An interference modeling and symbol error rate estimation method for an OTFS communication system

Abstract

This invention discloses an interference modeling and symbol error rate estimation method for OTFS communication systems, relating to the field of wireless communication technology. The purpose of this invention is to address the problems of inaccurate and incomplete interference modeling in existing OTFS systems under real-world, non-ideal environments. It proposes a complete interference analysis and modeling method for OTFS communication systems, including IFI, IDoI, and IDeI, and further derives the corresponding symbol error rate estimation method. This enables end-to-end quantitative evaluation of the OTFS system's performance under complex channel conditions including IFI, IDoI, and IDeI, providing a reliable basis for QoS evaluation of OTFS communication systems.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and in particular to a method for interference modeling analysis and system performance evaluation for orthogonal time-frequency-space (OTFS) communication systems. Background Technology

[0002] With the continuous advancement of research on sixth-generation mobile communication technology, achieving reliable and efficient data transmission in high-speed mobile scenarios has become a key research objective in the field of wireless communication. Traditional Orthogonal Frequency Division Multiplexing (OFDM) systems are extremely sensitive to Doppler frequency shift, which can lead to severe inter-carrier interference in high-dynamic scenarios, making it difficult to meet the performance requirements of high-speed mobile applications such as high-speed railways, UAV communications, and low-Earth orbit satellites.

[0003] OTFS modulation is a novel two-dimensional modulation technique. Unlike traditional OFDM, which modulates symbols in the frequency domain, OTFS performs signal modulation and demodulation in the delay-Doppler (DD) domain. By converting the time-frequency domain bidispersive channel into a quasi-static channel in the DD domain, OTFS allows each information symbol to experience approximately uniform channel gain, thereby significantly improving the system's robustness to time-frequency biselective fading and exhibiting superior transmission performance compared to OFDM in high-speed mobile scenarios.

[0004] Although OTFS has strong resistance to dichromatic dispersion, various non-ideal factors can still introduce complex interference in practical wireless transmission, limiting system performance. When the channel has fractional path delay and fractional Doppler shift—that is, when the path delay and Doppler shift are not strictly aligned with the DD domain grid points—the system will generate inter-delay interference (IDeI) and inter-Doppler interference (IDoI). Simultaneously, when the path delay is long, OTFS signals reflected from distant obstacles will also introduce inter-frame interference (IFI). In practical OTFS communication systems, IDeI, IDoI, and IFI usually coexist, collectively affecting system reliability.

[0005] Currently, existing interference analysis studies of OTFS systems have significant limitations: existing technologies [1] and [2] only analyze IDoI; existing technologies [3] and [4] study IDoI and Doppler interference IDeI. Among them, existing technology [1] considers multipath fading and Doppler effect in IDoI analysis; existing technologies [2], [3] and [4] further introduce cyclic prefix coding, but all adopt a single assumption: existing technologies [2] and [3] only consider that only a single cyclic prefix is ​​configured in each frame, while existing technology [4] assumes that the cyclic prefix length of all blocks (columns) in the frame is equal. None of the above studies have incorporated IFI into a unified analysis framework, the interference model is incomplete, the assumptions are idealized, and it is difficult to support the performance analysis and engineering design of actual OTFS systems.

[0006] For OTFS system quality-of-service (QoS) assessment, there is an urgent need to construct a complete mathematical analysis system that can uniformly characterize the three types of interference: IFI, IDoI, and IDeI, and comprehensively reflect the impact of practical factors such as Doppler effect, carrier frequency offset, multipath fading, and variable-length cyclic prefix. To date, no complete solution has been found. Therefore, this invention addresses the shortcomings of existing technologies by proposing an interference modeling and symbol error rate estimation method for OTFS communication systems. This method aims to fill the theoretical gap and provide reliable theoretical support and technical basis for the performance analysis, parameter design, and engineering implementation of OTFS systems in high-speed mobile scenarios.

