CN110149127A - A kind of D2D communication system precoding vector optimization method based on NOMA technology - Google Patents

A kind of D2D communication system precoding vector optimization method based on NOMA technology Download PDF

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CN110149127A
CN110149127A CN201910530716.5A CN201910530716A CN110149127A CN 110149127 A CN110149127 A CN 110149127A CN 201910530716 A CN201910530716 A CN 201910530716A CN 110149127 A CN110149127 A CN 110149127A
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沈鑫梦
杜毅豪
吴伟
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Nanjing Post and Telecommunication University
Nanjing University of Posts and Telecommunications
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H04B7/0456—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W24/00—Supervisory, monitoring or testing arrangements
    • H04W24/02—Arrangements for optimising operational condition
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W4/00—Services specially adapted for wireless communication networks; Facilities therefor
    • H04W4/70—Services for machine-to-machine communication [M2M] or machine type communication [MTC]

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Abstract

The invention discloses a kind of D2D communication system precoding vector optimization method based on NOMA technology, a wireless device directly can send information to two internal users under the non-orthogonal multiple access way with low time delay.Wherein, two users are all made of successive interference cancellation technology to be decoded by given decoding order to information.The constraint of transmission power based on given quality of service requirement and wireless device, the maximum rate and corresponding precoding vectors of decoding information after being obtained by application positive semidefinite relaxing techniques and Lagrange duality method.The present invention obtains best precoding vector by optimization method, it was demonstrated that the sigma compactness of positive semidefinite relaxation to improve wireless communication transmissions rate, while reducing the outage probability of communication system.The invention also provides a kind of radio communication systems based on singular value decomposition, and computation complexity can be effectively reduced.

Description

A kind of D2D communication system precoding vector optimization method based on NOMA technology
Technical field:
The present invention relates to fields of communication technology, more particularly to a kind of D2D for being based on non-orthogonal multiple access technology (NOMA) Communication system precoding vector optimization method.
Background technique:
Non-orthogonal multiple (NOMA) is the communication mode for realizing that one kind that 5G challenge requires is rising, is had in big The advantages that scale connection, high data rate and low latency.Facts proved that it is the feasible of the following dense network and internet of things equipment Solution.The different NOMA design of many combination multiple-input and multiple-outputs (MIMO), millimetre-wave attenuator and cooperative relaying has gone out Now in a recent study.Zhao Rui distinguishes user using power by the function division multiple access technology of NOMA, and user can simultaneously, together Defeated signal is kept pouring in, power system capacity is substantially increased.The scholars such as Stelios Timotheou specifically have studied NOMA and single user MIMO technology, NOMA in conjunction with multiuser MIMO technology after related communication resource allocation algorithm problem.Stelios The scholars such as Timotheou are based on user power distribution and propose a kind of multinomial algorithm, are in transient channel solving transmission user CSI under state and average channel condition acquires optimal solution.The scholars such as Wang Qianzhu mainly have studied the letter of NOMA downlink Number test problems, by eliminating the design of (SIC) receiver, subscriber signal detection algorithm, channel coding etc. to simple interference It is studied, realizes receiving end subscriber signal and efficiently separate, so that system communication performance is preferably promoted.Random chance Wave beam forming is a kind of signal processing technology for beam communication in wireless system, it is proposed for MIMO NOMA first System, transmitter generate multiple wave beams and are superimposed multiple users wherein.Assuming that complete channel state information (CSI) can be used for Transmitter proposes beam forming and user's pairing scheme based on force zero for downlink multiuser NOMA system.Therefore, NOMA and multi-user beam-forming are integrated with the advantages of may having both NOMA and beam forming.Device-to-device (D2D) communication Neighbouring user is directly in communication with each other without relying on base station, therefore it is a kind of reliable and the communication of low latency Mode.
