Address for Correspondence

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1 Mrndn et l., Interntionl Journl of Advnced Engineering Technology E-ISSN Reserch Pper A LATTICE REDUCTION-AIDED INFORMATION PRECODER FOR MULTIUSER COMMUNICATION SYSTEM S. Mrndn, N. Venteswrn 2 Address for Correspondence Deprtment of ECE, Annd Institute of higher Technology, IT ighwy, Kzhipttur, Chenni, 60303, Indi, 2 Deprtment of ECE, SSN College of Engineering, Old Mhblipurm Rod, Klvm, Chenni, 6030, Indi ABSTRACT: Recent demnd for high rte of informtion trnsmission in wireless communiction hs resulted in multiple-input/multiple output (MIMO) systems which offer high spectrl efficiency. Though mssive Multi-user MIMO (MU-MIMO) system introduces interference, it produces considerble increse in cpcity by the use of lrge number of trnsmit nd receive ntenns to communicte with multiple users. Precoding of informtion is technique, which helps in elimintion of inter symbol interference nd minimizes the receiver complexity. In this pper, lttice reduction technique combined with the Vector Perturbtion (VP) is proposed to provide reduced bit error rte t ll signl to noise rtios with no reduction in cpcity. Two schemes hve been formulted nmely lttice reduction ided VP- ZF nd lttice reduction ided VP -MMSE precoders. Its performnce is lso compred ginst tht of the conventionl VP-ZF nd VP MMSE. The simultion results show tht the lttice reduction ided Vector Perturbtion Precoder schemes performs better thn the other conventionl techniques for mssive MU-MIMO systems. KEYWORDS: MIMO, Interference suppression, Complexity, Precoding.. INTRODUCTION Wireless communiction hs been the subject of interest nd ctive reserch over the pst two decdes. The requirements for higher dt rte in complex spce time vrying wireless environment with the limited vilbility of rdio frequency spectrum resulted in highly promising wireless technology nmely the Multiple Input Multiple Output (MIMO). When the number of users ccessing the wireless system becomes lrge, the system is clled s the Multi-User MIMO (MU-MIMO). Mssive multiuser MIMO mes use of lrge number of service ntenns over ctive terminls in TDD mode opertion. It hs mjor benefits lie improved throughput nd high rdited energy efficiency. Precoding techniques hve been considered s solution to solve multiuser interference in wireless communiction []. In downlin, precoders re designed in TDD mode, which vlidtes chnnel reciprocity. Precoding is one of the trnsmitter functions, which mes use of Chnnel Stte Informtion (CSI) to correct the received signl errors t the trnsmitter end. In cse of multi-user MIMO, lrge number of trnsmitter ntenns simultneously communicte with multiple receivers. It therefore suffers from huge inter-user interference. Vrious precoding techniques re discussed in [5]- [2], for MIMO systems. In [], MMSE precoding is considered with chnnel estimtion error s n integrl prt of the system design nd users hving different dptive gin control units t the receiver. In [2] MU-MIMO schemes enble the simultneous multiplexing of multiuser dt strems which produces significnt throughput gin. Investigtions in [3] conclude tht, if the number of ctive trnsmits ntenns re reduced, the system performnce is lso reduced. In [8] low complexity liner precoding scheme clled the bloc digonliztion for downlin multiuser MIMO is considered which ttempts to completely remove the Multi-User Interference (MUI). But it does not consider the contribution of noise. At high dt rtes the mximum diversity order cn be chieved by decomposing MU-MIMO brodcst chnnel into prllel single user MIMO chnnels [9]. A receiver bem former design nmely Tomlinson- rshim precoding (TP) is developed in [9] for multiple receiver ntenn users to reduce the multi user interference. The precoding techniques considered in [0] re the two bsic TP structures nmely centrlized nd decentrlized TP. The quntized chnnel stte informtion is considered for Tomlinson-rshim precoding method proposed in []. In [2] the precoder design with nowledge of the chnnel for both single user