CN112865893A - Intelligent reflector assisted SM-NOMA system resource allocation method - Google Patents

Intelligent reflector assisted SM-NOMA system resource allocation method Download PDF

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CN112865893A
CN112865893A CN202110085028.XA CN202110085028A CN112865893A CN 112865893 A CN112865893 A CN 112865893A CN 202110085028 A CN202110085028 A CN 202110085028A CN 112865893 A CN112865893 A CN 112865893A
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李国权
马佳娣
徐勇军
林金朝
庞宇
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Chongqing University of Post and Telecommunications
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B17/00—Monitoring; Testing
    • H04B17/30—Monitoring; Testing of propagation channels
    • H04B17/309—Measuring or estimating channel quality parameters
    • H04B17/336—Signal-to-interference ratio [SIR] or carrier-to-interference ratio [CIR]
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B17/00—Monitoring; Testing
    • H04B17/30—Monitoring; Testing of propagation channels
    • H04B17/382—Monitoring; Testing of propagation channels for resource allocation, admission control or handover
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B17/00—Monitoring; Testing
    • H04B17/30—Monitoring; Testing of propagation channels
    • H04B17/391—Modelling the propagation channel
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Abstract

The invention relates to an intelligent reflector assisted SM-NOMA system resource allocation method, which belongs to the technical field of communication and comprises the following steps: for the intelligent reflector assisted SM-NOMA system, dynamic user grouping is carried out by considering the effective channel gain of each user; and establishing a power distribution model with the aim of maximizing the system and the speed according to the maximum transmitting power constraint of the base station and the user and the incident signal phase shift constraint of the intelligent reflection unit. The system resource allocation algorithm can effectively improve the system and the rate and reduce the system error rate on the premise of ensuring the maximum difference of each group of user channels.

Description

Intelligent reflector assisted SM-NOMA system resource allocation method
Technical Field
The invention belongs to the technical field of communication, and relates to an intelligent reflector assisted SM-NOMA system resource allocation method.
Background
With the gradual deployment of 5G network commercialization, 6G communication technologies are also under investigation. An Intelligent Reflection Surface (IRS) is used as a passive reflection array, and by adjusting a wireless propagation environment, the frequency spectrum and energy efficiency of a system are further improved, and meanwhile, energy consumption and hardware cost are reduced, which has attracted extensive attention of people. The intelligent reflecting surface is composed of a large number of small-sized and low-cost reflecting units made of thin-layer electromagnetic materials, is controlled by a programmable intelligent device, and simultaneously realizes the reflection of incident signals by adjusting the phase of the reflecting units. The biggest difference from the traditional communication system is that the propagation environment is improved by the reflection unit, only the propagation direction of the signal is changed, and the amplitude of the incident signal is not influenced. In order to improve the frequency spectrum utilization rate of a cellular network and reduce energy consumption, the service quality of each user is ensured by adjusting the phase offset of an intelligent reflecting surface and the transmitting power of a base station in an intelligent reflecting surface system.
Non-Orthogonal Multiple Access (NOMA) technology is a key technology of 5G. The principle of the technology is as follows: carrying out superposition coding at a transmitting end to form a superposition signal; serial Interference Cancellation (SIC) is performed at the receiving end, and the original signal is recovered. In addition, the NOMA technology allows multiple users to share the same time domain, frequency domain and code domain resources, and realizes multiplexing of the power domain. However, as the number of antennas at the transmitting end of the base station increases, there is a large interference between the antennas. Since the Spatial Modulation (Spatial Modulation) technique has the advantages of low complexity and no inter-antenna interference, the effect of the inter-antenna interference on the system can be reduced, and the Spatial Modulation technique has gradually become a research hotspot in recent years. Resource allocation based on non-orthogonal multiple access plays an important role in wireless communication networks, and each user is guaranteed to have good sum rate by performing power allocation on the base station side.
Currently, research on the combination of intelligent reflective surfaces with NOMA networks has yielded some valuable research results. The document "ZHEN B, WU Q and ZHANG R. Intelligent deflecting surface-assisted multiple access with user pairing: NOMA or OMA [ J ]. IEEE Communications Letters,2020,24(4): 753-. The literature, "DING Z and VINCENTENT POOR H.A Simple design of IRS-NOMA Transmission [ J ]. IEEE Communications Letters,2020,24 (5): 1119-. The documents "SHI Y J, FANG. F, ZHOU X T, et al. Joint beamforming and phase shift design in downlink UAV Networks with IRS-assisted NOMA [ J ]. Journal of Communications and Information Networks,2020,5(2): 138-149" propose a resource allocation problem in the communication scene of IRS assisted unmanned aerial vehicle, considering the joint optimization problem of the beamforming vector at the base station and the phase offset of IRS. And the minimum rate of the edge users is improved and the fairness of the users is ensured through resource allocation. To overcome the hardware limitation, the document "WANG H, LIU C, SHI Z, et al. on power minimization for IRS-aided downlink NOMA systems [ J ]. IEEE Wireless Communications Letters,2020,9(11): 1808-NOMA 1811" designs an IRS-NOMA transmission system, and derives a closed solution of the interruption probability of a single user by controlling IRS through a switch, and the result shows that the Intelligent reflector-Non-Orthogonal frequency division Multiple Access (IRS-NOMA) has better interruption rate capability than the Intelligent reflector-Orthogonal Multiple Access (IRS-OMA). However, the IRS-NOMA system has large interference at the transmitting end, and the receiving end needs a complex SIC detection technology, which affects the overall performance of the system.
