An OTFS communication method and system based on four-dimensional spherical code

Abstract

The present invention discloses an OTFS communication method and system based on four-dimensional spherical code, specifically: at the transmitting end, DD domain data is grouped into multiple sub-blocks, each sub-block is index modulated and four-dimensional spherical code modulated, and the outputs of all sub-blocks form a frame of DD domain signal X DD ;Signal X DD After OTFS modulation, it is transmitted to the receiving end, and the receiving end performs OTFS demodulation to obtain the DD domain receiving signal Y DD ; Receive signal Y DD After equalization and elimination of intersymbol interference, a preliminary detection signal #imgabs0# is obtained. This preliminary detection signal #imgabs1# is divided into sub-blocks equal to the number of transmitting terminals, and ML detection is performed on each sub-block. Based on the mathematical model corresponding to the input-output relationship of OTFS modulation, the average bit error rate (ABER) and the upper bound of the PAPR (Paper-likely Recognized Prediction Rate) of the communication system are determined. This invention leverages the increased distance between constellation points in high-dimensional modulation to improve the system's detection performance and communication capacity compared to traditional two-dimensional modulation communication systems.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technology, and in particular to an OTFS communication method and system based on four-dimensional spherical codes. Background Art

[0002] In high-speed communication systems, as the terminal's speed changes, users are affected by Doppler spread during communication, reducing communication quality. To address these communication issues in high-speed mobile scenarios, the industry has proposed Orthogonal Time-Frequency-Space Modulation (OTFS). This is a new modulation scheme in the Delay-Doppler Domain (DD). By performing a two-dimensional convolution of the modulation symbols in the DD domain with the effective channel, it fully utilizes time and frequency diversity. Furthermore, the dual-frequency channel is sparse in the DD domain, facilitating receiver design.

[0003] The key characteristic of index modulation (IM) is that it uses specific indices of transmission resources (such as antennas and subcarriers) to convey information. The resulting transmitted signal is sparsely distributed across one or a few resource domains, increasing the robustness of the communication system. Index modulation modulates information bits onto the index of the transmission resource based on the on / off keying principle of the available signal resource domain, which plays a significant role in improving spectral efficiency and bit error rate performance.

[0004] Combining these two technologies, research has been conducted on OTFS systems based on index modulation, also known as OTFS-IM modulation. By conveying bit information through the activation symbol index in the DD domain and the modulation constellation symbol, OTFS-IM modulation results in sparser DD domain transmitted data compared to traditional OTFS modulation, effectively reducing the effects of latency and Doppler. Building on this research, numerous studies have been conducted, such as increasing index information density by adding an in-phase orthogonal dimension to PAM modulated signals and increasing index information density by adding a modulation mode selection dimension to a two-mode modulation constellation. While maintaining the same spectral efficiency, increasing the index dimension increases the sparsity of the modulated signal, thereby improving signal detection performance. However, this approach increases the complexity of index detection, requiring separate detection for the added dimension. Current research is primarily based on two-dimensional modulated signals (such as BPSK and QAM). According to traditional detection theory, higher modulation dimensions increase the minimum Euclidean distance between constellation points, leading to better detection performance. Summary of the Invention

[0005] The object of the present invention is to provide an OTFS communication method and system based on four-dimensional spherical codes, which can increase the minimum distance between constellation points to be detected and improve the OTFS signal detection performance.

[0006] The technical solution for achieving the purpose of the present invention is: an OTFS communication method based on a four-dimensional spherical code, comprising the following steps:

[0007] Step 1: At the transmitter, the DD domain data is grouped into multiple sub-blocks. Each sub-block is index modulated and modulated with a four-dimensional spherical code. The outputs of all sub-blocks form a frame of DD domain signal X. DD ;

[0008] Step 2: Signal X DD After OTFS modulation, it is transmitted to the receiving end, and the receiving end performs OTFS demodulation to obtain the DD domain receiving signal Y DD ;

[0009] Step 3: Receive signal Y DD After equalization and elimination of inter-symbol interference, a preliminary detection signal is obtained

[0010] Step 4: Initial detection signal Divide into sub-blocks equal to the number of transmitting ends, and perform ML detection on each sub-block;

[0011] Step 5: Determine the average bit error rate approximation and the PAPR upper bound of the communication system based on the mathematical model corresponding to the input-output relationship of OTFS modulation.

[0012] Furthermore, in step 1, the DD domain data is grouped into multiple sub-blocks, and each sub-block is subjected to index modulation and four-dimensional spherical code modulation, as follows:

[0013] Step 1.1: Assume that the total number of symbols in a sub-block is n and the number of active symbols is k. Then, an M×N OTFS frame is divided into g=MN / n groups. The transmitted bit stream set u is evenly divided into g groups. Each sub-block transmits p bits of information, where bit p1 is used for index modulation and bit p2 is used for four-dimensional modulation.

