Intelligent reflection surface auxiliary simulation radio frequency division multiplexing modulation system in high-speed mobile environment

Abstract

The invention discloses an intelligent reflection surface (RIS)-assisted AFDM (Amplified Frequency Division Multiplexing) simulation modulation system in a high-speed moving environment, and relates to the field of radio frequency division multiplexing (AFDM) simulation modulation systems. The intelligent reflection surface (RIS)-assisted AFDM simulation modulation system in the high-speed moving environment can be applied to the field of radio frequency division multiplexing (AFDM) simulation modulation of the high-speed moving environment and the high-speed moving environment of the high-speed moving environment and the high-speed moving environment of the high-speed moving environment and the high-speed moving environment of the high-speed moving environment. In the system, the RIS is firstly used as relay auxiliary information transmission from an AFDM transmitting end to a receiving end, and the multipath diversity gain of the system is increased. As a multipath effect and Doppler frequency shift interference exist in high-speed mobile communication, an output solution of an AFDM demodulation end on a discrete affine Fourier domain is solved by constructing a delay Doppler cascade channel of the RIS, and a reflection phase of the RIS is optimized according to the formula, so that the power of a received signal is maximized. As the reflection optimization problem of the RIS under the multipath channel is a non-convex form, the problem can be solved by using a traditional method to cause relatively high complexity. According to the method, the MF-STC method based on norm maximization is provided by deducing the upper limit of the maximization problem to solve the suboptimal solution, and compared with a random phase method, it is verified that the MF-STC method can remarkably reduce the bit error rate of the RIS-AFDM system. Simulation results show that compared with a traditional RIS-assisted orthogonal frequency division multiplexing system, the system scheme provided by the invention can obtain better bit error rate performance.

Description

Technical Field

[0001] The present invention relates to the field of communication technology, in particular to multi-carrier modulation, RIS-assisted MIMO system, and RIS phase design, and specifically to an intelligent reflective surface-assisted radio frequency division multiplexing modulation system in a high-speed mobile environment. Background Art

[0002] The next generation of wireless systems and standards are expected to meet the needs of ultra-reliable, high data rate, and low-latency communications in high-mobility scenarios. However, under high-mobility conditions, Doppler shift and multipath effects will inevitably occur, causing the channel characteristics to change over time. This time-varying nature of the channel poses a challenge to the current mainstream orthogonal frequency division multiplexing (OFDM). In time-varying channels, Doppler shift can cause significant inter-carrier interference in OFDM, which seriously affects its performance. Therefore, in order to meet communication needs, new modulation techniques and waveforms are needed that can have good robustness in high-mobility scenarios.

[0003] In order to combat dual-dispersion channels, researchers have developed several new modulation techniques, including Orthogonal Chirp Division Multiplexing (OCDM) and Orthogonal Time Frequency Space (OTFS). OCDM uses a series of frequency-modulated signals that change frequency linearly over time to help transmit information. It performs better than OFDM in time-varying channels, but its diversity order is affected by the channel delay Doppler and therefore cannot achieve the optimal diversity order. OTFS can convert time-varying channels into quasi-time-invariant channels in the Delay-Doppler (DD) domain by modulating information in the DD domain. The superiority of OTFS in dual-selective channels has been demonstrated in many works. However, OTFS is a two-dimensional modulation technique, and its pilot symbols used for channel estimation will generate high pilot overhead after being spread in the DD domain.

[0004] Based on the above background, A.Bemani et al. proposed a new multi-carrier waveform based on linear frequency modulation pulses, called Affine Frequency Division Multiplexing (AFDM). AFDM is based on Discrete Affine Fourier Transform (DAFT), which is a generalized form of Fourier transform. DAFT has two parameters, namely the pre-linear frequency modulation parameter and the post-linear frequency modulation parameter, which can handle dual-dispersion channels by modulating these two parameters. In AFDM, data symbols are multiplexed onto a set of orthogonal linear frequency modulation subcarriers through DAFT, thereby converting the dual-dispersion channel into a sparse quasi-static channel in the discrete affine Fourier domain. By appropriately adjusting the linear frequency modulation parameters, AFDM can achieve full diversity of linear time-varying (LTV) channels. This means that in high-mobility communication scenarios, AFDM may be a promising alternative to OFDM, and the one-dimensional transform of AFDM is less complex than OTFS.

[0005] There are some studies on AFDM technology, including channel estimation, index modulation on different domains of AFDM, multiple access of AFDM, and synaesthesia integration based on AFDM. First, H. Yin et al. proposed a novel AFDM channel estimation scheme, which improved the spectrum efficiency by introducing superimposed pilots in the DAF domain, and developed an effective pilot placement method to minimize the channel estimation error. Subsequently, the diagonal reconfigurability of the AFDM subchannel matrix was studied, and a low-complexity embedded pilot-assisted diagonal reconstruction channel estimation scheme was proposed, which essentially eliminated the serious inter-Doppler interference. In order to improve the bit error rate and energy efficiency performance, J. Zhu et al. combined AFDM with index modulation (IM) and proposed a new AFDM-IM scheme, which transmits additional energy-free information bits through the activation mode of subcarriers in the DAF domain. Different from the previous scheme, G.Liu et al. proposed another AFDM-PIM scheme, which focuses on the linear frequency modulation parameters of AFDM and transmits additional information bits by indexing different parameters c2, indicating the potential of AFDM-PIM system in improving bit error rate performance and energy efficiency. In terms of multiple access, Q.Luo studied AFDM-based sparse code division multiple access system to support large-scale connections in high mobility environments. Y.Ni et al. extended their research to AFDM-based integrated sensing and communication (ISAC), proposed AFDM-ISAC system, and proved that the system can maintain excellent sensing performance under large Doppler frequency shift.

