CN107689859A - SCMA systems code book and power distribution method based on game theory - Google Patents
SCMA systems code book and power distribution method based on game theory Download PDFInfo
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- CN107689859A CN107689859A CN201710757064.XA CN201710757064A CN107689859A CN 107689859 A CN107689859 A CN 107689859A CN 201710757064 A CN201710757064 A CN 201710757064A CN 107689859 A CN107689859 A CN 107689859A
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L5/00—Arrangements affording multiple use of the transmission path
- H04L5/0001—Arrangements for dividing the transmission path
- H04L5/0014—Three-dimensional division
- H04L5/0016—Time-frequency-code
- H04L5/0021—Time-frequency-code in which codes are applied as a frequency-domain sequences, e.g. MC-CDMA
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L5/00—Arrangements affording multiple use of the transmission path
- H04L5/003—Arrangements for allocating sub-channels of the transmission path
- H04L5/0058—Allocation criteria
- H04L5/0076—Allocation utility-based
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L5/00—Arrangements affording multiple use of the transmission path
- H04L5/003—Arrangements for allocating sub-channels of the transmission path
- H04L5/0058—Allocation criteria
- H04L5/006—Quality of the received signal, e.g. BER, SNR, water filling
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04W—WIRELESS COMMUNICATION NETWORKS
- H04W72/00—Local resource management
- H04W72/04—Wireless resource allocation
- H04W72/044—Wireless resource allocation based on the type of the allocated resource
- H04W72/0453—Resources in frequency domain, e.g. a carrier in FDMA
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04W—WIRELESS COMMUNICATION NETWORKS
- H04W72/00—Local resource management
- H04W72/04—Wireless resource allocation
- H04W72/044—Wireless resource allocation based on the type of the allocated resource
- H04W72/0466—Wireless resource allocation based on the type of the allocated resource the resource being a scrambling code
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04W—WIRELESS COMMUNICATION NETWORKS
- H04W72/00—Local resource management
- H04W72/04—Wireless resource allocation
- H04W72/044—Wireless resource allocation based on the type of the allocated resource
- H04W72/0473—Wireless resource allocation based on the type of the allocated resource the resource being transmission power
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04W—WIRELESS COMMUNICATION NETWORKS
- H04W72/00—Local resource management
- H04W72/50—Allocation or scheduling criteria for wireless resources
- H04W72/54—Allocation or scheduling criteria for wireless resources based on quality criteria
- H04W72/542—Allocation or scheduling criteria for wireless resources based on quality criteria using measured or perceived quality
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
- Y02D30/00—Reducing energy consumption in communication networks
- Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks
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Abstract
The invention discloses a kind of SCMA systems code book and power distribution method based on game theory, including：S1：Assuming that under a SCMA downlink cellular system, there are M orthogonal sub-carriers on a given SCMA block orthogonal resource block, there is H non-zero entry in SCMA encoders, then it is that codebook number is to transmit the number of pliesDownlink user number is K, and each user only carries out the user data transmission using a transport layer, then K=J, and the corresponding relation between J code book and M orthogonal sub-carriers meets incidence matrix F；S2：Code book distribution is carried out with noise power sum based on the interference under minimum and value, by successive ignition, until all code books are assigned；S3：Code book for being already allocated to user, betting model is established based on game theory and carries out power distribution, by successive ignition, until all power distributions finish.The present invention has the advantages of handling capacity and speed that can effectively improve SCMA systems, reduction error rate of system.
Description
Technical field
The present invention relates to wireless communication field.A kind of it is more particularly related to SCMA systems based on game theory
Code book and power distribution method.
Background technology
In a wireless communication system, Sparse Code multiple access access (SCMA) is a kind of multiple access technique, that is, base station is such as
What services and distinguished simultaneously a kind of mode of multiple users.The performance of Sparse Code multiple access system depends primarily on SCMA code books
Design and the research of resource allocation algorithm.Main resource in communication is bandwidth and power, in bandwidth and the situation of power limited
Each user wants to take more frequency spectrum resources down.In Sparse Code multiple access system, same SCMA encoders are same
Same spectrum resources are shared between user on layer, interference to each other be present.On specific SCMA resources are fast, due to different codes
The orthogonal orthogonal sub-carriers of this actual association are different, and these orthogonal orthogonal sub-carriers are for different users, channel status letter
It is also different to cease (CSI).Because SCMA code books can be considered as a kind of code resource of channelizing, so we can use for reference
The orthogonal orthogonal sub-carriers allocation algorithm based on RA algorithms, code is carried out according to the channel condition information of user in OFDMA system
This selection, to improve the availability of frequency spectrum.Due to the concept of sparse spread spectrum in SCMA systems, by the data of different user in frequency domain
On be diffused in limited orthogonal sub-carriers, the user in same orthogonal sub-carriers can interfere with each other, can not between these users
Shared channel status information, so the method that each user can only be in a distributed manner maximizes the performance of oneself, channel congestion is caused,
Throughput of system is low.
