Available online at www.sciencedirect.com ScienceDirect Procedia Computer Science 4 (04 ) 7 79 9th International Conference on Future Networks and Communications (FNC-04) Space Time Block Code for Next Generation Multi-user MIMO Systems Nidhi Sharma a a Department of Electrical and Computer Engineering, Queen s University, Kingston K7L N6, Canada Abstract Space-time block codes (STBCs) based single user multiplexing techniques are already part of the LTE standard. However, the rapid increase in demand for high speed and reliable communications is propelling us towards the next generation cellular networks. Multi-user MIMO based techniques are a promising candidate to meet this demand. In this paper, an STBC is designed for a multiuser MIMO system containing two users, transmitting independently. The transmission matrix is designed with the criterion of maximizing coding gain for the two users. Further, the proposed STBC enables independent decoding of symbols of both the users. A pair-wise maximum likelihood (ML) decoder for the proposed STBC is also derived. The performance of the proposed STBC is compared with the existing work and it is shown through simulations that the proposed code design performs significantly better than the existing STBC. c 04 Elsevier The Authors. B.V. This Published an open by Elsevier access article B.V. under the CC BY-NC-ND license Selection (http://creativecommons.org/licenses/by-nc-nd/.0/). and peer-review under responsibility of Elhadi M. Shakshuki. Selection and peer-review under responsibility of Conference Program Chairs Keywords: Full-diversity, full-rate, minimum determinant, multiple input-multiple output (MIMO), space-time block code (STBC).. Main Text Space-time coding, for multiple input-multiple output (MIMO) systems has been used to enhance the data rate and increase the reliability of a wireless communication systems. Space-time block codes (STBCs) for single user MIMO system have been extensively studied over the last decade. Single user schemes for various antenna configurations are already part of the latest LTE standard. The next generation cellular networks are being designed for an expected multi-fold increase in user demand. Single user MIMO system may not be able to cope up with this huge surge in demand. Multi-user MIMO is one of the promising techniques that is expected to meet this demand 4. STBCs for multi-user MIMO systems have recently gained attention. Multi-user communication system allows users to simultaneously transmit data by sharing the same frequency and time interval. Multi-user MIMO channels can be divided into two categories: multiple access channel (MAC) and broadcast channel (BC). In the MAC (typically uplink), decentralized mobile users transmit to a base station (BS), while in the BC (typically downlink), the BS Corresponding author. Tel.: +-6-888-759. E-mail address: sharma.nidhi.iitd@gmail.com 877-0509 04 Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/.0/). Selection and peer-review under responsibility of Conference Program Chairs doi:0.06/j.procs.04.07.08
Nidhi Sharma / Procedia Computer Science 4 ( 04 ) 7 79 7 Fig.. Multi-user MIMO System. transmits to decentralized mobile users. A scheme that utilizes single-user STBC for different users with interference cancellation at the receiver has been proposed in 5. Space-time/frequency code design criteria for multi antenna MACs has been proposed in 6. In 7, Alamouti STBC is used by multiple users and different ways of decoding the transmitted signals by using the algebraic structure of Alamouti STBC have been suggested. A code design criteria for MIMO MAC channels with frequency selective fading has been designed in 8, where the diversity multiplexing trade-off for point-to-point selective-fading channels has been extended to the multi-point channels. Similar concept for diversity multiplexing trade-off has been proposed in 9. A multi-user STBC for MIMO uplink channel has been proposed in 0.TheSTBCin 0 considers quasi-static channel and is based on algebraic rotation achieving full diversity. Similar codes were