lower latency Internet of Vehicles, due to the limitation of frame length, the Doppler resolution of OTFS becomes low, and the actual Doppler frequency shift is difficult to represent with integer taps in the delay Doppler domain, resulting in a fractional Doppler channel. In a fractional Doppler channel, the peak of the channel response of each path may not fall on the sampling point, and its side lobes will extend to the entire Doppler domain. This inevitable diffusion is called inter-Doppler interference, which poses a challenge to the performance of the system. Summary of the invention

[0004] In view of the performance deterioration of the OTFS system in the low-latency scenario of the Internet of Vehicles, the present invention proposes a Doppler interference suppression method based on the Gaussian learning factor particle swarm algorithm. In view of the Doppler interference problem caused by the reduction of data frames in the OTFS system in the low-latency scenario of the Internet of Vehicles, an effective interference suppression method is proposed, which has strong practical application significance.

[0005] In order to solve the above technical problems, the technical solution of the present invention is:

[0006] A method for suppressing inter-Doppler interference based on a Gaussian learning factor particle swarm algorithm comprises the following steps:

[0007] Step 1: Encode the pilot and data symbols onto a resource grid in a two-dimensional delay-Doppler domain through an orthogonal time-frequency space;

[0008] Step 2: At the transmitter, the data on the delay-Doppler domain grid is mapped to the time-frequency domain by inverse symplectic finite Fourier transform to obtain a time-frequency domain signal;

[0009] Step 3, performing Heisenberg transform on the time-frequency domain signal to obtain a time-domain transmission signal;

[0010] Step 4: The time domain transmission signal is transmitted through the wireless channel to obtain a time domain reception signal;

[0011] Step 5: Perform Doppler compensation processing on the time domain received signal using Doppler frequency shift to obtain a Doppler compensated signal;

[0012] Step 6: First, generate a receiving pulse locally, then match filter the Doppler compensated signal and the receiving pulse, and sample to obtain a matched filter output signal;

[0013] Step 7: Perform sigma Fourier transform on the matched filter output signal to obtain a received signal in the delay Doppler domain.

[0014] Preferably, in step 5, the method for acquiring the Doppler frequency shift is:

[0015]

[0016] Where v′ is the Doppler frequency shift, κ refers to the fractional Doppler, N is the total number of data symbols, and T is the duration of a single symbol.

[0017] Preferably, the fractional Doppler κ is estimated by using a Gaussian learning factor particle swarm algorithm based on a Doppler leakage power minimum criterion of a pilot signal in a delay Doppler domain.

[0018] Preferably, in step 5, the Doppler leakage power of the pilot signal in the delay-Doppler domain is used as the objective function for obtaining the fractional Doppler κ.

[0019] Preferably, the method for establishing the objective function is:

[0020] First, the time domain pilot signal passing through the wireless channel is converted to the delay Doppler domain. At this time, the input and output relationship of the time domain pilot signal in the delay Doppler domain is expressed as:

[0021]

[0022] Where P represents the count of channel paths in the delay-Doppler domain, k∈[1,M], l∈[1,N], l and k represent the delay tap and Doppler tap of the received signal in the delay-Doppler domain, respectively, M represents the number of subcarriers, N represents the number of symbols, and h i is the channel amplitude corresponding to the tap, α i represents the attenuation coefficient of the fractional Doppler of the i-th path to the signal amplitude, [·] M represents the mod M operation, and denote the delay taps, integer and fractional Doppler taps of the i-th path received in the delay-Doppler domain, respectively;

[0023] Then the total power of the time domain pilot signal in the delay Doppler domain is:

[0024]

[0025] Then select the first J signals y(k m ,l m ), where J can be set to three times the number of channel multipaths, m∈[1J], then the power of the first J selected grid signals is:

[0026]

[0027] At this time, the leakage power of the time domain pilot signal, that is, the objective function, is:

[0028] Q k (κ) = Q s -Q m .

[0029] As a preference, when the channels have different fractional Dopplers κ, the pilot signals will have different leakage powers Q k (κ), when κ = 0, the leakage power of the pilot signal will also reach the minimum value. The next step is to use the particle swarm optimization algorithm based on Gaussian learning factor to search for κ so that the objective function Q k (κ) is minimized, that is:

[0030]

[0031] Preferably, the Gaussian learning factor particle swarm algorithm calculates the fractional Doppler κ method as follows:

[0032] (1) Set the maximum number of iterations T = 40, the population size Y = 10, and the maximum speed v max =0.1, upper and lower limits of position vector b h =0.5, b l=-0.5, inertia coefficient W = 2, learning factor C1 = C2 = 2;

[0033] (2) First, initialize each particle x i The speed is v i =rand(0,1)v max , position x i =rand(0,1)(b h -b l )+b l , set the current position to the historical optimal position P i =x i , calculate x i The corresponding fitness function Q i , where position x i And the fitness function Q i Corresponding to fractional Doppler κ and objective function Q respectively k (κ);

[0034] (3) For each iteration t∈[1,T], Gaussian distribution is used to update the learning factors C1 and C2:

[0035]

[0036] Where: C1 and C2 are the self-Gaussian learning factor and the global Gaussian learning factor respectively.