Summary of the invention
Goal of the invention: of the existing technology in order to solve the problems, such as, the object of the present invention is to provide one kind based on nonopiate The D2D communication system precoding vector optimization method of multiple access technique (NOMA), the optimization method computation complexity is low, can Wireless communication transmissions rate is significantly improved, while reducing the outage probability of communication system.
A kind of technical solution: D2D communication system precoding vector optimization method based on NOMA, comprising the following steps:
Step 1: under beehive network system, a wireless device is inside under the non-orthogonal multiple agreement with low latency Portion user 1 and user 2 send message, and the user 1 and user 2 are decoded message by given decoding order, provide use Family 1 and user 2 are to message s1And s2Signal to Interference plus Noise Ratio；
Step 2: according to decoding order, providing the achievable transmission rate of user 1 and user 2 respectively；
Step 3: transmission power is completely used for forwarding message s1With message s2, excess power wirelessly sets for receiving and amplify Standby middle information determines the condition that transmission power needs to meet；
Step 4: quality of service requirement and the transmission power constraint given based on user is up to mesh with message transmission rate Mark, completes the mathematical expression of optimization problem；
Step 5: define security interrupt probability to analyze the communication performance of whole system transmission process, while according to step 2, The analysis of step 3 and step 4 is as a result, provide the expression formula of the Transmission probability of whole system, and derive result.
Further, in the step 1, fairness and about definite decoding sequence is transmitted based on user message, provide use respectively Family 1 sends s1And s2Signal to Interference plus Noise Ratio SINRi,1And user 2 sends s1And s2Signal to Interference plus Noise Ratio SINRi,2:
Wherein,The multiple Gauss channel vector of user 1 and user 2 are respectively indicated, they are independent same distributions Fading channel；The mean square deviation of σ expression Gaussian noise；It is s respectively1And s2Precoding vector.
Further, in the step 2, s2Achievable rate are as follows:
R2=min [log2(1+SINR1,2),log2(1+SINR2,2)]
s1Achievable rate are as follows:
R1=[log2(1+SINR1,1)-log2(1+SINR2,1)]+。
Further, in the step 3, the sum of power needed for receiving and amplifying is no more than default emission maximum function Rate, i.e. transmission power need to meet:
E[xHX]=| | w1||2+||w2||2≤P
Wherein, E [xHX] indicate transmission power, | | w1||2Indicate power needed for sending information 1, | | w2||2It indicates to send letter Power needed for breath 2, P indicate default maximum transmission power.
In the step 4, using objective programming, with s1Achievable rate maximum turn to target, establish objective function； Using given quality of service requirement and wireless device transmission power as constraint condition, problem is optimized, optimization algorithm is as follows:
s.t.R2≥γM
||w1||2+||w2||2≤P
Wherein,RmIt is s2Targeted rate, meet corresponding quality of service requirement.
Further, in the step 5, objective function is rewritten are as follows:
Meanwhile utilizing s2Signal to Interference plus Noise Ratio indicate step 4 in quality of service requirement constraint, obtain following semi definite programming Problem:
||w1||2+||w2||≤P
Using the optimal solution of positive semidefinite relaxation Solve problems, algorithm is as follows:
||w1||2+||w2||≤P
Parameter t is introduced, following formula is obtained:
Wherein,For vector A, tr (A) are the order of vector A.
Preferably, the semi definite programming problem is solved based on singular value decomposition method:
||w1||2+||w2||≤P
IfWithIndicate that dual variable, dual problem are expressed as follows:
Wherein, To solve centre set by dual problem Variable, I are unit matrix；
Obtain the precoding vector based on singular value decomposition:
Wherein,
The utility model has the advantages that compared to the prior art, the present invention has following marked improvement 1, is obtained most preferably by optimization method Precoding vector, it was demonstrated that the sigma compactness of positive semidefinite relaxation, to improve wireless communication transmissions rate 2, can reduce communication system Outage probability；3, using a kind of radio communication system based on singular value decomposition, computation complexity is effectively reduced.