proposed in,,. A low peak-to-average power (PAPR) STBC for two-user MIMO system is proposed in 4 to remove co-channel interference in a multi-cell environment. The STBC in 4 is constructed to provide decoupled decoding of the symbols at the receiver. However, the STBC in 4 does not consider maximizing the coding gain. Hence, in this work a multi-user STBC with low PAPR and high coding gain is proposed that ensure more reliable communication. This is the motivation of this work. Symbol mapping has been proposed in the literature 5,6,7 to design high coding gain STBCs for single-user MIMO system. Despite the evident increase in performance, the concept of symbol mapping has not been used for designing STBCs for multi-user MIMO system. Hence, in this paper, an STBC for two user MIMO system for a quasi-static channel is presented that achieves high coding gain with decoupled decoding of symbols transmitted by the two users at the receiver. The STBC is designed using the concept of symbol mapping proposed earlier in 5,6,7 for PAM/QAM constellation. The proposed STBC is compared with the recently proposed STBC in 4 for multi-user MIMO system (using quasi-orthogonal STBCs). The rest of the paper is organized as follows. In Section, the system model for multi-user MIMO system is discussed. The code design for multi-user MIMO system is proposed in Section. In Section 4, pair-wise ML decoder for the proposed STBC is derived. The performance of the proposed STBC is compared with the existing STBC in Section 5. It is shown through Monte-Carlo simulations that the proposed code design performs significantly better than the existing STBCs. Finally, some concluding remarks are presented in Section 6.. System Model In this section, two individual users transmitting independently of each other are considered. Both the users are assumed to be equipped with N t =, transmit antennas and N r receive antennas, N r. Each user can transmit using T time slots as depicted in Fig.. The transmission of the both the users is considered to be synchronized in time. Further, it is assumed that the channel between the transmit and receive antennas is quasi-static flat fading
74 Nidhi Sharma / Procedia Computer Science 4 ( 04 ) 7 79 channel, i.e., the channelcoefficientsremain constant over T time slots. The symbols transmitted from both the users are received simultaneously at the receiver and the received signal can be represented as, R = C H + C H + N, () where R C Nr T is the received signal matrix, and C C Nt T and C C Nt T are the transmission matrix or the transmitted signal matrix from the two users, H and H C N r N t are the channel matrices for the two users containing independent and identically distributed (i.i.d.) circularly symmetric Gaussian random variables with zero mean and unit variance, and N C Nr T is the noise matrix containing i.i.d. complex Gaussian random variables with zero mean and σ variance. Some of the design criterion for space-time codes are defined below Definition. Coding gain of an STBC X is given by Δ g c = min (X X )(X X ) /N t, () X X where X and X are the codeword matrices belonging to the STBC X, (X X )(X X ) is the determinant, and (.) denotes the hermitian of a matrix. For all possible combinations of the constellation symbols the value of the determinant in () is calculated and the minimum value (minimum determinant) is chosen. Definition. Diversity gain of an STBC X is given by, { g d = N r min rank (X X )(X X ) }. () X X To check the diversity order of an STBC, the rank of all possible difference matrices (X X )(X X ) with X X is calculated. Definition. The PAPR measures the peak amplitude of a signal divided by its root mean square value. The PAPR of an STBC is given by max st,nt t {,...,T} PAPR = { ( st,nt (4) T t {,...,T} E )}, where T represents the time slots over which the STBC is transmitted, N t represents the number of transmit antennas, and s t,nt is the transmitted symbol in t th time slot from Nt th transmit antenna. In the next section, the code design for multi-user MIMO is presented.. Multi-user Code Design The STBCs proposed in can only be used for a single-user MIMO systems due to their structure. Hence, STBCs for multi-user MIMO systems need to be designed. Various STBCs 0,,, for MAC based MIMO systems are proposed in the literature. Amongst the existing STBCs for multi user MIMO, the one proposed in 4 for two-user MIMO system provides good performance without any compromise on PAPR. The code matrix of the STBC in 4 is given by [ ] Ak A X k = k, (5) B k B k where A k and B k are Alamouti STBCs for user and, respectively, represented as [ ] p p A k = (6) p p [ ] p p B k = 4 p 4 p, (7)
