RIS-NOMA bit allocation method under limited feedback

Abstract

The invention discloses an RIS-NOMA (Reconfigurable Intelligent Metasurface) bit allocation method under limited feedback, which considers the situation of limited feedback overhead widely existing in a non-orthogonal multiple access (NOMA) RIS-NOMA system assisted by a key technology reconfigurable intelligent metasurface (RIS) in a next-generation communication system, and the limited feedback enables a base station to only acquire quantized downlink channel state information (CSI) instead of perfect CSI. The inaccurate CSI misleads the coding and decoding sequence and deteriorates the system performance. According to the method, a feedback bit allocation scheme of two users in the RIS-NOMA system under limited feedback is deduced based on the improved random vector quantization (RVQ) codebook, the quantization rate loss of the system is reduced on the premise of considering the fairness of the NOMA users, the correct decoding sequence of the NOMA system is ensured, and compared with a traditional equal bit allocation scheme, the quantization performance of the system is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless communications, and in particular relates to a RIS-NOMA bit allocation method under limited feedback. Background Art

[0002] As a key technology in the next generation of communication technology, RIS can effectively improve the system capacity and coverage area of ​​the wireless communication system, while NOMA technology can effectively increase the number of communication devices accessed in the system, realize the propagation of multiple signals at the same frequency, and greatly improve the spectrum efficiency (Liu F, Wang M, Liu Y, et al. Hybrid NOMA Offloading for Delay-Sensitive Applications in MEC-Based NB-IoT Networks [J]. IEEE Internet of Things Journal, 2024.). Most existing analyses assume that perfect CSI is known and analyze the system performance of RIS-NOMA. In actual systems, it is extremely difficult to obtain perfect downlink CSI. This is because the user end needs to feed back the downlink CSI to the base station (BS) through limited feedback overhead, and the feedback overhead cannot be increased indefinitely. Therefore, the BS end can only obtain quantized downlink CSI, which will lead to a decrease in system performance. In NOMA systems, the impact of imperfect CSI is even greater, because the BS needs to allocate power and encode according to the accurate downlink CSI of different users. Inaccurate channel estimation may cause errors in the order of continuous interference elimination at the user end, which will sharply deteriorate system performance. In RIS-assisted systems, due to the large number of RIS units and the existence of cascaded channels, the complexity of the channel state matrix is ​​greatly increased, which increases the feedback overhead and difficulty. At present, there is a lack of research on the limited feedback problem of RIS-NOMA systems in this field. Summary of the invention

[0003] Purpose of the invention: The purpose of the present invention is to provide a RIS-NOMA bit allocation method under limited feedback. When the user end has limited ability to feedback downlink channel state information (CSI), channel modeling is performed, the optimal quantized channel gain is derived, the user's power allocation coefficient is analyzed, and on this basis, a user feedback bit allocation scheme is proposed, which improves the fairness, traversal reachability and rate of the system.

[0004] Technical solution: The present invention provides a RIS-NOMA bit allocation method under limited feedback. For a non-orthogonal multiple access NOMA communication system assisted by a reconfigurable intelligent metasurface RIS, the optimal quantized channel gain is derived when the user's feedback channel state information CSI capability is limited. The user's power allocation coefficient is analyzed, and on this basis, a user feedback bit allocation scheme is proposed, including the following steps:

[0005] S1, the base station BS and RIS are equipped with uniform planar antenna array UPA. The two users receive the BS signal with the help of RIS and are in a NOMA cluster. According to Jensen's inequality, the ergodic reachability and rate R in this system with perfect CSI are derived. p,sum As an upper bound;

[0006] S2. The downlink channel is quantized based on the improved random vector quantization RVQ codebook. The user feeds back its own codebook index to the BS, and the downlink channel is reconstructed at the BS. The influence of the quantized channel state information on the power allocation coefficient of the NOMA system is considered.