[0014] Step 1.2: Each sub-block is modulated independently, and the M in the unit sphere is taken in the L-dimensional space. c point as the modulation constellation point c i =(c i,1 ,c i,2 ,c i,3 ,c i,4 ), since the constellation point is a four-dimensional vector, two two-dimensional symbols will be used to carry a four-dimensional symbol in system transmission, that is, c i From s1=c i,1 +jc i,2 and s2=c i,3 +jc i,4Therefore, the number of activated symbols k should be an integer multiple of 2, and the modulation symbol vector of a sub-block is s β =[s β (1),s β (2),…,s β (k)] T , the number of bits used for four-dimensional modulation in the sub-block p2=k / 2log2(M c );

[0015] Step 1.3: Select k consecutive and non-repeated symbols from the n data symbols of the sub-block as activation symbols, then the index set I of the βth sub-block is β is a subset of the lookup table I, where I = {k(i-1)+1, k(i-1)+2, …, k(i-1)+k}, i∈[1, 2, …, n / k], and the number of bits used for index modulation in the subblock is

[0016] Step 1.4: The total number of bits transmitted in one sub-block is:

[0017]

[0018] So the spectral efficiency SE = p / n, the transmitted information X of the βth sub-block β Expressed as:

[0019]

[0020] Furthermore, in step 2, the sub-blocks are combined into a frame of DD domain signal X DD , after OTFS modulation, the receiving end performs OTFS demodulation to obtain the DD domain receiving signal Y DD , as follows:

[0021] After the modulation of each sub-block is completed, it is spliced ​​into an OTFS frame along the Doppler dimension for conventional OTFS modulation, that is, the inverse symplectic finite Fourier transform, Heisenberg transform and transmit pulse shaping are used to obtain the time domain transmit signal s; after passing through the time-frequency dual-selective channel, the receiving end obtains the DD domain receive signal Y through receive pulse shaping, Wigner transform and symplectic finite Fourier transform. DD .

[0022] Furthermore, the received signal Y in step 3 DD After equalization and elimination of inter-symbol interference, a preliminary detection signal is obtained The details are as follows:

[0023] Assuming that the channel information is known at the receiving end, MMSE equalization or MRC equalization is used for equalization;

[0024] The MMSE equalization is as follows:

[0025]

[0026] in is the estimated transmitted signal vector, y is the received signal vector, H is the channel matrix, σ 2 is the noise variance, and the MN×1 pre-estimated transmission vector Rewritten as an M×N matrix, we get

[0027] MRC equalization is consistent with MRC detection. It transforms the hard decision in the MRC detection algorithm into a soft decision. When using MRC equalization, a zero-padding OTFS structure is required. That is, the frame structure delay dimension is padded with δ zeros, where δ is greater than the maximum delay.

[0028] Furthermore, in step 4, the preliminary detection signal Divide into sub-blocks equal to the number of transmitters, and perform ML detection on each sub-block as follows:

[0029] According to the rule of forming OTFS frame by sub-blocks in step 1, the estimated transmission signal, i.e. the preliminary detection signal Re-divide into the same number of sub-blocks, use the ML detector to detect each sub-block, and obtain index information and four-dimensional modulation information:

[0030]

[0031] in, is the estimated transmission information of the βth sub-block, s β is the modulation symbol of the βth sub-block, β is the index set of the βth sub-block.

[0032] Furthermore, in step 5, based on the mathematical model corresponding to the input-output relationship of OTFS modulation, the average bit error rate approximation and the PAPR upper bound of the OTFS communication system are determined as follows:

[0033] When the channel information is known, x is wrongly judged as Conditional matching error probability for:

[0034]

[0035] Where Q(·) is the Gaussian Q function, H eff is the equivalent channel matrix in DD domain, N 0,DD is the variance of the noise in the DD domain;

[0036] After simplified derivation, the unconditional pairing probability is obtained for:

[0037]

[0038] Where P is the number of propagation paths, σ 2 is the channel gain h i The variance of i are the eigenvalues ​​of the Hermitian matrix Θ, The details are as follows: is the DD domain transmission signal matrix after the delay and Doppler effect, is the DD domain estimated transmit signal matrix after delay and Doppler influence, is the delay and Doppler influence matrix of the i-th path, F N is the N×N normalized Fourier transform matrix, G rx and G tx are the receiving shaped pulse matrix and the transmitting shaped pulse matrix, is the forward cyclic matrix reflecting the delay impact of the i-th path, is a diagonal matrix reflecting the Doppler effect of the i-th path;

[0039] The average bit error rate is then approximately:

[0040]

[0041] Among them, n x =((M c ) k / 2 n / k) g is the number of possible cases of transmitting signal x, M c represents the total number of four-dimensional constellation points, n represents the total number of symbols in the sub-block, k represents the number of activated symbols in the sub-block, and g represents the number of sub-blocks contained in an OTFS frame. To misjudge x as The number of error bits when

[0042] The PAPR upper bound of the system is derived as:

[0043]

[0044] Where k and l are the Doppler index and delay index in the DD domain respectively. For X DD The average power of the data in row u.

