CN103354485A - Adaptive feedback method based on power distribution in MISO interference broadcast system - Google Patents

Adaptive feedback method based on power distribution in MISO interference broadcast system Download PDF

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CN103354485A
CN103354485A CN2013102995255A CN201310299525A CN103354485A CN 103354485 A CN103354485 A CN 103354485A CN 2013102995255 A CN2013102995255 A CN 2013102995255A CN 201310299525 A CN201310299525 A CN 201310299525A CN 103354485 A CN103354485 A CN 103354485A
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唐海龙
苗萌
罗汉文
韦祥云
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WUXI JIAOTONG UNIVERSITY LIANYUN TECHNOLOGY Co Ltd
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Abstract

The invention discloses an adaptive feedback method based on power distribution in a MISO interference broadcast system and provides a combined adaptive limit feedback idea based on the power distribution in the MISO interference broadcast system. A power distribution scheme with a low complexity is provided. A rate loss caused by a quantization error is analyzed. On this basis, a combined distribution scheme of the adaptive power and a feedback bit is provided. According to the invention, on the basis of not increasing feedback cost in the system, through adaptive feedback channel state information of a user, a throughput of the system is finally and effectively increased. An adaptive limit bit feedback algorithm complexity of the user is low.

Description

In a kind of MISO interference broadcast system based on the adaptive feedback method of power division
Technical field
The invention discloses in the MISO interference broadcast channel system of a kind of many residential quarters based on the associating self adaptation limited feedback method of power division, relate to the single output of many inputs (MISO) technical fields of radio communication.
Background technology
The limit bit feedback is the key technology that solves the client feeds back channel information in the descending multi-user mimo system.How effectively to reduce the user feedback expense, guarantee that simultaneously power system capacity is a main study hotspot in the current space division multi-access.
In traditional descending multi-user mimo system, each user's number of bits of feedback is fixed.It is generally acknowledged that the raising number of bits of feedback can make the channel information of feedback more accurate, thereby improve user rate, but when certain user's channel was relatively relatively poor in the system, it was also not obvious for this user's speed lifting to improve number of bits of feedback.Therefore adopt fixing number of bits of feedback must cause overhead waste to a certain degree.
In the Multi-users MIS O interference broadcast system of many residential quarters, the impact of the interference between the multi-user and the serious interference of minizone the performance of throughput of system.Therefore how effectively eliminating these two kinds of interference is main study hotspots.
In the article " Two-cell MISO interfering broadcast channel with limited feedback:adaptive feedback strategy and multiplexing gains " (referring to " IEEE International Conference on Communication; Page (s): 1-5; June2011. ") of Namyoon Lee, the speed loss of at first having derived and having caused owing to quantization error, a kind of cooperation close-to zero beam forming technique has been proposed, the relation of the loss of the throughput of system of definition and channel quantitative error.The feedback bits scheme that proposes is the performance degradation that causes for the lower quantization error.And in the article " Antenna Combining for the MIMO Downlink Channel " (referring to " Wireless Communications; IEEE Transactions on Volume7; Issue10; October2008Page (s): 3834 – 3844. ") of Niha Jindal, then studied when system's code book produces at random (RVQ), relation between number of bits of feedback and the CDI feedback error, and a kind of scaling feedback scheme proposed, this scheme can cause larger feedback overhead when base station and user side antenna number differ larger, and the user can't adjust the feedback ratio paricular value according to residing system performance self adaptation.
Summary of the invention
Technical problem to be solved by this invention is: for the defective of prior art, proposed a kind of in MISO interference broadcast system the associating self adaptation Limited Feedback thought based on power division, provided a kind of power allocation scheme of low complex degree, analyze the speed loss that causes owing to quantization error, proposed on this basis the co-allocation scheme of a kind of adaptive power and feedback bits.
