Performance Analysis of an AMC System with an Iterative V-BLAST Decoding Algorithm

I. J. Counications, Network and Syste Sciences, 008,, 105-06 Published Online May 008 in SciRes (http://www.srpublishing.org/journal/ijcns/). Perforance Analysis of an AMC Syste with an Iterative V-BLAST Decoding Algorith Sangjin RYOO 1, Kyunghwan LEE, Intae HWANG 3 1 Departent of Electronics Engineering, Chonna National University, Korea T&M Algorith Research, Innowireless, Inc., Korea 3 Departent of Electronics & Coputer Engineering, Chonna National University, Korea E-ail: 1 sjryoo@epal.co, signalds@innowireless.co.kr, 3 hit@chonna.ac.kr Abstract In this paper, the iterative Vertical-Bell-lab Layered Space-Tie (V-BLAST) algorith of an Adaptive Modulation and Coding (AMC) syste is proposed, and the corresponding MIMO schee is analyzed. The proposed algorith adopts iteratively extrinsic inforation fro a Maxiu A Posteriori (MAP) decoder as an a priori probability in the two procedures of the V-BLAST schee of ordering and slicing in an AMC syste. Furtherore, the perforance of the proposed algorith is copared with that of a conventional V-BLAST algorith and a Maxiu Likelihood (ML) algorith in the cobined syste of an AMC schee and a V-BLAST schee. In this analysis, each MIMO schees are assued to be parts of the syste for perforance iproveent. Keywords: Iterative V-BLAST Decoding, MAP Decoder, AMC, STD, Turbo Code 1. Introduction To iprove the throughput perforance together with the developent of the MIMO schee, the AMC schee has attracted considerable attention as the forerunner of next-generation obile counication systes [1]. The AMC schee adapts a coding rate and odulation schee to the channel condition [], resulting in iproved throughput perforance. Consequently, the cobination of a MIMO schee and an AMC schee can potentially iprove the throughput perforance. V-BLAST [3,4] was selected as the MIMO ultiplexing schee [5] and the turbo-coding [6] was chosen as the channel coding schee of the AMC due to the coplexity of the aforeentioned cobined syste. The turbo-coding schee with iterative iplies the use of parallel concatenated recursive systeatic convolutional codes. Such a schee is iteratively decoded with a Posteriori Probabilities (APP) algoriths for the constituent codes [7,8]. In addition, the turbo algoriths used with MIMO is currently an area that is actively researched [9,10]. A perforance analysis is offered here of AMC systes with several V-BLAST algoriths including the turbo algorith used with MIMO. For greater perforance iproveent, the proposed syste utilizes a MIMO channel using two transitter antennas and two receiver antennas, a 4- MIMO channel applying a Selection Transit Diversity (STD) schee [11] that selects two antennas fro four transitter antennas, a 4 4 MIMO channel using four transitter antennas and four receiver antennas, and a 8 8 MIMO channel using eight transitter antennas and eight receiver antennas.. The AMC Syste with the Proposed Iterative V-BLAST Decoding Algorith Figure 1 shows the structure of the AMC syste used with the proposed iterative V-BLAST algorith. An AMC syste that uses a conventional V- BLAST algorith cobines a V-BLAST schee with a turbo-coded AMC syste. The proposed algorith of an AMC syste differs fro the conventional V-BLAST algorith insofar as the extrinsic inforation fro a MAP decoder is used as an a priori probability in the ordering and slicing procedures of the V-BLAST schee [1]. Copyright 008 SciRes. I. J. Counications, Network and Syste Sciences, 008,, 105-06

10 S.J. RYOO ET AL. l k = arg in (H k ) (3) Figure 1. Transitter-receiver structure of an AMC syste with the proposed iterative V-BLAST algorith This schee operates iteratively and is defined as the ain MAP iteration. Furtherore, whenever the schee operates internally, iterative of the MAP decoder is perfored. This ethod is defined as sub MAP iteration. For the proposed syste, a syste equipped with M transitter antennas and N receiver antennas is considered. It is assued that each transission channel is odeled as a flat Rayleigh fading channel. The received signal in the V-BLAST receiver is denoted by X = Hs + n (1) where X=[x 1,,x N ] T is the received signal vector, s=[s 1,,s M ] T is the transitted sybol vector, H is the N M channel atrix, n=[n 1,,n N ] T is the noise vector. The superscript