[0007] [1] P. Raviteja, KT Phan, Y. Hong, and E. Viterbo, “Interferencecancellation and iterative detection for orthogonal time frequency spacemodulation,” IEEE Transactions on Wireless Communications, vol. 17, no. 10, pp. 6501–6515, October 2018.

[0008] [2] A. Tusha and H. Arslan, “Low complex inter-Doppler interferencemitigation for OTFS systems via global receiver windowing,” IEEE Transactionson Vehicular Technology, vol. 72, no. 6, pp. 7685–7698, June 2023.

[0009] [3] SE Zegrar, AS Sümer, and H. Arslan, “Fractional delay and fractional Doppler estimation and mitigation framework in OTFS systems,” IEEETransactions on Vehicular Technology, vol. 74, no. 2, pp. 2884–2896, February2025.

[0010] [4] H. Qu, G. Liu, L. Zhang, S. Wen, and MA Imran, “Low-complexitysymbol detection and interference cancellation for OTFS system,” IEEETransactions on Communications, vol. 69, no. 3, pp. 1524–1537, March 2021. Summary of the Invention

[0011] The purpose of this invention is to address the problem of inaccurate and incomplete interference modeling in existing OTFS systems under real-world non-ideal environments. It proposes a complete interference analysis and modeling approach for OTFS communication systems, including IFI, IDoI, and IDeI, and further derives a corresponding symbol error rate estimation method. This enables end-to-end quantitative evaluation of the OTFS system's performance under complex channel conditions including IFI, IDoI, and IDeI, providing a reliable basis for QoS evaluation of OTFS communication systems.

[0012] The technical solution of this invention is: an interference modeling and symbol error rate estimation method for OTFS communication systems. The OTFS communication system architecture includes a transmitter, a wireless channel, and a receiver, and its specific system architecture diagram is attached. Figure 1 As shown; according to the appendix Figure 1 At the transmitting end, each DD domain frame contains Information symbols, among which and The DD domain represents the number of time slots and subcarriers within a frame, respectively, and the DD domain represents the time delay-Doppler domain; the DD domain represents the time delay-Doppler domain. Each DD domain frame is denoted as , of which Each symbol is denoted as , and These represent the time-delay index and the Doppler index, respectively. , Then, for the DD field symbols Performing a symplectic finite Fourier inverse transform yields the corresponding time-frequency domain symbol. as follows:

[0013] (1);

[0014] in, Indicates the first Each TF field transmits a frame, where the TF field represents the time-frequency domain. express The One entry, and These represent the frequency index and the time index, respectively. , Next, along the frequency axis... Performing the inverse discrete Fourier transform yields the first... Time-delay domain frames Then, for A cyclic prefix code is added, and a parallel-to-serial conversion is performed to obtain a continuous symbol stream. This symbol stream then passes sequentially through a digital-to-analog converter, a low-pass filter, and an up-converter to finally generate a bandpass transmit OTFS signal. According to the appendix Figure 1 , Through a continuous-time impulse response The wireless channel transmission is superimposed with additive white Gaussian noise. At the receiving end, firstly, the received signal... The baseband received signal is obtained by performing down-conversion processing. Subsequently It performs signal processing operations that are the opposite of those at the transmitting end, and finally completes the reconstruction of the information bit stream;

[0015] This includes establishing an interference analysis model and estimating the symbol error rate;

[0016] Step 1: The specific method for establishing the interference analysis model is as follows:

[0017] Step 1.1: The first TF domain OTFSOTFS Include The TF domain frame is divided into several information symbols. Each block contains [number] blocks. A single information symbol, making Indicates the transmission time of each block; OTFS represents the transmit frame; transmit signal. Represented as:

[0018] (2);

[0019] in:

[0020] ;

[0021] ;