The present invention is for solving the problems of the technologies described above by the following technical solutions:
Based on the adaptive feedback method of power division, concrete steps are as follows in a kind of MISO interference broadcast system:
Step 1: in MISO interference broadcast system, initial parameter is set, comprises the optimization problem closed solutions of the number of bits of feedback of system's code book, number of bits of feedback, each user's service channel and interference channel; In the described MISO interference broadcast system, the number of transmit antennas of base station is M, and the user is single antenna, and total transmitting power of base station is P, and the base station has identical code book with the user
Figure BDA00003520976300027
Wherein B is the maximum feedback bit number, and the code word in each code book is 1 * M type matrix, adopts different code books between the base station;
Step 2: user side carries out channel estimating, obtains channel condition information; The channel condition information that user side obtains dominant base is h K, i, what k represented is user's sequence number, and what i represented is the dominant base of service-user k, and the channel condition information of interference base station is
Figure BDA00003520976300021
What represent is the interference base station of service-user k, described h K, iWith
Figure BDA00003520976300022
Be M * 1 matrix; The user is respectively to dominant base and interference base station feedback channel directional information and channel quality information;
Step 3: the user accesses after the MISO interference broadcast system channel gain and the channel condition information according to self, adaptive distribution power and select number of bits of feedback B k,
Dominant base is to the transmitting power of user k
Figure BDA00003520976300023
Interference base station is to the transmitting power of user k
Figure BDA00003520976300024
Wherein, || h K, i|| and
Figure BDA00003520976300029
Expression is the average gain of system service channel and the average gain of interference channel respectively;
Step 4: the user is according to the codeword matching criterion, before system's code book
Figure BDA00003520976300028
Search for the code word of mating most in the individual code word, and the code word sequence number is fed back to the base station;
User's service channel directional information is
Figure BDA00003520976300025
The interference channel directional information is z ~ k , i ‾ = z k , i ‾ / | | z k , i ‾ | | ,
The channel directional information of each BTS channel all adopts random vector to quantize, and interchannel adopts different random vectors to quantize code book, and dominant base is
Figure BDA00003520976300039
C SWhat represent is the code book that dominant base adopts, B iWhat represent is the needed number of bits of feedback of service channel; Interference base station is
Figure BDA00003520976300036
, C IWhat represent is the code book that interference base station adopts,
Figure BDA00003520976300037
What represent is the needed number of bits of feedback of interference channel; Adopt minimum distance criterion to choose the quantization code word of mating most,
The quantization code word of dominant base and interference base station is respectively
n i = arg max 1 ≤ m ≤ 2 B i | c S , m H h ~ k , i | , n i ‾ = arg max max 1 ≤ l ≤ 2 B i ‾ | c I , l H z ~ k , i ‾ | - - - ( 1 )
And this code word sequence number fed back to the base station; That wherein, m represents is code book C SThat the sequence number of middle code word, l represent is code book C IThe conjugate transpose of the matrix that the sequence number of middle code word, H represent;
Step 5: the base station reconstructs channel condition information after obtaining the code word sequence number of user feedback in the code book of self, rebuilds resulting quantized channel directional information to be
Figure BDA00003520976300032
(k={1,2 ... K i) and
Figure BDA00003520976300033
Figure BDA000035209763000310
Wherein, K iThe total number of users order of the dominant base service of expression, L represents is the user's that serves of interference base station sequence number,
Figure BDA00003520976300038
The total number of users order of the interference base station service of expression;
Be expressed as rebuilding the channel directional information of gained and the error between the actual channel directional information:
sin 2 θ k = sin 2 ( h ~ k , i , h ~ k , i ) - - - ( 2 )
θ wherein kWhat represent is the angle of quantized channel directional information and actual channel directional information;
Step 6: power division and pre-coding matrix design are carried out according to channel quality information and channel directional information in the base station, and transmitting data is to user side.
Further, in the described step 6, the concrete grammar of pre-coding matrix design is as follows:
Order
Figure BDA00003520976300035
H sWhat represent is channel matrix, the transpose of a matrix that T represents; Then pre-coding matrix is:
W s=H s *(H sH s *) -1 (3)
Wherein, *The expression adjoint matrix;
Adopt cooperation close-to zero beam shaping scheme to eliminate simultaneously the interference of user and minizone in the MISO interference broadcast channel, beamforming vectors is designed according to the quantized channel directional information of its service channel and interference channel in each base station; Specific as follows:
User's (k, i) beamforming vectors is w K, i, eliminate inter-user interference and presence of intercell interference, namely
Figure BDA00003520976300041
Wherein
Figure BDA00003520976300042
The user of expression in the residential quarter be to user's (k, i) channel,
H ^ k , i = [ h ^ 1 , i , · · · , h ^ k + 1 , i , h ^ k + 1 , i · · · , h ^ K i , i ] H ;
The channel of the user to user (k, i) in the expression interfered cell,
Figure BDA00003520976300045