[0007] S3. Derive the optimal bit allocation for a single user when the feedback bit is fixed to achieve the maximum quantized channel gain for the user. Based on this bit allocation, perform the total bit allocation in the NOMA cluster to determine the system quantization and rate R when the feedback is limited. q,sum ;

[0008] S4. According to the characteristics of NOMA users sharing the BS-RIS subchannel in the model, this part of the feedback overhead is saved for redistribution, the quantization accuracy of other subchannels is improved, and then the system quantization and rate are improved to complete the allocation plan of user feedback bits.

[0009] Furthermore, step S1 specifically includes the following steps:

[0010] S1.1. The two-segment sub-channel BS-RIS and RIS-user are modeled according to the Rice channel. Taking the BS-RIS sub-channel as an example, we have

[0011]

[0012] in g B,l =e jη , a is the angular response of the UPA array, a R,l , a R , are the angular responses at RIS and BS, respectively, where the subscript is R, B is the response for the line-of-sight path, subscript l is the lth response for the non-line-of-sight path, and K B , K1 are the Rice factors of BS-RIS and RIS-user 1, LB , L1 is the number of paths of these two cascaded sub-channels, N B ,N R are the number of antennas and the number of RIS elements at the base station respectively. The downlink cascade channel of two users can be expressed as:

[0013]

[0014] Θ is the phase information at RIS, represents the cascaded sub-channel matrix from RIS to user 1 and user 2;

[0015] S1.2. The two users are divided into strong and weak users in the NOMA cluster according to their distance from the BS. User 1 is a strong user and user 2 is a weak user. The signal-to-noise ratio of the two users is expressed as:

[0016]

[0017] P is the BS transmit power, α is the power allocation coefficient at the BS, and f1 and f2 are the precoding of the base station for the two users.

[0018] δ 2 is the noise power. In which, continuous interference cancellation SIC is applied at the user end, user 1 directly decodes its own signal, user 2 decodes its own signal after removing the signal of user 1, and f is the precoding at the base station;

[0019] S1.3. According to Jensen's inequality, the traversal reachability and rate of the system are derived as:

[0020]

[0021] According to the result of formula (4), the system and rate under perfect CSI can be obtained as the upper bound;

[0022] S1.4. In order to ensure fairness between two users in the NOMA system and maximize the system sum rate, the power allocation coefficient is obtained by maximizing the minimum rate of the two users:

[0023] maxmin{log2(1+γ1),log2(1+γ2)} (5)

[0024] When log2(1+γ1)=log2(1+γ2), equation (5) is satisfied, so the optimal power allocation coefficient can be obtained:

[0025]

[0026] Where H1 and H2 are the channel gains of the two users respectively, and H1=E[|h1f1| 2 ],H2=E[|h2f2| 2].

[0027] Furthermore, step S2 specifically includes the following steps:

[0028] S2.1, the channel gain is composed of the inner product of two cascaded sub-channel gains. The codebook is designed according to this structure. Each codebook is also composed of the inner product of two cascaded sub-codebooks. The cascaded sub-codebook is the RVQ codebook. For b i There are users with feedback bits in the codebook. The code words are:

[0029]

[0030] Each codeword satisfies the normalization condition, ||w i,n ||=1, and for each sub-codebook, it can be decomposed into the inner product of the cascaded sub-channel codebooks at both ends,

[0031] S2.2. After applying the codebook at the BS, the concatenated channel is quantized to h 1,q ,h 2,q , taking user 1 as an example:

[0032]

[0033] in g1 imitates g B is the normalized path gain of RIS-user 1. After applying the codebook, the user only needs to feed back its own codebook index to the BS, and the downlink channel can be reconstructed at the BS.

