Interference Cancellation Method without Feedback Amount for Three Users Interference Channel

Transcription

1 Open Access Librry Journl 07, Volume, e57 ISSN Online: -97 ISSN Print: Interference Cncelltion Method without Feedbc Amount for Three Users Interference Chnnel Xini Tin, otin Zhng, Wenie Ji School of Physics & Electronic Informtion Engineering, enn Polytechnic University, Jiozuo, Chin ow to cite this pper: Tin, X.J., Zhng,.T. nd Ji, W.J. (07) Interference Cncelltion Method without Feedbc Amount for Three Users Interference Chnnel. Open Access Librry Journl, : e57. Received: Mrch 0, 07 Accepted: My, 07 Published: My, 07 Copyright 07 by uthors nd Open Access Librry Inc. This wor is licensed under the Cretive Commons Attribution Interntionl License (CC BY.0). Open Access Abstrct In this pper, we investigte how to cncel multi-user interference without feedbc mount over multiple-input multiple-output (MIMO) interference chnnel using spce-time code. Three trnsmitter-receiver pirs re considered nd ech node is equipped with four ntenns. Spce-time codeword with dimension is designed for three trnsmitters, respectively. The number of interfering codeword is reduced through the design of codeword. Then, multi-user interference is cncelled by liner opertion on the received signls. Compred with the existing scheme for the sme scene, the trnsmission efficiency is improved, nd the unidirectionl coopertive lin is not required. Simultion results demonstrte the vlidity of theoreticl nlysis. Subect Ares Informtion nd Communiction Theory nd Algorithms Keywords Interference Chnnel, Spce-Time Codeword, Multi-User Interference, Interference Cncelltion, Trnsmission Efficiency. Introduction Relibility nd effectiveness re importnt fctors for wireless communictions. Multiple-input multiple-output (MIMO) systems hve the bility to improve both nd hence, re immensely populr. In theory, MIMO systems cn chieve extremely high spectrl efficiency by trnsmitting independent dt strem simultneously. owever, multiple users, trnsmitting different codewords to multiple receivers simultneously using the sme bnd, re not ble to collborte with ech other []. There is serious interference t ech receiver, nd the DOI: 0.6/olib.057 My, 07

2 effectiveness becomes limited. Therefore, it is quite importnt to design trnsmission techniques to eliminte multi-user interference []. Severl inds of interference cncelltion methods hve been conducted, such s pre-coding t the trnsmitters, multi-user detection of the receivers, nd interference lignment [] []. Interference lignment methods lign the interference cused t ech receiver from ll the trnsmitters long the sme direction while the desired signls occupy linerly independent signl dimensions. In this cse, the desired signls cn be decoded free from interference by zero-forcing lgorithm. A populr wy to pproximting the sum-cpcity for interference lignment is using the concept of degrees of freedom (DoF), in terms of trnsmission efficiency. Mny wors hve been conducted to evlute DoF [5] [6]. owever, effectiveness is contrct to relibility in communiction systems. With high DoF, relibility in terms of the diversity gin is needed to be improved. Therefore, it is meningful to combine interference lignment nd spce-time code, which cn offer diversity gin [7] [8]. [9] proposes new interference lignment scheme using Almouti code for two users MIMO X chnnel, in which zero vector is introduced into ech codeword. The diversity gin of [9] is, which is brought by Almouti code. Spce-time codeword with dimension is designed nd zero vectors re introduced into ech codeword over two users MIMO X chnnel with four ntenns t ech user, in which the diversity gin is [0]. The multi- user interference is mitigted through interference lignment nd liner opertion on the received signls. Motivted by [9], interference lignment nd Almouti code re introduced into MIMO interference chnnel with three trnsmitter- receiver pirs []. The multi-user interference is mitigted through interference lignment nd unidirectionl coopertive lin. owever, chnnel stte informtion (CSI) is required t the trnsmitters. It is very difficult to estimte the CSI in mobility environment. Therefore, it is crucil to consider trnsmission scheme combined interference lignment nd spce-time code without CSI. Under this motivtion, interference cncelltion method without feedbc is proposed for MIMO interference chnnel with three trnsmitter-receiver pirs where ech node is equipped with four ntenns. Spce-time codeword with dimension is designed for three trnsmitters, respectively. Ech codeword includes eight independent modulted symbols nd zero mtrices re introduced into ech codeword, through which the number of interfering codeword is reduced. Then, multi-user interference is cncelled by liner opertion on the received signls. The trnsmission efficiency of the proposed scheme is higher thn tht of []. Theoreticl nlysis shows tht the diversity of the proposed scheme is the sme s tht of []. Nottion: The opertors ( ) nd ( ) conugtion trnspose, respectively. stnd for complex conugtion nd denotes Frobenius norm of the enclosed term. E ( ) is the expecttion opertions. /0