nd multiple users is proposed. In [4], performnce of MU-MIMO is incresed by using the prerrnged power scling t the receiver. The vector perturbtion precoder proposed in [5] uses the instntneous power nd instntneous pe power of the trnsmitted signl. In [7], vector perturbtion precoding is used with MMSE criterion nd per-ntenn-group power constrint. In [8], for Mssive MU-MIMO system with single ntenn per user, different liner precoding techniques re nlyzed for different chnnel models. A multi-brnch TP, Vector Perturbtion Precoding nd Lttice reduction ided Bloc digonliztion precoder re proposed nd nlyzed in [9] for MU-MIMO system. Point lttices in MIMO systems [20] nd the Lenstr Lenstr Lovsz (LLL) lttice reduction techniques outperform their other counterprts when integrted with the precoder design. In [2], verge trnsmitted energy reduction is considered. It uses lttice reduction ided precoding with Lenstr Lenstr Lovsz lgorithm for MMSE V-BLAST structure. The performnce of liner precoded MIMO system is shown to improve by the use of LLL lgorithm in [24]. In this pper, lttice reduction combined with the Vector Perturbtion (VP) is proposed to provide the reduced bit error rte t ll signl to noise rtios with no reduction in the cpcity. We formulted two schemes nmely Lttice reduction ided VP- ZF nd Lttice reduction ided VP -MMSE precoders nd compre the performnce ginst the conventionl VP-ZF nd VP MMSE. The rest of the pper is orgnized s follows; Section-2 introduces the chnnel model. Section -3 nlyzes the vrious precoder designs for mssive MIMO systems nmely MMSE, Bloc digonliztion, Tomlinson

2 Mrndn et l., Interntionl Journl of Advnced Engineering Technology E-ISSN rshim, Vector perturbtion precoding. Section -4 introduces the proposed Lttice reduction ided vector perturbtion precoding. In Section -5 nlysis nd comprison of results is performed. 2. MASSIVE MU- MIMO SYSTEM MODEL Fig.. Mssive Multiuser MIMO system Consider the mssive MU-MIMO downlin system with M number of trnsmitter ntenns t the bse sttion. Let there be K number of users nd N number of ntenns per user. The totl number of receiving ntenns [8] cn be represented s, K () Nr Ni i For the downlin the signl received by the th user is represented by y y x Iz n (2) N M Where, C represents the th user s chnnel gin mtrix between the BS nd th user. I is the interference mtrix due to the other users, z is the received signl mtrix of interfering users nd N r n C represents the th user s dditive complex Gussin noise n N(0,I) in the entire chnnel. The two unitry mtrices re used to perform equliztion in the both pre nd post trnsmission of dt strems. This ids the dt to be trnsmitted without interference. Non liner precoding bsed on Dirty pper coding cncels the interference with complete or prtil CSI. owever complete CSI is required for cpcity mximiztion. If the chnnel stte informtion is nown t the trnsmitter then the system cn be designed to produce dt trnsmission t high cpcity when compred to the scenrio, where the chnnel stte informtion is nown only t the receiver. In the non-liner method of precoding the interference is removed t the trnsmitter. Performnce of the nonliner precoding is better when compred to liner precoding. owever, the complexity of non-liner precoding surpsses tht of liner precoding. A. MMSE Precoding The MMSE bsed precoding is used to overcome the drwbcs presented by the zero-forcing bsed precoder [3]. The precoding mtrix is given s [2]. W I 6 Where, W represents the precoding mtrix for the i th user with the size M N nd represents the regulriztion fctor nd it is given by M 7 SNR As the number of ntenns t the bse sttion increses the cpcity lso increses for both the perfect CSI nd imperfect CSI ssumptions. The cpcity lso increses s the signl to noise rtio (SNR) increses. B. Bloc digonliztion Precoding The bloc digonliztion method considers the elimintion of multi-user interference.the bloc digonliztion precoding is done in two steps [8]. To K z y i i (3) i¹ Let x represents the trnsmitted symbol vector of size ( MX ) of user, the informtion trnsmitted