[0034] S2.3, the quantization gain of the downlink cascade channel of the two users can be expressed as H 1,q ,H 2,q , taking user 1 as an example, there are:

[0035]

[0036] in The quantized channel gain is a function of the number of feedback bits, b 1,BR,L ,b 1,BR,N ,b 1,R1,L ,b 1,R1,N They are the line-of-sight and non-line-of-sight path feedback bits of the BS-RIS path of user 1, and the line-of-sight and non-line-of-sight path feedback bits of RIS-user 1, and the same applies to user 2;

[0037] S2.4. After the BS reconstructs the quantized downlink channel gain, power allocation is required. However, the power allocation coefficient under perfect CSI is no longer applicable. For the power allocation coefficient of quantized CSI, the quantized power allocation coefficient α can be obtained according to the principle of formula (5):q :

[0038]

[0039] H 1,q ,H 2,q is the quantized channel gain of the two users. When reconstructing the downlink channel, the BS may misjudge the strong and weak users, that is, H 1,q <H 2,q , at this time the performance of the NOMA system will deteriorate sharply.

[0040] Furthermore, step S3 specifically includes the following steps:

[0041] S3.1. Analyze the quantized channel gain formula (9) and construct a function of the number of bits in the line-of-sight path

[0042]

[0043] where b 1,L is the feedback bit of the line-of-sight path of user 1, for b 1,BR,L Seeking guidance can be done properly When , the function reaches its maximum value, that is, the optimal bit allocation for the line-of-sight path is

[0044] S3.2. The bit number function for non-line-of-sight paths is:

[0045]

[0046] When the feedback bit tends to infinity, tends to zero, so the function about the non-line-of-sight path is approximately:

[0047]

[0048] b can be obtained 1,BR,N The optimal allocation is

[0049] S3.3, Substitute the optimal allocation of line-of-sight and non-line-of-sight paths into the quantized channel gain and construct the function f1(b 1,N ):

[0050]

[0051] After derivation, the bit allocation of each user's internal line-of-sight and non-line-of-sight paths can be obtained:

[0052]

[0053] in

[0054] S3.4. Based on the optimal bit allocation, construct the optimal quantized channel gain H for a single user i,q,max (b i ),i∈{1,2}, to ensure the fairness of the NOMA system, the same feedback bits are allocated to the two users, that is, b1=b2; the quantization gain of user 1 is H 1,q,max (b / 2), the quantization gain of user 2 is H 2,q,max (b / 2), the power allocation coefficient can be obtained by equation (10); therefore, the system quantization and rate are:

[0055]

[0056] Furthermore, step S4 specifically includes the following steps:

[0057] S4.1. Since both users need RIS-assisted communication, it can be seen that the BS-RIS subchannel is shared by the two users. Only one reconstruction of BS-RIS is required at the base station, without the need for both users to feedback cascade path information. Extract the feedback bit b allocated by user 2 to the BS-RIS subchannel 2,BR , and redistribute;

[0058] S4.2, considering the reallocation to b 1,BR The quantization gain of both users can be increased at the same time, and the 1,R1 or b 2,R2 The quantization gain of the subchannel of user 1 or user 2 can only be enhanced separately. Therefore, all the bits to be allocated are first allocated to the BS-RIS subchannel. At this time, the feedback bit of this subchannel is b 1,BR +b 2,BR ;

[0059] S4.3. As the number of feedback bits allocated to the subchannel increases, the quantization gain of the subchannel approaches the channel gain of perfect CSI. Therefore, when the number of feedback bits is large, as the feedback bits continue to increase, the growth of the quantization channel gain gradually slows down. From the perspective of the maximum quantization sum rate, the overhead allocated to BS-RIS can be gradually reduced and allocated to RIS-User 1 and RIS-User 2. When the quantization sum rate is greater than the sum rate obtained in step S52, the bit allocation is updated to this scheme. Let the reduced feedback bits be b red. , satisfying b red. ≤ b 2,BR , at this time the system quantization rate and the equivalent feedback bit are:

[0060]

[0061] Among them, H 1,q,pr ,α q,prThey are respectively the quantized channel gain of user 1 after applying the scheme and the system power allocation coefficient.

[0062] The present invention also discloses a computer device, comprising a memory, a processor and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method of the present invention.