The content of the invention
It is an object of the invention to solve at least the above, and provide the advantages of at least will be described later.
, should it is a still further object of the present invention to provide a kind of SCMA systems code book and power distribution method based on game theory
Method not only increases the handling capacity and speed of SCMA systems, also reduces the bit error rate of system.
In order to realize according to object of the present invention and further advantage, there is provided a kind of SCMA systems based on game theory
Code book and power distribution method, comprise the following steps：
S1：Initialization system model, it is assumed that under a SCMA downlink cellular system, consider a given SCMA
There are M orthogonal sub-carriers on block orthogonal resource blocks, there is H non-zero entry in SCMA encoders, then the transmission number of plies is code accordingly
This number isDownlink user number is K, and each user only carries out the user data transmission using a transport layer, then K=J,
And the corresponding relation between J code book and M orthogonal sub-carriers meets that incidence matrix F, F are a J row M row matrix, in each column
There is a H non-zero entry, the corresponding code book of each row in F, an orthogonal sub-carriers numbering, non-zero entry in often going are represented per a line
Position represents to be multiplexed the user that the row corresponds to orthogonal sub-carriers；
S2：It is assumed that transmission power is averagely allocated to all orthogonal sub-carriers by base station, then on each transport layer j individually
Code book distribution is carried out, j ∈ { 1,2 ..., J }, is tried to achieveH non-zero entry institute that will each in code book
The interference of H orthogonal sub-carriers of association to each user are summed with noise power sum, and the positive jiao zi under minimum and value is carried
Ripple combines m*Corresponding code book XkDistribute to user Uk, by successive ignition, each user distributes code book in turn, until all codes
Originally it is assigned, now, code book corresponds with user, wherein,Represent user U on transport layer jkOn orthogonal sub-carriers m
Interference and noise power sum, m ∈ { 1,2 ..., M }, k={ 1,2 ..., K }；
S3：Based on game theory, establish non-cooperative game model and carry out power distribution, try to achieveBase station is by power distribution
To the code book l for meeting above formula, and the watt level that base station is distributed on the code book meetsIt is remaining to the user
Performance numberIf dump power value is negative number representation, the user does not have enough power to meetThen willThe code book is distributed to, by successive ignition, until all power distributions finish, wherein,For strategic function, user U is representedkIn code book XkThe power of upper distribution,Actually active channel gain is represented, τ is represented
Work factor, C represents code book allocation matrix, if code book XkDistribute to user Uk, thenOtherwise it is 0,Represent
User UkMaximum transmission power.
Preferably, the SCMA systems code book and power distribution method based on game theory, specifically wrapped in step S2
Include following steps：
S21：User U corresponding to line link receiving terminal will be engraved some timeskThe information received be expressed as：
Wherein, if k-th of user UkThe code book used is Xk, user data by SCMA encoders mapping after code word be
xk=(xk1,xk2,...,xkN)(xk∈Xk), pkUser U is distributed in expressionkTransmission power, hk=(hk1,hk2,...,hkN)HTable
Show user UkChannel gain onto each orthogonal sub-carriers, wkAdditive noise is represented, is that a variance is δ2Zero-mean gaussian with
Machine variable；
S22：Assuming that user UkAdditive noise w on to each orthogonal sub-carrierskIt is all equal, and hkIt is the path fading factor
With the product of the frequency selective fading factor, then user U in j layerskThe Signal to Interference plus Noise Ratio SINR of receiving terminal is：
WhereinRepresent user UkInterference and noise power sum in receiving terminal；||xk|
|2Represent corresponding signal power；
S23：All users in unit bandwidth and speed be：
S24：Assuming that all users are used uniformly qam mode, the bit error rate of user, and given known interference are given
Vector, the then distribution in downlink to each orthogonal sub-carriers on j layers meet：
S25：Assuming that user U on j layerskSINR on orthogonal sub-carriers m isWhen, net utility is optimal, then j layers exist
The power distributed on orthogonal sub-carriers m is
Substituting into above formula can obtain
ThenThe orthogonal sub-carriers group for minimum that interference on j layers and noise power sum are summed
Close code book X corresponding to m*kDistribute to user Uk,
The interference level I of each user is known by base station testingk,jAnd maximum transmission powerBy each positive jiao zi
Carrier wave is pre-assigned to user at random, and all channels are pre-allocated by following scheme：A={ 1,2 ..., K }, is looked for from A
To user UkCorresponding unappropriated orthogonal sub-carriers combination m*,By m*Corresponding code book XkDistribution
Give user Uk, meanwhile,A=A- { m*, by successive ignition, each user distributes code book in turn, until institute
There is code book to be assigned, now code book corresponds with user.