[0037] (4) For each particle x i , update its velocity according to the following formula:

[0038]

[0039] when make

[0040] Where: t is the current iteration number, r1 and r2 are random numbers uniformly distributed in (0,1).

[0041] (5) Update each particle x i Location:

[0042]

[0043] (6) Then calculate the new position x i+1 The fitness function Q under t+1 ;

[0044] (7) Update the individual historical optimal position of each particle:

[0045] When Q t+1 <Q t hour, Otherwise P i t+1 =P i t

[0046] (8) Update the historical optimal position of particles in the entire population:

[0047]

[0048] (9) Repeat steps (3) to (8) until t>T.

[0049] (10) Finally, the global optimal fitness and its corresponding position are obtained The global optimal position obtained at this time is also the size of the channel fractional Doppler, that is

[0050] Preferably, in step 5, the method for performing Doppler compensation on the time domain data signal is:

[0051] r′(t)=r(t)e j2π(-v′)(t-τ)

[0052] =∫∫h(τ,v)x(t-τ)e j2π(v+v′)(t-τ) e j2π(-v′)(t-τ) dvd

[0053] =∫∫h(τ,v)x(t-τ)e j2πv(t-τ) dvd

[0054] in, Represent integer and fractional Doppler shifts respectively. The Doppler tap size of the signal after Doppler compensation is When the channel environment is single-path, the received signal only has integer Doppler.

[0055] Preferably, in step 6, the time domain data signal and the received pulse are matched filtered. If the received pulse is g tx (t), the mutual ambiguity function between it and the received signal is:

[0056]

[0057] Then, the matched filter output signal is obtained by sampling at intervals t = mT, f = nΔf:

[0058]

[0059] Preferably, in step 7, the received signal in the delay Doppler domain can be obtained by performing a sigma Fourier transform on the matched filter output signal y[m,n]:

[0060]

[0061] The present invention has the following characteristics and beneficial effects:

[0062] The inter-Doppler interference suppression method proposed in the present invention estimates the fractional Doppler based on the minimum Doppler leakage power criterion of the pilot signal in the delay Doppler domain through the Gaussian learning factor particle swarm algorithm, and then performs Doppler compensation on the received data signal, thereby improving the sparsity of the delay Doppler domain channel, and can effectively suppress the inter-Doppler interference problem caused by the small data frame of the OTFS system, thereby reducing the complexity of channel estimation and obtaining a better system bit error rate. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0064] Figure 1 It is a system model diagram of the Doppler inter-interference suppression method based on Gaussian learning factor particle swarm algorithm in the present invention;

[0065] Figure 2 It is a schematic diagram of the structure of the pilot and data frames of the orthogonal time-frequency space modulation in the present invention;

[0066] Figure 3 It is a channel amplitude diagram in the delay Doppler domain of the pilot signal before and after Gaussian learning factor particle swarm Doppler compensation in the single-path scenario of the present invention;

[0067] Figure 4 This is a performance comparison diagram of the Gaussian learning factor particle swarm algorithm in the present invention and the traditional particle swarm algorithm in the application scenario of the present invention;

[0068] Figure 5 This is a comparison diagram of bit error rates under different Doppler compensations when the data frame size of orthogonal time-frequency space modulation is M=N=16 in the present invention. DETAILED DESCRIPTION

[0069] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0070] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like indicate positions or positional relationships based on the positions or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first", "second", and the like are only used for descriptive purposes, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, features defined as "first", "second", and the like may explicitly or implicitly include one or more of the features. In the description of the present invention, unless otherwise specified, "multiple" means two or more.

[0071] In the description of the present invention, it should be noted that, unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood by specific circumstances.