Nidhi Sharma / Procedia Computer Science 4 ( 04 ) 7 79 75 such that p i s, i =,,, 4 are the symbols transmitted from user and respectively. The 4 4 STBC proposed in (5) can be used for a two-user MIMO system. The STBC is designed such that at the receiver the symbols of both the users can be separated to remove interference. A diversity order of N r is achieved. Motivated by these results, an STBC for two-user MIMO system is proposed in this paper which achieves a higher coding, without compromising on the PAPR, as compared to the STBC in (5) with the same diversity order. STBC for two users MIMO system is proposed where each user transmits using two transmit antennas over four time slots. The transmission matrix of the two users is represented as [ θp p C = θp ] p q q q q (8) and [ θp p C = 4 θp ] p 4 q 4 q q 4 q, (9) where the rows of C and C represent the transmit antennas and the columns represent the time slots. p i, q i are the information symbols that are drawn from any real or complex valued QAM constellation, i = {,,, 4}. θ = e iλ represents the angle of rotation. The symbol q i is obtained from p i using the following function defined in 5,6,7 q i = p i 5p i p i. (0) The function q i in (0) is defined such that both q i and p i A-QAM, where A is the size of the constellation. The function q i maps the symbol p i to a symbol in QAM constellation such that q i p i. The concept of mapping has been proposed earlier in 5,6,7 for a single user MIMO system. In 6,7, non-orthogonal STBCs were proposed for N t = 4, transmit antennas and N r receive antennas, N r using symbol mapping. The mapping was proposed in order to maximize the Euclidean distance between the symbols to increase the coding gain. This paper uses mapping to design STBC for multi-user MIMO case. The joint transmission of the two users can be represented as where C and C are given by (8) and (9), respectively... Minimum Determinant C = [ C C ] T, () The transmission matrix C and C are designed so as to maximize the value of minimum determinant as defined in () with respect to θ. Since, the two users are transmitting independently, therefore, the minimum determinant can be maximized by optimizing C and C independently with respect to θ. A simplified expression for minimum determinant for C can be obtained as follow. The codeword difference matrix for C can be written as [ θa a X = θa ] a θb b θb b = [ AB ], () where [ ] [ ] θa a A = θa a θa a, B = θb b and a i, b i, a i, b i, i =,,, 4 represent the symbol difference. From (), XX can be calculated as [ ] [ ] A AB = A + B. () B It can be observed from (), that minimizing { A + B } is equal to minimizing A and B individually, i.e., min X = min{ A } + min{ B }. (4) X
76 Nidhi Sharma / Procedia Computer Science 4 ( 04 ) 7 79 6 x 04 Minimum determinant of Multi user Scheme for 6 QAM 5 4 Minimum determinant 0 0 0.5.5 Angle of rotation (λ) Fig.. Minimum Determinant of Proposed STBC for 6-QAM Since A and B have similar structure, only one term in (4) is minimized, i.e., [ ][ ] min A = θa a θa b b b a = a + a θa b a b b θ a b a b b + b. (5) Further, (5) can be simplified to min A = min {( a + a )( b + b ) ( θa b a b )( θ a b a b ) }. (6) Since the minimum determinant is to be maximized over θ, the terms containing only θ in (6) are considered. Thus, (6) can be rewritten as min A = min { θa b θ a b + θa b a b a b θ a b a b } θ a b = min { a b + a b + θa a θ b b + a b θ a b }. (7) Neglecting the non θ terms, (7) can be further simplified to min A = θa a θ b b + a b θ a b = Re. { θa a θ b b }. (8) Similar expression can be obtained by minimizing B. The minimum determinant maximizing value of θ =.08 can be obtained using (8) as shown in Fig.. The next section presents the decoder for the proposed scheme. 4. Pair-wise ML Decoder In this section, a pairwise ML decoder has been derived for the proposed STBC. It is shown that the symbols transmitted by the two users can be decoded separately at the receiver by solving the ML decision metric. However, the symbols of the individual users are jointly decoded. For simplicity of the decoder, it is assumed that N r =,