Detailed description of the invention
Fig. 1 is the schematic diagram that a kind of D2D communication network sends message by NOMA agreement to two users.
Fig. 2 is the maximum rate performance and transmission power of different schemes as WD antenna amount N=4 and N=4bps/Hz The relationship of P.
Fig. 3 is targeted rate (the i.e. R as WDM) be 4bps/Hz and 6bps/Hz when, in the transmission power P=25dBm of WD Under conditions of, the R of different schemes1Maximum rate and the ratio between the antenna amount of WD.
Fig. 4 is the antenna amount N=4 as WD, when transmission power is respectively 25dBm and 20dBm, R under different schemes1's Maximum rate and targeted rate RM。
Fig. 5 is the antenna amount N=4 as WD, when transmission power P is 25dBm, R under different schemes1Outage probability with RM Variation.
Specific embodiment
In the following with reference to the drawings and specific embodiments, technical solution of the present invention is described in detail.
One kind being based on the D2D communication system precoding vector optimization method of non-orthogonal multiple access technology (NOMA), including Following steps:
Step 1: as shown in Figure 1, consider the cellular communications networks system of a D2D, including base station and K first floor system, One base station can serve one group of phone user by wireless device (WD).Base station can be assisted by NOMA in each subsystem It discusses to two internal users and sends message.Wherein, it is contemplated that the fairness and reliability of user message transmission, two with adopting per family Message is decoded by given decoding order with successive interference cancellation technology (SIC).
S is used respectively1And s2Indicate the message of user 1 and user 2.Assuming that s1And s2It is there is unit averaged power any Independent random signal, i.e. E [| s1|2]=E [| s2|2]=1.Therefore, the composite baseband of WD sends signal and can be expressed as:
X=w1s1+w2s2 (1)
WhereinIt is s respectively1And s2Precoding vector.The observation result of two users is as follows:
y1=h1 Hx+n1=h1 H(w1s1+w2s2)+n1 (2)
y2=h2 Hx+n2=h2 H(w1s1+w2s2)+n2 (3)
Wherein,The multiple Gauss channel vector of user 1 and user 2 are respectively indicated, they are independent same distributions Fading channel.n1,n2It is additive white Gaussian noise (AWGN), meets n1,n2~CN (0, σ2)。
Consider two user's signal intelligences, fairness and about definite decoding sequence are transmitted based on user message, provide two use Family sends s1And s2Signal to Interference plus Noise Ratio:
Step 2: according to decoding principle, s2Priority with higher, takes s2To smaller in 2 Signal to Interference plus Noise Ratio of user 1 and user Person is as its achievable rate R2。
R2=min [log2(1+SINR1,2),log2(1+SINR2,2)] (6)
Indeed it is contemplated that s1It will be received by user 1, therefore s1Achievable rate are as follows:
R1=[log2(1+SINR1,1)-log2(1+SINR2,1)]+ (7)
It is worth noting that, being only just able to verify that and depositing when bad channel conditions of the channel condition of user 1 unlike user 2 In effective s1Rate.
Step 3: the transmission power that wireless device (WD) needs is discussed.Since transmission power P almost all is for forwarding s1 And s2, and the energy for receiving and amplifying message in WD is provided by excess power, so the sum of power needed for reception and amplification is no It can exceed that default maximum transmission power, i.e. transmission power needs to meet:
E[xHX]=| | w1||2+||w2||2≤P (8)
Step 4: in order to realize s1Maximumlly achievable rate, establishes objective programming equation, with s1Achievable rate Maximum turns to target, using the given transmission power of the predetermined QoS of user 2 and WD as constraint condition, optimizes to problem, optimization Algorithm is as follows:
s.t.R2≥γM (10)
||w1||+||w2||2≤P (11)
Wherein,RMIt is s2Targeted rate, meet given qos requirement.