[0006] In addition, RIS, as an emerging wireless communication technology in recent years, is composed of a large number of reflection units. These reflection units can be configured individually according to different channel conditions, and the signal strength of the reflected signal in the direction of the receiving end can be enhanced by changing the phase and amplitude of the incident signal at the transmitting end, thereby obtaining a significant signal-to-noise ratio gain (SNR). At present, research based on RIS has expanded to multiple fields, including RIS and index modulation, RIS and multiple access, RIS and wireless energy-carrying communication, and the combination of RIS and multi-carrier modulation waveforms such as OFDM and OTFS. Among them, the work of B.Zheng et al. is specifically aimed at RIS-OFDM systems, and two channel estimation techniques and RIS phase optimization techniques are proposed. Y.Huang et al. proposed a novel RIS-assisted OFDM wireless communication system based on maximum distance separable codes. AS Bora et al. applied RIS to a high-mobility environment and proposed a multi-input multi-output RIS-assisted OTFS communication system with MMSE detection function, which verified that the bit error rate is significantly reduced compared with the RIS-assisted OFDM system for terrestrial and non-terrestrial high-Doppler communications. Summary of the invention

[0007] In view of the defects existing in the above-mentioned background technology, the present invention provides an intelligent reflective surface assisted affine Fourier transform (AFFT) radio frequency division multiplexing (RFDM) modulation system based on discrete affine Fourier transform (DFT) and the strongest tap coefficient RIS optimization method based on norm maximization.

[0008] The present invention is implemented by the following technical solutions:

[0009] 1. A Reconfigurable Intelligent Surface (RIS) assisted Affine Frequency Division Multiplexing (AFDM) modulation system in a high-speed mobile environment, characterized in that the method comprises the following steps:

[0010] 1) Deploy an AFDM modulator at the transmitter (T) and an AFDM demodulator at the receiver (R) to build modulation and demodulation of AFDM signals;

[0011] 2) Deploy RIS between the T-end and the R-end, and complete the cascade channel modeling from the T-end to the RIS and then to the R-end under the dual-dispersion channel;

[0012] 3) Derive the output signal of the RIS-AFDM system from the perspective of the Discrete Affine Fourier Transform (DAFT) on which AFDM is based;

[0013] 4) Model the phase shift optimization problem of RIS and complete the reflection phase design of RIS;

[0014] 2. The method according to claim 1, characterized in that the specific method described in step 1) is:

[0015] 1.1) At the AFDM modulation end, let is a PSK modulation symbol vector in the DAF domain, x[m] is one of its elements, and m represents the index of the DAF domain. The modulation operation is to convert the signal from the DAF domain to the transmission signal in the time domain through an N-point inverse discrete affine Fourier transform (IDAFT). The specific expression is:

[0016]

[0017] Where s = [s[0], s[1], ..., s[N-1]] is the time domain signal, n = 0, ..., N-1, c1 and c2 are DAFT parameters. The above transformation can be written in matrix form as:

[0018]

[0019] Where A is the DAFT matrix, A H represents the conjugate transpose of matrix A, F is the N-point normalized discrete Fourier transform matrix, and its elements are Before sending the signal s, AFDM also needs to add a prefix to combat the multipath effect. However, unlike the cyclic prefix (CP) of OFDM, since the signal in the DAF domain of AFDM is periodic, a chirp-periodic prefix (CPP) is used instead of CP, with a length of L. CP The CPP formula is given by:

[0020]

[0021] 1.2) At the AFDM demodulation end, assuming that the received time domain sample is r(n), demodulation requires a discrete affine Fourier transform to convert the time domain signal into an output symbol in the DAF domain, expressed as:

[0022]

[0023] in,

[0024] 3. The method according to claim 1, characterized in that the specific method described in step 2) is:

[0025] 2.1)RIS-assisted AFDM system deploys RIS-assisted information transmission between the AFDM transmitter and the AFDM receiver. The RIS has U reflection units, and the reflection coefficient of the u-th reflection unit is defined as u=1,2,···U. Among them, β u ∈[0,1],θ u ∈[0,2π) represent the reflection amplitude and reflection phase respectively. In order to maximize the reflection power of each RIS unit, the amplitude β of each reflection element is set u =1. Due to the characteristics of high-speed mobile scenarios, the channel between the transmitter and each RIS element is a time-varying channel (also called a dual-dispersion channel or a dual-selection channel), and the channel between each RIS element and the receiver is also a time-varying channel. Under the time-varying channel, the channel contains multiple paths with time delay and Doppler shift parameters, and the path parameters of the time-varying channel passing through each RIS element are different.