To solve the above problems, the spatial modulation based NOMA system starts to receive a great attention from the academic world. The literature "WANG X, WANG J, HE L, et al, on the spatial modulation aid Non-Orthogonal multiple access [ J ]. IEEE Communications Letters,2017,21(9): 1937-. Compared with the traditional NOMA system, the technology has remarkable improvement in spectral efficiency. The document "ZHU X, WANG Z and CAO J. NOMA-based modulation [ J ]. IEEE Access,2017,5(99): 3790-. However, no spatial modulation technique has been studied for the intelligent reflector based NOMA system.
Disclosure of Invention
In view of the above, the present invention aims to provide a resource allocation method for an intelligent reflector-assisted SM-NOMA system, which provides a scheme for dynamic user grouping by considering the effective channel gain (i.e. the sub-channel corresponding to the transmit antenna selected by spatial modulation) of each user. And establishing a power distribution model aiming at maximizing the system and the speed by considering the maximum transmitting power constraint of the base station and the user and the incident signal phase shift constraint of the intelligent reflection unit. Since the constructed problem is a non-convex problem, it is difficult to solve directly. The problem of maximizing the sum rate is first translated into the problem of maximizing the signal to interference plus noise ratio according to the criterion of maximizing the minimum. And then decomposing the original problem into two non-convex sub-problems based on the grouping result: (1) fixing a power distribution coefficient, and converting a non-convex sub problem based on the maximum channel gain into a convex problem by using a semi-definite relaxation algorithm; (2) and fixing the phase shift of the intelligent reflecting surface, and converting the non-convex power distribution subproblem of multiple users into a convex optimization problem to solve by introducing auxiliary variables.
In order to achieve the purpose, the invention provides the following technical scheme:
a resource allocation method of an intelligent reflector assisted SM-NOMA system comprises the following steps:
for the intelligent reflector assisted SM-NOMA system, dynamic user grouping is carried out by considering the effective channel gain of each user; and establishing a power distribution model taking a maximized system and speed as targets according to the maximum transmitting power constraint of the base station and the user and the incident signal phase shift constraint of the intelligent reflection unit.
Further, the intelligent reflecting surface assisted SM-NOMA system comprises a base station transmitting end, an intelligent reflecting surface and a user receiving end; wherein:
the user connectsThe receiving end includes: w users are divided equally into T groups, each group has K users, the channel state information is known; users in each group
Figure BDA0002907551170000031
m belongs to {1,2,. T } as the serial number of the group, i belongs to {1,2, …, K } as the serial number of the user in the group;
equipping N at the transmitting end of a base stationtA transmitting antenna, a receiving end having NrA root receiving antenna; selecting a transmitting antenna at a transmitting end of a base station through spatial modulation, transmitting a superposed signal at the same time and at the same frequency, reflecting the superposed signal through an intelligent reflector IRS (infrared receiver) and reaching a receiving end of a user;
the IRS consists of N passive reflective elements, each of which changes the phase shift of the incident signal by reflection, thereby assisting NOMA transmission.
Further, at the transmitting end of the base station, the bit stream transmitted by each time slot is divided into two blocks, which are log in total2(Nt)+log2(M) bits; wherein log2(M) bits are used to determine a corresponding transmitted symbol in a signal constellation, where M represents a modulation order; log (log)2(Nt) The bits are used for determining the serial number of the transmitting antenna in the space constellation diagram; the total power of the transmitted signal is P, and the power occupied by each data stream is P
Figure BDA0002907551170000032
Wherein the content of the first and second substances,
Figure BDA0002907551170000033
is a user
Figure BDA0002907551170000034
Power allocation factor, the transmitted superimposed signal is:
Figure BDA0002907551170000035
user' s
Figure BDA0002907551170000036
Of a data stream
Figure BDA0002907551170000037
Comprises the following steps:
Figure BDA0002907551170000038
wherein the content of the first and second substances,
Figure BDA0002907551170000039
representing a user
Figure BDA00029075511700000310
The serial number of the selected antenna is selected,
Figure BDA00029075511700000311
indicating the modulated transmission symbols.
Further, based on the intelligent reflector assisted SM-NOMA system, a channel is divided into two parts, wherein one part is a direct channel from a base station to a user, and the other part is a reflection channel from the base station to the intelligent reflector to the user; rayleigh fading channels subject to independent equal distribution between base station and user i, i.e.