Step 5: in order to solve above-mentioned non-convex problem, propose two kinds of algorithms:
The non-trivial situation (9) to consider a problem, wherein objective function is positive and can rewrite are as follows:
Obviously, using identical constraint,WithThere is identical optimal solution.
Meanwhile (11) are divided into about s2Two of SINR constraints.So what problem (9) similarly had the following problems Best solution:
The optimal solution of Solve problems (9) is gone using SDR, defines W1=w1w1 H, W2=w2w2 H,H1=h1h1 H, H2=h2h2 HAnd Ignore rank (W1)=rank (W2The constraint of)=1, available:
In order to solve this problem, using parameter t by molecule and denominator with separate.
Wherein,Being in (14) can Capable.(14) will be optimized first against given t.For convenience, (15) are rewritten as following form:
s.t.tr(H1W2)≥γM[tr(H2W1)+σ2] (17)
tr(H2W2)≥γM[tr(H2W1)+σ2] (18)
tr(W1)+tr(W2)≤P (19)
Meanwhile problem (16) belongs to SDP problem, it is possible to be efficiently solved by convex optimization solver.
Proposition 1: the optimal solution of problem (16) meets rank (W1 *)=rank (W2 *)=1.
Prove: obviously, problem (16) is an individual SDP, and there are three Generalized Constraineds.Optimal solution (W1 *, W2 *) arrive (16) Always meet rank2(W1 *)+rank2(W2 *)≤3.Here consider W1 *≠ 0 and W2 *≠ 0 non-trivial situation, then can obtain rank(W1 *)=rank (W2 *)=1.Proposition 1 is proved to, and demonstrates the sigma compactness of SDR.
Enable α1,α2And α3It respectively indicates and constraint (17), (18) and (19) associated dual variable.Dual problem extension Are as follows:
s.t.A≤0,B≤0 (21)
α1≤0,α2≤0,α3≥0 (22)
Wherein,
A=- α3I+(1-α1γM)H1-(t+α2γM)H2 (23)
B=- α3I+α1H1+α2H2 (24)
Utilize the optimal dual solution (α obtained by Solve problems (20)1 *, α2 *, α3 *), it can be by by (α1 *, α2 *, α3 *) It substitutes into (23) and (24) and acquires A respectively*And B*.In addition, obtaining A according to the complementary slackness condition of (21)*W1 *=0, B*W2 *=0. Due to rank (W1 *)=1 and rank (W2 *)=1 obtains rank (A*)=N-1 and rank (B*)=N-1, allows u1And u2Respectively as A*And B*Kernel basis, and defineIt obtains:
Wherein, τ1And τ2Namely for sending information s1And s2Power partition coefficient
Therefore, best precoding vector is the w of given t1 *=τ1u1,w2 *=τ2u2。
Proposition 2: the optimal bilingual α of problem (20)3 *Meet α3 *> 0.
It proves: proving optimal solution α using reduction to absurdity3 *> 0.
Assuming that α3 *=0, only work as α1 *=α2 *When=0, matrix B*Just meet constraint condition (21), i.e. α1 *H1+α2 *H2≤0。 In addition, (16) are convex functions and meet Slater condition, gap between the two is 0, i.e., (16) and (20) are 0.Therefore F (t) =(1-t) σ2.According to lemma 2, as F (t*When)=0, the optimal solution of problem (16) is identical as problem (14).So t*=1, and R1Maximum rate be log2t*=0.It is unreasonable, then α3 *> 0 is necessary for very, so that proposition 2 is proved to.
It by using positive semidefinite relaxing techniques and solves dual problem in algorithm 1 and derives the optimal solution of (13) of ging wrong. But find optimal t*Cyclic search reduce the feasibility of optimal solution to a certain extent.So in order to solve this problem, The invention proposes a kind of sub-optimum solutions based on SVD, to further decrease computational complexity.
Problem (20) has computation complexity more lower than problem (14), and with the increase of WD antenna amount, complexity Reduction it is also very significant.The detailed step of the optimal algorithm proposed is summarized as algorithm 1.