Further, in the described step 1, the optimization problem closed solutions of the number of bits of feedback of each user's service channel and interference channel, method for solving is specific as follows:
With the speed difference Δ R under perfect information feedback and the limited information feedback K, i, namely the speed attrition table is shown:
ΔR k , i ( P k , i , P k , i ‾ , K i , K i ‾ , M ) = Δ E [ R k , i PFB - R k , i LPE ] , - - - ( 5 )
Wherein, E represents is to get desired value, Be illustrated in the total speed of user (k, i) under the perfect information feedback, the implication of PFB is perfect information feedback, that is:
R k , i PFB = log 2 ( 1 + P k , i | h k , i H w k , i PZF | 2 ) , - - - ( 6 )
Figure BDA00003520976300049
Total speed of user (k, i) under the limited information feedback of expression, what LFB represented is limited information feedback,
Figure BDA000035209763000410
Expression be the beamforming vectors of user (k, i) under perfect channel condition information, PZF represents is that close-to zero beam under the perfect channel condition information is shaped;
Compare with perfect channel information, there is residual volume in the interference of inter-user interference and minizone under the Limited Feedback system, and the speed that user (k, i) can reach under the Limited Feedback system is:
R k , i LFB = log 2 ( 1 + P k , i | | h k , i | | 2 | h ~ k , i H w k , i | 2 I IUI + I ICI + 1 ) - - - ( 7 )
Wherein, I IUIWhat represent is the interference between the user in the residential quarter, I IUI = | | h k , i | | 2 Σ j = 1 j ≠ k K i | | h k , j | | P Σ | | h k , j | | | h ~ k , i H w j , i | 2 ;
I ICIExpression be interference between inter-cell user, I ICI = | | z k , i ‾ | | 2 Σ L = 1 K i ‾ | | z k , L | | P Σ | | z k , L | | | z ~ k , i ‾ H w L , i ‾ | 2 ;
w J, iWhat represent is the beamforming vectors of the user j of dominant base service, h K, jThe expression be user j to the channel condition information of user k,
Figure BDA000035209763000513
What represent is the beamforming vectors of the user L of interference base station service, z K, LWhat represent is that user L is to the interference channel state information of user k;
Utilize Orthogonal Decomposition that the channel directional information is decomposed into:
k ~ k , i = h ^ k , i ( cos θ k , i ) + q k , i ( sin θ k , i )
Z ~ k , i ‾ = Z ^ k , i ‾ ( cos θ k , i ‾ ) + r k , i ‾ ( sin θ k , i ‾ ) (8)
In the formula, θ K, iWith
Figure BDA000035209763000511
The angle that represents respectively real channel directional information and quantized channel directional information, q K, iWith Expression is the error vector that service channel and interference channel cause owing to channel quantitative respectively;
The speed that user k can reach under the Limited Feedback system is:
R k , i LFB = log 2 ( 1 + P k , i | | h k , i | | 2 | h ~ k , i H w k , i | 2 I ~ IUI + I ~ ICI + 1 ) - - - ( 9 )
Wherein, I ~ IUI = | | h k , i | | 2 sin 2 θ ki , Σ j = 1 j ≠ k K i | | h k , j | | P Σ | | h k , j | | | q k i H , w ji | 2 , ,
I ~ ICI = | | z k , i ‾ | | 2 sin 2 θ k , i ‾ Σ L = 1 K i ‾ | | z k , L | | P Σ | | z k , L | | | r k , i ‾ H w L , i ‾ | 2 , (10)
Figure BDA00003520976300057
What represent is the interference between the user in the residential quarter under the Limited Feedback system,
Figure BDA00003520976300058
What represent is in the interference between inter-cell user under the Limited Feedback system;
The speed attrition table is shown:
ΔR k , i ≤ E [ log 2 ( 1 + P k , i | h k , i H w k , i PZF | 2 ) ] - E [ log 2 ( 1 + P k , i | h k , i H w k , i | 2 ) ] + E [ log 2 ( I ~ IUI + I ~ ICI + 1 ) ]
= E [ log 2 ( I ~ IUI + I ~ ICI + 1 )
(11)
Wherein, what E represented gets desired value to formula, and the condition that equal sign is set up is:
Figure BDA00003520976300061
And w K, iHave identical distribution, and and
Figure BDA00003520976300062
All be separate;
According to the Jensen inequality, be expressed as:
ΔR k , i ≤ log 2 ( E [ I ~ IUI ] + E [ I ~ ICI ] + 1 ) - - - ( 12 )
Figure BDA00003520976300064
With
Figure BDA00003520976300065
Obey (1, β distribution M-1), stochastic variable
Figure BDA00003520976300066
Figure BDA00003520976300067
,
Figure BDA00003520976300068
,
Figure BDA00003520976300069
,
Figure BDA000035209763000610
Independent mutually, so the upper bound of speed loss is expressed as:
ΔR k , i ≤ log 2 ( 1 + MP M - 1 Σ j = 1 , j ≠ k K i | | h k , j | | Σ | | h k , j | | 2 - B i M - 1 + MP M - 1 Σ L = 1 K i ‾ | | z k , L | | Σ | | z k , L | | 2 - B i ‾ M - 1 ) - - - ( 13 )
Speed loss in this formula is from the interference of remaining inter-user interference and inter-cell user, as total number of bits of feedback B of each user tIn the time of fixing, how to distribute the optimization problem of the number of bits of feedback of each user's service channel and interference channel, be expressed as:
min B i , B i ‾ ⋐ { 0 , z + } P s 2 - B i M - 1 + P I 2 - B i ‾ M - 1 - - - ( 14 )
s . t . B i + B i ‾ = B t
Wherein: P s = MP M - 1 Σ j = 1 j ≠ k K i | | h k , j | | Σ | | h k , j | | , P I = MP M - 1 Σ M - 1 K i ‾ | | z k , L | | Σ | | z k , L | | ;
According to protruding optimum theory and method of Lagrange multipliers, order
L ( B i , B i ‾ , λ ) = P s 2 - B i M - 1 + P I 2 - B i ‾ M - 1 + λ ( B i + B i ‾ - B t ) - - - ( 15 )
Then ∂ L ( B i , B i ‾ , λ ) ∂ B i = - ln ( 2 ) P S M - 1 2 - B i M - 1 + λ = 0 - - - ( 16 )
∂ L ( B i , B i ‾ , λ ) ∂ B i ‾ = - ln ( 2 ) P I M - 1 2 - B i ‾ M - 1 + λ = 0 - - - ( 17 )
∂ L ( B i , B i ‾ , λ ) ∂ λ = B i + B i ‾ - B t = 0 - - - ( 18 )
What wherein, λ represented is indefinite multiplier;
The above-mentioned formula of simultaneous solution (15), (16), (17), (18), the closed solutions that obtains this optimization problem is:
Figure BDA00003520976300071
The present invention adopts above technical scheme compared with prior art, has following technique effect: on the basis that does not increase system's internal feedback expense, and by the adaptive feedback of user CDI, the throughput of final Effective Raise system; User's self adaptation limit bit feedback algorithm complexity is lower.