Figure BDA00029075511700000312
The channel of the base station-intelligent reflecting surface is a Rice channel, and the channel vector is
Figure BDA00029075511700000313
Wherein N is the number of intelligent plane of reflection, then:
Figure BDA0002907551170000041
wherein eta is1Is the rayleigh fading coefficient of the channel f,
Figure BDA0002907551170000042
and
Figure BDA0002907551170000043
direct-view path and non-direct-view path, respectively;
Figure BDA0002907551170000044
each element in (a) is independent and follows a distribution with a mean of 0 and a variance of 1;
the phase shift matrix theta of the intelligent reflecting surface is expressed by a diagonal matrix, namely
Figure BDA0002907551170000045
Wherein theta isn∈[0,2π](ii) a Intelligent reflecting surface to user
Figure BDA0002907551170000046
Is a channel of
Figure BDA0002907551170000047
User' s
Figure BDA0002907551170000048
The channel description of (c) is:
Figure BDA0002907551170000049
the channel gain order is:
Figure BDA00029075511700000410
and
Figure BDA00029075511700000411
rayleigh channels representing user 1, user 2, user 3 and user K, respectively, wherein
Figure BDA00029075511700000412
User' s
Figure BDA00029075511700000413
The received signals are:
Figure BDA00029075511700000414
wherein
Figure BDA00029075511700000415
Is a user
Figure BDA00029075511700000416
Of the received signal, n0Is additive white Gaussian noise, obeys a mean value of 0 and has a variance of sigma2Complex Gaussian distribution of jiRepresenting a user
Figure BDA00029075511700000417
Is subject to spatial modulation of the selected jth antenna,
Figure BDA00029075511700000418
representing a user
Figure BDA00029075511700000419
And the jth transmit antenna.
Further, the dynamic user grouping comprises the steps of:
user pre-allocation: there are W alternative users, and the user set is divided into 3 types according to the distance between the base station and each user: near users, center users, and far users;
sorting in descending order of users: sorting the alternative users of each initial set in a descending order according to the effective channel gain;
and (3) selecting by the user: and selecting the users with the largest difference of effective channel gains from the corresponding initial set, grouping the users into one group, and returning all grouping conditions until all the users finish grouping. After the optimization of the reflecting surface is finished, carrying out one iteration on the reflecting surface;
the channel gain referenced when users are grouped is: channels before IRS optimization, i.e.
Figure BDA00029075511700000420
First, only one transmitting antenna is selected from IRS-SM-NOMA, and consideration is given toEffective direct channel gain for the ith user, i.e.
Figure BDA00029075511700000421
Further, the power allocation model targeted to maximize system and rate includes:
each group has K users
Figure BDA0002907551170000051
When decoding the signal, the signal from other weak users is regarded as interference, and the user
Figure BDA0002907551170000052
The Signal to Interference plus Noise Ratio (SINR) of (1) is expressed as:
Figure BDA0002907551170000053
user' s
Figure BDA0002907551170000054
The corresponding rates are:
Figure BDA0002907551170000055
according to equation (11), an optimization scheme is adopted to maximize the SINR, i.e. by jointly optimizing the power distribution coefficients of the users
Figure BDA0002907551170000056
And the phase shift Θ of IRS, maximizing user and rate:
Figure BDA0002907551170000057
optimal maximization-the minimum SINR is Q, where Q is a relaxation variable, i.e.
Figure RE-GDA0003031237140000058
The optimization problem is then transferred to:
Figure BDA0002907551170000059
under the condition of a given signal-to-noise ratio, the power is assumed to have a determined value to optimize theta so as to achieve the aim of maximizing channel gain; and then, carrying out power distribution according to the number of users in the group, determining beta, and dividing (P1) into two optimization problems to maximize the sum rate of the users, namely a phase shift optimization sub-problem and a power distribution optimization sub-problem.
Further, the phase shift optimization sub-problem comprises:
for the user
Figure BDA0002907551170000061
Given a fixed power distribution coefficient, and then splitting (P2) into two parts, the channel gain is maximized by optimizing the intelligent reflector phase, starting with the following problem:
Figure BDA0002907551170000062
let I ═ l1,…,lN]H，
Figure BDA0002907551170000063
And is
Figure BDA0002907551170000064
Further order
Figure BDA00029075511700000617
Then
Figure BDA0002907551170000065
To obtain
Figure BDA0002907551170000066
Therefore (P3)The optimization problem is equivalent to:
Figure BDA0002907551170000067
(P3) is a problem of non-convex quadratic constraints, restated (P3) as a non-convex homogeneous problem by introducing an auxiliary variable t, (P4) transforms the equivalent write:
Figure BDA0002907551170000068
wherein the content of the first and second substances,
Figure BDA0002907551170000069
due to the fact that
Figure BDA00029075511700000610
When L satisfies L ≧ 0 and
Figure BDA00029075511700000611
when, define
Figure BDA00029075511700000612
The first constraint is non-convex, and the semi-definite relaxation (SDR) method is used to relax this constraint, and the problem (P5) is simplified as:
Figure BDA00029075511700000613
rank of L is reduced to 1 by using semi-deterministic relaxation techniques and gaussian randomization:
(1) decomposing L as characteristic value, L being U ∑ UHWhere U is a unitary matrix and Σ is a diagonal matrix, both of which have dimensions of (N +1) × (N + 1);
(2)
Figure BDA00029075511700000614
obtaining a random vector
Figure BDA00029075511700000615
Wherein r is a random variable, r-CN (0, 1);
(3) to obtain
Figure BDA00029075511700000616
Wherein [ X ]](1:N)Represents the vector of [ X ]]The first N elements of (a); obtaining an optimized reflecting surface; by generating enough random variables r, an approximation of (P3) is optimized using the SDR method.