Algorithm 1
Precoding vector w based on SVD1It can be expressed asWhereinIndicate the new vector to be designed, and And the s to be designed2Correspondence precoding vector beIt is obvious that in order to keep the solution based on SVD feasible, must be requested that N≥2.Problem (13) is to be expressed as:
DefinitionThere is the SDP based on SVD:
Obviously, optimal solution also meets the constraint of order one.IfWithIndicate that dual variable, dual problem are expressed as follows:
Wherein,
Different from problem (14), problem (27) is convex, and the duality gap between (28) and (29) is also zero.With calculation As method 1, the lagrange duality problem (29) of problem (27) can use, also to reduce computation complexity.(29) are utilized to ask Obtain the solution based on SVDIt is obtained further according to (30) and (31)WithIt enablesWithIt is respectivelyWithKernel base, and defineIt is similar with (25), have the precoding based on SVD to AmountWherein
Sub-optimal algorithm based on SVD is algorithm 2, and compared with algorithm 1, the suboptimal design based on SVD proposed in algorithm 2 exists Do not have to further reduced computation complexity in the case where Dinkelbach method.Algorithm 2 is summarized as follows:
Algorithm 2
Fig. 2 is shown in WD antenna amount N=4 and RMUnder conditions of=4bps/Hz, the maximum rate performance of different schemes With the relationship of transmission power P.In the case where without loss of generality, TDMA is used for the representative of OMA, and wherein WD is only in a time slot In for single user service, between two time slots for two users provide joint Power distribute.It is observed that proposed Optimal and suboptimal design is in R1Maximum rate in terms of be better than tradition TDMA, and this performance advantage is in high transmitting power region In become apparent from.And compared with optimal case, the suboptimal design based on SVD only has slight performance loss.
Fig. 3 compares targeted rate (the i.e. R as WDM) be 4bps/Hz and 6bps/Hz when, in the transmission power P=of WD Under conditions of 25dBm, the R of different schemes1Maximum rate and the ratio between the antenna amount of WD.It is obvious that with antenna amount Increase, R1Maximum rate also will increase, but growth trend is gradually slack-off.In R1Maximum rate in terms of, the optimal side proposed Gap between case and scheme based on SVD is with RMIncrease and reduce.
Fig. 4 is the antenna amount N=4 of WD, when transmission power is respectively 25dBm and 20dBm, R under different schemes1Most Big rate and targeted rate RM.It can be seen that optimal case is R more achievable than the scheme based on SVD1Maximum rate it is bigger.This Outside, with s2The desired increase of targeted rate, optimal difference between suboptimal design reduces.Simultaneously it can be seen that certain Under power, work as RMWhen big, R1Rate may be zero.The reason is that meet s2Targeted rate demand, by all power point Dispensing precoding vector w2, therefore precoding vector w1System performance is had little effect.
Fig. 5 shows the antenna amount N=4 as WD, when transmission power P is 25dBm, R under different schemes1Outage probability with RMVariation.As given antenna amount N, transmission power P and targeted rate RMWhen, outage probability is represented byAs seen from the figure, work as N=4, when transmission power is 25dBm, optimal and suboptimum solution party Case performance is similar, and R is significantly reduced compared with TDMA scheme1Cut off probability.
By simulation result it is found that proposed by the present invention optimal and suboptimum precoding algorithms, are significantly better than TDMA scheme.
To sum up, the present invention is based on the constraints of the transmission power of predefined QoS and wireless device, using positive semidefinite relaxation skill Art and Lagrange duality method obtain the maximum rate and corresponding precoding vectors of latter decoded information, pass through optimization algorithm Precoding vector is obtained, to improve wireless communication transmissions rate, while reducing the outage probability of communication system.In addition, this hair It is bright also by defining a kind of radio communication system based on singular value decomposition, effectively reduce computation complexity.