T signifies the transpose atrix, and the noise vector, n, is odeled as a coplex Gaussian rando process. In addition, s is the -ary odulated sybol; that is s =f(d 1,,d ) Φ={φ 1,,φ }, where denotes the bit nuber per sybol, f( ) denotes the sybol odulation function, {d q } q=1,, represents the q-th inforation bits that correspond to s, and {φ i } i=1,, represents the i-th sybol. The proposed slicing algorith does not ake a hard decision with the received signal but akes a decision with the extrinsic inforation fro the MAP decoder [13]. This extrinsic inforation fro the MAP decoder is the log-likelihood function, which can be described as L q, p d = log p d ( q = 1) ( q = 0) () where L,q is the extrinsic inforation that corresponds to d q [14]. Specifically, {d q } q=1,, is deterined by {L,q } q=1,,, respectively. (e.g., if L,q is greater than 0, d q is deterined to be 1. Otherwise, d q is deterined to be 0.) The proposed slicing algorith then perfors the quantization operation appropriate to the constellation in use corresponding to {d q } q=1,,. In a conventional V-BLAST ordering procedure, the order is deterined by the SNR of the corresponding layer. The conventional V-BLAST ordering is described as where k denotes the stage and the superscript represents the pseudo-inverse atrix. The SNR is a function of the channel power, and the layer with the largest channel power is the first layer that is decoded. A high SNR signifies a low sybol error rate. Fro this fact, it follows that the axiu SNR criterion can be considered to be a specific version of the iniu sybol error criterion. The proposed ordering algorith is a function not only of the SNR but also of the extrinsic inforation. It can be odified accordingly to l k = arg in P (e X k, H k, L (i) ) (4) where P (e X k, H k, L (i) ) is the sybol error probability of the -th layer and L (i) =[L (i),1,,l (i), ] T is the extrinsic inforation vector of the l k -th layer at the i-th ain MAP iteration. The sybol error probability, P, can be calculated fro = P(e Xk, Hk, L(i)) 1 P(φ q L (i) )P(φ q φ p X k, H k, L (i) ) (5) q= 1 p= 1, p q where φ q is the original transitted sybol, φ p is the possible sybol excluding the original transitted sybol (φ q ), and P(φ q φ p X k, H k, L (i) ) is the pair-wise sybol error probability, which can be obtained fro P (φ q φ p X k, H k, L (i) ) = P [ p(φ q y ) < p(φ p y ) ] = P [ log p(φ q y ) < log p(φ p y )] (6) where y is the desired sybol that deletes the interference of other sybols after the nulling process of the V-BLAST in the received sybol of the -th layer, x. With the assuption that the variance of noise corresponding to the -th layer is σ /, in Eq. (6), the log posteriori function of φ p is described by log p(φ p y ) (7) = log [ p(φ p L (i) ) p(y φ p )/p(y ) ] =log p(φ p L (i) ) + [Re(φp-φ q )(y -(φ p +φ q )) * ]/σ where the superscript * signifies a coplex conjugate. 3. Siulation Results 3.1. MCS Level and Paraeters for Siulation Table 1 shows the Modulation and Coding Schee Copyright 008 SciRes. I. J. Counications, Network and Syste Sciences, 008,, 105-06

PERFORMANCE ANALYSIS OF AN AMC SYSTEM WITH AN ITERATIVE 11 V-BLAST DECODING ALGORITHM (MCS) level selection thresholds, and Table shows the siulation paraeters. The detailed paraeters in Table 1 are established on the basis of the 1X EV-DO standards [15]. There are any references in the selection of the MCS level selection threshold. For exaple, the threshold can be selected to satisfy the required Bit Error Rate (BER) and the required Frae Error Rate (FER). As ore ephasis is placed here on the data transission rate, the threshold that axiizes the throughput perforance was selected. That is, the threshold of the selected MCS level is derived fro the MCS level transission rate perforance intersection in each syste. One frae is set up with one transission slot with a frae length of,048 sybols. If one bit error occurs in one frae, it is assued to be a frae error. When a frae error does not occur, the transission rate is calculated in accordance with the V- BLAST technique in the order of (bit length data rate nuber of transit antenna). The perforance of the transission rate closely corresponds to the capacity of the FER. Thus, in accordance with the transission rate, a perforance analysis is obtained by the error probability. MCS level Data rate (Kbps) Table 1. MCS levels Nuber of bits per frae Code rate Modulation 1 614.4 1,04 1/3 PSK 1,8.8,048 /3 PSK 3 1,843. 