is s, K eliminte or blnce the multi-user interference with x W s (4) noise n initil precoding filter P used is represented s in [8], The received signl y hevily depends on the nture 0 of the CSI vilble. Accordingly, the impct of CSI P V 8 on the precoder design is considered in this pper. 0 Where, V C M M R is obtined by performing The Chnnel Stte Informtion (CSI) vilble is SVD decomposition of ssumed to be either Perfect or Imperfect. In cse of. R is the rn of the perfect Chnnel Stte Informtion (CSI) received t chnnel gin mtrix [8]. the bse sttion (trnsmitter) the chnnel gin mtrix 0 is represented s nd in cse of imperfect CSI, it U V V 9 is given by noisy chnnel mtrix [5] Ĥ E (5) To prllelize ech user strem the second precoding b The ccurcy of CSI is influenced by the error filter P is used. For the th user equipment the mtrix E. precoding mtrix is given s 3. LINEAR AND NON-LINEAR PRECODER FOR MASSIVE MU-MIMO SYSTEM W P P b 0 In this section, we review the liner nd non liner M L Where, P precoding techniques for mssive MIMO systems. C b L nd N P C. The Liner precoding cn be performed using MMSE or prmeter L depends on the precoding lgorithm. By Bloc Digonliztion precoders. The populr nonliner precoding techniques considered here include Nr N M excluding the th user chnnel mtrix, the Tomlinson-rshim nd Vector Perturbtion C is [8] Precoding. T, T,..., T, T,..., T Liner precoding employs SVD of the CSI t the K trnsmitter. SVD digonlizes the chnnel mtrix.

3 Mrndn et l., Interntionl Journl of Advnced Engineering Technology E-ISSN The interference generted by the other users is given by P. The second precoding mtrix is found by decomposing the MU-MIMO chnnel into multiple prllel SU-MIMO chnnels. For the i th user the effective chnnel mtrix is given by eff P 2 Singulr vlue decomposition is pplied to the effective chnnel mtrix in order to obtin the second precoding mtrix. b P V 3 is the power loding mtrix. Generlly the performnce of bloc digonliztion bsed precoding is better thn tht of MMSE bsed precoding. The complexity increse since the first nd second precoding mtrices need to be implemented K times to find nd. The totl number of the receiver ntenns required is less thn the totl number of trnsmitter ntenns. C. Tomlinson-rshim Precoding eff Fig. 2- System model for Tomlinson-rshim precoding [9]. Tomlinson-rshim precoding cn be considered for both the time domin s well s sptil domin equliztion. The function of TP is similr to tht of decision feedbc equlizer t the receiver. But for precoding it is plced t the trnsmitter. Figure 2 shows the system model for TP precoding. The vrious filters used re the scling filter G, feedforwrd filter F nd the feedbc filter B. The LQ decomposition is performed. The scling, feedforwrd nd the feed-bcwrd filters re represented jointly s [0] F Q 4,, 2,2,..., 5 G dig l l l N t M B LG 6 The trnsmitted symbol vector x for the input i bits s is xi si bi, j x j j In order to reduce the mplitude of the trnsmitted symbols modulo opertion is performed. The received signl is represented s r FGx n 7 Where, is the normliztion fctor. It is E FGx represented s. The complexity of the E s Tomlinson-rshim precoding increses t greter rte when compred to the bloc digonliztion bsed precoding. If the chnnel stte informtion received is perfect then the interference from other users cn be completely subtrcted. D. Vector Perturbtion Precoding In Vector Perturbtion Precoding the instntneous power nd the pe-to-verge-powers re considered. For this purpose it uses the p -sphere encoding. The p -sphere encoder minimizes the error rte. The trnsmitted symbol vector is represented by [4] P x s z 8 Where, represents the power normliztion fctor nd it is given by M i M i. ere is i instntneous trnsmit power nd is given by i s z 9 The z represents the perturbtion vector nd it is given by z rg min s z 20 zg Where represents the rel vlued trnsltionl prmeter. The p - sphere encoder is used to find the instntneous pe-power. The short term power constrint is used for simple MIMO system while long-term power constrint is used for