[0045] An OTFS communication system based on a four-dimensional spherical code is used to implement the OTFS communication method based on a four-dimensional spherical code. The system includes a transmitting end and a receiving end, wherein:

[0046] The transmitting end includes a bit separator, a modulation module, an OTFS frame generator, an ISFFT unit, and a Heisenberg transform unit arranged in sequence; the modulation module includes a plurality of modulation units arranged in parallel, each modulation unit includes an index selector and a four-dimensional modulator, and performs index modulation and four-dimensional spherical code modulation;

[0047] The receiving end includes a Wigner transform unit, a SFFT unit, an equalizer, a sub-block generator, a detection module and a bit integrator which are arranged in sequence. The detection module includes a plurality of detectors which are arranged in parallel.

[0048] Furthermore, the specific working process of the OTFS communication system based on four-dimensional spherical code is as follows:

[0049] At the transmitter, the bit separator groups the DD domain data into multiple sub-blocks. Each sub-block is modulated by index and four-dimensional spherical code through the modulation module. The outputs of all sub-blocks are spliced ​​into an OTFS frame along the Doppler dimension by the OTFS frame generator, and then conventional OTFS modulation is performed. That is, the ISFFT unit performs the inverse symplectic finite Fourier transform, the Heisenberg transform unit performs the Heisenberg transform, and finally the transmit pulse is shaped to obtain the time domain transmit signal s.

[0050] After the time-frequency dual-selection channel, the receiving end performs OTFS demodulation to obtain the DD domain receiving signal Y DD First, the received pulse is shaped, then the Wigner transform unit is used to perform Wigner transform, and the SFFT unit is used to perform symplectic finite Fourier transform to obtain the DD domain received signal Y DD ; Receive signal Y DD After equalization by the equalizer, inter-symbol interference is eliminated and a preliminary detection signal is obtained. The sub-block generator will initially detect the signal It is divided into sub-blocks equal to the number of transmitting ends. The detection module performs ML detection on each sub-block through parallel detectors. The ML detection results of each sub-block are processed by the bit integrator to obtain the final received signal.

[0051] Compared with the prior art, the present invention has the following significant advantages: (1) by introducing four-dimensional spherical code modulation into the OTFS-IM system, the distance between the constellation points to be detected is increased, thereby improving the detection performance and communication capacity of the system; (2) the equalization method before signal detection can choose MMSE with higher spectrum efficiency or MRC with lower complexity; (3) by analyzing and deriving the average bit error rate approximation and the PAPR upper limit, the PAPR performance of the present invention is better than that of the traditional OTFS communication system. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 Schematic diagram of the process of the OTFS communication method based on four-dimensional spherical code modulation.

[0053] Figure 2 This is a comparison chart of the theoretical and simulated BER values ​​of the OTFS-IM system based on four-dimensional spherical code modulation.

[0054] Figure 3 This is a comparison chart of the BER performance of the OTFS-IM system based on four-dimensional spherical codes and the traditional OTFS-IM system under two propagation paths.

[0055] Figure 4 This is a comparison chart of the BER performance of the OTFS-IM system based on four-dimensional spherical codes and the traditional OTFS-IM system under EVA channels.

[0056] Figure 5 This is a comparison chart of the PAPR performance of the OTFS-IM system based on four-dimensional spherical codes, the traditional OTFS-IM system, and the traditional OTFS system at different activation ratios. DETAILED DESCRIPTION

[0057] Combine Figure 1 The OTFS communication system based on four-dimensional spherical codes of the present invention comprises the following steps:

[0058] Step 1: At the transmitter, the DD (delay-Doppler) domain data is grouped into multiple sub-blocks. Each sub-block is index modulated and modulated with a four-dimensional spherical code. The outputs of all sub-blocks form a frame of DD domain signal X. DD ;

[0059] Step 2: Signal X DD After OTFS modulation, it is transmitted to the receiving end, and the receiving end performs OTFS demodulation to obtain the DD domain receiving signal Y DD ;

[0060] Step 3: Receive signal Y DD After equalization and elimination of inter-symbol interference, a preliminary detection signal is obtained

[0061] Step 4: Initial detection signal Divide into sub-blocks equal to the number of transmitting ends, and perform ML detection on each sub-block;

[0062] Step 5: Based on the mathematical model corresponding to the input-output relationship of OTFS modulation, determine the approximate average bit error rate and the upper bound of the PAPR (Peak to Average Power Ratio) of the communication system. The system has better PAPR performance.