3 . System Model The system model is shown in Figure. There re three dedicted trnsmitterreceiver pirs, where ech trnsmitter hs n individul messge to be communicted to its respectively receiver. All the trnsmitters nd receivers re ssumed to hve four ntenns. We ssume CSI is not vilble t ech trnsmitter., b nd c, which te vlues from set such tht E = = = E b E c, =,,, 8, represent the modulted signls t trnsmitter, trnsmitter nd trnsmitter, respectively., b nd c re encoded into spce-time codeword, denoted by A i, B i nd C i, respectively, i =,. A i, B i nd C i re expressed s e e i i i i Ai = i e i i e i b e e i b i b i bi Bi = bi e bi bi e bi ci e ci ci e c i Ci = ci e ci ci e ci where, =, 0< θ < π. The elements of A i, the elements of B i nd the elements of C i re nonzero by the proper vlue of θ. Ech element of A i, ech element of B i nd ech element of C i includes two independent symbols, with the purpose of improving trnsmission efficiency. If we see the elements of A i, the elements of B i nd the elements of C i s the modulted signls, i =,, A i, B i nd C i hve n Almouti structure. The motive for such design is tht the effective chnnel mtrix of Almouti code hs orthogonl columns, which cn be used to reduce decoding complexity. At trnsmitter, A nd A re combined ccording to certin rule to get codeword A. Similrly, B nd B re combined to obtin codeword B while C nd C re combined to obtin codeword C. A, B nd C re given by () Trnsmitter A A A Receiver Trnsmitter B B B Receiver Trnsmitter C C Receiver C Figure. The system model of the proposed scheme. /0

4 A 0 B 0 0 C A=, B =, C = A 0 0 B 0 C where, 0 represents zero mtrix. 0 is introduced becuse it cn be used to mitigte prtil multi-user interference, s shown lter. A, B nd C re the desired codewords for the three receivers, respectively. As shown in Figure, three trnsmitters send A, B nd C on the sme frequency bnd t the sme time. The received signls t receiver i, denoted by Y i, re expressed s () Y = A B C N () Y = A B C N () Y = A B C N (5) where, i =,,, i is the chnnel from trnsmitter to receiver i nd N i is the complex dditive white ussin noise t receiver i. The dimension of i nd N i re both. To void degenerte chnnel conditions, we ssume tht the chnnel coefficient vlues re drwn i.i.d. from continuous distribution nd the bsolute vlue of ll the chnnel coefficients is bounded between nonzero minimum vlue nd finite mximum vlue. The term A in Eqution () is the desired signls for receiver nd the term B C in Eqution () is the interference signls for receiver. The term B in Eqution () is the desired signls for receiver nd the term A C in Eqution () is the interference signls for receiver. The term C in Eqution (5) is the desired signls for receiver nd the term A B in Eqution (5) is the interference signls for receiver.. Interference Cncelltion Method We describe the interference cncelltion method t R. It cn be similrly used to mitigte interference t R nd to mitigte interference R... Remove the Undesired Codeword Let = [ ], = [ ], = [ 5 6 ], Y = [ Y Y ] nd = [ ] Y i re both, N N N. The dimension of l, N i nd l =,,, 6, i =,. Then, () cn be expressed s [ ] = [ ] [ ] Y Y A A B B C C N N (6) 5 6 (6) is equivlent to the following two equtions, Y = A A B N (7) Y = B C 5 C 6 N (8) The codeword of trnsmitter nd the prtil codeword of trnsmitter re encompssed by Y. The codeword of trnsmitter nd the prtil codeword of trnsmitter re encompssed by Y. So, the number of interfering codeword is reduced by the introduction of zero mtrices. owever, both the desired codeword for receiver nd the undesired codeword for receiver in terms of /0

5 B re included by Y. In wht follows, we represent how to cncel the undesired codeword B. h h h h h h h h h h h h h h h h h h Let =, = nd h h =. Use y nd i h h h h n to denote the element of i Y nd N, i =,,,, =,. The elements Y cn be effectively written s of y e e b e b n 5 7 = e 6 e 8 b e b y e e b e b n 5 7 = e 6 e 8 b e b y e e b e b n 5 7 = e 6 e 8 b e b y e e b e b n 5 7 = e 6 e 8 b e b h i hi yi ni where, i =, y =, i n = hi hi y, i i =,,,, =,,. y i i ni nd n i re the effective received signls nd the effective noise t the i-th n e 5 e 7 b e b tenn, respectively., θ nd θ re the effec e 6 e 8 b e b tive trnsmitted signls of the three trnsmitters. i is the effective chnnel mtrix corresponding to the effective trnsmitted signls, i =,,,, i i =,,. i, hving orthogonl columns, stisfies = I, where I is unit mtrix with dimension. The third terms t the right side of Eqution (9-) re the interference signls, which cn be mitigted using interference cncelltion method s follows e e z P P w y y 5 7 = = θ e 6 e 8 e e z P P w y y 5 7 = = θ e 6 e 8 i i ( ) ( ) where, Pi =, P =, n n n n w =, w =, =, = i (9) (0) () () () () i,,. z i nd w i re the signls nd the noise fter liner opertion, respectively, i =,. P i is effective chnnel mtrix fter liner opertion, i =,,,. The dimension of z i nd the dimension w i re both, i =,. The dimension of P i is, 5/0