[0026] 2.2) The present invention is based on The impulse response of the total reflection channel from the transmitter to the RIS and then to the receiver at time n and delay l is expressed as:

[0027]

[0028] Where δ(·) is the Dirac function, P1 and P2 are the number of paths from the transmitter to the u-th unit of RIS and from the u-th unit of RIS to the receiver, respectively. u,i and h u,j are the complex channel gains of the i-th path from the transmitter to the u-th unit of RIS and the j-th path from the u-th unit to the receiver, respectively, and they obey the distribution and and is the integer delay of path i and path j, respectively, and the maximum delay and Take the path i passing through the u-th RIS unit as an example, is relative to the subcarrier spacing Δ f Normalized Doppler shift, where α u,i ∈[-α max ,α max ] is the integer part, and the fractional part a is assumed to be zero in this paper.

[0029] Then the channels on both sides of each RIS unit are cascaded, and the channel response pulse expression after cascading is:

[0030]

[0031] For each path of each transmitter-RIS-receiver cascade channel, where the Doppler shift is f u,ij =f u,i +f u,j , the delay is l u,ij = l u,i +l u,j , the effective DD channel gain is h u,ij =h u,i h u,j .

[0032] 2.3) The matrix of each link is expressed in matrix form below. The cascade channel matrix from the transmitter through the u-th RIS unit to the receiver is:

[0033]

[0034] in in is the channel matrix from the transmitter to the u-th RIS unit, is the channel matrix from the uth unit to the receiving end. u For example, So l u,ij is the forward cyclic shift matrix of the shift number, and the Doppler frequency shift matrix is is an N×N diagonal matrix, expressed as:

[0035]

[0036] Where n = 0, 1, ..., N-1. The final total cascade channel matrix is ​​constructed as

[0037] 4. The method according to claim 1, characterized in that the specific method described in step 3) is:

[0038] 3.1) The signal s(n) in formula (1) in step 1) is the transmitted signal that completes AFDM modulation. After the transmitted signal is transmitted through the reflection channel of RIS, the time domain signal obtained by the receiving end is:

[0039]

[0040] in is additive Gaussian white noise, which obeys a complex Gaussian distribution with a mean of 0 and a variance of N0. It can be written in matrix form as:

[0041]

[0042] in Indicates that the mean is 0 and the covariance is N0I N The noise matrix, I N is an N×N unit matrix. After DAFT transformation of the time domain received signal, the output signal at the AFDM demodulation end is:

[0043]

[0044] in, is the effective channel matrix in DAF domain, For the detection of constellation symbols, the present invention uses a minimum mean square error (MMSE) detector based on the channel matrix for detection, which is expressed as:

[0045]

[0046] 3.2) In order to establish a further input-output relationship, the present invention superimposes the paths in each RIS unit channel in the Delay-Doppler (DD) channel, and obtains P as the total number of taps in the superimposed DD channel. Each tap p represents a group of delay Dopplers, and the same delay Doppler may contain multiple paths. The coefficient of tap p is the sum of the coefficients of these paths. The range of P is between the number of paths P1 and UP1P2 and is much smaller than N. Formula (11) can be simplified as:

[0047]

[0048] in, is the effective channel matrix of each RIS unit under single tap. According to the single tap effective channel matrix characteristics of AFDM, There is only one non-zero element in each row and column of , and the position of the column where the non-zero element is located has a corresponding relationship with the position of the row. Specifically, the channel matrix No. The non-zero elements in the row and column m It can be expressed as:

[0049]

[0050] in, Therefore, the input-output relationship between the initial PSK modulation symbol and the final output symbol in the DAF domain is constructed as follows:

[0051]

[0052] 5. The method according to claim 1, characterized in that the specific method described in step 4) is:

[0053] Due to the existence of multipath in the double-dispersion channel, RIS cannot perfectly phase-cancel all paths, so a set of RIS phases can be found to maximize the signal-to-noise ratio at the receiving end. The optimization problem of RIS phase shift in the single-input single-output (SISO) case can be modeled as:

[0054]

[0055] Where P t Set to unit transmit power. Considering the complexity of this non-convex optimization problem, in order to simplify the problem, this method first derives the upper limit of equation (22), and then proposes a RIS-AFDM system optimization method that maximizes this upper limit, called the Strongest Tap Coefficient (SPT). First, the problem is decomposed into the phase design problem for each RIS unit:

[0056]

[0057] Substituting into the channel matrix expression, the problem can be restated as:

[0058]

[0059] According to formula (13) in step 3), the above formula can be simplified to:

[0060]

[0061] The corresponding upper limit is:

[0062]

[0063] In order to achieve the best diversity order of AFDM, it is set to c1=(2α max +1) / 2N, and N is an even number in this paper, so For the unit array. For a circulant matrix, the norm size is not affected. After substituting the expression into , the optimization problem becomes:

[0064]

[0065] Therefore, we can consider searching for the strongest path tap in the superimposed DD domain channel. The phase of the RIS is then configured according to the phase of this tap coefficient. By adding and comparing the complex gains corresponding to each tap in different RIS unit channels, the strongest tap can be expressed as:

[0066]