Mssive MU- MIMO system. Eqution (20) represents the power constrint E x 2 P 2 Fig.3 System model for Vector Perturbtion precoding [4] The usge of p -sphere encoder increses the complexity. When the noise nd interference re less the detector produces correct decisions. VP precoding method is sensitive to CSI imperfections when the instntneous trnsmit power is lrge. 4. PROPOSED LATTICE-REDUCTION-AIDED VECTOR PERTURBATION PRECODING Fig. 4. Proposed System model for LR ided Vector Perturbtion precoder using LLL lgorithm Comprison of the liner nd non-liner precoding techniques hs been presented in the previous section. It is well nown tht the Vector Perturbtion Precoding performs well, compred to the other techniques. owever, VP precoding inherently cncels the residul interference t ech of the user s receiver nd does not completely remove inter user interference. The performnce of the VP precoding cn still be improved by Lttice reduction lgorithm. The LLL lgorithm solves the problems tht occur in

4 Mrndn et l., Interntionl Journl of Advnced Engineering Technology E-ISSN point lttices by orthogonlizing the columns nd reducing the lttice bsis. An improved bsis for the lttice is generted by using lttice reduction. Figure 4 shows the proposed system model for LR ided Vector Perturbtion precoder using LLL lgorithm. The reduced bsis nd the originl bsis re interrelted vi unimodulr mtrix. The Precoding mtrix is QR decomposed s i Qi Ri 22 The size of the R mtrix is reduced when the condition Rl, Rl, l is not stisfied, 2 where l, M. Orthogonliztion is chieved by exchnging the two column vectors if the condition R, R, R, is not stisfied for given 4 prmeter. This is clled the Lovsz condition. The qulity of the reduced bsis depends on the prmeter. owever, higher the vlue of, greter the complexity. Therefore the optiml vlue of used is 3 / 4. All the trnsformtions preformed on R re registered within the trnsformtion mtrix T. By Lenstr Lenstr Lovsz lgorithm the lttice reduced precoding mtrix is given by, Q R T 23 The LR ided Vector Perturbtion Precoded signl is represented s P x Q R T T s z (24) The flowchrt of the LLL lgorithm is shown in figure 5, where m represents the rn of the precoding mtrix. A. LR- VP- ZF precoding Chnnel inversion done in trnsmitter side by zero forcing yields the by considering perfect CSI, (25) From Eqution (8) the instntneous trnsmit power is clculted nd zero forced perturbtion vector is, rg min zg z s z (26) The LR- VP- ZF precoded signl will converge to better error rte under the condition of perfect CSI for minimum. B. LR- VP- MMSE precoding From eqution (6), the scling fctor β reduces the chnnel impirments, thus regulting trnsmit power I (27) From Eqution (8), the perturbtion vector is, z rg min I s z zg Since the impirments re regulted by β, even under imperfect CSI, the totl trnsmit power Г is regulted bsed on the SNR. 5. SIMULATION RESULTS Extensive numericl simultions hve been performed to evlute the performnce of the proposed LR ided VP precoding schemes nmely LR ided VP-MMSE nd LR ided VP-ZF. The performnce of the proposed LR ided Fig. 5. Flow chrt of Lenstr Lenstr Lovsz Lttice Reduction Technique Vector perturbtion precoding scheme for mssive MU-MIMO system hs been evluted with 00 ntenns t the trnsmitter nd 4 ntenns per user. Considering tht 0 users re present we rrive t {(00 4),0} system. The MIMO chnnels re ssumed s AWGN chnnels. They re independent identiclly distributed with zero men normlly distributed noise. 6-QAM modultion hs been used for higher spectrl efficiency. For comprison, the following precoding techniques hve been considered, Liner Precoding Schemes: Bloc Digonliztion Precoding, MMSE Precoding, Zero forcing(zf) bsed precoding Non liner precoding schemes: Tomlinson rshim Precoding (TP), Vector Perturbtion Precoding (VP), VP-ZF, VP - MMSE LR ided precoding schemes: LR- VP ZF, LR- VP-MMSE. A. Bit Error Rte Performnce Anlysis Fig. 6 Signl to noise rtio vs. BER using Perfect Chnnel Stte Informtion for M 00 number of trnsmitter ntenns for K 0 number of users ech hving 4 ntenns ech.