3,07 /3 8PSK 4,457.6,096 /3 16AM Table. Siulation paraeters Paraeter Turbo-coding schee MAP iteration of the AMC syste with a conventional V-BLAST technique Main MAP iteration of the AMC syste with the proposed V-BLAST technique Sub MAP iteration of the AMC syste with the proposed V-BLAST technique Channel Value PCCC 4 4 Flat fading 3.. Coplexity of Each Decoding Algorith This section outlines the coplexity of the proposed algorith, the conventional V-BLAST algorith, and the ML algorith in the cobined syste of an AMC schee and a V- BLAST schee. The ultiplication operation contributes to the coplexity of ipleenting the syste. Except for the procedures of a channel deinterleaver and the MAP decoder in the receiver, each algorith was copared to the nuber of ultiplication operations, as shown in Table 3 [16]. In this table, C is the nuber of sybols, S is the nuber of sub MAP iterations, L is the nuber of ain MAP iterations, and B is the nuber of bits per sybol. Soe exaples of the table show that the proposed algorith is ore coplex than a conventional V- BLAST algorith but less coplex than an ML algorith. In particular, when used with a higher-order odulation, the proposed algorith is less coplex than the ML algorith. According to the table, as the odulation changes fro PSK to 16AM in the case of M=N=4, the coputational coplexity of the proposed algorith ranges fro approxiately 4% to 0.1% of the coplexity of the ML algorith. Furtherore, coparing with the coplexity of the proposed schee in [16], the coplexity of the proposed schee is relatively less coplex for M=N=4, PSK, and L=3 or 4. Table 3. Coplexity of each algorith (L=4, S=, M=N=4) Required ultiplications ML C M (M+1)N Conventional (M+1)N 3 + (3/)M N+ [(7/)M-1]N-1 Proposed (M+1)N 3 + L[M N(B+1)+ (3M-1)N-1] PSK 5,10 467 1,60 8PSK 81,90 467 1,516 16AM 1,310,70 467 1,77 3.3. Perforance of the AMC Systes with Several V-BLAST Decoding Algoriths Figure shows the throughputs of the AMC systes with several V-BLAST algoriths in a MIMO schee. It is clear that the proposed algorith achieves a better throughput perforance copared to the conventional V-BLAST algorith over the entire SNR range. Additionally, the proposed algorith is close to the existing ML algorith in ters of the throughput perforance. Figure 3 shows the throughputs of the AMC systes with several V-BLAST algoriths in a and 4- MIMO channel. It is deonstrated that the systes in a 4- MIMO channel achieve superior throughput perforance relative to the others. The systes in the 4- MIMO channel that utilize a STD schee show iproveents in the SNR through the selection diversity gain. These iproveents lead to a reduced error rate and an increase in the probability of selecting the MCS level with a higher data rate. These systes therefore achieve greater throughput Copyright 008 SciRes. I. J. Counications, Network and Syste Sciences, 008,, 105-06

1 S.J. RYOO ET AL. perforance copared to the other systes. In addition, the proposed algorith achieves superior throughput perforance relative to the conventional V- BLAST algorith in 4- MIMO channel using a STD schee. It can be inferred that the proposed algorith achieves this effect as well in conjunction with a STD and a MIMO diversity schee. Figure 4 shows the throughputs of the AMC systes with several V- BLAST algoriths in a, a 4 4, and an 8 8 MIMO schee. The results show that the approxiate axiu throughput iproveent for these three MIMO schees is 41 Kbps, 545 Kbps, and 880 Kbps, respectively. Accordingly, it can be inferred that the effect of the proposed algorith increases as the nuber of syste antennas increases. Moreover, when each MIMO schee is applied, the perforance is enhanced significantly. Figure. Throughputs of the AMC systes with several V- BLAST algoriths in a MIMO schee Figure 3. Throughputs of the AMC systes with several V- BLAST algoriths in a and 4- MIMO schee Figure 4. Throughputs of the AMC systes with several V- BLAST algoriths in a, 4 4, and 8 8 MIMO schee 4. Conclusions In this paper, to iprove the throughput perforance in a downlink, AMC systes with several V-BLAST algoriths were ipleented and copared. It was found that the perforance can be iproved through application of the STD as a MIMO diversity schee. Through