[0072] The present invention provides a method for suppressing inter-Doppler interference based on a Gaussian learning factor particle swarm algorithm. Figure 1 The system model framework diagram of orthogonal time-frequency space modulation is shown in FIG. 1 , and data transmission is performed in the form of pilot plus data frame. The structure of the pilot and data frame is as follows: Figure 2 As shown, both experience the same channel. Specifically, the following steps are included:

[0073] Step 1: OTFS encodes the pilot and data symbols onto a resource grid in the two-dimensional delay-Doppler domain, which can be expressed as follows:

[0074]

[0075] Wherein, M represents the number of subcarriers, N represents the number of symbols, Δf represents the subcarrier spacing, T represents the duration of a single symbol, and l and k represent the delay tap and Doppler tap of the received signal in the delay-Doppler domain, respectively.

[0076] Step 2: At the transmitter, the data on the delay-Doppler domain grid is mapped to the time-frequency domain through the inverse symplectic finite Fourier transform (ISFFT). The time-frequency domain signal is:

[0077]

[0078] Step 3: Use Heisenberg transform to transform the obtained time-frequency domain signal to the time domain. The time domain signal is:

[0079]

[0080] Among them, g tx (t) represents the transmitted pulse.

[0081] Step 4: After the time domain transmission signal x(t) passes through the channel, a time domain reception signal r(t) can be obtained, where the time domain reception signal includes a time domain pilot signal and a time domain data signal, which can be expressed as:

[0082] r(t)=∫ ν ∫ τ h(τ,ν)x(t-τ)e j2πν(t-τ) dτdν

[0083] Step 5: Use the Gaussian learning factor particle swarm algorithm to estimate the channel fractional Doppler κ based on the Doppler leakage power minimum criterion of the pilot signal in the delay-Doppler domain.

[0084] First, let’s introduce how to establish the objective function:

[0085] The time domain pilot signal passing through the wireless channel is converted to the delay Doppler domain. When the data frame in the orthogonal time-frequency space becomes smaller, the system Doppler resolution decreases. After the transmitted signal is transmitted through the wireless channel, the received signal inevitably has a fractional Doppler frequency shift. At this time, the input and output relationship of the signal in the delay Doppler domain can be expressed as:

[0086]

[0087] Where P represents the count of channel paths in the delay-Doppler domain, k∈[1,M], l∈[1,N], l and k represent the delay tap and Doppler tap of the received signal in the delay-Doppler domain, respectively, M represents the number of subcarriers, N represents the number of symbols, and h i is the channel amplitude corresponding to the tap, α i represents the attenuation coefficient of the fractional Doppler of the i-th path to the signal amplitude, [·] M represents the mod M operation, and denote the delay taps, integer and fractional Doppler taps, and fractional Doppler taps of the i-th path received in the delay-Doppler domain, respectively. represents the offset from the integer Doppler tap.

[0088] Then the total power of the pilot signal in the delay-Doppler domain is:

[0089]

[0090] Then select the first J signals y(k m ,l m ), where J can be set to three times the number of channel multipaths, m∈[1J], then the power of the first J selected grid signals is:

[0091]

[0092] At this time, the leakage power of the pilot signal, that is, the objective function, is:

[0093] Q k (κ) = Q s -Q m

[0094] When the channel has different fractional Doppler κ, the pilot signal will have different leakage power Q k (κ), when κ = 0, the leakage power of the pilot signal will also reach the minimum value. The next step is to use the particle swarm optimization algorithm based on Gaussian learning factor to search for κ so that the objective function Q k (κ) is minimized, that is:

[0095]

[0096] Next, the specific content of the Gaussian learning factor particle swarm algorithm in this embodiment is as follows:

[0097] Step 5-1: Set the maximum number of iterations T = 40, the population size Υ = 10, and the maximum speed v max =0.1, upper and lower limits of position vector b h =0.5, b l =-0.5, inertia coefficient W = 2, learning factor C1 = C2 = 2.

[0098] Step 5-2: First initialize each particle x i The speed is v i =rand(0,1)v max , position x i =rand(0,1)(b h -b l )+b l , set the current position to the historical optimal position P i =x i , calculate x i The corresponding fitness function Q i . Where position x i And the fitness function Q i Corresponding to fractional Doppler κ and objective function Q respectively k (κ).

[0099] Step 5-3: For each iteration t∈[1,T], use Gaussian distribution to update the learning factors C1 and C2:

[0100]

[0101] Where: C1 and C2 are the self-Gaussian learning factor and the global Gaussian learning factor respectively.

[0102] Step 5-4: For each particle x i , update its velocity according to the following formula:

[0103]

[0104] when make

[0105] Where: t is the current iteration number, r1 and r2 are random numbers uniformly distributed in (0,1).

[0106] Step 5-5: Update each particle x i Location:

[0107]

[0108] Step 5-6: Then calculate the new position x i+1 The fitness function Q under t+1 .