[0063] Furthermore, the DD domain data is grouped into multiple sub-blocks as described in step 1, and each sub-block is subjected to index modulation and four-dimensional spherical code modulation, as follows:

[0064] Step 1.1: Assume that the total number of symbols in a sub-block is n and the number of active symbols is k. Then, an M×N OTFS frame can be divided into g=MN / n groups. The transmitted bit stream set u is evenly divided into g groups. Each sub-block transmits p bits of information, where bit p1 is used for index modulation and bit p2 is used for four-dimensional modulation.

[0065] Step 1.2: Each sub-block is modulated independently. In the L-dimensional space, are all points on the surface of the unit sphere, then

[0066]

[0067] Take M in the unit sphere c Points constitute a constellation set The spherical code can be expressed as K(L,M c ,θ), θ is the angle that maximizes the distance between constellation points; since constellation point c i =(c i,1 ,c i,2 ,c i,3 ,c i,4 ) is a four-dimensional vector. In system transmission, two two-dimensional symbols will be used to carry a four-dimensional symbol, that is, c i From s1=c i,1 +jc i,2 and s2=c i,3 +jc i,4 Therefore, the number of activated symbols k should be an integer multiple of 2, and the modulation symbol vector of a sub-block is s β =[s β (1),s β (2),…,s β (k)] T , the number of bits used for four-dimensional modulation in the sub-block p2=k / 2log2(M c );

[0068] Step 1.3: To facilitate signal detection, select k consecutive and non-repeated symbols from the n data symbols of the sub-block as activation symbols. Then the index set I of the βth sub-block is β is a subset of the lookup table I, where I = {k(i-1)+1, k(i-1)+2, …, k(i-1)+k}, i∈[1, 2, …, n / k], and the number of bits used for index modulation in the subblock is

[0069] Step 1.4: The total number of bits transmitted in one sub-block is:

[0070]

[0071] So the spectral efficiency is SE = p / n, and the transmission information of the βth sub-block can be expressed as:

[0072]

[0073] Furthermore, the sub-blocks are combined into a frame of DD domain signal X in step 2. DD , after OTFS modulation, the receiving end performs OTFS demodulation to obtain the DD domain receiving signal Y DD , as follows:

[0074] After the modulation of each sub-block is completed, it is spliced ​​into an OTFS frame along the Doppler dimension and conventional OTFS modulation is performed. The transmit signal in the time-frequency domain is obtained by the inverse symplectic finite Fourier transform (ISFFT). Then, the time-domain transmit end signal s is obtained through the Heisenberg transform and transmit pulse shaping:

[0075]

[0076]

[0077] Where F represents the normalized Fourier transform matrix, vec(·) represents the column-vectorized operation, represents the Kronecker product, X is the column vector of the transmitted signal in the DD domain;

[0078] After the signal s passes through the time-frequency dual-selective channel, the receiving end obtains the DD (delay-Doppler) domain received signal Y through receiving pulse shaping, Wigner transform and Symplectic Finite Fourier Transform (SFFT) DD , whose column vector is represented by y, so far we can get the input-output relationship of the DD domain:

[0079]

[0080] The DD domain equivalent channel matrix h i represents the channel gain of the i-th path, is a circulant matrix reflecting the delay effect of the channel, is a diagonal matrix reflecting the Doppler effect of the channel.

[0081] Furthermore, the received signal Y in step 3 DD After equalization and elimination of inter-symbol interference, a preliminary detection signal is obtained The details are as follows:

[0082] Assuming that the channel information is known at the receiving end, MMSE equalization or MRC equalization can be used for equalization. The MMSE equalization concept is as follows:

[0083]

[0084] in y, H, and σ 2 are the estimated transmitted signal vector, received signal vector, channel matrix and noise variance respectively, and the MN×1 pre-estimated transmitted vector Rewritten as an M×N matrix, we can get It can be seen that MMSE equalization requires a high inverse complexity of the matrix;

[0085] The concept of MRC equalization is consistent with MRC detection. It only requires converting the hard decisions in the detection algorithm into soft decisions. When using MRC equalization, a zero-padding OTFS structure is required. That is, the delay dimension of the frame structure needs to be padded with zeros greater than the maximum delay, resulting in reduced spectrum utilization and additional overhead.