Description of drawings
Fig. 1 be throughput of system with the graph of relation between the number of users,
Wherein: B refers to average feedback bits, and value is respectively 6 and 12.
Fig. 2 is the MISO interference broadcast channel model of two residential quarter Limited Feedback.
Embodiment
Below in conjunction with accompanying drawing technical scheme of the present invention is described in further detail:
The MISO broadcast channel schematic diagram of two residential quarter Limited Feedback as shown in Figure 2.The number of transmit antennas M=4 of base station, user's reception antenna number is N=1, system's code book
Figure BDA00003520976300074
Be that user's maximum feedback bit number is 12.The average number of bits of feedback 6 of user and 12, the average SNR P of transmitting terminal is 0~30db, number of users 4, Channel Modeling is the rayleigh distributed channel.
Step 1: system's code book
Figure BDA00003520976300075
N=2 12, the average number of bits of feedback B={6 of user, 12}, the average SNR P of transmitting terminal are 0~30db, number of users 4, Channel Modeling is the rayleigh distributed channel.
Step 2: suppose that each user's receiving terminal can the perfect channel condition information (Channel State Information, CSI) that obtains dominant base and interference base station, h K, iWith
Figure BDA00003520976300076
H wherein K, iWith
Figure BDA00003520976300077
Be M * 1 matrix.And each user is to dominant base and interference base station difference feedback channel directional information (Channel Direction Information, CDI) and channel quality information.
Step 3, behind the subscriber access system, power can be distributed according to the subscriber channel state information in the base station, P k , i = | | h k , i | | Σ k | | h k , i | | P With P k , i ‾ = | | z k , i ‾ | | Σ k | | z k , i ‾ | | P , Wherein || h K, i|| and
Figure BDA00003520976300078
Be respectively the average gain of service channel of system and the average gain of interference channel.
Step 4, user's service channel directional information and interference channel directional information are defined as respectively
Figure BDA00003520976300081
With
Figure BDA00003520976300082
Each BTS channel CDI all adopts random vector to quantize (Random Vector Quantization, RVQ), and interchannel adopts different RVQ code books, C S = { c S , 1 , c S , 2 · · · , c S , 2 B i } With C I = { c I , 1 , c I , 2 , · · · c I , 2 B i ‾ } 。And adopt minimum distance criterion to choose the quantization code word of mating most, that is:
n i = arg max 1 ≤ m ≤ 2 B i | c S , m H h ~ k , i | , n i ‾ = arg max 1 ≤ l ≤ 2 B i ‾ | c I , l H z ~ k , i ‾ | - - - ( 20 )
And the code word sequence number fed back to the base station.
Step 5, base station reconstruct channel condition information after obtaining the code word sequence number of user feedback in the code book of self, rebuild resulting quantification CDI to be
Figure BDA00003520976300084
With
Figure BDA00003520976300085
Rebuilding the CDI of gained and the error between the actual CDI can be expressed as:
sin 2 θ k = sin 2 ( ∠ ( h ~ k , i , h ~ k , i ) ) - - - ( 21 )
Step 6 is specially:
(1) power division
The base station reconstructs channel condition information, distributes power according to user's channel quality information (Channel Quality Information, CQI), that is:
P k , i = | | h k , i | | Σ k | | h k , i | | P With P k , i ‾ = | | z k , i ‾ | | Σ k | | z k , i ‾ | | P ,
Wherein || h K, i|| and
Figure BDA000035209763000812
Be respectively service channel average gain and the interference channel average gain of system.