[0063] The present invention also discloses a computer-readable storage medium on which a computer program / instruction is stored. When the computer program / instruction is executed by a processor, the steps of the method of the present invention are implemented.

[0064] The present invention also discloses a computer program product, comprising a computer program / instruction, which implements the steps of the method of the present invention when executed by a processor.

[0065] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages:

[0066] The present invention takes into account the limited feedback overhead in the next generation of communication technology. This limited feedback allows the base station to only obtain quantized downlink channel state information (CSI) instead of perfect CSI. Inaccurate CSI will mislead the encoding and decoding order and deteriorate system performance. Based on the improved random vector quantization (RVQ) codebook, the present invention derives the feedback bit allocation scheme of two users in the RIS-NOMA system under limited feedback. Under the premise of taking into account the fairness of NOMA users, the quantization rate loss of the system is reduced, the correct decoding order of the NOMA system is guaranteed, and the power allocation of the base station when quantizing CSI is provided. The BS realizes the reconstruction of the downlink channel through the feedback codebook index and its own codebook. The user only needs to feedback the index instead of the high-dimensional channel matrix, which reduces the feedback overhead. Especially after the introduction of RIS for assistance, a large number of RIS elements make the dimension of the downlink cascade channel matrix increase sharply. The problem is effectively solved after using the codebook; the characteristics of the two users sharing the BS-RIS cascade subchannel in the system model are used to reallocate the bits. Compared with the simple bit allocation scheme, the scheme reduces the feedback overhead, improves the equivalent feedback bits of the system, and achieves higher quantization performance under the same number of feedback. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 This is the system model diagram of the RIS-NOMA system;

[0068] Figure 2 The rate loss of the bit allocation scheme proposed by the present invention compared with the traditional bit allocation scheme varies with the base station transmission power;

[0069] Figure 3The rate loss of the bit allocation scheme proposed by the present invention compared with the traditional equal bit allocation scheme varies with the total number of feedback bits. DETAILED DESCRIPTION

[0070] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

[0071] The present invention proposes a limited feedback bit allocation scheme for RIS-NOMA. Both the base station (BS) and the RIS are equipped with a uniform planar antenna array (UPA). Two users receive BS signals with the help of RIS and are in a NOMA cluster for channel modeling. The ergodic reachable sum rate R in this system with perfect CSI is derived according to Jensen's inequality. p,sum As the upper bound; quantize the downlink channel based on the improved random vector quantization (RVQ) codebook, and consider the impact of the quantized channel state information on the power allocation coefficient of the NOMA system; derive the optimal bit allocation for a single user when the feedback bit is fixed to achieve the maximum quantized channel gain for the user. According to this bit allocation, the total bit allocation in the NOMA cluster is performed to determine the system quantization and rate R when the feedback is limited. q,sum According to the characteristics of NOMA users sharing the BS-RIS subchannel, this part of the feedback overhead is saved for redistribution, and the quantization accuracy of other subchannels is improved, thereby improving the system quantization and rate.

[0072] Both the base station (BS) and the RIS are equipped with a uniform planar antenna array (UPA). The two users receive the BS signal with the help of the RIS and are in a NOMA cluster. The ergodic reachability and rate R of the perfect CSI in this system are derived according to the Jensen inequality. p,sum As an upper bound:

[0073] The two sub-channels BS-RIS and RIS-user are modeled according to the Rice channel. Taking the BS-RIS sub-channel as an example, we have

[0074]

[0075] in g B,l =e jη , a is the angular response of the UPA array, K B , K1 are the Rice factors of BS-RIS and RIS-user 1, L B , L1 is the number of paths of these two cascaded sub-channels, N B ,N R are the number of antennas and RIS elements at the base station, respectively. Similarly, RIS-subchannel of user i It can be expressed as:

[0076]

[0077] here a Ri,l =a R (θ i,l ,φ i,l ) is the angle response of the lth path from RIS to user i. R (θ, φ) as an example, we have (assuming that the distance between the antenna and the RIS element is half a wavelength):