[0086] Furthermore, the preliminary detection signal in step 4 is Divide into sub-blocks equal to the number of transmitters, and perform ML detection on each sub-block as follows:

[0087] According to the rule of forming OTFS frame by sub-blocks in step 1, the estimated transmission signal, i.e. the preliminary detection signal Re-divide into the same number of sub-blocks, use the ML detector to detect each sub-block, and obtain index information and four-dimensional modulation information:

[0088]

[0089] in, is the estimated transmission information of the βth sub-block, s β is the modulation symbol of the βth sub-block, β is the index set of the βth sub-block.

[0090] Furthermore, according to the mathematical model corresponding to the input-output relationship of OTFS modulation in step 5, the average bit error rate approximation and the PAPR upper bound of the OTFS communication system are determined as follows:

[0091] According to the input-output relationship of OTFS modulation, when the channel information is known, x is misjudged as Conditional matching error probability for:

[0092]

[0093] Where Q(·) is the Gaussian Q function, H eff is the equivalent channel matrix in DD domain, N 0,DD is the variance of the noise in the DD domain;

[0094] After simplified derivation, the unconditional pairing probability is obtained for:

[0095]

[0096] Where P is the number of propagation paths, σ 2 is the channel gain h i The variance of i are the eigenvalues ​​of the Hermitian matrix Θ, The details are as follows: is the DD domain transmission signal matrix after the delay and Doppler effect, is the DD domain estimated transmit signal matrix after delay and Doppler influence, is the delay and Doppler influence matrix of the i-th path, F N is the N×N normalized Fourier transform matrix, G rx and G tx are the receiving shaped pulse matrix and the transmitting shaped pulse matrix, is the forward cyclic matrix reflecting the delay impact of the i-th path, is a diagonal matrix reflecting the Doppler effect of the i-th path;

[0097] The average bit error rate is then approximately:

[0098]

[0099] Among them, n x =((M c ) k / 2 n / k) g is the number of possible cases of transmitting signal x, M c represents the total number of four-dimensional constellation points, n represents the total number of symbols in the sub-block, k represents the number of activated symbols in the sub-block, and g represents the number of sub-blocks contained in an OTFS frame. To misjudge x as The number of error bits when

[0100] According to the mathematical model in step 2, the upper bound of the PAPR of the OTFS-IM system under four-dimensional modulation is derived as:

[0101]

[0102] Where k and l are the Doppler index and delay index in the DD domain respectively. For X DD The average power of the data in row u;

[0103] Compared to the OTFS system, the PAPR of the OTFS-IM system changes from being linearly related to N to being linearly related to the number of active symbols per row of the DD domain signal, indicating that the peak-to-average ratio of the index modulation system is lower. Under the same sub-block parameters, the constellation points of 4D modulation are carried by two 2D signals. These 2D signals do not have uniform amplitudes, unlike 2D modulation, which has uniform amplitudes. Therefore, the PAPR of 4D modulation communication systems differs slightly from that of 2D modulation communication systems.

[0104] The present invention also provides an OTFS communication system based on a four-dimensional spherical code, for implementing the OTFS communication method based on a four-dimensional spherical code. The system includes a transmitting end and a receiving end, wherein:

[0105] The transmitting end includes a bit separator, a modulation module, an OTFS frame generator, an ISFFT unit, and a Heisenberg transform unit arranged in sequence; the modulation module includes a plurality of modulation units arranged in parallel, each modulation unit includes an index selector and a four-dimensional modulator, and performs index modulation and four-dimensional spherical code modulation;

[0106] The receiving end includes a Wigner transform unit, a SFFT unit, an equalizer, a sub-block generator, a detection module and a bit integrator which are arranged in sequence. The detection module includes a plurality of detectors which are arranged in parallel.

[0107] Furthermore, the specific working process of the OTFS communication system based on four-dimensional spherical code is as follows:

[0108] At the transmitter, the bit separator groups the DD domain data into multiple sub-blocks. Each sub-block is modulated by index and four-dimensional spherical code through the modulation module. The outputs of all sub-blocks are spliced ​​into an OTFS frame along the Doppler dimension by the OTFS frame generator, and then conventional OTFS modulation is performed. That is, the ISFFT unit performs the inverse symplectic finite Fourier transform, the Heisenberg transform unit performs the Heisenberg transform, and finally the transmit pulse is shaped to obtain the time domain transmit signal s.

[0109] After the time-frequency dual-selection channel, the receiving end performs OTFS demodulation to obtain the DD domain receiving signal Y DD First, the received pulse is shaped, then the Wigner transform unit is used to perform Wigner transform, and the SFFT unit is used to perform symplectic finite Fourier transform to obtain the DD domain received signal Y DD ; Receive signal Y DD After equalization by the equalizer, inter-symbol interference is eliminated and a preliminary detection signal is obtained. The sub-block generator will initially detect the signal It is divided into sub-blocks equal to the number of transmitting ends. The detection module performs ML detection on each sub-block through parallel detectors. The ML detection results of each sub-block are processed by the bit integrator to obtain the final received signal.