(2) pre-coding matrix design
Order H s = [ ( h ^ 1 , i ) T , ( h ^ 2 , i ) T · · · ( h ^ k , i ) T ] T , Then pre-coding matrix is:
W s=H s *(H sH s *) - (22)
The beam forming that user k is corresponding is W sK row, be designated as w k
Adopt a kind of simple cooperation close-to zero beam shaping (Coordinate Zero-Forcing Beamforming, CZFBF) scheme is eliminated the interference of user and minizone in the MISO interference broadcast channel simultaneously, and each base station is according to its service channel and the quantized channel directional information design beamforming vectors of interference channel.User's (k, i) beam forming w K, iEliminate simultaneously inter-user interference and presence of intercell interference, namely
Figure BDA00003520976300091
Wherein,
Figure BDA00003520976300092
User in the expression residential quarter is defined as to user's (k, i) channel
Figure BDA00003520976300093
Figure BDA00003520976300094
The channel of the user to user (k, i) in the expression interfered cell is defined as Z ^ i = [ z ^ 1 , i , · · · , z ^ K i ‾ , i ] H ·
(3) transmitting data
Suppose that transmission data corresponding to user k are s k, then base station place antenna transmit for
Figure BDA00003520976300096
Below adaptive power and Limited Feedback technology are described:
In two residential quarter MISO interference broadcast systems, the number of transmit antennas of each base station is M, and the user is single antenna, and total transmitting power of base station is P.System's code book is
Figure BDA000035209763000915
Code word in the code book is 1 * M type matrix.Article " MIMO broadcast channels with finite rate feedback " according to Niha Jindal, the speed loss refers to the speed difference under perfect information feedback and the limited information feedback, and we are defined as the speed loss:
ΔR k , i ( P k , i P k , i ‾ , K i , K i ‾ , M ) = Δ E [ R k , i PFB - R k , i LPF ] , - - - ( 24 )
Wherein
Figure BDA00003520976300098
Be illustrated in total speed of the lower user (k, i) of perfect CSI feedback, that is:
R k , i PFB = log 2 ( 1 + P k , i | h k , i H w k , i PZF | 2 ) , - - - ( 25 )
Compare with perfect channel information, the interference of inter-user interference and minizone still has certain residual volume under the Limited Feedback system, so the speed that user (k, i) can reach under the Limited Feedback system is:
R k , i LFB = log 2 ( 1 + P k , i | | h k , i | | 2 | h ~ k , i H w k , i | 2 I IUI + I ICI + 1 ) - - - ( 26 )
Wherein I IUI = | | h k , i | | 2 Σ j = 1 j ≠ k K i | | h k , j | | P Σ | | h k , j | | | h ~ k , i H w j , i | 2 , I ICI = | | z k , i ‾ | | 2 Σ L = 1 K i ‾ | | z k , L | | P Σ | | z k , L | | | z ~ k , i ‾ H w L , i ‾ | 2 ,
Utilize Orthogonal Decomposition that the channel directional information is decomposed into:
k ~ k , i = h ^ k , i ( cos θ k , i ) + q k , i ( sin θ k , i )
z ~ k , i ‾ = z ^ k , i ‾ ( cos θ k , i ‾ ) + r k , i ‾ ( sin θ k , i ‾ ) (27)
θ in the formula K, iWith The angle that represents respectively real channel directional information and quantized channel directional information, q K, iWith
Figure BDA00003520976300101
Expression is the error vector that service channel and interference channel cause owing to channel quantitative respectively.
Therefore, the speed that user (k, i) can reach under the Limited Feedback system is:
R k , i LFB = log 2 ( 1 + P k , i | | h k , i | | 2 | h ~ k , i H w k , i | 2 I ~ IUI + I ~ ICI + 1 ) - - - ( 28 )
Wherein I ~ IUI = | | h k , i | | 2 sin 2 θ k i , Σ j = 1 j ≠ k K i | | h k , j | | P Σ | | h k , j | | | q k , i , H w ji | 2 , ,
I ~ ICI = | | z k , i ‾ | | 2 sin 2 θ k , i ‾ Σ L = 1 K i ‾ | | z k , L | | P Σ | | z k , L | | | r k , i ‾ H w L , i ‾ | 2 , (29)
Therefore the speed loss can be expressed as
ΔR k , i ≤ E [ log 2 ( 1 + P k , i | h k , i H w k , i PZF | 2 ) ] - E [ log 2 ( 1 + P k , i | h k , i H w k , i | 2 ) ] + E [ log 2 ( I ~ IUI + I ~ ICI + 1 ) ]
= E [ log 2 ( I ~ IUI + I ~ ICI + 1 ) ]
(30)
In (30) formula, equal sign set up be because And w K, iHave identical distribution, and and
Figure BDA00003520976300108
All be separate, according to the Jensen inequality, can be expressed as:
ΔR k , i ≤ log 2 ( E [ I ~ IUI ] + E [ I ~ ICI ] + 1 ) - - - ( 31 )
Because
Figure BDA000035209763001010
With Obey (1, β M-1) distributes, stochastic variable || h K, i|| 2, sin 2θ K, i,
Figure BDA000035209763001012
, ,
Figure BDA000035209763001014
Figure BDA000035209763001015
All be separate, so the upper bound of speed loss can be expressed as:
ΔR k , i ≤ log 2 ( 1 + MP M - 1 Σ j = 1 , j ≠ k K i | | h k , j | | Σ | | h k , j | | 2 - B i M - 1 + MP M - 1 Σ L = 1 K i ‾ | | z k , L | | Σ | | z k , L | | 2 - B i ‾ M - 1 ) - - - ( 32 )
Compare with the MISO interference broadcast channel of single residential quarter, the speed loss in this formula is mainly from two aspects, the interference of remaining inter-user interference and inter-cell user.Therefore the total number of bits of feedback B that works as each user tIn the time of fixing, minimize in order to make the caused speed loss of quantization error, how to distribute the optimization problem of the number of bits of feedback of each user's transmission channel and interference channel, can be expressed as:
min B i , B i ‾ ⋐ { 0 , z + } P s 2 - B i M - 1 + P I 2 - B i ‾ M - 1 (3)
s . t . B i + B i ‾ = B t
Wherein: P S = MP M - 1 Σ j = 1 j ≠ k K i | | h k , j | | Σ | | h k , j | | , P I = MP M - 1 Σ l = 1 K i ‾ | | z k , L | | Σ | | z k , L | | ,
According to protruding optimum theory and method of Lagrange multipliers, order
L ( B i , B i ‾ , λ ) = P S 2 - B i M - 1 + P I 2 - B i ‾ M - 1 + λ ( B i + B i ‾ - B t ) - - - ( 34 )
∂ L ( B i , B i ‾ , λ ) ∂ B i = - 1 n ( 2 ) P S M - 1 2 - B i M - 1 + λ = 0 - - - ( 35 )
∂ L ( B i , B i ‾ , λ ) ∂ B i ‾ = - 1 n ( 2 ) P I M - 1 2 - B i ‾ M - 1 + λ = 0 - - - ( 36 )
∂ L ( B i , B i ‾ , λ ) ∂ λ = B i + B i ‾ - B t = 0 - - - ( 37 )
Unite and find the solution above (34), (35), (36), (37), we can obtain the closed solutions of this optimization problem:
Figure BDA00003520976300117
As shown in Figure 1, Fig. 1 is base station 4 transmit antennas, 1 antenna of user's receiving terminal, and SNR P is 0~30db, user's code book is 2 12, average feedback bits is respectively 6 and at 12 o'clock, and throughput of system is with the graph of relation between the number of users.The performance of three kinds of different schemes has been compared in emulation:
1) traditional bit allocative decisions such as constant power;
2) the adaptive power tradition waits the bit allocative decision;
3) adaptive power Bit Allocation in Discrete scheme;
We compare the size of the throughput of system under three kinds of schemes, and the distribution of the bits such as conventional power refers to that the bit such as constant power distribution and each interchannel of user distributes between each user.As can be seen from the figure, adaptive power tradition waits the allocative decision of bit to be better than the scheme that the bit such as conventional power distributes, and its main cause is that the base station can be according to channel conditions different between the user, and adaptive is the preferably more power of user assignment of channel.And the adaptive power bit co-allocation division that proposes is better than the bit allocative decisions such as adaptive power tradition, its main cause is the feedback quantization precision that the user can decide according to signal strength signal intensities different between transmission channel and the interference channel each channel, namely distributes adaptively the number of bits of feedback between the different channels.Therefore show from simulation result, the adaptive power bit co-allocation scheme that proposes, in the situation that does not change feedback overhead, the adaptive power Bit Allocation in Discrete that we propose can comparatively significantly improve the throughput of system.

Claims (3)

  1. In the MISO interference broadcast system based on the adaptive feedback method of power division, it is characterized in that concrete steps are as follows:
    Step 1: in MISO interference broadcast system, initial parameter is set, comprises the optimization problem closed solutions of the number of bits of feedback of system's code book, number of bits of feedback, each user's service channel and interference channel; In the described MISO interference broadcast system, the number of transmit antennas of base station is M, and the user is single antenna, and total transmitting power of base station is P, and the base station has identical code book with the user
    Figure FDA00003520976200017
    Wherein B is the maximum feedback bit number, and the code word in each code book is 1 * M type matrix, adopts different code books between the base station;
    Step 2: user side carries out channel estimating, obtains channel condition information; The channel condition information that user side obtains dominant base is h K, i, what k represented is user's sequence number, and what i represented is the dominant base of service-user k, and the channel condition information of interference base station is
    Figure FDA00003520976200011
    What represent is the interference base station of service-user k, described h K, iWith
    Figure FDA00003520976200012
    Be M * 1 matrix; The user is respectively to dominant base and interference base station feedback channel directional information and channel quality information;
    Step 3: the user accesses after the MISO interference broadcast system channel gain and the channel condition information according to self, adaptive distribution power and select number of bits of feedback B k,
    Dominant base is to the transmitting power of user k
    Figure FDA00003520976200013
    Interference base station is to the transmitting power of user k
    Figure FDA00003520976200014
    Wherein, || h K, i|| and
    Figure FDA00003520976200018
    Expression is the average gain of system service channel and the average gain of interference channel respectively;
    Step 4: the user is according to the codeword matching criterion, before system's code book