the SNR iproveent of the receiver of the systes that utilized a STD schee, the error probability was decreased in the range of a relatively low SNR and, ultiately, the throughput perforance was iproved. The throughput perforance can also be enhanced by increasing the nuber of antennas in the MIMO channel. The proposed algorith achieves a better throughput perforance than the conventional V- BLAST algorith over the entire SNR range. For the exaple of M=N=4 and PSK, it was deonstrated that the proposed algorith has nearly 4% lower coplexity than the existing ML algorith while it provides an approxiate increase of 8.3% in capacity copared to the conventional V-BLAST algorith. In addition, the siulation results show that the axiu throughput iproveent in each MIMO channel is nearly 41 kbps (a 17.7% increase in capacity) for a MIMO, 545 kbps (an 8.3% increase in capacity) for a 4 4 MIMO, and 880 kbps (a 5.5% increase in capacity) for an 8 8 MIMO. Thus, the effect of the proposed algorith increases while the nuber of syste antennas increases. Accordingly, if the MIMO schees or the MIMO channel can be applied in each case for a higher throughput perforance, the proposed algorith will then be a practical candidate for next-generation obile counication systes. 5. References [1] A.J. Goldsith and S.G. Chua, Adaptive Coded Modulation for Fading Channels, IEEE Trans. on Co., vol. 46, no. 5, pp. 595 60, May 1998. [] A. Bhargave and R.J.P. de Fegueiredo, A new MIMO detector for iterative with ultiple antenna systes, Military Counications Conference, MILCOM 005. IEEE, vol. 3, pp. 148 143, October 005. [3] G.J. Foschini, Layered Space-Tie Architecture for Wireless Counication in a Fading Environent When Using Multi-Eleent Antennas, Bell Labs Technical Journal, pp. 41 59, 1996. [4] A. Bhargave, R.J.P. de Figueiredo, and T. Eltoft, A Detection Algorith for the V-BLAST Syste, GLOBECOM 01. IEEE, vol. 1, pp. 494 498, Noveber Copyright 008 SciRes. I. J. Counications, Network and Syste Sciences, 008,, 105-06

PERFORMANCE ANALYSIS OF AN AMC SYSTEM WITH AN ITERATIVE 13 V-BLAST DECODING ALGORITHM 001. [5] A. Alaouti, A siple transit diversity technique for wireless counications, IEEE JSA on Co., vol. 16, pp. 1451 1458, October 1998. [6] S. Benedetto and G. Montorsi, Unveling Turbo Codes: soe results on parallel concatenated coding schees, IEEE Trans. on Infor. Theory, vol. 4, pp. 409 49, March 1996. [7].F. Chen, H.F. Wang, M. Chen, and S.X. Cheng, An Iproved Turbo-BLAST Syste for uasi-static Channel, The 15th IEEE International Syposiu on Personal, Indoor and Mobile Radio Counications, 004. PIMRC 004, vol. 3, no. 5 8, pp. 1588 1591, Septeber 004. [8] Y. Li, Y. Yang, and H.S. Yan, Using Turbo Code in BLAST Syste, Proceedings of the 003 International Conference on Neural Networks and Signal Processing, 003, vol., pp. 1477 1480, Deceber 003. [9] T. Matsuoto and R.S. Thoa, Turbo Transceivers for MIMO Wireless Counications and Their Perforance Verification via Multi-Diensional Channel Sounding, IEICE Trans. Coun. vol. E88-B, no. 6, pp. 39 51, June 005. [10] S. Haykin, McMaster University, M. Sellathurai, Y.D. Jong, and T. Willink, Turbo-MIMO for Wireless Counications, IEEE Counications Magazine, pp. 48 53, October 004. [11] M. Sandell, Analytical analysis of transit diversity in WCDMA on fading ultipath channels, PIMRC99, vol., pp. 946 950, Septeber 1999. [1] Z.W. Catherine, H. Sweatan, J.S. Thopson, B. Mulgrew, and P.M. Grant, Coparison of Detection Algorith including BLAST for Wireless Counication using Multiple Antennas, PIMRC 00, vol. 1, pp. 698 703, 000. [13] A. Elkhazin, N. Plataniotis, and S. Pasupathy, Reduced- Diension MAP Turbo-BLAST Detection, IEEE Transactions on Counications, vol. 54, no. 1, pp. 108 118, January 006. [14] R. Wang, H. Wang, C. Fan, X. Zhang, and D.C. Yang, Research on Modified Structure of Turbo-Blast Syste, The 17th Annual IEEE International Syposiu on Personal, Indoor and Mobile Radio Counications, PIMRC 06, pp. 1 5, Septeber 006. [15] 3GPP C.P9010, Draft baseline text for the physical layer portion of the 1X EV specification, pp. 9 78, August 000. [16] H.Z. Sung, J.W. Kang, and K.B. Lee, A Siplified Maxiu Likehood Detection for MIMO Systes, IEICE Trans. Coun., vol. E89-B, no. 8, pp. 41 44, August 006. Copyright 008 SciRes. I. J. Counications, Network and Syste Sciences, 008,, 105-06