6 i =,,,. Symbols trnsmitted from trnsmitter nd symbols trnsmitted from trnsmitter re not included in (-). So multi-user interference is mitigted through liner opertion on the received signls... Seprte the Desired Codewords Even if multi-user interference is cncelled, the desired codeword t receiver includes 8 independent modulted symbols, nmely,,, 8, s shown in (-). If we decode,,, 8 bsed on (-), the complexity of mximum lielihood (ML) lgorithm is proportionl to the 8th power of modultion order, which is extremely high. So, it is necessry to divide these symbols into severl groups. Te opertion on z nd z to get, where, = P P P Q P P P w = P w P w e x Q w P z P z = = P P e e x Q w P P P z P z 5 7 = = P P 6 e 8 = P P P P P w P w, Q, w = P P P P, (5) (6).,, nd re encompssed by A wheres 5, 6, 7 nd 8 re encompssed by A. So, the elements of A nd the elements of A re seprted, s shown in (5-6). The decoding complexity cn be reduced. From the bove nlysis, not only multi-user interference is cncelled, but lso the two desired codewords A nd A re seprted. Similr opertion cn be performed t the other two receivers. Note tht neither feedbc informtion nor the unidirectionl coopertive lin is required.. Decoding Method In this section, we will show how to decode, ting receiver s exmple. i hs n Almouti structure, i =,,,, =,,. Due to the completeness of mtrix ddition, mtrix multipliction, nd the sclr multipliction of the Almouti mtrix, Q nd Q still hve the Almouti structure. Let q q q q Q = nd Q =. Multiply both sides of (5) with Q to q q q q get 0 x q q e = = θ Q w x 0 q q e Q x Multiply both sides of (6) with Q to get x q q 0 5 e 7 = = θ Q w x 0 q q 6 e 8 Q x (7) (8) 6/0

7 In (7), the chnnel corresponding to e is orthogonl to the chnnel corresponding to e. So we cn decode e nd e seprtely. Similrly, we cn decode 5 e 7 nd 6 e 8 seprtely s well. According to the nlysis mentioned bove, the decoding method is s follows. Step, obtin,,, from the chnnel mtrices, nd then compute P, P, P nd P from,,, ; Step, compute = P P P P Q nd = P P P Q P through di- P P P P rect multiplictions nd subtrction ; Step, obtin y, y, y nd y ccording to the received signls, s in (9-); Step, te opertion on y, y, y nd y to get z nd z, y y y y z =, z = ; P z P z Step 5, te opertion on z nd z to get x = P P x = x = P z P z x x, furthermore, computer = Q x nd Q x P P x through direct multiplictions; Step 6, estimte nd by ( ˆ, ˆ) rg min = ( )( e θ ) x q q, where â nd â re the es-, timtion of nd, respectively; Step 7, estimte nd by ( ˆ, ˆ) rg min = ( )( e θ ) x q q, where â nd â re, the estimtion of nd, respectively; Step 8, estimte 5 nd 6 by ( ˆ5, ˆ6) rg min = ( )( 5 e θ 6) x q q, where â 5 nd â 6 re the 5, 6 estimtion of 5 nd 6, respectively; Step 9, estimte 7 nd 8 by ( ˆ7, ˆ8) rg min = ( )( 7 e θ 8) x q q, where â 7 nd â 8 re the 7, 8 estimtion of 7 nd 8, respectively; The ML decoding complexity in step (6-9) is proportionl to the squre of modultion order. It is esy to see from (7) tht the chnnel corresponding to e is q q, which includes two independent pth with gin q nd q. So e hs diversity gin of two, which is equl to tht of []. Similr rguments cn be used to prove tht other symbols chieve diversity of two s well. nd 7/0