[0110] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0111] Example

[0112] The present invention uses four-dimensional spherical code K (4, 16, 67.19°) modulation, constellation matrix C' 4,16 as follows:

[0113]

[0114] In the traditional OTFS-IM system, the total transmission energy of k symbols activated by a sub-block is k. In order to maintain the same transmission energy, the actual amplitude of each constellation point in the OTFS-IM system based on four-dimensional modulation should be That is, the constellation matrix is And the minimum distance between constellation points is Table 1 is an example of the index mapping relationship. In this case, one subblock transmits one four-dimensional constellation point, and the total number of bits, p, is 6. For convenience, the OTFS-IM system based on four-dimensional spherical code modulation is denoted as OTFS-IM4, and the OTFS-IM system using traditional two-dimensional modulation is denoted as OTFS-IM2.

[0115] Table 1 Index lookup table for n=8, k=2

[0116] Bit index Sub-block data 00

[12] <![CDATA[[s1,s2,0,0,0,0,0,0]]]> 01

[34] <![CDATA[[0,0,s1,s2,0,0,0,0]]]> 10

[56] <![CDATA[[0,0,0,0,s1,s2,0,0]]]> 11

[78] <![CDATA[[0,0,0,0,0,0s1,s2]]]>

[0117] Figure 2 The theoretical value and simulation results of the bit error rate of the OTFS-IM system based on four-dimensional spherical code modulation are compared. Since the theoretical value of the average bit error rate derived based on the union bound method needs to traverse the entire signal space, the simulation parameters are specified as follows for ease of solution. The operating frequency and subcarrier spacing of the system are respectively f c =3GHz, Δf=15kHz, OTFS frame size M=4, N=2, delay tap and Doppler tap are [l i ,k i ]={[0,0],[1,1]}, channel coefficient h i ~CN(0,1 / P). At this time, there is exactly one set of sub-blocks in one frame, that is, g=1, p=6, n x= 64. It can be seen that the simulation performance gradually approaches the theoretical approximation as the SNR increases. When the SNR exceeds 15dB, it is almost equal to the theoretical approximation, verifying the correctness of the theoretical approximation of the bit error rate.

[0118] In order to verify the performance of the OTFS-IM system based on four-dimensional spherical codes, Figure 3 The BER performance of the four-dimensional modulation system and the two-dimensional modulation system under two propagation paths is compared. The simulation uses a frame size of M = 64, N = 8, and an operating frequency of f c =3GHz, subcarrier spacing Δf=15kHz. In satellite communication and air-to-ground communication scenarios, the channel is generally modeled as a two-path model. The simulation channel based on the tapped delay line refers to the NTN-TDL series model of the 3GPP standard. The maximum terminal moving speed is 1000km / h, and the maximum delay is about 4us. In order to ensure fairness in comparison, the two-dimensional modulation lookup table selects n=4, k=1 and BPSK modulation. At this time, the lookup table is the same as the four-dimensional modulation, with only 4 mapping options, and the spectral efficiency is SE=3 / 4. Under MMSE equalization, four-dimensional modulation has a gain of about 2dB over two-dimensional modulation. Since MMSE equalization requires matrix inversion and has a high complexity, according to the idea of ​​the MRC detection algorithm, the hard decision is converted into a soft decision, which can be used for the equalization step in the index modulation system. The complexity is low and the performance is improved. For example Figure 3 As shown by the solid line, although the BER performance of MRC equalization is not as good as that of MMSE equalization at low signal-to-noise ratio, when the SNR exceeds 10dB, the performance of MRC equalization gradually exceeds that of MMSE. -4 When using MRC equalization, it has a gain of approximately 2dB over MMSE equalization. When using MRC equalization, a zero-padding OTFS structure is required. This means that the frame structure delay dimension must be padded with zeros greater than the maximum delay. This reduces spectrum utilization and generates additional overhead. Therefore, in actual use, the appropriate equalization method should be selected based on the application scenario. Figure 4 The BER performance diagram of MMSE equalization in EVA channel shows that the performance of four-dimensional modulation is still better than that of two-dimensional modulation.