[0067] The phase of each RIS unit is then adjusted to be opposite to the phase of the cascade path corresponding to the strongest tap in the unit channel:

[0068]

[0069] After adjusting the RIS phase, the input-output relationship of equation (15) in step 3) becomes:

[0070]

[0071] However, we find that for some RIS units, the cascade channel matrix H u , which may not contain the strongest tap The corresponding delay-Doppler combination. At this time, the taps in the cascaded channels of these RIS units The corresponding channel coefficient is 0, so the phase This situation is more obvious when the number of RIS units increases. In order to maximize the role of RIS and further improve the signal-to-noise ratio of the receiving end, this paper proposes the MF-SPT method based on the above method. Assume that after the path phase corresponding to the strongest tap in each RIS unit channel matrix is ​​offset, the phase of the remaining L RIS units is zero θ u =0 (u=1,...,L). For these zero values, random Q groups of phase vectors are given, each group contains L phase factors, where the phase of the qth group can be expressed as:

[0072]

[0073] And select a set of phases Φ that maximizes the channel Frobenius norm m To replace these zero values, it can be expressed as:

[0074]

[0075] Finally, the L phases are set to u=1,...,L.

[0076] The inventive principle of the present invention is:

[0077] In order to improve the reliability of the communication system in a high-speed mobile environment, on the one hand, the AFDM modulation technology is used to modulate and demodulate information in the DAF domain. By constructing a dual-dispersion cascade channel of RIS, the output solution of the AFDM demodulation end in the DAF domain is obtained, and the channel impulse response of the entire DAF domain is used to distinguish the paths of different delay Doppler parameters. On the other hand, for the reflection coefficient of RIS, the strongest tap is first searched in the superimposed delay Doppler channel, the phase of all RIS is configured according to the phase of this tap coefficient, and then the RIS unit with a phase of 0 is re-optimized to maximize the channel Frobenius norm, thereby maximizing the signal-to-noise ratio at the receiving end.

[0078] The advantages and beneficial effects of the present invention are:

[0079] The present invention proposes an intelligent reflective surface-assisted affine frequency division multiplexing modulation system in a high-speed mobile environment. The designed RIS-AFDM communication system uses discrete affine Fourier transform to modulate data symbols in the DAF domain, so that information symbols are multiplexed in the entire DAF domain, and each symbol experiences all resolvable paths, thereby combating delay Doppler interference in a dual-dispersion channel. In addition, a method for optimizing the strongest tap coefficients based on norm maximization is proposed to complete the RIS phase design while maintaining low complexity, improve the signal receiving power, and enhance the robustness of the RIS-AFDM system in a high Doppler environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] Figure 1 It is a schematic diagram of a smart reflective surface assisted radio frequency division multiplexing modulation system proposed in the present invention;

[0081] Figure 2 The BER performance comparison of the RIS-AFDM system proposed in the present invention using two RIS phase shift design methods and a random phase method under a dual dispersion channel is presented;

[0082] Figure 3 The BER performance of the RIS-AFDM system with different numbers of RIS units proposed by the present invention and the comparison with the single AFDM system;

[0083] Figure 4 It is a comparison of the BER performance of the RIS-AFDM system and the traditional RIS-OFDM system under different numbers of RIS units proposed by the present invention;

[0084] Figure 5 It is the BER performance of the RIS-AFDM system under different numbers of paths and considering the direct channel according to the present invention;

[0085] Figure 6The figure is a comparison of the BER performance of the RIS-AFDM system under different numbers of antennas proposed by the present invention. DETAILED DESCRIPTION

[0086] like Figure 1 The invention proposes an intelligent reflective surface assisted affine Fourier transform modulation system in a high-speed mobile environment. The modulation and demodulation of the AFDM in the system are realized by forward / inverse discrete affine Fourier transform, and RIS auxiliary information transmission is deployed between the transmitting end and the receiving end. The RIS has U reflection units, and the reflection coefficient of the uth reflection unit is defined as u=1,2,···U. Among them, β u ∈[0,1],θ u ∈[0,2π) represent the reflection amplitude and reflection phase respectively. In order to maximize the reflection power of each RIS unit, the amplitude β of each reflection element is set u = 1. Considering the dynamic time-varying property of the channel, the channel between each RIS element and the transmitting end or the receiving end is set as a time-varying channel, and the path parameters of the time-varying channel passing through each RIS element are different.

[0087] The present application proposes a Reconfigurable Intelligent Surface (RIS) assisted Affine Frequency Division Multiplexing (AFDM) modulation system in a high-speed mobile environment, characterized in that the method comprises the following steps:

[0088] 1) Deploy an AFDM modulator at the transmitter (T) and an AFDM demodulator at the receiver (R) to build modulation and demodulation of AFDM signals;

[0089] 2) Deploy RIS between the T-end and the R-end, and complete the cascade channel modeling from the T-end to the RIS and then to the R-end under the dual-dispersion channel;

[0090] 3) Derive the output signal of the RIS-AFDM system from the perspective of the Discrete Affine Fourier Transform (DAFT) on which AFDM is based;

[0091] 4) Model the phase shift optimization problem of RIS and complete the reflection phase design of RIS;

[0092] 2. The method according to claim 1, characterized in that the specific method described in step 1) is:

[0093] 1.1) At the AFDM modulation end, let is a PSK modulation symbol vector in the DAF domain, x[m] is one of its elements, and m represents the index of the DAF domain. The modulation operation is to convert the signal from the DAF domain to the transmission signal in the time domain through an N-point inverse discrete affine Fourier transform (IDAFT). The specific expression is:

[0094]

[0095] Where s = [s[0], s[1], ..., s[N-1]] is the time domain signal, n = 0, ..., N-1, c1 and c2 are DAFT parameters. The above transformation can be written in matrix form as:

[0096]

[0097] Where A is the DAFT matrix, A H represents the conjugate transpose of matrix A, F is the N-point normalized discrete Fourier transform matrix, and its elements are Before sending the signal s, AFDM also needs to add a prefix to combat the multipath effect. However, unlike the cyclic prefix (CP) of OFDM, since the signal in the DAF domain of AFDM is periodic, a chirp-periodic prefix (CPP) is used instead of CP, with a length of L. CP The CPP formula is given by:

[0098]

[0099] 1.2) At the AFDM demodulation end, assuming that the received time domain sample is r(n), demodulation requires a discrete affine Fourier transform to convert the time domain signal into an output symbol in the DAF domain, expressed as:

[0100]

[0101] in,

[0102] 3. The method according to claim 1, characterized in that the specific method described in step 2) is:

[0103] 2.1)RIS-assisted AFDM system deploys RIS-assisted information transmission between the AFDM transmitter and the AFDM receiver. The RIS has U reflection units, and the reflection coefficient of the u-th reflection unit is defined as u=1,2,···U. Among them, βu ∈[0,1],θ u ∈[0,2π) represent the reflection amplitude and reflection phase respectively. In order to maximize the reflection power of each RIS unit, the amplitude β of each reflection element is set u =1. Due to the characteristics of high-speed mobile scenarios, the channel between the transmitter and each RIS element is a time-varying channel (also called a dual-dispersion channel or a dual-selection channel), and the channel between each RIS element and the receiver is also a time-varying channel. Under the time-varying channel, the channel contains multiple paths with time delay and Doppler shift parameters, and the path parameters of the time-varying channel passing through each RIS element are different.

[0104] 2.2) The present invention is based on The impulse response of the total reflection channel from the transmitter to the RIS and then to the receiver at time n and delay l is expressed as:

[0105]

[0106] Where δ(·) is the Dirac function, P1 and P2 are the number of paths from the transmitter to the u-th unit of RIS and from the u-th unit of RIS to the receiver, respectively. u,i and h u,j are the complex channel gains of the i-th path from the transmitter to the u-th unit of RIS and the j-th path from the u-th unit to the receiver, respectively, and they obey the distribution and and is the integer delay of path i and path j, respectively, and the maximum delay and Take the path i passing through the u-th RIS unit as an example, is relative to the subcarrier spacing Δ f Normalized Doppler shift, where α u,i ∈[-α max ,α max ] is the integer part, and the fractional part a is assumed to be zero in this paper.

[0107] Then the channels on both sides of each RIS unit are cascaded, and the channel response pulse expression after cascading is:

[0108]

[0109] For each path of each transmitter-RIS-receiver cascade channel, where the Doppler shift is f u,ij =f u,i +f u,j , the delay is l u,ij = l u,i +l u,j, the effective DD channel gain is h u,ij =h u,i h u,j .

[0110] 2.3) The matrix of each link is expressed in matrix form below. The cascade channel matrix from the transmitter through the u-th RIS unit to the receiver is:

[0111]

[0112] in in is the channel matrix from the transmitter to the u-th RIS unit, is the channel matrix from the uth unit to the receiving end. u For example, So l u,ij is the forward cyclic shift matrix of the shift number, and the Doppler frequency shift matrix is is an N×N diagonal matrix, expressed as:

[0113]

[0114] Where n = 0, 1, ..., N-1. The final total cascade channel matrix is ​​constructed as

[0115] 4. The method according to claim 1, characterized in that the specific method described in step 3) is:

[0116] 3.1) The signal s(n) in formula (1) in step 1) is the transmitted signal that completes AFDM modulation. After the transmitted signal is transmitted through the reflection channel of RIS, the time domain signal obtained by the receiving end is:

[0117]

[0118] in is additive Gaussian white noise, which obeys a complex Gaussian distribution with a mean of 0 and a variance of N0. It can be written in matrix form as:

[0119]

[0120] in Indicates that the mean is 0 and the covariance is N0I N The noise matrix, I N is an N×N unit matrix. After DAFT transformation of the time domain received signal, the output signal at the AFDM demodulation end is:

[0121]

[0122] in, is the effective channel matrix in DAF domain, For the detection of constellation symbols, the present invention uses a minimum mean square error (MMSE) detector based on the channel matrix for detection, which is expressed as:

[0123]

[0124] 3.2) In order to establish a further input-output relationship, the present invention superimposes the paths in each RIS unit channel in the Delay-Doppler (DD) channel, and obtains P as the total number of taps in the superimposed DD channel. Each tap p represents a group of delay Dopplers, and the same delay Doppler may contain multiple paths. The coefficient of tap p is the sum of the coefficients of these paths. The range of P is between the number of paths P1 and UP1P2 and is much smaller than N. Formula (11) can be simplified as:

[0125]

[0126] in, is the effective channel matrix of each RIS unit under single tap. According to the single tap effective channel matrix characteristics of AFDM, There is only one non-zero element in each row and column of , and the position of the column where the non-zero element is located has a corresponding relationship with the position of the row. Specifically, the channel matrix No. The non-zero elements in the row and column m It can be expressed as:

[0127]

[0128] in, Therefore, the input-output relationship between the initial PSK modulation symbol and the final output symbol in the DAF domain is constructed as follows:

[0129]

[0130] 5. The method according to claim 1, characterized in that the specific method described in step 4) is:

[0131] Due to the existence of multipath in the double-dispersion channel, RIS cannot perfectly phase-cancel all paths, so a set of RIS phases can be found to maximize the signal-to-noise ratio at the receiving end. The optimization problem of RIS phase shift in the single-input single-output (SISO) case can be modeled as:

[0132]

[0133] Where P tSet to unit transmit power. Considering the complexity of this non-convex optimization problem, in order to simplify the problem, this method first derives the upper limit of equation (22), and then proposes a RIS-AFDM system optimization method that maximizes this upper limit, called the Strongest Tap Coefficient (SPT). First, the problem is decomposed into the phase design problem for each RIS unit:

[0134]

[0135] Substituting into the channel matrix expression, the problem can be restated as:

[0136]

[0137] According to formula (13) in step 3), the above formula can be simplified to:

[0138]

[0139] The corresponding upper limit is:

[0140]

[0141] In order to achieve the best diversity order of AFDM, it is set to c1=(2α max +1) / 2N, and N is an even number in this paper, so is a unit matrix. For a circulant matrix, the norm size is not affected. After substituting the expression into , the optimization problem becomes:

[0142]

[0143] Therefore, we can consider searching for the strongest path tap in the superimposed DD domain channel. The phase of the RIS is then configured according to the phase of this tap coefficient. By adding and comparing the complex gains corresponding to each tap in different RIS unit channels, the strongest tap can be expressed as:

[0144]

[0145] The phase of each RIS unit is then adjusted to be opposite to the phase of the cascade path corresponding to the strongest tap in the unit channel:

[0146]

[0147] After adjusting the RIS phase, the input-output relationship of equation (15) in step 3) becomes:

[0148]

[0149] However, we find that for some RIS units, the cascade channel matrix H u , which may not contain the strongest tap The corresponding delay-Doppler combination. At this time, the taps in the cascaded channels of these RIS units The corresponding channel coefficient is 0, so the phase This situation is more obvious when the number of RIS units increases. In order to maximize the role of RIS and further improve the signal-to-noise ratio of the receiving end, this paper proposes the MF-SPT method based on the above method. Assume that after the path phase corresponding to the strongest tap in each RIS unit channel matrix is ​​offset, the phase of the remaining L RIS units is zero θ u =0 (u=1,...,L). For these zero values, random Q groups of phase vectors are given, each group contains L phase factors, where the phase of the qth group can be expressed as:

[0150]

[0151] And select a set of phases Φ that maximizes the channel Frobenius norm m To replace these zero values, it can be expressed as:

[0152]

[0153] Finally, the L phases are set to

[0154] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0155] Figure 2 The BER performance of the RIS-AFDM system using two RIS phase shift design methods and the random phase method in a double dispersion channel is compared. In the parameter setting, unless otherwise specified, we set the carrier frequency of the AFDM system to f c =4GHZ, the sub-symbol interval in the DAF domain is set to f s =1KHZ, number of subcarriers N = 32, maximum normalized Doppler shift α max =2, the Doppler shifts of all paths are generated using the Jakes formula, which are and where θ u,i and θ u,j are evenly distributed in [-π,π]. In this figure, the number of cascade paths passing through each RIS unit is P1P2=2×2=4, and the maximum delay of path P1 Maximum delay of path P2 Through simulation, it is found that the MF-STC method has better bit error rate performance than the STC method, and this improvement becomes more and more obvious as the signal-to-noise ratio increases. At the same time, both are better than the random phase method. Moreover, as the number of RIS units U increases, the performance gap between the system using the two phase optimization methods and the system using the random optimization method becomes larger and larger.

[0156] Figure 3 The BER performance of the RIS-AFDM system with different numbers of RIS units is compared with that of the traditional AFDM system. Figure 2 In the AFDM system without RIS, the number of subcarriers N = 32, the number of paths P0 = 2, and the channel coefficient is Maximum delay of the path It can be found that the BER performance of the RIS-assisted AFDM system is much better than that of the single AFDM system, and the BER performance of the RIS-AFDM system improves with the increase of the number of RIS units.

[0157] exist Figure 4 In the parameter setting, the number of cascade paths passing through each RIS unit is P1P2 = 2 × 4 = 8, and the maximum delay of path P1 is Maximum delay of path P2 For the RIS-OFDM scheme, we use the same dual-dispersion channel condition and also set the number of subcarriers to 32. Under the above conditions, we compare the bit error rate performance of RIS-AFDM and traditional RIS-OFDM. The simulation shows that the BER performance of the RIS-AFDM system under dual-selection channels is significantly better than that of the RIS-OFDM system. This is because the AFDM system, due to its inherent advantages, can achieve full diversity of the LTV channel by reasonably setting the c1 and c2 parameters, while OFDM cannot separate different delay Doppler paths.