Claims (7)

1. a kind of D2D communication system precoding vector optimization method based on NOMA, which comprises the following steps:
Step 1: under beehive network system, a wireless device is internally used under the non-orthogonal multiple agreement with low latency Family 1 and user 2 send message, and the user 1 and user 2 are decoded message by given decoding order, provide 1 He of user User 2 is to message s1And s2Signal to Interference plus Noise Ratio；
Step 2: according to decoding order, providing the achievable transmission rate of user 1 and user 2 respectively；
Step 3: transmission power is completely used for forwarding message s1With message s2, excess power is for receiving and amplifying in wireless device Information determines the condition that transmission power needs to meet；
Step 4: quality of service requirement and the transmission power constraint given based on user is up to target with message transmission rate, Complete the mathematical expression of optimization problem；
Step 5: defining security interrupt probability to analyze the communication performance of whole system transmission process, while according to step 2, step 3 and step 4 analysis as a result, provide the expression formula of the Transmission probability of whole system, and derive result.
2. the D2D communication system precoding vector optimization method according to claim 1 based on NOMA, it is characterised in that: In the step 1, fairness and about definite decoding sequence are transmitted based on user message, user 1 is provided respectively and sends s1And s2Letter it is dry It makes an uproar and compares SINRi,1And user 2 sends s1And s2Signal to Interference plus Noise Ratio SINRi,2:
Wherein, h1,The multiple Gauss channel vector of user 1 and user 2 are respectively indicated, they are independent identically distributed decline Fall channel；The mean square deviation of σ expression Gaussian noise；w1,It is s respectively1And s2Precoding vector.
3. the D2D communication system precoding vector optimization method according to claim 1 based on NOMA, it is characterised in that: In the step 2, s2Achievable rate are as follows:
R2=min [log2(1+SINR1,2),log2(1+SINR2,2)]
s1Achievable rate are as follows:
R1=[log2(1+SINR1,1)-log2(1+SINR2,1)]+。
4. the D2D communication system precoding vector optimization method according to claim 1 based on NOMA, it is characterised in that: In the step 3, the sum of power needed for receiving and amplifying needs completely no more than default maximum transmission power, i.e. transmission power Foot:
E[xHX]=| | w1||2+||w2||2≤P
Wherein, E [xHX] indicate transmission power, | | w1||2Indicate power needed for sending information 1, | | w2||2It indicates to send 2 institute of information Power is needed, P indicates default maximum transmission power.
5. the D2D communication system precoding vector optimization method according to claim 3 based on NOMA, it is characterised in that: In the step 4, using objective programming, with s1Achievable rate maximum turn to target, establish objective function；With what is given Quality of service requirement and wireless device transmission power are constraint condition, are optimized to problem, optimization algorithm is as follows:
s.t.R2≥γM
||w1||2+||w2||2≤P
Wherein,RmIt is s2Targeted rate, meet corresponding quality of service requirement.
6. the D2D communication system precoding vector optimization method according to claim 5 based on NOMA, it is characterised in that: In the step 5, objective function is rewritten are as follows:
Meanwhile utilizing s2Signal to Interference plus Noise Ratio indicate step 4 in quality of service requirement constraint, obtain following semi definite programming problem:
||w1||2+||w2||≤P
Using the optimal solution of positive semidefinite relaxation Solve problems, algorithm is as follows:
||w1||2+||w2||≤P
Parameter t is introduced, following formula is obtained:
Wherein,For vector A, tr (A) order for being vector A.
7. the D2D communication system precoding vector optimization method according to claim 6 based on NOMA, it is characterised in that: The semi definite programming problem is solved based on singular value decomposition method:
||w1||2+||w2||≤P
IfWithIndicate that dual variable, dual problem are expressed as follows:
Wherein, To solve intermediate set by dual problem become Amount, I are unit matrix；
Obtain the precoding vector based on singular value decomposition:
Wherein,
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