[0022] Indicates the carrier frequency. Indicates the first Subcarrier frequencies, Indicates the first The transmission time required for the cyclic prefix of each block, Indicates adding to the The number of cyclic prefix symbols in each block, This indicates the first iteration after adding the loop prefix. Total transmission time required for each block; and These represent the first and second digits after adding the loop prefix. The total transfer time required for each block and the number of blocks after adding the cyclic prefix. Total transmission time required for each block; This represents a tightly supported pulse shaping function. In this invention, a rectangular pulse function is selected, namely:

[0023] (3);

[0024] Step 1.2: Rewrite the transmitted OTFS signal given by formula (2) as a continuous-time function of two variables: time and carrier frequency, i.e.:

[0025] (4);

[0026] when OTFS signals are received via a dual-dispersion channel. Represented as:

[0027] (5);

[0028] in, The DD-domain extension function represents the channel. and These represent the time delay variable and the Doppler variable, respectively. , Indicates the frequency offset of the local oscillator; Represents additive white Gaussian noise; assume the channel is... It consists of separable paths, namely:

[0029] (6);

[0030] in, , and They represent the first The path gain, path delay, and Doppler shift of each path. Representing the continuous-time impulse function, substitute equation (6) into equation (5) to receive the OTFS signal. for:

[0031] (7);

[0032] in, ;right Perform down-conversion processing to obtain the baseband received signal as follows:

[0033] (8);

[0034] in, This indicates the first iteration after adding the loop prefix. Total transmission time required for each block; , ; Due to signal processing and channel delay, the index of the OTFS transmitted frame... No need to compare with the index of the current OTFS demodulated frame at the receiving end Consistency; To Perform analog-to-digital conversion to obtain the corresponding discrete-time series. as follows:

[0035] (9);

[0036] in, This indicates a replacement;

[0037] (10);

[0038] Step 1.3: Because the first The front of each block The symbol is a cyclic prefix, so only one needs to be retained. The last one A symbol, namely , This is used for the reconstruction of information symbols; then, for... Do Discrete Fourier Transform yields the first TF domain demodulation frames , its first Each symbol is denoted as The expression is as follows:

[0039] (11);

[0040] in, and These represent the frequency index and the time index, respectively. , , Indicates the first The first TF domain demodulation frame suffered the first One noise sample;

[0041] Step 1.4: For Performing the symplectic finite Fourier transform yields the first... DD domain demodulation frames , its first Each symbol is denoted as The expression is as follows:

[0042] (12);

[0043] in, and These represent the time-delay index and the Doppler index, respectively. , , Indicates the first The first DD domain demodulation frame suffered the first One noise sample;

[0044] Step 1.5: Based on formulas (1)-(12), the OTFS transmission model including three types of interference: IFI, IDoI, and IDeI is obtained. as follows:

[0045] (13);

[0046] in, Indicates the receiver's first One DD domain demodulation frame Indicates the receiver's first One DD domain demodulation frame Indicates the first The first DD domain demodulation frame suffered the first The noise sample, the first The frame signal passes through the first The path to the receiving end is the current number. Each demodulated frame generates interference; Represents the IFI filter coefficients; Indicates the first The IDoI filter coefficients within each demodulated frame; Indicates the first The IDeI filter coefficients within each demodulated frame; Indicates that due to the first The path to the receiving end is the current number. All DD domain transmission frames that generate interference from the demodulated DD domain frames;

[0047] Step 2: The symbol error rate estimation method is as follows:

[0048] Step 2.1: According to the central limit theorem, when and / or When the noise level exceeds a set threshold, it is defined as "integrated noise". as follows:

[0049] (twenty four);

[0050] Represents the IFI filter coefficients. Represents the IDoI filter coefficients. Indicates the coefficients of the IDeI filter;

[0051] Caused by path delay and Doppler shift Phase drift for:

[0052] (25);

[0053] in, and Let represent the operations of extracting the imaginary part and the operations of extracting the real part, respectively; the rotation matrix resulting from this phase shift is:

[0054] (26);