[0078]

[0079] N Rv ,N Rh are the number of antennas in the vertical and horizontal directions in RIS, satisfying N R =N Rv ×N Rh (θ, φ) are the arrival or departure angles in the vertical and horizontal directions respectively. The downlink cascade channel of two users can be expressed as:

[0080]

[0081] Θ is the phase information at RIS, satisfying Take the cascade channel of user 1 as an example:

[0082]

[0083] Due to the different distances from the BS, the two users are divided into strong and weak users in the NOMA cluster, where user 1 is a strong user and user 2 is a weak user. The signal-to-noise ratio of the two users can be expressed as:

[0084]

[0085] In which, Successive Interference Cancellation (SIC) is applied at the user end, user 1 directly decodes its own signal, and user 2 decodes its own signal after removing the signal of user 1, and f is the precoding at the base station;

[0086] According to Jensen's inequality, the system traversal reachability and rate can be derived as:

[0087]

[0088] According to the result of this formula, the system and rate under perfect CSI can be obtained as the upper bound;

[0089] In order to ensure fairness between the two users in the NOMA system and maximize the system sum rate, the power allocation coefficient can be obtained by maximizing the minimum rate of the two users:

[0090] maxmin{log2(1+γ1),log2(1+γ2)} (32)

[0091] It is easy to obtain that when log2(1+γ1)=log2(1+γ2), equation (32) is satisfied. Therefore, the optimal power allocation coefficient can be obtained:

[0092]

[0093] Where H1 and H2 are the channel gains of the two users respectively, and H1=E[|h1f1| 2 ],H2=E[|h2f2| 2 ].

[0094] The downlink channel is quantized based on the improved RVQ codebook, and the impact of the quantized channel state information on the power allocation coefficient of the NOMA system is considered:

[0095] Since the channel gain is composed of the inner product of two cascaded sub-channel gains, the codebook is designed according to this structure. Each codebook is also composed of the inner product of two cascaded sub-codebooks. The cascaded sub-codebook is the RVQ codebook. i There are users with feedback bits in the codebook. The code words are:

[0096]

[0097] Each codeword satisfies the normalization condition, ||w i,n ||=1, and there is

[0098] After applying the codebook at the BS, the concatenated channel is quantized to h 1,q ,h 2,q , taking user 1 as an example:

[0099]

[0100] in g1 imitates g B is the normalized path gain of RIS-user 1. After applying this codebook, the user only needs to feed back its own codebook index to the BS, and the downlink channel can be reconstructed at the BS without feeding back the complete channel information, which greatly saves the system feedback overhead;

[0101] The quantization gain of the downlink cascade channel of two users can be expressed as H 1,q ,H 2,q , taking user 1 as an example, there are:

[0102]

[0103] in It can be seen that the quantized channel gain is a function of the number of feedback bits, b1,BR,L ,b 1,BR,N ,b 1,R1,L ,b 1,R1,N They are the line-of-sight and non-line-of-sight path feedback bits of the BS-RIS path of user 1, and the line-of-sight and non-line-of-sight path feedback bits of RIS-user 1, and the same applies to user 2;

[0104] After the BS reconstructs the quantized downlink channel gain, power allocation is required. However, the power allocation coefficient under perfect CSI is no longer applicable. For the power allocation coefficient of quantized CSI, the quantized power allocation coefficient α can be obtained. q :

[0105]

[0106] H 1,q ,H 2,q is the quantized channel gain of the two users. Note that when the BS reconstructs the downlink channel, it may misjudge the strong and weak users, that is, H 1,q <H 2,q , at this time the performance of the NOMA system will deteriorate sharply.