Further, in the power allocation optimization sub-problem, for power allocation of two users, a channel model is a rayleigh channel
Figure BDA0002907551170000071
Wherein d isiIs a base station and a user
Figure BDA0002907551170000072
Distance between, path loss is denoted by α;
Figure BDA0002907551170000073
is the Rayleigh fading coefficient, and the noise power of all users is σ2；
For an SM-NOMA system of two users, a sending symbol is a traditional APM symbol, and one antenna is selected at a sending end through spatial modulation, so that the reachable rates of the two users are represented as Rsum＝R1+R2：
Figure BDA0002907551170000074
The power allocation optimization problem of the two users is converted into:
Figure BDA0002907551170000075
F(β1,β2) SINR for two users, and beta1+β 21 is ═ 1, i.e：
Figure BDA0002907551170000076
For F (. beta.)1,β2) Beta inside1The partial derivative is calculated and then the first derivative is made equal to 0 as follows:
Figure BDA0002907551170000077
wherein the content of the first and second substances,
Figure BDA0002907551170000078
Figure BDA0002907551170000079
and c ═ σ2，q＝cb2-cb1，p＝cb1+c2；
To obtain
Figure BDA00029075511700000710
The power distribution coefficient of the far user is
Figure BDA0002907551170000081
The power distribution coefficient of the near user is (1-beta)*)。
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objectives and other advantages of the invention may be realized and attained by the means of the instrumentalities and combinations particularly pointed out hereinafter.
Drawings
For purposes of promoting a better understanding of the objects, aspects and advantages of the invention, reference will now be made to the following detailed description taken in conjunction with the accompanying drawings in which:
FIG. 1 is a model of an intelligent reflector assisted SM-NOMA communication system;
FIG. 2 is a diagram of two single antenna user systems and rate performance for different signal-to-noise ratios;
fig. 3 is a diagram of the bit error rate performance of two single antenna user systems under different signal-to-noise ratios.
Detailed Description
The embodiments of the present invention are described below with reference to specific embodiments, and other advantages and effects of the present invention will be easily understood by those skilled in the art from the disclosure of the present specification. The invention is capable of other and different embodiments and of being practiced or of being carried out in various ways, and its several details are capable of modification in various respects, all without departing from the spirit and scope of the present invention. It should be noted that the drawings provided in the following embodiments are only for illustrating the basic idea of the present invention in a schematic way, and the features in the following embodiments and examples may be combined with each other without conflict.
Wherein the showings are for the purpose of illustrating the invention only and not for the purpose of limiting the same, and in which there is shown by way of illustration only and not in the drawings in which there is no intention to limit the invention thereto; to better illustrate the embodiments of the present invention, some parts of the drawings may be omitted, enlarged or reduced, and do not represent the size of an actual product; it will be understood by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted.
The same or similar reference numerals in the drawings of the embodiments of the present invention correspond to the same or similar components; in the description of the present invention, it should be understood that if there is an orientation or positional relationship indicated by terms such as "upper", "lower", "left", "right", "front", "rear", etc., based on the orientation or positional relationship shown in the drawings, it is only for convenience of description and simplification of description, but it is not intended to indicate or imply that the referred device or element must have a specific orientation, be constructed in a specific orientation, and be operated, and therefore, the terms describing the positional relationship in the drawings are only used for illustrative purposes and are not to be construed as limiting the present invention, and it is possible for a person having ordinary skill in the art to understand the specific meaning of the above terms according to specific circumstances.
Consider a multi-user SM-NOMA network downlink communication system model based on intelligent reflective surfaces, as shown in fig. 1. It is assumed that W users are divided equally into T groups, thereby guaranteeing K users per group, and that the channel state information is known. For users in each group
Figure BDA0002907551170000091
Indicating that the rank of the group is m e {1, 2.. T }, and the rank of the user in the group is i e {1,2, …, K }. Further, assume that N is provided on the base station sidetA transmitting antenna and a receiving end NrThe root receives the antenna. A transmitting antenna is selected at a transmitting end through spatial modulation, a superposed signal is transmitted at the same time and within the same frequency, and the superposed signal is reflected through an IRS and reaches a receiving end. The IRS consists of N passive reflective elements, each of which, by reflection, can change the phase shift of the incident signal, thereby assisting NOMA transmission.
At the transmitting end of the base station, dividing the bit stream transmitted by each time slot into two blocks, wherein the total number is log2(Nt)+log2(M) bits. Wherein log2(M) bits are used to determine a corresponding transmitted symbol in a signal constellation, where M represents a modulation order; log (log)2(Nt) The bits are used to determine the serial number of the transmit antenna in the spatial constellation. Assuming that the total power of the transmitted signal is P, the power occupied by each data stream is P
Figure BDA0002907551170000092
Wherein the content of the first and second substances,
Figure BDA0002907551170000093
is a user
Figure BDA0002907551170000094
A power allocation factor. Thus, the transmitted superimposed signal can be described as:
Figure BDA0002907551170000095
then the user
Figure BDA0002907551170000096
Of a data stream
Figure BDA0002907551170000097
Can be described as:
Figure BDA0002907551170000098
wherein the content of the first and second substances,
Figure BDA0002907551170000099
representing a user
Figure BDA00029075511700000910
The serial number of the selected antenna is selected,
Figure BDA00029075511700000911
indicating the modulated transmission symbols.
Based on an IRS-SM-NOMA system, a channel is divided into two parts, wherein one part is a direct channel from a base station to a user, and the other part is a reflection channel from the base station, an intelligent reflecting surface and the user. Assuming independent identically distributed Rayleigh fading channels between base station and user i, i.e.