[0055] for In a phase-shift keying (OTFS) communication system, a phasor probability distribution is assumed, and each decision region used during demodulation is based on the minimum distance detection criterion. Due to the symmetry of the constellation diagram, the system symbol error rate is related to the transmission of the first signal constellation phasor. The error probabilities are equal at all times, where To represent the average symbolic energy; first, define two variables. and ; probability density function for:

[0056] (27);

[0057] in, , Indicates statistical expectation;

[0058] Step 2.2: IQ vector after phase compensation for;

[0059] (28);

[0060] express The inverse matrix, , ;

[0061] Step 2.3: Transfer variables and Convert to:

[0062] (29);

[0063] (30);

[0064] Step 2.4: Establish The joint probability density function is :

[0065] (31);

[0066] right exist Integrating over the range of values ​​of , we can obtain information about marginal probability density function as follows:

[0067] (32);

[0068] in, express The noise power spectral density, according to formulas (24)-(32), is... In the PSK-OTFS communication system, Symbol error rate for:

[0069] (33);

[0070] therefore, Average symbol error rate for:

[0071] (34);

[0072] Assuming the transmitted information symbols are independent and identically distributed, the estimated symbol error rate for different received frames within the channel coherence period is as follows: Keep constant .

[0073] Further, in step 1.5, due to the first The path to the receiving end is the current number. All DD domain transmission frames that generate interference from the demodulated DD domain frames. The specific calculation method is as follows:

[0074] (14);

[0075] Further, in step 1.5, the first... The first transmitted DD domain frame interference Each demodulated DD domain frame is used as an IFI filter coefficient. The calculation method is as follows:

[0076] (15);

[0077] and This represents the set of two path indices that lead to IFI, namely:

[0078] (16)

[0079] (17).

[0080] Further, in step 1.5, the IDoI filter coefficients The specific expression is as follows:

[0081] (18);

[0082] in, and This represents the set of two path indices that lead to IDoI, namely:

[0083] (19)

[0084] (20).

[0085] Further, in step 1.5, the IDeI filter coefficients The specific expression is as follows:

[0086] (twenty one);

[0087] in, and This represents the set of two path indices that lead to IDeI, namely:

[0088] (twenty two);

[0089] (twenty three).

[0090] Compared with the prior art, the present invention has the following main advantages:

[0091] (1) This invention is the first to theoretically realize a comprehensive analysis of inter-frame interference (IFI), inter-Doppler interference (IDoI), and time delay interference (IDeI) in the OTFS communication system;

[0092] (2) Under the comprehensive consideration of key factors such as Doppler effect, carrier frequency offset of local oscillator, multipath fading and cyclic prefix coding, this invention establishes a new mathematical representation of IFI, IDoI and IDeI, and derives the transmission model of OTFS communication system.

[0093] (3) Based on the constructed OTFS transmission model including IFI, IDoI and IDeI, this invention proposes a symbol error rate estimation method for PSK-OTFS communication system, which can effectively achieve accurate evaluation of OTFS receiver performance. Attached Figure Description

[0094] Figure 1 This is a schematic diagram of the architecture of the OTFS communication system described in this invention, which mainly includes three parts: the transmitter, the wireless channel, and the receiver.

[0095] Figure 2 This is a comparison chart showing the estimated and actual symbol error rate of the QPSK-OTFS communication system under a short-delay spread EVA channel, based on the present invention and existing technologies. Two carrier frequency offset scenarios.

[0096] Figure 3 This is a comparison chart showing the estimated and actual symbol error rate of the QPSK-OTFS communication system under a long-delay spread EVA channel, based on the present invention and existing technologies. Two carrier frequency offset scenarios. Detailed Implementation

[0097] (1) Overall setup of the embodiment;

[0098] This embodiment aims to verify the accuracy of the interference modeling and symbol error rate estimation method of the present invention. The Extended Vehicle A (EVA) channel model from the 3GPP standard is selected as the wireless transmission channel, and its power delay spectrum parameters are shown in Table 1. Using the symbol error rate (SER) as the core performance indicator, the Quality of Service (QoS) of the QPSK-OTFS communication system under different signal-to-noise ratio conditions in the EVA channel is quantitatively evaluated. The symbol error rate obtained from Monte Carlo simulation experiments is used as the true value. By comparing the deviations between the estimated values ​​of the present invention method and existing methods and the true values, the effectiveness and superiority of the present invention are verified.