Preferably, the SCMA systems code book and power distribution method based on game theory, specifically wrap in step S3
Include following steps：
S31：This allocation matrix of definitions isIf code book XkDistribute to user Uk, that
Otherwise it is 0；Assuming that all users use QAM modulation, then in speedUnder, user UkCorresponding code book XkUnder
Bit error rate be
S32：Power distribution is carried out using game theory, its revenue function is：
Wherein, ΩkFor user UkAnd power efficiency function,Represent user UkIn code book XkOn power efficiency,Represent actually active channel gain；
S33：The distribution of code book is considered simultaneously, then revenue function is：
S34：Work factor τ is introduced, then non-cooperative game model is：
S35：Lagrange relaxations are carried out to the non-cooperative game model, can be obtained：
Wherein, uk,For the non-negative Lagrange factors；
S36：Above formula is asked on transmission powerFirst derivative obtain：
If code book XkIt is not allocated to user Uk, thenAnd
Otherwise haveSet up, then
I.e. base station will
Power distribution gives the code book l for meeting this condition, and the watt level distributed on the code book meets
To remaining performance numberIf dump power value is negative, user UkThere is no enough power
To meetTherefore by dump powerThe code book is distributed to, by successive ignition, until all power
It is assigned.
The beneficial effects of the invention are as follows：H orthogonal sub-carriers associated by H non-zero entry in each code book are arrived first
The interference of each user is summed with noise power sum, and code book corresponding to the orthogonal sub-carriers combination under minimum and value is distributed to
User, through successive ignition, until code book is assigned, then carries out power distribution based on game theory, by successive ignition, until work(
Rate is assigned, and now, code book and power distribution all obtain optimal solution, and systematic function is optimal, and correlation model is established with traditional
The resource allocation methods for carrying out combined optimization are compared, and not only amount of calculation is small by the present invention, can also effectively improve handling up for SCMA systems
Amount and speed, reduce the bit error rate of system.
Further advantage, target and the feature of the present invention embodies part by following explanation, and part will also be by this
The research and practice of invention and be understood by the person skilled in the art.
Brief description of the drawings
Fig. 1 is the FB(flow block) of the present invention.
Embodiment
With reference to embodiment and accompanying drawing, the present invention is described in further detail, to make those skilled in the art's reference
Specification word can be implemented according to this.
It should be noted that experimental method described in following embodiments, is conventional method unless otherwise specified, institute
Reagent and material are stated, unless otherwise specified, is commercially obtained；In the description of the invention, term " transverse direction ", " vertical
To ", " on ", " under ", "front", "rear", "left", "right", " vertical ", " level ", " top ", " bottom ", " interior ", the instruction such as " outer " side
Position or position relationship are based on orientation shown in the drawings or position relationship, are for only for ease of the description present invention and simplify description,
It is not instruction or implies signified device or element there must be specific orientation, with specific azimuth configuration and operation, because
This is not considered as limiting the invention.
As shown in figure 1, present invention offer a kind of SCMA systems code book and power distribution method based on game theory, including with
Lower step：
S1：Initialization system model, it is assumed that under a SCMA downlink cellular system, consider a given SCMA
There are M orthogonal sub-carriers on block orthogonal resource blocks, there is H non-zero entry in SCMA encoders, then the transmission number of plies is code accordingly
This number isDownlink user number is K, and each user only carries out the user data transmission using a transport layer, then K=J,
And the corresponding relation between J code book and M orthogonal sub-carriers meets that incidence matrix F, F are a J row M row matrix, in each column
There is a H non-zero entry, the corresponding code book of each row in F, an orthogonal sub-carriers numbering, non-zero entry in often going are represented per a line
Position represents to be multiplexed the user that the row corresponds to orthogonal sub-carriers；
Such as have 4 orthogonal sub-carriers, 2 non-zero entries, then there are 6 code books, between 6 code books and 4 orthogonal sub-carriers
The incidence matrix F of corresponding relation is：
The corresponding code book of each row in F, 1 position represents the non-zero entry position of code word in the code book in each column,
I.e. using the user of the code book by using the orthogonal sub-carriers corresponding to 1, as non-zero entry in the 2nd, 4 rows, representing should in the 1st row
The orthogonal sub-carriers numbering that code book/user uses is 2,4；An orthogonal sub-carriers numbering, 1 institute in often going are represented in F per a line
Be multiplexed those users that the row corresponds to orthogonal sub-carriers in positional representation, as in the first row non-zero entry in the positions of 2,3,5 row, generation
Table using the code book of No. 1 orthogonal sub-carriers have in F the 2nd, 3,4 row corresponding to code book.