Figure BDA00029075511700000912
Assuming that the channel of the base station-intelligent reflecting surface is a Rice channel and the channel vector is
Figure BDA00029075511700000913
Wherein N is the number of the intelligent reflecting surfaces, then
Figure BDA00029075511700000914
Wherein eta is1Is the rayleigh fading coefficient of the channel f,
Figure BDA00029075511700000915
and
Figure BDA00029075511700000916
respectively a direct-view path and a non-direct-view path.
Figure BDA00029075511700000917
Each element in (a) is independent and follows a distribution with a mean of 0 and a variance of 1. Further, the phase shift matrix theta of the intelligent reflecting surface is expressed by a diagonal matrix, namely
Figure BDA00029075511700000918
Wherein theta isn∈[0,2π]. Intelligent reflecting surface to user
Figure BDA00029075511700000919
Is a channel of
Figure BDA00029075511700000920
Thus users
Figure BDA00029075511700000921
The channels of (a) may be described as:
Figure BDA00029075511700000922
since IRS channels have uncertainty before optimization, it is assumed
Figure BDA0002907551170000101
And the order of the channel gains is:
Figure BDA0002907551170000102
herein, the
Figure BDA0002907551170000103
And
Figure BDA0002907551170000104
rayleigh channels representing user 1, user 2, user 3 and user K, respectively, since here single antenna users are considered, i.e. users with single antenna
Figure BDA0002907551170000105
So that the user
Figure BDA0002907551170000106
The received signals are:
Figure BDA0002907551170000107
herein, the
Figure BDA0002907551170000108
Is a user
Figure BDA0002907551170000109
Of the received signal, n0Is additive white Gaussian noise, obeys a mean value of 0 and has a variance of sigma2Complex gaussian distribution. j is a function ofiRepresenting a user
Figure BDA00029075511700001010
Is subject to spatial modulation of the selected jth antenna,
Figure BDA00029075511700001011
representing a user
Figure BDA00029075511700001012
And the jth transmit antenna.
The user grouping algorithm based on the effective channel gain comprises the following steps:
the channel gain referenced when users are grouped is: channels before IRS optimization, i.e.
Figure BDA00029075511700001013
First, only one transmit antenna is selected in the IRS-SM-NOMA, because the effective channel gain is different from the overall channel gain,so only the effective direct channel gain of the ith user needs to be considered, i.e.
Figure BDA00029075511700001014
The steps of grouping users are as follows:
(1) user pre-allocation: assuming that there are W alternative users, according to the distance between the base station and each user, the user set is divided into 3 types: near users, center users, and far users.
(2) Sorting in descending order of users: and each alternative user of the initial set is sorted in a descending order according to the effective channel gain.
(3) And (3) selecting by the user: the users with the largest difference in effective channel gain can be selected from the corresponding initial set to be grouped, and all grouping conditions are returned until all users complete grouping. And after the optimization of the reflecting surface is finished, performing iteration once again.
Constructing a joint optimization model of intelligent reflecting surface phase shift and power distribution:
suppose there are K users per group, users
Figure BDA00029075511700001015
When decoding the signal, the signals from other weak users are regarded as interference, and in this time, the users
Figure BDA00029075511700001016
The Signal to Interference Noise Ratio (SINR) of (1) can be expressed as:
Figure BDA0002907551170000111
then, the user
Figure BDA0002907551170000112
The corresponding rates are:
Figure BDA0002907551170000113
in order to maximize the transmission rate of the system while ensuring fairness for each user, an optimization scheme for maximizing SINR (by jointly optimizing power allocation coefficients of users) is adopted according to equation (11)
Figure BDA0002907551170000114
And IRS, to maximize user and rate).
Figure BDA0002907551170000115
Thus, the optimal maximization is assumed-the minimum SINR is Q, where Q is a relaxation variable, i.e.
Figure BDA0002907551170000116
The optimization problem can be transferred as:
Figure BDA0002907551170000117
the method comprises the following steps: under the condition of a given signal-to-noise ratio, the power is assumed to have a determined value to optimize theta so as to achieve the purpose of maximizing channel gain; then, power allocation is performed (determining β) according to the number of users in the group, so that (P1) is divided into two optimization problems, and the sum rate of the users is maximized.
Wherein the phase shift optimization sub-problem solving comprises:
in accordance with the foregoing, for the user
Figure RE-GDA0003031237140000116
Given a fixed power distribution coefficient and then splitting (P2) into two parts, the channel gain can be maximized by optimizing the intelligent reflector phase, starting with the following problem:
Figure BDA0002907551170000122
let I ═ l1,…,lN]H，
Figure BDA0002907551170000123
And is
Figure BDA0002907551170000124
Further order
Figure BDA0002907551170000125
Then
Figure BDA0002907551170000126
Thus, can obtain
Figure BDA0002907551170000127
The optimization problem of (P3) can be equivalent to:
Figure BDA0002907551170000128
(P3) is a problem of non-convex quadratic constraints, (P3) can be restated as a non-convex homogeneous problem by introducing an auxiliary variable t, so (P4) can be transformed into equivalent write:
Figure BDA0002907551170000129
wherein the content of the first and second substances,
Figure BDA00029075511700001210
however, it is difficult to solve the problem (P5) directly. Due to the fact that
Figure BDA00029075511700001211
When L satisfies L ≧ 0 and
Figure BDA00029075511700001212
when, define
Figure BDA00029075511700001213
Because the first constraint is non-convex, the semi-definite relaxation (SDR) method is used to relax this constraint, so the problem (P5) can be simplified as:
Figure BDA00029075511700001214
it can be seen that (P6) is non-convex, but since rank (l) ≠ 1, the optimal value of (P6) does not satisfy the optimization target of (P3), but only satisfies the upper bound of (P5). Therefore, in order to obtain a condition satisfying the first-stage optimization, the rank of L needs to be reduced to 1, and a semi-definite relaxation technique and a gaussian randomization scheme are adopted:
(1) decomposing L as characteristic value, L being U ∑ UHWhere U is a unitary matrix and Σ is a diagonal matrix, both of which have dimensions of (N +1) × (N + 1).