[0109] Step 5-7: Update the individual historical optimal position of each particle:

[0110] When Q t+1 <Q t hour, Otherwise P i t+1 =P i t

[0111] Step 5-8: Update the historical optimal position of particles in the entire population:

[0112]

[0113] Step 5-9: Repeat steps 5-3 to 5-8 until t>T.

[0114] Steps 5-10: Finally, obtain the global optimal fitness and its corresponding position The global optimal position obtained at this time is also the size of the channel fractional Doppler, that is Figure 3This is a channel amplitude diagram of the pilot signal in the delay Doppler domain before and after Gaussian learning factor particle swarm Doppler compensation in a single-path scenario in the present invention. The results show that the effect of inter-Doppler interference suppression is achieved. Figure 4 The performance comparison diagram of the Gaussian learning factor particle swarm algorithm in the present invention and the traditional particle swarm algorithm in the scenario of the present invention shows that the Gaussian learning factor particle swarm algorithm has stronger global search ability and local development ability.

[0115] Step 6: The fractional Doppler κ of the channel is obtained through step 5 and converted into the Doppler frequency shift v′ in the time domain:

[0116]

[0117] Step 7: Using the Doppler frequency shift v′, perform the following Doppler compensation processing on the received signal r(t) in the time domain:

[0118] r′(t)=r(t)e j2π(-v′)(t-τ)

[0119] =∫∫h(τ,v)x(t-τ)e j2π(v+v′)(t-τ) e j2π(-v′)(t-τ) dvd

[0120] =∫∫h(τ,v)x(t-τ)e j2πv(t-τ) dvd

[0121] in, Represent integer and fractional Doppler shifts respectively. The Doppler tap size of the signal after Doppler compensation is When the channel environment is single-path, the received signal only has integer Doppler.

[0122] Step 8: Match the received signal and the received pulse. If the received pulse is g tx (t), the mutual ambiguity function between it and the received signal is:

[0123]

[0124] Step 9: Then sample at intervals t = mT, f = nΔf to obtain the matched filter output signal:

[0125]

[0126] Step 10: Performing a sigmoid Fourier transform on the matched filter output signal y[m,n] can obtain the received signal in the delay Doppler domain:

[0127]

[0128] Figure 5This is a comparison diagram of bit error rates under different Doppler compensations when the data frame of orthogonal time-frequency space modulation is M=N=16 in the present invention. The simulation results show that the present invention achieves the expected effect.

[0129] The embodiments of the present invention are described in detail above with reference to the accompanying drawings, but the present invention is not limited to the described embodiments. For those skilled in the art, various changes, modifications, substitutions and variations of these embodiments including components are made without departing from the principles and spirit of the present invention, and still fall within the scope of protection of the present invention.

Claims

1. A method for suppressing inter-Doppler interference based on Gaussian learning factor particle swarm algorithm, characterized in that: The steps include: Step 1: Encode the pilot and data symbols onto a resource grid in a two-dimensional delay-Doppler domain through an orthogonal time-frequency space; Step 2: At the transmitter, the data on the delay-Doppler domain grid is mapped to the time-frequency domain by inverse symplectic finite Fourier transform to obtain a time-frequency domain signal; Step 3, performing Heisenberg transform on the time-frequency domain signal to obtain a time-domain transmission signal; Step 4: After the time domain transmission signal passes through the wireless channel, a time domain reception signal is obtained, wherein the time domain reception signal includes a time domain pilot signal and a time domain data signal; Step 5: Perform Doppler compensation processing on the time domain received signal using Doppler frequency shift to obtain a Doppler compensated signal; Step 6: First, generate a receiving pulse locally, then match filter the Doppler compensated signal and the receiving pulse, and sample to obtain a matched filter output signal; Step 7: Perform sigma Fourier transform on the matched filter output signal to obtain a received signal in the delay Doppler domain.

2. The method for suppressing inter-Doppler interference based on Gaussian learning factor particle swarm algorithm according to claim 1, characterized in that: In step 5, the method for obtaining the Doppler frequency shift is: Where v′ is the Doppler frequency shift, κ refers to the fractional Doppler, N is the total number of data symbols, and T is the duration of a single symbol.

3. The method for suppressing inter-Doppler interference based on Gaussian learning factor particle swarm algorithm according to claim 2, characterized in that: The fractional Doppler κ is estimated by using a Gaussian learning factor particle swarm algorithm based on a Doppler leakage power minimum criterion of a pilot signal in a delay Doppler domain.

4. The method for suppressing inter-Doppler interference based on Gaussian learning factor particle swarm algorithm according to claim 3, characterized in that: In step 5, the Doppler leakage power of the pilot signal in the delay-Doppler domain is used as the objective function for obtaining the fractional Doppler κ.