S2：It is assumed that transmission power is averagely allocated to all orthogonal sub-carriers by base station, then on each transport layer j individually
Code book distribution is carried out, j ∈ { 1,2 ..., J }, is tried to achieveH non-zero entry institute that will each in code book
The interference of H orthogonal sub-carriers of association to each user are summed with noise power sum, and the positive jiao zi under minimum and value is carried
Ripple combines m*Corresponding code book XkDistribute to user Uk, by successive ignition, each user distributes code book in turn, until all codes
Originally it is assigned, now, code book corresponds with user, wherein,Represent user U on transport layer jkOn orthogonal sub-carriers m
Interference and noise power sum, m ∈ { 1,2 ..., M }, k={ 1,2 ..., K }；To all code book have been chosen during each iteration
User and corresponding code book first reject, the code book under minimum and value is only distributed to a user, K user's need by each iteration
Carry out K-1 iteration；
S3：Based on game theory, establish non-cooperative game model and carry out power distribution, try to achieveBase station is by power distribution
To the code book l for meeting above formula, and the watt level that base station is distributed on the code book meetsIt is remaining to the user
Performance numberIf dump power value is negative number representation, the user does not have enough power to meetThen willThe code book is distributed to, by successive ignition, until all power distributions finish, wherein,For strategic function, user U is representedkIn code book XkThe power of upper distribution,Actually active channel gain is represented, τ is represented
Work factor, C represents code book allocation matrix, if code book XkDistribute to user Uk, thenOtherwise it is 0,Represent
User UkMaximum transmission power；All the code book of the power distributed and corresponding power are first rejected during each iteration,
Each iteration all distributes power to a code book for meeting above formula, and K code book needs to carry out K-1 iteration.
The described SCMA systems code book and power distribution method based on game theory, following step is specifically included in step S2
Suddenly：
S21：User U corresponding to line link receiving terminal will be engraved some timeskThe information received be expressed as：
Wherein, if k-th of user UkThe code book used is Xk, user data by SCMA encoders mapping after code word be
xk=(xk1,xk2,...,xkN)(xk∈Xk), pkUser U is distributed in expressionkTransmission power, hk=(hk1,hk2,...,hkN)HTable
Show user UkChannel gain onto each orthogonal sub-carriers, wkAdditive noise is represented, is that a variance is δ2Zero-mean gaussian with
Machine variable；
S22：Assuming that user UkAdditive noise w on to each orthogonal sub-carrierskIt is all equal, and hkIt is the path fading factor
With the product of the frequency selective fading factor, then user U in j layerskThe Signal to Interference plus Noise Ratio SINR of receiving terminal is：
WhereinRepresent user UkInterference and noise power sum in receiving terminal；||xk|
|2Represent corresponding signal power；
S23：All users in unit bandwidth and speed be：
S24：Assuming that all users are used uniformly qam mode, the target of the bit error rate, then resource allocation of user is given
Function is：
Above formula is nonlinear optimal problem under a constraints, it is to be understood that the power distribution feelings on each subcarrier
Condition, amount of calculation is excessive if being optimized using multi-user association, is generally difficult to realize, so we use the framework of game theory here
Seek optimal solution, greatly reduce complexity；
Given known interference vector, the then distribution in downlink to each orthogonal sub-carriers on j layers meet：
S25：Assuming that user U on j layerskSINR on orthogonal sub-carriers m isWhen, net utility is optimal, then j layers exist
The power distributed on orthogonal sub-carriers m is
Substituting into above formula can obtain
ThenThe orthogonal sub-carriers group for minimum that interference on j layers and noise power sum are summed
Close code book X corresponding to m*kDistribute to user Uk,
The interference level I of each user is known by base station testingk,jAnd maximum transmission powerPositive jiao zi is carried
Ripple is pre-assigned to user at random, and tentatively to be judged channel condition, all channels are pre-allocated by following scheme：
ωk,j=φ, A=1,2 ..., K }
For k=1 to K
while A≠φ
User U is found from AkCorresponding unappropriated orthogonal sub-carriers combination m*,By m*
Corresponding code book XkDistribute to user Uk, meanwhile,By successive ignition, each user
Code book is distributed in turn, until all code books are assigned, now code book corresponds with user, wherein,A
=A- { m*It is assignment statement.
The described SCMA systems code book and power distribution method based on game theory, following step is specifically included in step S3
Suddenly：
S31：This allocation matrix of definitions isIf code book XkDistribute to user Uk, that
Otherwise it is 0；Assuming that all users use QAM modulation, then in speedUnder, user UkCorresponding code book XkUnder
Bit error rate be
S32：Power distribution is carried out using game theory, its revenue function is：
Wherein, ΩkFor user UkAnd power efficiency function,Represent user UkIn code book XkOn power efficiency,Represent actually active channel gain；
S33：The distribution of code book is considered simultaneously, then revenue function is：
S34：All be present the optimal solution of either system in not all game Nash Equilibrium Solution, have in orthogonal sub-carriers
On the premise of limit, user can fight for limited resource, between form the relation of competition, while the peak power constraint of each user
Down between the orthogonal sub-carriers of each user there is also the problem of power competition, so we, which introduce work factor τ, makes user
Between there is implicit non-cooperative relationship, then non-cooperative game model is：
Game theory different from the past solves, and it is not optimal solution that may have Nash Equilibrium Solution, the receipts that the present invention designs
Beneficial function Nash Equilibrium Solution certainly exists, and is optimal solution
It will be proven below：
If the excessively a certain function of theorem 1. is recessed (convex) function, secondary function is to intend recessed (convex) function certainly.