(2) At this time, the process of the present invention,
Figure BDA00029075511700001215
a random vector can be obtained
Figure BDA00029075511700001216
Where r is a random variable, r-CN (0, 1).
(3) Thus can obtain
Figure BDA0002907551170000131
Wherein [ X ]](1:N)Represents the vector of [ X ]]The first N elements in (a). An optimized reflecting surface can be obtained. In summary, by generating enough random variables r, an approximation of (P3) can be optimized using the SDR method.
Wherein, the power distribution optimization sub-problem solution comprises two-user power distribution and multi-user power distribution, and the two-user power distribution comprises:
consider first the case where there are two users in a group. Assuming the channel model as a Rayleigh channel
Figure BDA0002907551170000132
Wherein d isiIs a base station and a user
Figure BDA0002907551170000133
Distance between, path loss is denoted by α;
Figure BDA0002907551170000134
is the rayleigh fading coefficient. In general, the noise power of all users is σ2。
For the two-user NOMA-SM system, the transmit symbols are conventional APM symbols. When one antenna is selected by spatial modulation at the transmitting end, the reachable rate of two users can be represented as Rsum＝R1+R2：
Figure BDA0002907551170000135
Figure BDA0002907551170000136
In order to guarantee the service quality of each user and simultaneously realize the maximum sum rate of the users, the power allocation scheme of the double users in the SM-NOMA system is applied to the IRS-SM-NOMA system, but the current selected antenna is only considered for the narrow-band channel gain, and other antennas are not considered. Thus, the power allocation optimization problem for dual users can be translated into:
Figure BDA0002907551170000137
F(β1,β2) SINR for two users, and beta1+β 21, namely:
Figure BDA0002907551170000138
by mathematical analysis, for F (. beta.)1,β2) Beta inside1Calculating a deviation, thenLet the first derivative equal 0, as follows:
Figure BDA0002907551170000141
wherein the content of the first and second substances,
Figure BDA0002907551170000142
and c ═ σ2，q＝cb2-cb1，p＝cb1+c2。
It is obvious that
Figure BDA0002907551170000143
B is obtained according to the distance relation between the user and the base station1＞b2And q is less than 0. Therefore, the temperature of the molten metal is controlled,
Figure BDA0002907551170000144
the feasible region of beta is exceeded, so it is discarded. Therefore, the power distribution coefficient of the far user is
Figure BDA0002907551170000145
The power distribution coefficient of the near user is (1-beta)*)。
In this embodiment, the validity of the algorithm will be verified by simulation. The proposed IRS-SM-NOMA scheme is verified in simulation in FIG. 2 to be superior to conventional SM-NOMA, SM-OMA, MISO-NOMA, which compared to SM-OMA, demonstrates the effectiveness of the power allocation scheme IRS-SM-NOMA over SM-NOMA because the effective channel gain becomes large.
In FIG. 3, the error rate performance of IRS-SM-NOMA and conventional SM-NOMA are compared. As can be seen from the figure: the error rate of the IRS-SM-NOMA scheme is superior to that of the traditional SM-NOMA scheme.
Finally, the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting, although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions may be made on the technical solutions of the present invention without departing from the spirit and scope of the technical solutions, and all that should be covered by the claims of the present invention.

Claims (8)

1. An intelligent reflector assisted SM-NOMA system resource allocation method is characterized in that: the method comprises the following steps:
for the intelligent reflector assisted SM-NOMA system, dynamic user grouping is carried out by considering the effective channel gain of each user; and establishing a power distribution model with the aim of maximizing the system and the speed according to the maximum transmitting power constraint of the base station and the user and the incident signal phase shift constraint of the intelligent reflection unit.
2. The intelligent reflector assisted SM-NOMA system resource allocation method according to claim 1, characterized in that: the intelligent reflecting surface assisted SM-NOMA system comprises a base station transmitting end, an intelligent reflecting surface and a user receiving end; wherein:
the user receiving end includes: w users are divided equally into T groups, each group has K users, the channel state information is known; users in each group
Figure RE-FDA0002999051890000011
Is the serial number of the group, i belongs to {1,2, …, K } is the serial number of the user in the group;
equipping N at the transmitting end of a base stationtA transmitting antenna, a receiving end having NrA root receiving antenna; selecting a transmitting antenna at a transmitting end of a base station through spatial modulation, transmitting a superposed signal at the same time and at the same frequency, reflecting the superposed signal through an intelligent reflector IRS (infrared receiver) and reaching a receiving end of a user;
the IRS consists of N passive reflective elements, each of which, by reflection, changes the phase shift of the incident signal, thereby assisting NOMA transmission.