5. The method for suppressing inter-Doppler interference based on Gaussian learning factor particle swarm algorithm according to claim 4, characterized in that: The objective function is established as follows: First, the time domain pilot signal passing through the wireless channel is converted to the delay Doppler domain. At this time, the input and output relationship of the time domain pilot signal in the delay Doppler domain is expressed as: Where P represents the count of channel paths in the delay-Doppler domain, k∈[1,M], l∈[1,N], l and k represent the delay tap and Doppler tap of the received signal in the delay-Doppler domain, respectively, M represents the number of subcarriers, N represents the number of symbols, and h i is the channel amplitude corresponding to the tap, α i represents the attenuation coefficient of the fractional Doppler of the i-th path to the signal amplitude, [·] M represents the mod M operation, and denote the delay taps, integer and fractional Doppler taps of the i-th path received in the delay-Doppler domain, respectively; Then the total power of the time domain pilot signal in the delay Doppler domain is: Then select the first J signals y(k m ,l m ), where J can be set to three times the number of channel multipaths, m∈[1J], then the power of the first J selected grid signals is: At this time, the leakage power of the time domain pilot signal, that is, the objective function, is: Q k (κ)=Q s -Q m 。 6. The method for suppressing inter-Doppler interference based on Gaussian learning factor particle swarm algorithm according to claim 5, characterized in that: When the channel has different fractional Doppler κ, the pilot signal will have different leakage power Q k (κ), when κ = 0, the leakage power of the pilot signal will also reach the minimum value. The next step is to use the particle swarm optimization algorithm based on Gaussian learning factor to search for κ so that the objective function Q k (κ) is minimized, that is:

7. The method for suppressing inter-Doppler interference based on Gaussian learning factor particle swarm algorithm according to claim 5, characterized in that: The Gaussian learning factor particle swarm algorithm searches for fractional Doppler κ as follows: (1) Set the maximum number of iterations T = 40, the population size Y = 10, and the maximum speed v max = 0.1, upper and lower limits of position vector b h =0.5, b l =-0.5, inertia coefficient W = 2, learning factor C1 = C2 = 2; (2) First, initialize each particle x i The speed is v i =rand(0,1)v max , position x i =rand(0,1)(b h -b l )+b l , set the current position to the historical optimal position P i =x i , calculate x i The corresponding fitness function Q i , where position x i And the fitness function Q i Corresponding to fractional Doppler κ and objective function Q respectively k (κ); (3) For each iteration t∈[1,T], Gaussian distribution is used to update the learning factors C1 and C2: Where: C1 and C2 are the self-Gaussian learning factor and the global Gaussian learning factor respectively, (4) For each particle x i , update its velocity according to the following formula: when make Where: t is the current iteration number, r1 and r2 are random numbers uniformly distributed in (0,1), (5) Update each particle x i Location: (6) Then calculate the new position x i+1 The fitness function Q under t+1 ; (7) Update the individual historical optimal position of each particle: When Q t+1 <Q t hour, Otherwise P i t+1 =P i t (8) Update the historical optimal position of particles in the entire population: (9) Repeat steps (3) to (8) until t>T, (10) Finally, the global optimal fitness and its corresponding position are obtained The global optimal position obtained at this time is also the size of the channel fractional Doppler, that is 8. The method for suppressing inter-Doppler interference based on Gaussian learning factor particle swarm algorithm according to claim 2, characterized in that: In step 5, the Doppler compensation method for the time domain received signal is: r′(t)=r(t)e j2π(-v′)(t-τ) =∫∫h(τ,v)x(t-τ)e j2π(v+v′)(t-τ) e j2π(-v′)(t-τ) DVD =∫∫h(τ,v)x(t-τ)e j2πv(t-τ) DVD in, Represent integer and fractional Doppler shifts respectively. The Doppler tap size of the signal after Doppler compensation is When the channel environment is single-path, the received signal only has integer Doppler.

9. The method for suppressing inter-Doppler interference based on Gaussian learning factor particle swarm algorithm according to claim 1, characterized in that: In step 6, the time domain Doppler compensated signal is matched filtered with the received pulse. If the received pulse is g tx (t), the mutual ambiguity function between it and the received signal is: Then, the matched filter output signal is obtained by sampling at intervals t = mT, f = nΔf:

10. The method for suppressing inter-Doppler interference based on Gaussian learning factor particle swarm algorithm according to claim 1, characterized in that: In step 7, the received signal in the delay Doppler domain can be obtained by performing a sigmoid Fourier transform on the matched filter output signal y[m,n]:

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