Revenue function G=[M, { P of the theorem 2. for this paperk,C},{uk() }], it is assumed that all code books are assigned, that
Corresponding remaining power distribution function can be expressed as G=[M, { Pk,C},{uk() }], if its do not have in the case of errored bit
Policy space { the p of rate compositionkBe non-NULL convex set, and revenue function uk() is on strategic functionIntend recessed (convex) letter for one
Number, now there is at least one Nash Equilibrium point in this function.
Prove：For given revenue function, policy space is a non-NULL convex set certainly, for theorem 2, if to receiving
Beneficial function seeks the second dervative of its policy space, can obtainI.e. our revenue function is a concave function,
Understand that concave function is quasiconcave function certainly by theorem 1, then can with the card revenue function Nash Equilibrium Solution at least be present.
S35：Lagrange relaxations are carried out to the non-cooperative game model, can be obtained：
Wherein, uk,For the non-negative Lagrange factors；
S36：Above formula is asked on transmission powerFirst derivative obtain：
If code book XkIt is not allocated to user Uk, thenAnd
Otherwise haveSet up, then
I.e. base station will
Power distribution gives the code book l for meeting this condition, and the watt level distributed on the code book meets
To remaining performance numberIf dump power value is negative, user UkThere is no enough power
To meetTherefore by dump powerThe code book is distributed to, by successive ignition, until all power
It is assigned, wherein,For assignment statement.
Although embodiment of the present invention is disclosed as above, it is not restricted in specification and embodiment listed
With it can be applied to various suitable the field of the invention completely, can be easily for those skilled in the art
Other modification is realized, therefore under the universal limited without departing substantially from claim and equivalency range, it is of the invention and unlimited
In specific details and shown here as the legend with description.
Claims (3)
1. a kind of SCMA systems code book and power distribution method based on game theory, it is characterised in that comprise the following steps：
S1：Initialization system model, it is assumed that under a SCMA downlink cellular system, consider a given SCMA block
There are M orthogonal sub-carriers on orthogonal resource block, there is H non-zero entry in SCMA encoders, then the transmission number of plies is codebook number accordingly
ForDownlink user number is K, and each user only carries out the user data transmission using a transport layer, then K=J, and J
Corresponding relation between individual code book and M orthogonal sub-carriers meets that incidence matrix F, F are a J row M row matrix, has H in each column
Individual non-zero entry, the corresponding code book of each row in F, an orthogonal sub-carriers numbering, non-zero entry institute in often going are represented per a line
The user that the row corresponds to orthogonal sub-carriers is multiplexed in positional representation；
S2：It is assumed that transmission power is averagely allocated to all orthogonal sub-carriers by base station, then individually carried out on each transport layer j
Code book distributes, and j ∈ { 1,2 ..., J }, tries to achieveWill be each associated by H non-zero entry in code book
H orthogonal sub-carriers summed to interference and the noise power sum of each user, and by the orthogonal sub-carriers group under minimum and value
Close m*Corresponding code book XkDistribute to user Uk, by successive ignition, each user distributes code book in turn, until all code books point
With finishing, now, code book corresponds with user, wherein,Represent user U on transport layer jkIt is dry on orthogonal sub-carriers m
Disturb and noise power sum, m ∈ { 1,2 ..., M }, k ∈ { 1,2 ..., K }；
S3：Based on game theory, establish non-cooperative game model and power distribution is carried out to each user, try to achieveBase station is by power distribution
To the code book l for meeting above formula, and the watt level that base station is distributed on the code book meetsIt is remaining to the user
Performance numberIf dump power value is negative number representation, the user does not have enough power to meetThen willThe code book is distributed to, by successive ignition, until all power distributions finish, wherein,For strategic function, user U is representedkIn code book XkThe power of upper distribution,Actually active channel gain is represented, τ is represented
Work factor, C represents code book allocation matrix, if code book XkDistribute to user Uk, thenOtherwise it is 0,Represent
User UkMaximum transmission power.