3. The intelligent reflector assisted SM-NOMA system resource allocation method according to claim 2, characterized in that: at the transmitting end of the base station, dividing the bit stream transmitted by each time slot into two blocks, wherein the total number is log2(Nt)+log2(M) bits; wherein log2(M) bits are used to determine a corresponding transmitted symbol in a signal constellation, where M represents a modulation order; log (log)2(Nt) The bits are used for determining the serial number of the transmitting antenna in the space constellation diagram; the total power of the transmitted signal is P, and the power occupied by each data stream is P
Figure RE-FDA0002999051890000012
Wherein the content of the first and second substances,
Figure RE-FDA0002999051890000013
is a user
Figure RE-FDA0002999051890000014
Power allocation factor, the transmitted superimposed signal is:
Figure RE-FDA0002999051890000015
user' s
Figure RE-FDA0002999051890000016
Of a data stream
Figure RE-FDA0002999051890000017
Comprises the following steps:
Figure RE-FDA0002999051890000018
wherein the content of the first and second substances,
Figure RE-FDA0002999051890000019
representing a user
Figure RE-FDA00029990518900000110
The serial number of the selected antenna is selected,
Figure RE-FDA00029990518900000111
indicating the modulated transmission symbols.
4. The intelligent reflector assisted SM-NOMA system resource allocation method according to claim 3, characterized in that: based on the intelligent reflector assisted SM-NOMA system, a channel is divided into two parts, wherein one part is a direct channel from a base station to a user, and the other part is a reflection channel from the base station to the intelligent reflector to the user; rayleigh fading channels subject to independent equal distribution from base station to user i, i.e.
Figure RE-FDA0002999051890000021
The channel of the base station-intelligent reflecting surface is a Rice channel, and the channel vector is
Figure RE-FDA0002999051890000022
Wherein N is the number of intelligent plane of reflection, then:
Figure RE-FDA0002999051890000023
wherein eta is1Is the rayleigh fading coefficient of the channel f,
Figure RE-FDA0002999051890000024
and
Figure RE-FDA0002999051890000025
direct-view path and non-direct-view path, respectively;
Figure RE-FDA0002999051890000026
each element in (a) is independent and follows a distribution with a mean of 0 and a variance of 1;
the phase shift matrix theta of the intelligent reflecting surface is expressed by a diagonal matrix, namely
Figure RE-FDA0002999051890000027
Wherein theta isn∈[0,2π](ii) a Intelligent reflecting surface to user
Figure RE-FDA0002999051890000028
Is a channel of
Figure RE-FDA0002999051890000029
User' s
Figure RE-FDA00029990518900000210
The channel description of (c) is:
Figure RE-FDA00029990518900000211
the channel gain order is:
Figure RE-FDA00029990518900000212
Figure RE-FDA00029990518900000213
and
Figure RE-FDA00029990518900000214
rayleigh channels representing user 1, user 2, user 3 and user K, respectively, wherein
Figure RE-FDA00029990518900000215
User' s
Figure RE-FDA00029990518900000216
The received signals are:
Figure RE-FDA00029990518900000217
wherein
Figure RE-FDA00029990518900000218
Is a user
Figure RE-FDA00029990518900000219
Of the received signal, n0Is additive white Gaussian noise, obeys a mean value of 0 and has a variance of sigma2Complex Gaussian distribution of jiRepresenting a user
Figure RE-FDA00029990518900000220
Is subject to spatial modulation of the selected jth antenna,
Figure RE-FDA00029990518900000221
representing a user
Figure RE-FDA00029990518900000222
And the jth transmit antenna.
5. The intelligent reflector assisted SM-NOMA system resource allocation method according to claim 1, characterized in that: the dynamic user grouping comprises the steps of:
user pre-allocation: there are W alternative users, and the user set is divided into 3 types according to the distance between the base station and each user: near users, center users, and far users;
sorting in descending order of users: sorting the alternative users of each initial set in a descending order according to the effective channel gain;
and (3) selecting by the user: selecting the users with the largest difference of effective channel gains from the corresponding initial set to divide the users into a group, and returning all grouping conditions until all the users finish grouping; after the optimization of the reflecting surface is finished, carrying out one iteration on the reflecting surface;
the channel gain referenced when users are grouped is: channels before IRS optimization, i.e.
Figure RE-FDA0002999051890000031
Firstly, only one transmitting antenna is selected in IRS-SM-NOMA, and the ith user is consideredEffective direct channel gain, i.e.