    Figure FDA00003520976200019
    Search for the code word of mating most in the individual code word, and the code word sequence number is fed back to the base station;
    User's service channel directional information is
    Figure FDA00003520976200015
    The interference channel directional information is z ~ k , i ‾ = z k , i ‾ / | | z k , i ‾ | | ,
    The channel directional information of each BTS channel all adopts random vector to quantize, and interchannel adopts different random vectors to quantize code book, and dominant base is
    Figure FDA000035209762000110
    C SWhat represent is the code book that dominant base adopts, B iWhat represent is the needed number of bits of feedback of service channel; Interference base station is
    Figure FDA00003520976200021
    C IWhat represent is the code book that interference base station adopts, What represent is the needed number of bits of feedback of interference channel; Adopt minimum distance criterion to choose the quantization code word of mating most,
    The quantization code word of dominant base and interference base station is respectively
    n i = arg max 1 ≤ m ≤ 2 B i | c S , m H h ~ k , i | , n i ‾ = arg max max 1 ≤ l ≤ 2 B i ‾ | c I , l H z ~ k , i ‾ | - - - ( 1 )
    And this code word sequence number fed back to the base station; That wherein, m represents is code book C SThat the sequence number of middle code word, l represent is code book C IThe conjugate transpose of the matrix that the sequence number of middle code word, H represent;
    Step 5: the base station reconstructs channel condition information after obtaining the code word sequence number of user feedback in the code book of self, rebuilds resulting quantized channel directional information to be
    Figure FDA00003520976200023
    (k={1,2 ... K i) and
    Figure FDA000035209762000210
    Wherein, K iThe total number of users order of the dominant base service of expression, L represents is the user's that serves of interference base station sequence number,
    Figure FDA00003520976200029
    The total number of users order of the interference base station service of expression;
    Be expressed as rebuilding the channel directional information of gained and the error between the actual channel directional information:
    sin 2 θ k = sin 2 ( h ~ k , i , h ~ k , i ) - - - ( 2 )
    θ wherein kWhat represent is the angle of quantized channel directional information and actual channel directional information;
    Step 6: power division and pre-coding matrix design are carried out according to channel quality information and channel directional information in the base station, and transmitting data is to user side.
  2. In a kind of MISO interference broadcast as claimed in claim 1 system based on the adaptive feedback method of power division, it is characterized in that in the described step 6, the concrete grammar of pre-coding matrix design is as follows:
    Order
    Figure FDA00003520976200026
    H sWhat represent is channel matrix, the transpose of a matrix that T represents; Then pre-coding matrix is:
    W s=H s *(H sH s *) - (3)
    Wherein, *The expression adjoint matrix;
    Adopt cooperation close-to zero beam shaping scheme to eliminate simultaneously the interference of user and minizone in the MISO interference broadcast channel, beamforming vectors is designed according to the quantized channel directional information of its service channel and interference channel in each base station; Specific as follows:
    User's (k, i) beamforming vectors is w K, i, eliminate inter-user interference and presence of intercell interference, namely
    Wherein
    Figure FDA00003520976200032
    The user of expression in the residential quarter be to user's (k, i) channel,
    H ^ k , i = [ h ^ 1 , i , · · · , h ^ k - 1 , i , h ^ k + 1 , i · · · , h ^ K i , i ] H ;
    The channel of the user to user (k, i) in the expression interfered cell,
    Figure FDA00003520976200035
  3. In a kind of MISO interference broadcast as claimed in claim 1 system based on the adaptive feedback method of power division, it is characterized in that: in the described step 1, the optimization problem closed solutions of the number of bits of feedback of each user's service channel and interference channel, method for solving is specific as follows:
    With the speed difference Δ R under perfect information feedback and the limited information feedback K, i, namely the speed attrition table is shown:
    ΔR k , i ( P k , i , P k , i ‾ , K i , K i ‾ , M ) = Δ E [ R k , i PFB - R k , i LPE ] , - - - ( 5 )
    Wherein, E represents is to get desired value, Be illustrated in the total speed of user (k, i) under the perfect information feedback, the implication of PFB is perfect information feedback, that is:
    R k , i PFB = log 2 ( 1 + P k , i | h k , i H w k , i PZF | 2 ) , - - - ( 6 )
    Figure FDA00003520976200039
    Total speed of user (k, i) under the limited information feedback of expression, what LFB represented is limited information feedback,
    Figure FDA000035209762000310