2. SCMA systems code book and power distribution method based on game theory as claimed in claim 1, it is characterised in that step
Specifically comprise the following steps in S2：
S21：User U corresponding to line link receiving terminal will be engraved some timeskThe information received be expressed as：
Wherein, if k-th of user UkThe code book used is Xk, code word of the user data after the mapping of SCMA encoders is xk=
(xk1,xk2,...,xkN)(xk∈Xk), pkUser U is distributed in expressionkTransmission power, hk=(hk1,hk2,...,hkN)HRepresent to use
Family UkChannel gain onto each orthogonal sub-carriers, wkAdditive noise is represented, is that a variance is δ2Zero-mean gaussian become at random
Amount；
S22：Assuming that user UkAdditive noise w on to each orthogonal sub-carrierskIt is all equal, and hkIt is the path fading factor and frequency choosing
The product of selecting property fading factor, then user U in j layerskThe Signal to Interference plus Noise Ratio SINR of receiving terminal is：
WhereinRepresent user UkInterference and noise power sum in receiving terminal；||xk||2Represent
Corresponding signal power；
S23：All users in unit bandwidth and speed be：
S24：Assuming that all users are used uniformly qam mode, give the bit error rate of user, and it is given it is known disturb to
Amount, the then distribution in downlink to each orthogonal sub-carriers on j layers meet：
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</msub>
<msub>
<mi>p</mi>
<mi>k</mi>
</msub>
</mrow>
<mrow>
<msub>
<mi>h</mi>
<mrow>
<mi>k</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<msub>
<mi>p</mi>
<mi>k</mi>
</msub>
</mrow>
</mfrac>
<mo>-</mo>
<msub>
<mi>&alpha;</mi>
<mi>k</mi>
</msub>
<msub>
<mi>h</mi>
<mrow>
<mi>k</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<msub>
<mi>p</mi>
<mi>k</mi>
</msub>
<mo>&rsqb;</mo>
<mo>;</mo>
</mrow>
S25：Assuming that user U on j layerskSINR on orthogonal sub-carriers m isWhen, net utility is optimal, then j layers are in positive jiao zi
The power distributed on carrier wave m is
Substituting into above formula can obtain
<mfenced open = "" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<munder>
<mrow>
<mi>arg</mi>
<mi>max</mi>
</mrow>
<mi>k</mi>
</munder>
<mo>&lsqb;</mo>
<mo>-</mo>
<mfrac>
<mn>1</mn>
<mover>
<mi>r</mi>
<mo>~</mo>
</mover>
</mfrac>
<mo>-</mo>
<msub>
<mi>&alpha;</mi>
<mi>k</mi>
</msub>
<mover>
<mi>r</mi>
<mo>~</mo>
</mover>
<msub>
<mi>I</mi>
<mrow>
<mi>k</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<mo>&rsqb;</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>=</mo>
<munder>
<mrow>
<mi>arg</mi>
<mi>min</mi>
</mrow>
<mi>k</mi>
</munder>
<msub>
<mi>I</mi>
<mrow>
<mi>k</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
ThenThe orthogonal sub-carriers combination m* for interference on j layers and noise power sum being summed minimum
Corresponding code book XkDistribute to user Uk,
The interference level I of each user is known by base station testingk,jAnd maximum transmission powerBy each orthogonal sub-carriers
Random to be pre-assigned to user, all channels are pre-allocated by following scheme：A={ 1,2 ..., K }, finds use from A
Family UkCorresponding unappropriated orthogonal sub-carriers combination m*,By m*Corresponding code book XkDistribute to use
Family Uk, meanwhile,A=A- { m*, by successive ignition, each user distributes code book in turn, until all codes
Originally it is assigned, now code book corresponds with user.