[0099] This embodiment sets up two typical scenarios to comprehensively verify the performance of the present invention under different interference conditions:

[0100] 1) Short-delay extended EVA channel scenario: Using the original tap delay of the EVA channel, the cyclic prefix length is long enough, that is, the cyclic prefix length is greater than the maximum path delay of the channel. The system only has inter-Doppler interference (IDoI) and inter-delay interference (IDeI), and no inter-frame interference (IFI). The corresponding simulation results are detailed in Figure 2.

[0101] 2) Long-delay extended EVA channel scenario: The original tap delay of the EVA channel is increased by 10 times. At this time, the cyclic prefix length is less than the maximum path delay of the channel. The system simultaneously has inter-frame interference (IFI), inter-Doppler interference (IDoI) and inter-delay interference (IDeI). The corresponding simulation results are detailed in Figure 3.

[0102] The remaining simulation parameters in this embodiment are set uniformly, and the specific parameter values ​​are shown in Table 2.

[0103] (2) Details of simulation experiment parameters;

[0104] Table 1 Power delay spectrum of EVA channel;

[0105]

[0106] Table 2 Simulation parameter settings;

[0107]

[0108] (3) Simulation results analysis and verification

[0109] 1) Short-latency spread EVA channel scenario (Figure 2) Figure 2 This represents a comparison between the estimated and true symbol error rate of the QPSK-OTFS communication system under a short-delay spread EVA channel. The symbol error rate estimate obtained by this invention and prior art is... This represents the true sign error rate obtained from the Monte Carlo experiment. (a) (b) As shown in Figure 2, in the short-latency spread scenario (where only IDoI and IDeI exist), the symbol error rate estimate obtained by the method proposed in this invention (labeled "this invention" in Figure 2) differs from the symbol error rate estimate obtained by existing methods (see Figure 2). Figure 2 The data marked as "Prior Art" showed a high degree of fit, and the local oscillator carrier frequency offset (Δf) was changed. o The value of ) has almost no impact on the estimation results of the two methods. This result shows that in the absence of IFI, both the method of this invention and the existing method can achieve a certain symbol error rate estimation, but the estimation curve of the method of this invention is closer to the true value (Monte Carlo simulation results).

[0110] 2) Long-delay spread EVA channel scenario (see appendix) Figure 3 This represents the comparison between the estimated and true symbol error rate of a QPSK-OTFS communication system under a long-delay spread EVA channel; where, The symbol error rate estimate obtained by this invention and prior art is... This represents the true sign error rate obtained from the Monte Carlo experiment. (a) (b) From the appendix Figure 3 As can be seen, in long-latency extended scenarios (where IFI, IDoI, and IDeI coexist), the symbol error rate estimate obtained by the method proposed in this invention (labeled "this invention" in Figure 3) deviates from the true value (Monte Carlo simulation results, labeled "true symbol error rate" in Figure 3) within one order of magnitude, demonstrating extremely high estimation accuracy. In contrast, the symbol error rate estimate obtained by existing methods deviates from the true value by more than ten orders of magnitude, completely failing to accurately reflect the actual performance of the system.

[0111] The simulation results fully verify that the interference model established in this invention, which includes IFI, IDoI, and IDeI, can comprehensively and accurately characterize the interference characteristics under actual non-ideal channels. The symbol error rate estimation method derived from this model has significantly better estimation accuracy than existing technologies in complex interference scenarios. It can effectively realize the quantitative evaluation of the end-to-end performance of the OTFS system and provide reliable support for system design and QoS optimization.