[0107] The optimal bit allocation for a single user when the feedback bit is fixed is derived to achieve the maximum quantized channel gain for the user and perform total bit allocation:

[0108] Analyze the quantized channel gain formula and construct a function for the number of bits in the line-of-sight path

[0109]

[0110] where b 1,L is the feedback bit of the line-of-sight path of user 1. 1,BR,L Seeking guidance,

[0111]

[0112] Can be sought When , the function reaches its maximum value, that is, the optimal bit allocation for the line-of-sight path is

[0113] The bit number function for non-line-of-sight paths is:

[0114]

[0115] When the feedback bit tends to infinity, tends to zero and is much smaller than the first two terms, so the function for non-line-of-sight paths can be approximated as:

[0116]

[0117] About b 1,BR,N Seeking guidance,

[0118]

[0119] b can be obtained 1,BR,N The optimal allocation is

[0120] Substitute the optimal allocation of line-of-sight and non-line-of-sight paths obtained in the first two steps into the quantized channel gain to construct the function f1(b 1,N ):

[0121]

[0122] After derivation, the bit allocation of each user's internal line-of-sight and non-line-of-sight paths can be obtained:

[0123]

[0124] in

[0125] According to the optimal bit allocation obtained in the previous step, the optimal quantized channel gain H for a single user is constructed. i,q,max (b i ),i∈{1,2}. To ensure the fairness of the NOMA system, the same feedback bits are allocated to the two users, that is, b1=b2. The quantization gain of user 1 is H 1,q,max (b / 2), the quantization gain of user 2 is H 2,q,max (b / 2), the power allocation coefficient can be obtained by equation (34). Therefore, the system quantization and rate are:

[0126]

[0127] Preferably, according to the characteristics of NOMA users sharing the BS-RIS subchannel in the model, this part of the feedback overhead is saved for redistribution to improve the quantization accuracy of other subchannels:

[0128] Since both users need RIS-assisted communication, it can be seen that the BS-RIS subchannel is shared by the two users. Only one reconstruction of BS-RIS is required at the base station, without the need for both users to feedback cascade path information. Extract the feedback bit b allocated by user 2 to the BS-RIS subchannel 2,BR , and redistribute;

[0129] Considering the reallocation to b 1,BR The quantization gain of both users can be increased at the same time, and the 1,R1 or b 2,R2 The quantization gain of the subchannel of user 1 or user 2 can only be enhanced separately. Therefore, all the bits to be allocated are first allocated to the BS-RIS subchannel. At this time, the feedback bit of this subchannel is b 1,BR +R2,BR ;

[0130] As the number of feedback bits allocated to the subchannel increases, the quantization gain of the subchannel approaches the channel gain of perfect CSI. Therefore, when the number of feedback bits is large, as the feedback bits continue to increase, the growth of the quantization channel gain gradually slows down. From the perspective of the maximum quantization sum rate, the overhead allocated to BS-RIS can be gradually reduced and allocated to RIS-User 1 and RIS-User 2. When the quantization sum rate is greater than the sum rate obtained in step S52, the bit allocation is updated to this scheme. Let the reduced feedback bits be b red. , satisfying b red. ≤ b 2,BR , at this time the system quantization rate and the equivalent feedback bit are:

[0131]

[0132] Among them, H 1,q,pr ,α q,pr They are respectively the quantized channel gain of user 1 after applying the scheme and the system power allocation coefficient.

[0133] Combination Figure 2 , 3 It can be seen that the bit allocation scheme proposed in the present invention effectively improves the quantization accuracy of the channel state information and reduces the system quantization error and rate loss compared with the traditional equal bit allocation scheme.

[0134] The preferred embodiments of the present invention are described in detail above in conjunction with the accompanying drawings. Some modifications and improvements can be made on the basis of the present invention. Modifications and improvements made without departing from the spirit of the present invention all belong to the protection scope of the present invention.