Figure RE-FDA0002999051890000032
6. The intelligent reflector assisted SM-NOMA system resource allocation method according to claim 1, characterized in that: the power allocation model targeted to maximize system and rate includes:
each group has K users
Figure RE-FDA0002999051890000033
When decoding the signal, the signal from other weak users is regarded as interference, and the user
Figure RE-FDA0002999051890000034
The signal to interference plus noise ratio SINR of (signal to interference plus noise ratio) is expressed as:
Figure RE-FDA0002999051890000035
user' s
Figure RE-FDA0002999051890000036
The corresponding rates are:
Figure RE-FDA0002999051890000037
according to equation (11), an optimization scheme is adopted to maximize the SINR, i.e. by jointly optimizing the power allocation coefficients of the users
Figure RE-FDA0002999051890000038
And the phase shift Θ of IRS, maximizing user and rate:
Figure RE-FDA00029990518900000315
s.t.C1:
Figure RE-FDA00029990518900000310
C2:
Figure RE-FDA00029990518900000311
C3:
Figure RE-FDA00029990518900000312
C4:
Figure RE-FDA00029990518900000313
optimal maximization-the minimum SINR is Q, where Q is a relaxation variable, i.e.
Figure RE-FDA00029990518900000314
The optimization problem is then transferred to:
Figure RE-FDA00029990518900000422
s.t.C1:
Figure RE-FDA0002999051890000042
C2:
Figure RE-FDA0002999051890000043
C3:
Figure RE-FDA0002999051890000044
C4:
Figure RE-FDA0002999051890000045
under the condition of a given signal-to-noise ratio, the power is assumed to have a determined value to optimize theta so as to achieve the purpose of maximizing channel gain; and then, carrying out power distribution according to the number of users in the group, determining beta, and dividing (P1) into two optimization problems to maximize the sum rate of the users, namely a phase shift optimization sub-problem and a power distribution optimization sub-problem.
7. The intelligent reflector assisted SM-NOMA system resource allocation method according to claim 6, characterized in that: the phase shift optimization sub-problem comprises:
for the user
Figure RE-FDA0002999051890000046
Given a fixed power distribution coefficient, and then splitting (P2) into two parts, the channel gain is maximized by optimizing the intelligent reflector phase, starting with the following problem:
Figure RE-FDA00029990518900000423
Figure RE-FDA0002999051890000048
let I ═ l1,…,lN]H，
Figure RE-FDA0002999051890000049
And is
Figure RE-FDA00029990518900000410
Further order
Figure RE-FDA00029990518900000411
Then
Figure RE-FDA00029990518900000412
To obtain
Figure RE-FDA00029990518900000413
The optimization problem of (P3) is equivalent to:
Figure RE-FDA00029990518900000424
Figure RE-FDA00029990518900000415
(P3) is a problem of non-convex quadratic constraints, restated (P3) as a non-convex homogeneous problem by introducing an auxiliary variable t, (P4) transforms the equivalent write:
Figure RE-FDA00029990518900000425
Figure RE-FDA00029990518900000417
wherein the content of the first and second substances,
Figure RE-FDA00029990518900000418
due to the fact that
Figure RE-FDA00029990518900000419
When L satisfies L ≧ 0 and
Figure RE-FDA00029990518900000420
when, define
Figure RE-FDA00029990518900000421
The first constraint is non-convex and is relaxed using a semi-deterministic relaxation SDR methodThis constraint, the problem (P5), reduces to:
Figure RE-FDA0002999051890000051
Figure RE-FDA0002999051890000052
Figure RE-FDA00029990518900000513
(P6) is non-convex, processed by reducing the rank of L to 1, by using a semi-deterministic relaxation technique and a gaussian randomization scheme:
(1) decomposing L as characteristic value, L being U ∑ UHWhere U is a unitary matrix and Σ is a diagonal matrix, both of which have dimensions of (N +1) × (N + 1);
(2)
Figure RE-FDA0002999051890000053
obtaining a random vector
Figure RE-FDA0002999051890000054
Wherein r is a random variable, r-CN (0, 1);
(3) to obtain
Figure RE-FDA0002999051890000055
Wherein [ X ]](1:N)Represents the vector of [ X ]]The first N elements of (a); obtaining an optimized reflecting surface; by generating enough random variables r, an approximation of (P3) is optimized using the SDR method.
8. The intelligent reflector assisted SM-NOMA system resource allocation method according to claim 6, characterized in that: in the power allocation optimization sub-problem, for power allocation of two users, the channel model is a rayleigh channel
Figure RE-FDA0002999051890000056
Wherein d isiIs a base station and a user
Figure RE-FDA0002999051890000057
Distance between, path loss is denoted by α;
Figure RE-FDA0002999051890000058
is the Rayleigh fading coefficient, and the noise power of all users is sigma2；
For an SM-NOMA system of two users, a sending symbol is a traditional APM symbol, and one antenna is selected at a sending end through spatial modulation, so that the reachable rates of the two users are represented as Rsum＝R1+R2：
Figure RE-FDA0002999051890000059
Figure RE-FDA00029990518900000510
The power allocation optimization problem of the two users is converted into:
Figure RE-FDA00029990518900000511
Figure RE-FDA00029990518900000512
F(β1,β2) SINR for two users, and beta1+β21, namely:
Figure RE-FDA0002999051890000061
for F (. beta.)1,β2) Beta inside1The partial derivative is calculated and then the first derivative is made equal to 0 as follows:
Figure RE-FDA0002999051890000062
wherein the content of the first and second substances,
Figure RE-FDA0002999051890000063
Figure RE-FDA0002999051890000064
and c ═ σ2，q＝cb2-cb1，p＝cb1+c2；
To obtain
Figure RE-FDA0002999051890000065
The power distribution coefficient of the far user is
Figure RE-FDA0002999051890000066
The power distribution coefficient of the near user is (1-beta)*)。
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