3. SCMA systems code book and power distribution method based on game theory as claimed in claim 2, it is characterised in that step
Specifically comprise the following steps in S3：
S31：This allocation matrix of definitions isIf code book XkDistribute to user Uk, thenOtherwise it is 0；Assuming that all users use QAM modulation, then in speedUnder, user UkCorresponding code book XkUnder
Bit error rate is
S32：Power distribution is carried out using game theory, its revenue function is：
<mrow>
<msub>
<mi>&Omega;</mi>
<mi>k</mi>
</msub>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>K</mi>
</munderover>
<msubsup>
<mi>&Omega;</mi>
<mi>k</mi>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</msubsup>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>K</mi>
</munderover>
<mfrac>
<msubsup>
<mi>R</mi>
<mi>k</mi>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</msubsup>
<msup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>p</mi>
<mi>k</mi>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</msubsup>
<mo>)</mo>
</mrow>
<mrow>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msup>
</mfrac>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>K</mi>
</munderover>
<mfrac>
<mrow>
<mi>l</mi>
<mi>o</mi>
<mi>g</mi>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<msub>
<mi>g</mi>
<mrow>
<mi>k</mi>
<mo>,</mo>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</mrow>
</msub>
<msubsup>
<mi>p</mi>
<mi>k</mi>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</msubsup>
<mo>)</mo>
</mrow>
</mrow>
<msup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>p</mi>
<mi>k</mi>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</msubsup>
<mo>)</mo>
</mrow>
<mrow>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msup>
</mfrac>
</mrow>
Wherein, ΩkFor user UkAnd power efficiency function,Represent user UkIn code book XkOn power efficiency,Represent actually active channel gain；
S33：The distribution of code book is considered simultaneously, then revenue function is：
<mrow>
<msub>
<mi>u</mi>
<mi>k</mi>
</msub>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>K</mi>
</munderover>
<msubsup>
<mi>c</mi>
<mi>k</mi>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</msubsup>
<msubsup>
<mi>&Omega;</mi>
<mi>k</mi>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</msubsup>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>K</mi>
</munderover>
<msubsup>
<mi>c</mi>
<mi>k</mi>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</msubsup>
<mfrac>
<mrow>
<mi>l</mi>
<mi>o</mi>
<mi>g</mi>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<msub>
<mi>g</mi>
<mrow>
<mi>k</mi>
<mo>,</mo>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</mrow>
</msub>
<msubsup>
<mi>p</mi>
<mi>k</mi>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</msubsup>
<mo>)</mo>
</mrow>
</mrow>
<msup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>p</mi>
<mi>k</mi>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</msubsup>
<mo>)</mo>
</mrow>
<mrow>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msup>
</mfrac>
</mrow>
S34：Work factor τ is introduced, then non-cooperative game model is：
<mrow>
<mi>G</mi>
<mo>:</mo>
<msub>
<mi>u</mi>
<mi>k</mi>
</msub>
<mo>=</mo>
<mi>argmax</mi>
<munder>
<mo>&Sigma;</mo>
<mi>P</mi>
</munder>
<msubsup>
<mi>c</mi>
<mi>k</mi>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</msubsup>
<msubsup>
<mi>Q</mi>
<mi>k</mi>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</msubsup>
<mo>-</mo>
<msub>
<mi>&tau;g</mi>
<mrow>
<mi>k</mi>
<mo>,</mo>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</mrow>
</msub>
<msubsup>
<mi>p</mi>
<mi>k</mi>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</msubsup>
</mrow>
<mrow>
<mi>s</mi>
<mo>.</mo>
<mi>t</mi>
<mo>.</mo>
<msubsup>
<mo>&Sigma;</mo>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>K</mi>
</msubsup>
<msubsup>
<mi>p</mi>
<mi>k</mi>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>P</mi>
<mi>max</mi>
<mi>k</mi>
</msubsup>
<mo>&le;</mo>
<mn>0</mn>
<mo>,</mo>
<mo>&ForAll;</mo>
<mi>k</mi>
<mo>,</mo>
</mrow>
<mrow>
<msubsup>
<mi>R</mi>
<mi>k</mi>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</msubsup>
<mo>,</mo>
<msubsup>
<mi>p</mi>
<mi>k</mi>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</msubsup>
<mo>&GreaterEqual;</mo>
<mn>0</mn>
<mo>,</mo>
<mo>&ForAll;</mo>
<mi>k</mi>
</mrow>
<mrow>
<msubsup>
<mi>&Sigma;</mi>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>K</mi>
</msubsup>
<msubsup>
<mi>c</mi>
<mi>k</mi>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</msubsup>
<mo>&le;</mo>
<mn>1</mn>
</mrow>
S35：Lagrange relaxations are carried out to the non-cooperative game model, can be obtained：
<mrow>
<mi>L</mi>
<mrow>
<mo>(</mo>
<msubsup>
<mi>c</mi>
<mi>k</mi>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</msubsup>
<mo>,</mo>
<msubsup>
<mi>p</mi>
<mi>k</mi>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</msubsup>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msubsup>
<mo>&Sigma;</mo>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>K</mi>
</msubsup>
<mfrac>
<mrow>
<msubsup>
<mi>c</mi>
<mi>k</mi>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</msubsup>
<msubsup>
<mi>R</mi>
<mi>k</mi>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</msubsup>
</mrow>
<msup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>p</mi>
<mi>k</mi>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</msubsup>
<mo>)</mo>
</mrow>
<mrow>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msup>
</mfrac>
<mo>-</mo>
<msub>
<mi>&tau;g</mi>
<mrow>
<mi>k</mi>
<mo>,</mo>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</mrow>
</msub>
<msubsup>