Claims

1. A RIS-NOMA bit allocation method under limited feedback, characterized in that: For the non-orthogonal multiple access NOMA communication system assisted by reconfigurable intelligent metasurface RIS, when the user feedback channel state information CSI capability is limited, the optimal quantized channel gain is derived, the user power allocation coefficient is analyzed, and on this basis, a user feedback bit allocation scheme is proposed, including the following steps: S1, the base station BS and RIS are equipped with uniform planar antenna array UPA. The two users receive the BS signal with the help of RIS and are in a NOMA cluster. According to Jensen's inequality, the ergodic reachability and rate R in this system with perfect CSI are derived. p,sum As an upper bound; S2. The downlink channel is quantized based on the improved random vector quantization RVQ codebook. The user feeds back its own codebook index to the BS, and the downlink channel is reconstructed at the BS. The influence of the quantized channel state information on the power allocation coefficient of the NOMA system is considered. S3. Derive the optimal bit allocation for a single user when the feedback bit is fixed to achieve the maximum quantized channel gain for the user. Based on this bit allocation, perform the total bit allocation in the NOMA cluster to determine the system quantization and rate R when the feedback is limited. q,sum ; S4. According to the characteristics of NOMA users sharing the BS-RIS subchannel in the model, this part of the feedback overhead is saved for redistribution, the quantization accuracy of other subchannels is improved, and then the system quantization and rate are improved to complete the allocation plan of user feedback bits.

2. The RIS-NOMA bit allocation method under limited feedback according to claim 1, characterized in that: Step S1 specifically includes the following steps: S1.

1. The two-segment sub-channel BS-RIS and RIS-user are modeled according to the Rice channel. Taking the BS-RIS sub-channel as an example, we have in g B,l =e jη , a is the angle response of the UPA array, a R,l , a R , are the angular responses at RIS and BS, respectively, where the subscript is R, B is the response for the line-of-sight path, subscript l is the lth response for the non-line-of-sight path, and K B , K1 are the Rice factors of BS-RIS and RIS-user 1, L B , L1 is the number of paths of these two cascaded sub-channels, N B ,N R are the number of antennas and the number of RIS elements at the base station respectively. The downlink cascade channel of two users can be expressed as: Θ is the phase information at RIS, represents the cascaded sub-channel matrix from RIS to user 1 and user 2; S1.

2. The two users are divided into strong and weak users in the NOMA cluster according to their distance from the BS. User 1 is a strong user and user 2 is a weak user. The signal-to-noise ratio of the two users is expressed as: P is the BS transmit power, α is the power allocation coefficient at the BS, f1, f2 are the precoding of the base station for the two users; δ 2 is the noise power; In which, continuous interference cancellation SIC is applied at the user end, user 1 directly decodes its own signal, and user 2 decodes its own signal after removing the signal of user 1, and f is the precoding at the base station; S1.

3. According to Jensen's inequality, the traversal reachability and rate of the system are derived as: According to the result of formula (4), the system and rate under perfect CSI can be obtained as the upper bound; S1.

4. In order to ensure fairness between two users in the NOMA system and maximize the system sum rate, the power allocation coefficient is obtained by maximizing the minimum rate of the two users: maxmin{log2(1+γ1),log2(1+γ2)} (5) When log2(1+γ1)=log2(1+γ2), equation (5) is satisfied, so the optimal power allocation coefficient can be obtained: Where H1 and H2 are the channel gains of the two users respectively, and H1=E[h1f1 2 ],H2=E[h2f2 2 ].

3. The RIS-NOMA bit allocation method under limited feedback according to claim 2, characterized in that: Step S2 specifically includes the following steps: S2.1, the channel gain is composed of the inner product of two cascaded sub-channel gains. The codebook is designed according to this structure. Each codebook is also composed of the inner product of two cascaded sub-codebooks. The cascaded sub-codebook is the RVQ codebook. For b i There are users with feedback bits in the codebook. The code words are: Each codeword satisfies the normalization condition, ||w i,n ||=1, and for each sub-codebook, it can be decomposed into the inner product of the cascaded sub-channel codebooks at both ends, S2.