[0119] In order to analyze the PAPR performance of the OTFS-IM system based on four-dimensional spherical code modulation, Figure 5 The CCDF curves of the four-dimensional modulation system and the traditional two-dimensional modulation system are simulated. Among them, when the frame parameters M = 64 and N = 16, the two-dimensional modulation uses BPSK modulation n = 4 and k = 1, which has the same spectral efficiency as the four-dimensional modulation using n = 8 and k = 2, that is, SE = 3 / 4. The CCDF curve is shown as follows Figure 5As shown in the solid line, it can be seen that the PAPR performance of two-dimensional modulation and four-dimensional modulation is close. When two-dimensional modulation uses BPSK modulation, n = 2, k = 1, it has the same spectral efficiency as four-dimensional modulation using n = 8, k = 4, that is, SE ≈ 1. The CCDF curve is shown in Figure 5 As shown by the dashed line, 4D modulation achieves approximately 0.1dB better PAPR performance than 2D modulation. As analyzed in Step 5 above, when using indexed modulation, there's only a slight difference in PAPR performance between 2D and 4D modulation. Furthermore, PAPR is linearly correlated with the symbol activation ratio k / n in the sub-block. Taking simulation parameters as an example, the PAPR when k / n = 1 / 4 is approximately 3dB lower than when k / n = 1 / 2, which is consistent with the simulation results. Since the sub-block activation ratio determines spectral efficiency, a higher activation ratio results in higher spectral efficiency, and vice versa. Therefore, a trade-off between spectral efficiency and PAPR is necessary during system design.

Claims

1. An OTFS communication method based on four-dimensional spherical codes, characterized in that: The following steps are involved: Step 1: At the transmitter, the DD domain data is grouped into multiple sub-blocks. Each sub-block is index modulated and modulated with a four-dimensional spherical code. The outputs of all sub-blocks form a frame of DD domain signal X. DD ; Step 2: Signal X DD After OTFS modulation, it is transmitted to the receiving end, and the receiving end performs OTFS demodulation to obtain the DD domain receiving signal Y DD ; Step 3: Receive signal Y DD After equalization and elimination of inter-symbol interference, a preliminary detection signal is obtained Step 4: Initial detection signal Divide into sub-blocks equal to the number of transmitting ends, and perform ML detection on each sub-block; Step 5: Determine the average bit error rate approximation and the PAPR upper bound of the communication system based on the mathematical model corresponding to the input-output relationship of OTFS modulation; In step 1, the DD domain data is grouped into multiple sub-blocks, and each sub-block is subjected to index modulation and four-dimensional spherical code modulation, as follows: Step 1.1: Assume that the total number of symbols in a sub-block is n and the number of active symbols is k. Then, an M×N OTFS frame is divided into g=MN / n groups. The transmitted bit stream set u is evenly divided into g groups. Each sub-block transmits p bits of information, where bit p1 is used for index modulation and bit p2 is used for four-dimensional modulation. Step 1.2: Each sub-block is modulated independently, and the M in the unit sphere is taken in the L-dimensional space. c point as the modulation constellation point c i =(c i,1 ,c i,2 ,c i,3 ,c i,4 ), since the constellation point is a four-dimensional vector, two two-dimensional symbols will be used to carry a four-dimensional symbol in system transmission, that is, c i From s1=c i,1 +jc i,2 and s2=c i,3 +jc i,4 Therefore, the number of activated symbols k should be an integer multiple of 2, and the modulation symbol vector of a sub-block is s β =[s β (1),s β (2),…,s β (k)] T , the number of bits used for four-dimensional modulation in the sub-block p2=k / 2log2(M c ); Step 1.3: Select k consecutive and non-repeated symbols from the n data symbols of the sub-block as activation symbols, then the index set I of the β-th sub-block is β is a subset of the lookup table I, where I = {k(i-1)+1, k(i-1)+2, …, k(i-1)+k}, i∈[1, 2, …, n / k], and the number of bits used for index modulation in the subblock is Step 1.4: The total number of bits transmitted in one sub-block is: So the spectral efficiency SE = p / n, the transmitted information X of the βth sub-block β Expressed as: The received signal Y in step 3 DD After equalization and elimination of inter-symbol interference, a preliminary detection signal is obtained The details are as follows: Assuming that the channel information is known at the receiving end, MMSE equalization or MRC equalization is used for equalization; The MMSE equalization is as follows: in is the estimated transmitted signal vector, y is the received signal vector, H is the channel matrix, σ 2 is the noise variance, and the MN×1 pre-estimated transmission vector Rewritten as an M×N matrix, we get MRC equalization is consistent with MRC detection. It converts the hard decision in the MRC detection algorithm into a soft decision. When using MRC equalization, it is necessary to use the zero-padding OTFS structure, that is, the frame structure delay dimension is padded with δ zeros, where δ is greater than the maximum delay. In step 4, the initial detection signal Divide into sub-blocks equal to the number of transmitters, and perform ML detection on each sub-block as follows: According to the rule of forming OTFS frame by sub-blocks in step 1, the estimated transmission signal, i.e. the preliminary detection signal Re-divide into the same number of sub-blocks, use the ML detector to detect each sub-block, and obtain index information and four-dimensional modulation information: in, is the estimated transmission information of the βth sub-block, s β is the modulation symbol of the βth sub-block, β is the index set of the βth sub-block; In step 5, based on the mathematical model corresponding to the input-output relationship of OTFS modulation, the average bit error rate approximation and the PAPR upper bound of the OTFS communication system are determined as follows: When the channel information is known, x is wrongly judged as The conditional matching error probability for: Where Q(·) is the Gaussian Q function, H eff is the equivalent channel matrix in DD domain, N 0,DD is the variance of the noise in the DD domain; After simplified derivation, the unconditional pairing probability is obtained for: Where P is the number of propagation paths, σ 2 is the channel gain h i The variance of i are the eigenvalues ​​of the Hermitian matrix Θ, The details are as follows: is the DD domain transmission signal matrix after the delay and Doppler effect, is the DD domain estimated transmit signal matrix after delay and Doppler influence, is the delay and Doppler influence matrix of the i-th path, F N is the N×N normalized Fourier transform matrix, G rx and G tx are the receiving shaped pulse matrix and the transmitting shaped pulse matrix, is the forward cyclic matrix reflecting the delay impact of the i-th path, is a diagonal matrix reflecting the Doppler effect of the i-th path; The average bit error rate is then approximately: Among them, n x =((M c ) k2 n / k) g is the number of possible cases of transmitting signal x, M c represents the total number of four-dimensional constellation points, n represents the total number of symbols in the sub-block, k represents the number of activated symbols in the sub-block, and g represents the number of sub-blocks contained in an OTFS frame. To misjudge x as The number of error bits when The PAPR upper bound of the system is derived as: Where k and l are the Doppler index and delay index in the DD domain respectively. For X DD The average power of the data in row u.