Claims

1. A method for interference modeling and symbol error rate estimation in OTFS communication systems, wherein the OTFS communication system architecture addressed by this method includes: The transmitter, wireless channel, and receiver; at the transmitter, each DD domain frame contains... Information symbols, among which and The DD domain represents the number of time slots and subcarriers within a frame, respectively, and the DD domain represents the time delay-Doppler domain; the DD domain represents the time delay-Doppler domain. Each DD domain frame is denoted as , of which Each symbol is denoted as , and These represent the time-delay index and the Doppler index, respectively. , Then, for the DD field symbols Performing a symplectic finite Fourier inverse transform yields the corresponding time-frequency domain symbol. as follows: (1)； in, Indicates the first Each TF field transmits a frame, where the TF field represents the time-frequency domain. express The One entry, and These represent the frequency index and the time index, respectively. , Next, along the frequency axis... Performing the inverse discrete Fourier transform yields the first... Time-delay domain frames Then, for A cyclic prefix code is added, and a parallel-to-serial conversion is performed to obtain a continuous symbol stream. This symbol stream then passes sequentially through a digital-to-analog converter, a low-pass filter, and an up-converter to finally generate a bandpass transmit OTFS signal. ; Through a continuous-time impulse response The wireless channel transmission is superimposed with additive white Gaussian noise. At the receiving end, firstly, the received signal... The baseband received signal is obtained by performing down-conversion processing. Subsequently It performs signal processing operations that are the opposite of those at the transmitting end, and finally completes the reconstruction of the information bit stream; This includes establishing an interference analysis model and estimating the symbol error rate; Step 1: The specific method for establishing the interference analysis model is as follows: Step 1.1: The TF domain OTFSOTFS Include The TF domain frame is divided into several information symbols. Each block contains [number] blocks. A single information symbol, making Indicates the transmission time of each block; OTFS represents the transmit frame; transmit signal. Represented as: (2)； in: ； ； Indicates the carrier frequency. Indicates the first Subcarrier frequencies, Indicates the first The transmission time required for the cyclic prefix of each block, Indicates adding to the The number of cyclic prefix symbols in each block, This indicates the first iteration after adding the loop prefix. Total transmission time required for each block; and These represent the first and second digits after adding the loop prefix. The total transfer time required for each block and the number of blocks after adding the cyclic prefix. Total transmission time required for each block; This represents a tightly supported pulse shaping function. In this invention, a rectangular pulse function is selected, namely: (3)； Step 1.2: Rewrite the transmitted OTFS signal given by formula (2) as a continuous-time function of two variables: time and carrier frequency, i.e.: (4)； when OTFS signals are received via a dual-dispersion channel. Represented as: (5)； in, The DD-domain extension function represents the channel. and These represent the time delay variable and the Doppler variable, respectively. , Indicates the frequency offset of the local oscillator; Represents additive white Gaussian noise; assume the channel is... It consists of separable paths, namely: (6)； in, , and They represent the first The path gain, path delay, and Doppler shift of each path. Representing the continuous-time impulse function, substitute equation (6) into equation (5) to receive the OTFS signal. for: (7)； in, ;right Perform down-conversion processing to obtain the baseband received signal as follows: (8)； in, This indicates the first iteration after adding the loop prefix. Total transmission time required for each block; , ; Due to signal processing and channel delay, the index of the OTFS transmitted frame... No need to compare with the index of the current OTFS demodulated frame at the receiving end Consistent; To Perform analog-to-digital conversion to obtain the corresponding discrete-time series. as follows: (9)； in, This indicates a replacement; (10)； Step 1.3: Because the first The front of each block The symbol is a cyclic prefix, so only one needs to be retained. The last one A symbol, namely , This is used for the reconstruction of information symbols; then, for... Do Discrete Fourier Transform yields the first TF domain demodulation frames , its first Each symbol is denoted as The expression is as follows: (11)； in, and These represent the frequency