2. After applying the codebook at the BS, the concatenated channel is quantized to h 1,q ,h 2,q , taking user 1 as an example: in g1 imitates g B is the normalized path gain of RIS-user 1. After applying the codebook, the user only needs to feed back its own codebook index to the BS, and the downlink channel can be reconstructed at the BS. S2.3, the quantization gain of the downlink cascade channel of the two users can be expressed as H 1,q ,H 2,q , taking user 1 as an example, there are: in The quantized channel gain is a function of the number of feedback bits, b 1,BR,L ,b 1,BR,N ,b 1,R1,L ,b 1,R1,N They are the line-of-sight and non-line-of-sight path feedback bits of the BS-RIS path of user 1, and the line-of-sight and non-line-of-sight path feedback bits of RIS-user 1, and the same applies to user 2; S2.

4. After the BS reconstructs the quantized downlink channel gain, power allocation is required. However, the power allocation coefficient under perfect CSI is no longer applicable. For the power allocation coefficient of quantized CSI, the quantized power allocation coefficient α can be obtained according to the principle of formula (5): q : H 1,q ,H 2,q is the quantized channel gain of the two users after quantization; When reconstructing the downlink channel, the BS may misjudge the strong and weak users, i.e. 1,q <H 2,q , at this time the performance of the NOMA system will deteriorate sharply.

4. The RIS-NOMA bit allocation method under limited feedback according to claim 3, characterized in that: Step S3 specifically includes the following steps: S3.

1. Analyze the quantized channel gain equation (9) and construct a function of the number of bits in the line-of-sight path where b 1,L is the feedback bit of the line-of-sight path of user 1, for b 1,BR,L Seeking guidance can be done properly When , the function reaches its maximum value, that is, the optimal bit allocation for the line-of-sight path is S3.

2. The bit number function for non-line-of-sight paths is: When the feedback bit tends to infinity, tends to zero, so the function about the non-line-of-sight path is approximately: b can be obtained 1,BR,N The optimal allocation is S3.3, Substitute the optimal allocation of line-of-sight and non-line-of-sight paths into the quantized channel gain and construct the function f1(b 1,B ): After derivation, the bit allocation of each user's internal line-of-sight and non-line-of-sight paths can be obtained: in S3.

4. Based on the optimal bit allocation, construct the optimal quantized channel gain H for a single user i,q,max (b i ),i∈{1,2}, to ensure the fairness of the NOMA system, the same feedback bits are allocated to the two users, that is, b1=b2; the quantization gain of user 1 is H 1,q,max (b / 2), the quantization gain of user 2 is H 2,q,max (b / 2), the power allocation coefficient can be obtained by equation (10); therefore, the system quantization and rate are:

5. The RIS-NOMA bit allocation method under limited feedback according to claim 1, characterized in that: Step S4 specifically includes the following steps: S4.

1. Since both users need RIS-assisted communication, the BS-RIS subchannel is shared by the two users. Only one reconstruction of BS-RIS is required at the base station to extract the feedback bit b allocated by user 2 to the BS-RIS subchannel. 2,BR , and redistribute; S4.2, allocating all the bits to be allocated to the BS-RIS subchannel. At this time, the feedback bit of the subchannel is b 1,BR +b 2,BR ; S4.3, gradually reduce the overhead allocated to BS-RIS and allocate it to RIS-user 1 and RIS-user 2. When the quantization sum rate is greater than the sum rate obtained in step S52, update the bit allocation to this scheme. Let the reduced feedback bits be b red. , satisfying b red. ≤ b 2,BR , at this time the system quantization rate and the equivalent feedback bit are: Among them, H 1,q,pr ,α q,pr They are respectively the quantized channel gain of user 1 after applying the scheme and the system power allocation coefficient.

6. A computer device comprising a memory, a processor and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the steps of the method of claim 1.

7. A computer-readable storage medium having a computer program / instruction stored thereon, characterized in that: When the computer program / instructions are executed by a processor, the steps of the method according to claim 1 are implemented.

8. A computer program product comprising a computer program / instructions, characterized in that When the computer program / instructions are executed by a processor, the steps of the method according to claim 1 are implemented.

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