Nidhi Sharma / Procedia Computer Science 4 ( 04 ) 7 79 77 similar analysis is applicable for N r. Using (), the received signal equation can be written as R = [ ] [ θa h h a θa ] a b b b b + [ ] [ θa h h a 4 θa ] a 4 4 b 4 b b 4 b. (9) Rearranging (9) results in which can be equivalently written as The ML decision metric for () can be written as where R is given by and HCR is given by Further simplification of (4) gives r r = [ θa a ] θa a b h r h h h b b b 4 θa a 4 θa a + 4 r 4 b 4 b b 4 b n n n n 4, (0) R = HC + N. () R HC = R Re { HCR } + H C CH, () R = 4 r i, () i= HCR = [ θa a ] θa a b h h h h b b b 4 θa a 4 θa a 4 b 4 b b 4 b r r r r4. (4) HCR = h (θa r a r + θa r a r 4) + h (b r b r + b r b r 4) +h (θa r a 4 r + θa r a 4 r 4) + h 4 (b 4 r + b r b 4 r b r 4). (5) Post some manipulations, (5) can be written as HCR = (r + r )(θh s + h b ) + (r r )(θh s + h 4 b 4 ) + (r + r 4 )( h a + h b ) + (r r 4 )( h a 4 + h 4b ). (6) In (), H C CH is given by where H C CH = [ h h h h 4 ] T C C [ h h h h 4 ], (7) ( a + a ) ( θa b a b ) 0 0 C ( θ a C = b ( a b) b ) + b ) 0 0 0 0 ( a + a 4 ) ( θa b 4 a 4 b ). (8) 0 0 ( θ a b ) ( 4 a 4 b b + b 4 ) On solving (7), we obtain H C CH = Re{ h h θa b h h θa b + h h 4 θa b 4 h h 4 θa 4 b } + h ( b + b ) + h 4 ( b + b 4 ) + h ( a + a ) + h ( a + a 4 ). (9)
78 Nidhi Sharma / Procedia Computer Science 4 ( 04 ) 7 79 0 0 SNR versus SER for 6 QAM STBC [] for 6QAM Proposed STBC for 6QAM 0 SER 0 0 0 4 6 8 0 4 6 8 0 SNR [db] Fig.. SER versus SNR Curve for Proposed STBC and Existing STBC 4 for 6-QAM. Substituting the values of R, HCR,andH C CH from (), (6), and (9), respectively, in () we get R HC = 4 i= r i + h (θa r a r + θa r a r 4) + h (b r b r + b r b r 4) + h ( a + a ) +h (θa r a 4 r + θa r a 4 r 4) + h 4 (b 4 r + b r b 4 r b r 4) + h ( b + b ) + h 4 ( b + b 4 )) +( Re{h h θa b h h θa b ) + h h 4 θa b 4 ) h h 4 θa 4 b } + h ( a + a 4 ). (0) The RHS of (0) represents the simplified ML decision metric. It can be seen from the expression in (0) that the terms containing a, a and a, a 4 can be separated and are given by f (a, a ) = h (θa r a r + θa r a r 4) + h (b )r b r + b r b r 4)+ {Re{h h θa b h h θa b } + h ( b ) + b ) + h ( a + a )}, () f (a, a 4 ) = h (θa r a 4 r + θa r a 4 r 4) + h 4 (b 4 r + b r b 4 r b r 4)+ {Re{h h 4 θb b 4 h h 4 θb 4 b } + h 4 ( b + b 4 ) + h ( a + a 4 )}. The expression in () and () are minimized to decode the symbols of two users independently. From () and (), the symbols a, a of User and a, a 4 of User are decoded separately. Hence, the proposed code design independently decodes the data transmitted from both the users; thereby removing inter-user interference. However, the symbols of any individual user have to be jointly decoded. () 5. Performance Results Simulation results for symbol error rate (SER) versus the SNR are presented for the proposed multi-user STBC for 6-QAM constellation using Monte-Carlo simulations. A block fading channel is considered with frequency flat fading. Additive white Gaussian noise with zero mean and unit variance is considered in the system. The SNR is varied from 0 to 6 db with a step size of db. The SER versus SNR is plotted on a logarithmic scale as shown