<mi>p</mi>
<mi>k</mi>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</msubsup>
<mo>-</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>K</mi>
</munderover>
<msub>
<mi>u</mi>
<mi>k</mi>
</msub>
<mrow>
<mo>(</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>K</mi>
</munderover>
<msubsup>
<mi>p</mi>
<mi>k</mi>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>P</mi>
<mi>max</mi>
<mi>k</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mo>-</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>K</mi>
</munderover>
<msub>
<mi>&lambda;</mi>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</msub>
<mrow>
<mo>(</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>K</mi>
</munderover>
<msubsup>
<mi>c</mi>
<mi>k</mi>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</msubsup>
<mo>-</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein, uk,For the non-negative Lagrange factors；
S36：Above formula is asked on transmission powerFirst derivative obtain：
<mrow>
<mfrac>
<mrow>
<mo>&part;</mo>
<mi>L</mi>
<mrow>
<mo>(</mo>
<msubsup>
<mi>c</mi>
<mi>k</mi>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</msubsup>
<msubsup>
<mi>p</mi>
<mi>k</mi>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</msubsup>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mo>&part;</mo>
<msubsup>
<mi>p</mi>
<mi>k</mi>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</msubsup>
</mrow>
</mfrac>
<mo>=</mo>
<mfrac>
<msubsup>
<mi>c</mi>
<mi>k</mi>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</msubsup>
<msubsup>
<mi>p</mi>
<mi>k</mi>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</msubsup>
</mfrac>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<msub>
<mi>g</mi>
<mrow>
<mi>k</mi>
<mo>,</mo>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</mrow>
</msub>
<msup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>p</mi>
<mi>k</mi>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</msubsup>
<mo>)</mo>
</mrow>
<mrow>
<mo>-</mo>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msup>
</mrow>
<mrow>
<mn>1</mn>
<mo>+</mo>
<msub>
<mi>g</mi>
<mrow>
<mi>k</mi>
<mo>,</mo>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</mrow>
</msub>
<msubsup>
<mi>p</mi>
<mi>k</mi>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</msubsup>
</mrow>
</mfrac>
<mo>-</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<msup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>p</mi>
<mi>k</mi>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</msubsup>
<mo>)</mo>
</mrow>
<mrow>
<mo>-</mo>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msup>
<mi>log</mi>
<mo>(</mo>
<mrow>
<mn>1</mn>
<mo>+</mo>
<msub>
<mi>g</mi>
<mrow>
<mi>k</mi>
<mo>,</mo>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</mrow>
</msub>
<msubsup>
<mi>p</mi>
<mi>k</mi>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</msubsup>
</mrow>
<mo>)</mo>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msub>
<mi>&tau;g</mi>
<mrow>
<mi>k</mi>
<mo>,</mo>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>u</mi>
<mi>k</mi>
</msub>
<mo>&le;</mo>
<mn>0</mn>
</mrow>
<mrow>
<msubsup>
<mi>p</mi>
<mi>k</mi>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</msubsup>
<mfrac>
<mrow>
<mo>&part;</mo>
<mi>L</mi>
<mrow>
<mo>(</mo>
<msubsup>
<mi>c</mi>
<mi>k</mi>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</msubsup>
<mo>,</mo>
<msubsup>
<mi>p</mi>
<mi>k</mi>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</msubsup>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mo>&part;</mo>
<msubsup>
<mi>p</mi>
<mi>k</mi>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</msubsup>
</mrow>
</mfrac>
<mo>=</mo>
<mn>0</mn>
</mrow>
If code book XkIt is not allocated to user Uk, thenAnd
<mrow>
<mfrac>
<msubsup>
<mi>c</mi>
<mi>k</mi>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</msubsup>
<msubsup>
<mi>p</mi>
<mi>k</mi>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</msubsup>
</mfrac>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<msub>
<mi>g</mi>
<mrow>
<mi>k</mi>
<mo>,</mo>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</mrow>
</msub>
<msup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>p</mi>
<mi>k</mi>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</msubsup>
<mo>)</mo>
</mrow>
<mrow>
<mo>-</mo>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msup>
</mrow>
<mrow>
<mn>1</mn>
<mo>+</mo>
<msub>
<mi>g</mi>
<mrow>
<mi>k</mi>
<mo>,</mo>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</mrow>
</msub>
<msubsup>
<mi>p</mi>
<mi>k</mi>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</msubsup>
</mrow>
</mfrac>
<mo>-</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<msup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>p</mi>
<mi>k</mi>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</msubsup>
<mo>)</mo>
</mrow>
<mrow>
<mo>-</mo>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msup>
<mi>l</mi>
<mi>o</mi>
<mi>g</mi>
<mo>(</mo>
<mrow>
<mn>1</mn>
<mo>+</mo>
<msub>
<mi>g</mi>
<mrow>
<mi>k</mi>
<mo>,</mo>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</mrow>
</msub>
<msubsup>
<mi>p</mi>
<mi>k</mi>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
</msubsup>
</mrow>
<mo>)</mo>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msub>
<mi>&tau;g</mi>
<mrow>
<mi>k</mi>
<mo>,</mo>
<msub>
<mi>X</mi>
<mi>k</mi>
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Otherwise haveSet up, then
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| CN110048985A (en) * | 2019-03-27 | 2019-07-23 | 天津大学 | The low complex degree SCMA codebook design method of suboptimum |
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