[0158] exist Figure 5 In this paper, we changed the number of multipaths in the RIS-receiver channel and added simulations under direct link to analyze the BER performance of the RIS-AFDM system under different channel conditions. The total number of multipaths in the channel is P = P d +P1P2, where P d is the number of multipaths in the direct link from the base station to the user, and P1P2 is the number of cascade paths from the transmitter-RIS-receiver. When P1P2 = 4, When P1P2=16,

[0159] Maximum delay of direct link Here we take the number of RISs U = 4, and we can see that, with the same number of RISs, the BER performance of the RIS-AFDM system improves as the number of system multipaths increases. And for a fixed number of multipaths, the BER performance of the RIS-AFDM system with direct links is better than that of the RIS-AFDM system without direct links.

[0160] Figure 6 The RIS-AFDM system is simulated with different numbers of antennas. The number of cascade paths from each transmitting antenna to each receiving antenna through RIS is P1P2 = 2×4. The number of RIS units is set to U=8. Through simulation, we compared the bit error rate performance of the RIS-AFDM system under four different numbers of antennas. It can be found that, under the same other conditions, the more antennas there are, the better the BER performance of the RIS-AFDM system. In addition, when the number of transmitting antennas remains unchanged and the number of receiving antennas increases, the BER performance of the system will increase significantly. This is because the increase in the number of receiving antennas brings additional spatial diversity gain and enhances the signal detection capability.

[0161] The specific 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 above embodiments. Those skilled in the art may make various modifications or alterations without departing from the spirit and scope of the claims of the present application.

Claims

1. A Reconfigurable Intelligent Surface (RIS) assisted Affine Frequency Division Multiplexing (AFDM) modulation system in a high-speed mobile environment, characterized in that: The method comprises the following steps: 1) Deploy an AFDM modulator at the transmitter (T) and an AFDM demodulator at the receiver (R) to build modulation and demodulation of AFDM signals; 2) Deploy RIS between the T-end and the R-end, and complete the cascade channel modeling from the T-end to the RIS and then to the R-end under the dual-dispersion channel; 3) Derive the output signal of the RIS-AFDM system from the perspective of the Discrete Affine Fourier Transform (DAFT) on which AFDM is based; 4) Model the phase shift optimization problem of RIS and complete the reflection phase design of RIS.