Nidhi Sharma / Procedia Computer Science 4 ( 04 ) 7 79 79 in Fig.. The channel coefficient matrix H is assumed to be a constant for each transmitted STBC and is varied independentlybetween different transmitted STBCs. The channel state information is assumed to be available at the receiver. This is a reasonable assumption given that the uplink and downlink channel coefficients are symmetric and can be estimated through training pilot symbols. The simulation results are averaged over 0 6 channel realizations. It is further assumed that both the users are transmitting to a single receive antenna, i.e., N r =. In the user devices, a reasonable number of equipments still use single antenna. Hence, this is a practical assumption. However, similar results can be obtained for higher number of antennas at the receiver as well. The optimal rotation angle for 6-QAM constellation, i.e.,.08 is used for the simulations. This value is obtained through exhaustive search amongst all possible values. Pair-wise ML decoding is used at the receiver to decode the transmitted symbols of each user. The SER performance of the proposed STBC is compared with the STBC proposed in 4. It is seen in Fig. that the proposed STBC achieves a higher coding gain and performs significantly better than the STBC in 4. 6. Conclusions In this paper, a multi-user MIMO STBC for two users for 6-QAM constellation is presented. It is shown that the symbols transmitted by the two users can be decoded separately at the receiver. The performance of the proposed scheme is compared with the existing STBC for multi-user MIMO and it is shown that the proposed STBC outperforms the existing STBC for two user MIMO system. The proposed STBC shows significant improvement in performance without compromising on PAPR and decoding complexity. Similar STBCs can be designed for arbitrary number of transmit and receive antennas for higher order constellations and is subject of future research. References. Tarokh V, Seshadri N, Calderbank AR. Space-time codes for high data rate wireless communication: Performance criterion and code construction. IEEE Trans. Inf. Theory 998; 44:744-65.. Alamouti SM. A simple transmit diversity technique for wireless communication. IEEE J. Selected Areas Commun. 998; 6: 45-8.. GPP-TSG-RAN-WG. Evolved universal terrestrial radio access (E-UTRA). GPP, Tech. Rep. TR 6.84 00. 4. Larsson EG, Edfors O, Tufvesson F, Marzetta TL. Massive MIMO for next generation wireless systems. IEEE Communications Magazine 04; : 86-95. 5. Ng BK, Sousa ES, On bandwidth-efficient multiuser-space-time signal design and detection. IEEE J. on Selected Areas in Commun. 00; 0: 0-9. 6. Gartner ME, Bolcskei H. Multiuser Space-Time/Frequency Code Design. in Proc. ISIT, Seattle, USA 006. 7. Tan CW, Calderbank AR. Multiuser detection of alamouti signals. IEEE J. on Selected Areas in Commun. 009; 57: 080-7. 8. Coronel P, Gartner M, Bolcskei H. Diversity multiplexing tradeoff in selective fading multiple-access MIMO channels. in Proc. IEEE ISIT, Toronto, ON 008; 95-9. 9. Tse D, Viswanath P, Zheng L. Diversity and multiplexing tradeoff in multiple-access channels. IEEE Trans. Inf. Theory 004; 50; 859-74. 0. Hong Y, Viterbo E. Algebraic multi-user space-time block codes for X MIMO. in Proc. IEEE PIMRC Cannes, France 008; -5.. Lu HF, Vehkalahti R, Hollanti C, Lahtonen J, Hong Y, Viterbo E. New space-time code constructions for two-user multiple access channels. IEEE J. on Selected topics in Signal Processing 009; : 99-55.. Lu HF, Hollanti C, Vehkalahti R, Lahtonen J. DMT optimal codes constructions for multiple-access MIMO channel IEEE Trans. on Inf. Theory 0; 6: 594-67.. Badr M, Belfiore JC. Distributed space-time block codes for the MIMO multiple access channel. in Proc. IEEE ISIT, Toronto, Ontario 008; 55-7. 4. Bhatnagar MR, Hjorungnes A, Song L. Interference cancellation by using Quasi-orthogonal STBC in two-user MIMO system. in Proc. APCC, Shanghai, China 009; 89-9. 5. Willems FMJ. Rotated and scaled alamouti coding. in Proc. ISIT, Toronto, Ontario, Canada 008; 88-9. 6. Sharma N, Bhatnagar MR, Agrawal M. A high coding gain and low decoding complexity STBC for four transmit antennas. in Proc. NCC, IIT Kharagpur, West Bengal, India 0; -5. 7. Sharma N, Bhatnagar MR, Agrawal M. Non-orthogonal STBC for four transmit antennas with high coding gain and low decoding complexity. in Proc. ICSPCS, Honolulu, Hawaii, USA 0; -5.