8 5. Simultion Results 6 independent modulted signls re sent over two time slots in []. Feedbc informtion, nmely 6 complex numbers, re required t the trnsmitters, which occupy 6/ time slot if these three receivers dopt the sme trnsmission nd the sme code mode s the trnsmitters. So, / time slot is required to send 6 independent modulted signls in []. The trnsmission efficiency is / symbol per ntenn per time slot. independent modulted signls re sent over four time slots in the proposed scheme. The trnsmission efficiency is / symbol per ntenn per time slot, which is / times s tht of []. Performnce of the proposed scheme nd performnce of the scheme in [] re compred in Tble. Two schemes hve the sme diversity gin. The dvntge of the proposed scheme is tht neither feedbc informtion nor unidirectionl coopertive lin is required, nd the trnsmission efficiency is improved. The disdvntge is tht the decoding complexity is proportionl to the squre of modultion order, higher thn tht of [], which is proportionl to the modultion order. In Figure, we simulte the verge BER curves of the proposed scheme nd the scheme in []. We consider uncoded systems, in which ll the underlying lins experience Ryleigh fding chnnels. The dt symbols re ssumed to be QAM symbols nd 6QAM symbols, generted independently t ech trnsmitter. The verge BER is determined through monte-crlo simultions. The BER [] 6QAM Proposed 6QAM [] QAM Proposed QAM SNR/dB Figure. The BER curves of the two schemes. Tble. Performnce of the two schemes. Scheme Proposed Ref. [] Trnsmission efficiency / symbol/ntenn/time slot / symbol/ntenn/time slot Diversity gin Feedbc No Locl CSI Unidirectionl coopertive lin No Trnsmit two complex number Decoding complexity Proportionl to the squre of modultion order Proportionl to the modultion order 8/0

9 slope of BER curves represents diversity gin, which is in these two schemes. It cn be seen from this figure tht the slope of BER curves of the proposed scheme is lmost the sme s tht of [], which demonstrte the vlidity of theoreticl nlysis. 6. Conclusion In this pper, the multi-user interference is cncelled by the design of the codeword nd liner opertion on the received signls. Compred with the existing scheme for the sme scene, the proposed scheme doesn t require feedbc informtion nd doesn t require unidirectionl coopertive lin, while eeping the sme diversity gin. owever, the scheme is limited to three trnsmitter-receiver pirs, where ech node is equipped with four ntenns. Future wor on this scheme includes extending the ppliction scene. Acnowledgements The uthors would lie to thn the reviewers for their detiled reviews nd constructive comments, which hve helped improve the qulity of this pper. This wor ws supported in prt by Ntionl Nturl Science Foundtion of Chin under rnt No References [] esbert, D., Shfi, M. nd Shiu, D. (0) From Theory to Prctice: An Overview of Mimo Spce-Time Coded Wireless Systems. IEEE Journl on Selected Ares in Communictions,, [] Chen, X., Song, S.. nd Letief, K.B. (0) Interference Alignment in Dul-op MIMO Interference Chnnel. IEEE Trnsctions on Wireless Communictions,, [] Lu, L. nd Zhng, W. (0) Blind Interference Alignment with Diversity in K-User Interference Chnnels. IEEE Trnsctions on Communiction, 6, [] Mddh-Ali, M., Mothri, A. nd Khndni, A. (008) Communiction over MIMO X Chnnels: Interference Alignment, Decomposition, nd Performnce Anlysis. IEEE Trnsctions on Informtion Theory, 5, [5] Xie, B., Li, Y., Minn,. nd Nosrtini, A. (0) Adptive Interference Alignment with CSI Uncertinty. IEEE Trnsctions on Communictions, 6, [6] Chen, X., Song, S.. nd Letief, K.B. (0) Interference Alignment in Dul-op MIMO Interference Chnnel. IEEE Trnsctions on Wireless Communictions,, [7] nesn, A. nd Rn, B.S. (0) Interference Alignment with Diversity for the X Networ with Three Antenns. rxiv:0.[cs.it] [8] Shi, L., Zhng, W. nd Xi, X.. (0) Spce-Time Bloc Code Designs for Two-User MIMO X Chnnels. IEEE Trnsctions on Communictions, 6, [9] Li, L.B. nd Jfrhni,. (0) Mximum-Rte Trnsmission with Improved Di- 9/0

10 versity in for Interference Networs. IEEE Trnsctions on Informtion Theory, 59, [0] nesn, A. nd Rn, B.S. (0) Interference Alignment with Diversity for the X Networ with Four Antenns. IEEE Trnsctions on Informtion Theory, 60, [] Zi, A., Wng, C. nd Rsmussen, L.K. (0) Combining Interference Alignment nd Almouti Codes for the -User Mimo Interference Chnnel. IEEE Wireless Communictions nd Networing Conference, Shnghi, Submit or recommend next mnuscript to nd we will provide best service for you: Publiction frequency: Monthly 9 subect res of science, technology nd medicine Fir nd rigorous peer-review system Fst publiction process Article promotion in vrious socil networing sites (LinedIn, Fceboo, Twitter, etc.) Mximum dissemintion of your reserch wor Submit Your Pper Online: Clic ere to Submit Or Contct service@olib.com 0/0