2. The method according to claim 1, characterized in that The specific method described in step 1) is: 1.1) At the AFDM modulation end, let is a PSK modulation symbol vector in the DAF domain, x[m] is one of its elements, and m represents the index of the DAF domain. The modulation operation is to convert the signal from the DAF domain to the transmission signal in the time domain through an N-point inverse discrete affine Fourier transform (IDAFT). The specific expression is: Where s = [s[0], s[1], ..., s[N-1]] is the time domain signal, n = 0, ..., N-1, c1 and c2 are DAFT parameters. The above transformation can be written in matrix form as: Where A is the DAFT matrix, A H represents the conjugate transpose of matrix A, F is the N-point normalized discrete Fourier transform matrix, and its elements are Before sending the signal s, AFDM also needs to add a prefix to combat the multipath effect. However, unlike the cyclic prefix (CP) of OFDM, since the signal in the DAF domain of AFDM is periodic, a chirp-periodic prefix (CPP) is used instead of CP, with a length of L. CP The CPP formula is given by: 1.2) At the AFDM demodulation end, assuming that the received time domain sample is r(n), demodulation requires a discrete affine Fourier transform to convert the time domain signal into an output symbol in the DAF domain, expressed as: in, 3. The method according to claim 1, characterized in that The specific method described in step 2) is: 2.1)RIS-assisted AFDM system deploys RIS-assisted information transmission between the AFDM transmitter and the AFDM receiver. The RIS has U reflection units, and the reflection coefficient of the u-th reflection unit is defined as where β u ∈[0,1],θ u ∈[0,2π) represent the reflection amplitude and reflection phase respectively. In order to maximize the reflection power of each RIS unit, the amplitude β of each reflection element is set u =1. Due to the characteristics of high-speed mobile scenarios, the channel between the transmitter and each RIS element is a time-varying channel (also called a dual-dispersion channel or a dual-selection channel), and the channel between each RIS element and the receiver is also a time-varying channel. Under the time-varying channel, the channel contains multiple paths with time delay and Doppler shift parameters, and the path parameters of the time-varying channel passing through each RIS element are different. 2.2) The present invention is based on The impulse response of the total reflection channel from the transmitter to the RIS and then to the receiver at time n and delay l is expressed as: Where δ(·) is the Dirac function, P1 and P2 are the number of paths from the transmitter to the u-th unit of RIS and from the u-th unit of RIS to the receiver, respectively. u,i and h u,j are the complex channel gains of the i-th path from the transmitter to the u-th unit of RIS and the j-th path from the u-th unit to the receiver, respectively, and they obey the distribution and and is the integer delay of path i and path j, respectively, and the maximum delay and Take the path i passing through the u-th RIS unit as an example, is relative to the subcarrier spacing Δ f Normalized Doppler shift, where α u,i ∈[-α max ,α max ] is the integer part, and the fractional part a is assumed to be zero in this paper. Then the channels on both sides of each RIS unit are cascaded, and the channel response pulse expression after cascading is: For each path of each transmitter-RIS-receiver cascade channel, where the Doppler shift is f u,ij =f u,i +f u,j , the delay is l u,ij = l u,i +l u,j , the effective DD channel gain is h u,ij =h u,i h u,j . 2.3) The matrix of each link is expressed in matrix form below. The cascade channel matrix from the transmitter through the u-th RIS unit to the receiver is: in in is the channel matrix from the transmitter to the u-th RIS unit, is the channel matrix from the uth unit to the receiving end. u For example, So l u,ij is the forward cyclic shift matrix of the shift number, and the Doppler frequency shift matrix is is an N×N diagonal matrix, expressed as: Where n = 0, 1, ..., N-1. The final total cascade channel matrix is ​​constructed as 4. The method according to claim 1, characterized in that: The specific method described in step 3) is: 3.1) The signal s(n) in formula (1) in step 1) is the transmitted signal that completes AFDM modulation. After the transmitted signal is transmitted through the reflection channel of RIS, the time domain signal obtained by the receiving end is: in is additive Gaussian white noise, which obeys a complex Gaussian distribution with a mean of 0 and a variance of N0. It can be written in matrix form as: in Indicates that the mean is 0 and the covariance is N0I N The noise matrix, I N is an N×N unit matrix. After DAFT transformation of the time domain received signal, the output signal at the AFDM demodulation end is: in, is the effective channel matrix in DAF domain, For the detection of constellation symbols, the present invention uses a minimum mean square error (MMSE) detector based on the channel matrix for detection, which is expressed as: 3.2) In order to establish a further input-output relationship, the present invention superimposes the paths in each RIS unit channel in the Delay-Doppler (DD) channel, and obtains P as the total number of taps in the superimposed DD channel. Each tap p represents a group of delay Dopplers, and the same delay Doppler may contain multiple paths. The coefficient of tap p is the sum of the coefficients of these paths. The range of P is between the number of paths P1 and UP1P2 and is much smaller than N. Formula (11) can be simplified as: in, is the effective channel matrix of each RIS unit under single tap. According to the single tap effective channel matrix characteristics of AFDM, There is only one non-zero element in each row and column of , and the position of the column where the non-zero element is located has a corresponding relationship with the position of the row. Specifically, the channel matrix No. The non-zero elements in the row and column m It can be expressed as: in, Therefore, the input-output relationship between the initial PSK modulation symbol and the final output symbol in the DAF domain is constructed as follows:

5. The method according to claim 1, characterized in that The specific method described in step 4) is: Due to the existence of multipath in the double-dispersion channel, RIS cannot perfectly phase-cancel all paths, so a set of RIS phases can be found to maximize the signal-to-noise ratio at the receiving end. The optimization problem of RIS phase shift in the single-input single-output (SISO) case can be modeled as: Where P t Set to unit transmit power. Considering the complexity of this non-convex optimization problem, in order to simplify the problem, this method first derives the upper limit of equation (22), and then proposes a RIS-AFDM system optimization method that maximizes this upper limit, called the Strongest Tap Coefficient (SPT). First, the problem is decomposed into the phase design problem for each RIS unit: Substituting into the channel matrix expression, the problem can be restated as: According to formula (13) in step 3), the above formula can be simplified to: The corresponding upper limit is: In order to achieve the best diversity order of AFDM, it is set to c1=(2α max +1) / 2N, and N is an even number in this paper, so For the unit array. For a circulant matrix, the norm size is not affected. After substituting the expression into , the optimization problem becomes: Therefore, we can consider searching for the strongest path tap in the superimposed DD domain channel. The phase of the RIS is then configured according to the phase of this tap coefficient. By adding and comparing the complex gains corresponding to each tap in different RIS unit channels, the strongest tap can be expressed as: The phase of each RIS unit is then adjusted to be opposite to the phase of the cascade path corresponding to the strongest tap in the unit channel: After adjusting the RIS phase, the input-output relationship of equation (15) in step 3) becomes: However, we find that for some RIS units, the cascade channel matrix H u , which may not contain the strongest tap The corresponding delay-Doppler combination. At this time, the taps in the cascaded channels of these RIS units The corresponding channel coefficient is 0, so the phase This situation is more obvious when the number of RIS units increases. In order to maximize the role of RIS and further improve the signal-to-noise ratio of the receiving end, this paper proposes the MF-SPT method based on the above method. Assume that after the path phase corresponding to the strongest tap in each RIS unit channel matrix is ​​offset, the phase of the remaining L RIS units is zero θ u =0 (u=1,...,L). For these zero values, random Q groups of phase vectors are given, each group contains L phase factors, where the phase of the qth group can be expressed as: And select a set of phases Φ that maximizes the channel Frobenius norm m To replace these zero values, it can be expressed as: Finally, the L phases are set to

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