index and the time index, respectively. , , Indicates the first The first TF domain demodulation frame suffered the first One noise sample; Step 1.4: For Performing the symplectic finite Fourier transform yields the first... DD domain demodulation frames , its first Each symbol is denoted as The expression is as follows: (12)； in, and These represent the time-delay index and the Doppler index, respectively. , , Indicates the first The first DD domain demodulation frame suffered the first One noise sample; Step 1.5: Based on formulas (1)-(12), the OTFS transmission model including three types of interference: IFI, IDoI, and IDeI is obtained. as follows: (13)； in, Indicates the receiver's first One DD domain demodulation frame Indicates the receiver's first One DD domain demodulation frame Indicates the first The first DD domain demodulation frame suffered the first The noise sample, the first The frame signal passes through the first The path to the receiving end is the current number. Each demodulated frame generates interference; Represents the IFI filter coefficients; Indicates the first The IDoI filter coefficients within each demodulated frame; Indicates the first The IDeI filter coefficients within each demodulated frame; Indicates that due to the first The path to the receiving end is the current number. All DD domain transmission frames that generate interference from the demodulated DD domain frames; Step 2: The symbol error rate estimation method is as follows: Step 2.1: According to the central limit theorem, when and / or When the noise level exceeds a set threshold, it is defined as "integrated noise". as follows: (24)； Represents the IFI filter coefficients. Represents the IDoI filter coefficients. Indicates the coefficients of the IDeI filter; Caused by path delay and Doppler shift Phase drift for: (25)； in, and Let represent the operations of extracting the imaginary part and the operations of extracting the real part, respectively; the rotation matrix resulting from this phase shift is: (26)； for In a phase-shift keying (OTFS) communication system, a phasor probability distribution is assumed, and each decision region used during demodulation is based on the minimum distance detection criterion. Due to the symmetry of the constellation diagram, the system symbol error rate is related to the transmission of the first signal constellation phasor. The error probabilities are equal at the same time, where To represent the average symbolic energy; first, define two variables. and ; probability density function for: (27)； in, , Indicates statistical expectation; Step 2.2: IQ vector after phase compensation for; (28)； express The inverse matrix, , ; Step 2.3: Transfer variables and Convert to: (29)； (30)； Step 2.4: Establish The joint probability density function is : (31)； right exist Integrating over the range of values ​​of , we can obtain information about marginal probability density function as follows: (32)； in, express The noise power spectral density, according to formulas (24)-(32), is... In the PSK-OTFS communication system, Symbol error rate for: (33)； therefore, Average symbol error rate for: (34)； Assuming the transmitted information symbols are independent and identically distributed, the estimated symbol error rate for different received frames within the channel coherence period is as follows: Keep constant .

2. The interference modeling and symbol error rate estimation method for OTFS communication systems as described in claim 1, characterized in that, In step 1.5, because the first The path to the receiving end is the current number. All DD domain transmission frames that generate interference from the demodulated DD domain frames. The specific calculation method is as follows: (14)。 3. The interference modeling and symbol error rate estimation method for OTFS communication systems as described in claim 1, characterized in that, In step 1.5, the first... The first transmitted DD domain frame interference Each demodulated DD domain frame is used as an IFI filter coefficient. The calculation method is as follows: (15); and This represents the set of two path indices that lead to IFI, namely: (16) （17)。 4. The interference modeling and symbol error rate estimation method for OTFS communication systems as described in claim 1, characterized in that, In step 1.5, the IDoI filter coefficients The specific expression is as follows: (18)； in, and This represents the set of two path indices that lead to IDoI, namely: ， (19) (20)。 5. The interference modeling and symbol error rate estimation method for OTFS communication systems as described in claim 1, characterized in that, In step 1.5, the IDeI filter coefficients The specific expression is as follows: (21)； in, and This represents the set of two path indices that lead to IDeI, namely: (22)； (23)。

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