5 Mrndn et l., Interntionl Journl of Advnced Engineering Technology E-ISSN Figure 6 shows comprison of the performnce of LR-VP schemes in terms of Bit Error Rte Vs SNR with other conventionl precoding schemes for the chnnel conditions nmely with perfect CSI. In MMSE precoding regulriztion fctor is used. It reduces the ill-posed problems which occur when the solutions behvior chnges continuously with initil conditions. Due to this reson the performnce of MMSE outperforms the Bloc Digonliztion, Tomlinson-rshim precoding nd Vector Perturbtion for both the perfect nd the imperfect CSI ssumptions. The function similr to the decision feedbc equliztion is performed t the trnsmitter in Tomlinson-rshim precoder. ence the bit error rte performnce is higher for the Bloc digonliztion method of precoding for perfect CSI. outperforms ll the other conventionl precoding such s the MMSE, Tomlinson-rshim precoding. But it pproches the cpcity of Vector Perturbtion precoding with zero-forcing. The Cpcity of Tomlinson-rshim precoding flls behind other methods of precoding considered, becuse the size of the precoding mtrix increses, s the number of trnsmit ntenn increse. Fig. 7- Signl to noise rtio vs. BER using Imperfect Chnnel Stte informtion for M 00 number of trnsmitter ntenns for K=0 number of users ech hving 4 ntenns ech In Figure 7, for the cse of imperfect CSI the Bloc digonliztion method of precoding BER performnce is better thn tht of the Tomlinson- rshim precoding becuse it reduces the multiuser interference. The Vector Perturbtion precoding uses perturbed dt for reducing the error rte to level which is lower thn wht cn be chieved using the Bloc digonliztion nd TP bsed precoding. The error rte of vector perturbtion precoder cn be reduced further by using the LLL lttice reduction lgorithm s shown in figure. B. Cpcity Anlysis Fig. 9. Signl to Noise Rtio vs. Cpcity of MMSE precoding, Bloc Digonliztion precoding, Tomlinson-rshim Precoding, VP-MMSE, VP-ZF, VP-MMSE-LLL nd VP-ZF- LLL for M 00, K0 N 4 nd 6-QAM using perfect CSI. C. Cumultive distributive function Anlysis Figure 8 shows the bit error rte vs. cumultive distributive function (CDF) plot for perfect nd imperfect chnnel stte informtion. The CDF describes tht the given probbility distribution will hve vlue less thn or equl to the BER. If the system hs perfect nowledge of the chnnel stte, there is greter probbility tht the dt will be decoded correctly. If only Imperfect nowledge of CSI is vilble the probbility of decoding error is completely high. Thus for ny given BER threshold the CDF for perfect CSI is greter thn tht for imperfect CSI. Fig. 8 Number of trnsmitter ntenns Vs. Cpcity of MMSE precoding, Bloc Digonliztion precoding, Tomlinson- rshim Precoding, VP-MMSE, VP-ZF, VP-MMSE-LLL nd VP-ZF-LLL for M=00, 200, 300, nd 400, K=0, N=4, nd 6 QAM using perfect CSI. Figure 8 shows plot of cpcity ginst the number of trnsmitter ntenns of MMSE, Bloc digonliztion, Tomlinson-rshim precoding nd Vector Perturbtion Precoding schemes for the cse of perfect CSI. As the number of trnsmitter ntenns increses, the Cpcity of LR ided Vector Perturbtion with MMSE method of precoding Fig. 0. Bit error rte vs. Cumultive distributive function for perfect nd imperfect CSI 6. CONCLUSIONS In this pper, we demonstrte the performnce of lttice reduction ided vector perturbtion Precoder for mssive MU-MIMO system. The pper suggested the use of lttice reduction lgorithm in the design of vector perturbtion precoding to further orthogonlize the bsis. Simultion results conclude tht the LR ided Vector Perturbtion precoding hs better performnce when compred to ll the other conventionl precoding lgorithms nmely Bloc digonliztion, Tomlinson-rshim precoding nd Vector Perturbtion Precoding in terms of Bit Error rte for Mssive MU-MIMO system. In ddition, LR ided Vector Perturbtion performnce is the best for vrying number of trnsmit ntenns. owever, in generl s number of users nd the number of user

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