    Expression be the beamforming vectors of user (k, i) under perfect channel condition information, PZF represents is that close-to zero beam under the perfect channel condition information is shaped;
    Compare with perfect channel information, there is residual volume in the interference of inter-user interference and minizone under the Limited Feedback system, and the speed that user (k, i) can reach under the Limited Feedback system is:
    R k , i LFB = log 2 ( 1 + P k , i | | h k , i | | 2 | h ~ k , i H w k , i | 2 I IUI + I ICI + 1 ) - - - ( 7 )
    Wherein, I IUIWhat represent is the interference between the user in the residential quarter,
    Figure FDA000035209762000312
    I ICIExpression be interference between inter-cell user, I ICI = | | z k , i ‾ | | 2 Σ L = 1 K i ‾ | | z k , L | | P Σ | | z k , L | | | z ~ k , i ‾ H w L , i ‾ | 2 ;
    w J, iWhat represent is the beamforming vectors of the user j of dominant base service, h K, jThe expression be user j to the channel condition information of user k,
    Figure FDA00003520976200042
    What represent is the beamforming vectors of the user L of interference base station service, z K, LWhat represent is that user L is to the interference channel state information of user k;
    Utilize Orthogonal Decomposition that the channel directional information is decomposed into:
    k ~ k , i = h ^ k , i ( cos θ k , i ) + q k , i ( sin θ k , i )
    Z ~ k , i ‾ = Z ^ k , i ‾ ( cos θ k , i ‾ ) + r k , i ‾ ( sin θ k , i ‾ ) (8)
    In the formula, θ K, iWith
    Figure FDA000035209762000412
    The angle that represents respectively real channel directional information and quantized channel directional information, q K, iWith
    Figure FDA000035209762000413
    Expression is the error vector that service channel and interference channel cause owing to channel quantitative respectively;
    The speed that user k can reach under the Limited Feedback system is:
    R k , i LFB = log 2 ( 1 + P k , i | | h k , i | | 2 | h ~ k , i H w k , i | 2 I ~ IUI + I ~ ICI + 1 ) - - - ( 9 )
    Wherein, I ~ IUI = | | h k , i | | 2 sin 2 θ k , i Σ j = 1 j ≠ k K i | | h k , j | | P Σ | | h k , j | | | q k , i H , w ji | 2 , ,
    I ~ ICI = | | z k , i ‾ | | 2 sin 2 θ k , i ‾ Σ L = 1 K i ‾ | | z k , L | | P Σ | | z k , L | | | r k , i ‾ H w L , i ‾ | 2 , (10)
    Figure FDA00003520976200048
    What represent is the interference between the user in the residential quarter under the Limited Feedback system,
    Figure FDA00003520976200049
    What represent is in the interference between inter-cell user under the Limited Feedback system;
    The speed attrition table is shown:
    ΔR k , i ≤ E [ log 2 ( 1 + P k , i | h k , i H w k , i PZF | 2 ) ] - E [ log 2 ( 1 + P k , i | h k , i H w k , i | 2 ) ] + E [ log 2 ( I ~ IUI + I ~ ICI + 1 ) ]
    = E [ log 2 ( I ~ IUI + I ~ ICI + 1 ) ]
    (11)
    Wherein, what E represented gets desired value to formula, and the condition that equal sign is set up is:
    Figure FDA00003520976200051
    With
    Figure FDA00003520976200052
    Distribution together, and and
    Figure FDA00003520976200053
    All be separate;
    According to the Jensen inequality, be expressed as:
    ΔR k , i ≤ log 2 ( E [ I ~ IUI ] + E [ I ~ ICI ] + 1 ) - - - ( 12 )
    Figure FDA00003520976200055
    With
    Figure FDA00003520976200056
    Obey (1, β M-1) distributes, stochastic variable || h K, i|| 2, sin 2θ K, i,
    Figure FDA00003520976200057
    ,
    Figure FDA00003520976200058
    ,
    Figure FDA00003520976200059
    Figure FDA000035209762000510
    Independent mutually, so the upper bound of speed loss is expressed as:
    ΔR k , i ≤ log 2 ( 1 + MP M - 1 Σ j = 1 , j ≠ k K i | | h k , j | | Σ | | h k , j | | 2 - B i M - 1 + MP M - 1 Σ L = 1 K i ‾ | | z k , L | | Σ | | z k , L | | 2 - B i ‾ M - 1 ) - - - ( 13 )
    Speed loss in this formula is from the interference of remaining inter-user interference and inter-cell user, as total number of bits of feedback B of each user tIn the time of fixing, how to distribute the optimization problem of the number of bits of feedback of each user's service channel and interference channel, be expressed as:
    min B i , B i ‾ ⋐ { 0 , z + } P s 2 - B i M - 1 + P I 2 - B i ‾ M - 1 (14)
    s . t . B i + B i ‾ = B t
    Wherein: P S = MP M - 1 Σ j = 1 , j ≠ k K i | | h k , j | | Σ | | h k , j | | , P I = MP M - 1 Σ L = 1 K i ‾ | | z k , L | | Σ | | z k , L | | ;
    According to protruding optimum theory and method of Lagrange multipliers, order
    L ( B i , B i ‾ , λ ) = P S 2 - B i M - 1 + P I 2 - B i ‾ M - 1 + λ ( B i + B i ‾ - B t ) - - - ( 15 )
    Then ∂ L ( B i , B i ‾ , λ ) ∂ B i = - 1 n ( 2 ) P S M - 1 2 - B i M - 1 + λ = 0 - - - ( 16 )
    ∂ L ( B i , B i ‾ , λ ) ∂ B i ‾ = - ln ( 2 ) P I M - 1 2 - B i ‾ M - 1 + λ = 0 - - - ( 17 )
    ∂ L ( B i , B i ‾ , λ ) ∂ λ B i + B i ‾ - B t = 0 - - - ( 18 )
    What wherein, λ represented is indefinite multiplier;
    The above-mentioned formula of simultaneous solution (15), (16), (17), (18), the closed solutions that obtains this optimization problem is:
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