2. The OTFS communication method based on four-dimensional spherical code according to claim 1, characterized in that: In step 2, the sub-blocks are combined into a frame of DD domain signal X DD , after OTFS modulation, the receiving end performs OTFS demodulation to obtain the DD domain receiving signal Y DD , as follows: After the modulation of each sub-block is completed, it is spliced ​​into an OTFS frame along the Doppler dimension for conventional OTFS modulation, that is, the inverse symplectic finite Fourier transform, Heisenberg transform and transmit pulse shaping are used to obtain the time domain transmit signal s; after passing through the time-frequency dual-selective channel, the receiving end obtains the DD domain receive signal Y through receive pulse shaping, Wigner transform and symplectic finite Fourier transform. DD .

3. An OTFS communication system based on four-dimensional spherical codes, characterized in that: The system is used to implement the OTFS communication method based on four-dimensional spherical codes according to any one of claims 1 to 2, comprising a transmitting end and a receiving end, wherein: The transmitting end includes a bit separator, a modulation module, an OTFS frame generator, an ISFFT unit, and a Heisenberg transform unit arranged in sequence; the modulation module includes a plurality of modulation units arranged in parallel, each modulation unit includes an index selector and a four-dimensional modulator, and performs index modulation and four-dimensional spherical code modulation; The receiving end includes a Wigner transform unit, a SFFT unit, an equalizer, a sub-block generator, a detection module and a bit integrator which are arranged in sequence. The detection module includes a plurality of detectors which are arranged in parallel.

4. The OTFS communication system based on four-dimensional spherical codes according to claim 3, characterized in that: The specific working process of the system is as follows: At the transmitter, the bit separator groups the DD domain data into multiple sub-blocks. Each sub-block is modulated by index and four-dimensional spherical code through the modulation module. The outputs of all sub-blocks are spliced ​​into an OTFS frame along the Doppler dimension by the OTFS frame generator, and then conventional OTFS modulation is performed. That is, the ISFFT unit performs the inverse symplectic finite Fourier transform, the Heisenberg transform unit performs the Heisenberg transform, and finally the transmit pulse is shaped to obtain the time domain transmit signal s. After the time-frequency dual-selection channel, the receiving end performs OTFS demodulation to obtain the DD domain receiving signal Y DD First, the received pulse is shaped, then the Wigner transform unit is used to perform Wigner transform, and the SFFT unit is used to perform symplectic finite Fourier transform to obtain the DD domain received signal Y DD ; Receive signal Y DD After equalization by the equalizer, inter-symbol interference is eliminated and a preliminary detection signal is obtained. The sub-block generator will initially detect the signal It is divided into sub-blocks equal to the number of transmitting ends. The detection module performs ML detection on each sub-block through parallel detectors. The ML detection results of each sub-block are processed by the bit integrator to obtain the final received signal.

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