Design of Adaptive Modulation and Coding Scheme for Truncated Hybrid ARQ

Transcription

1 Wireless Pers Commun DOI /s Design of Adaptive Modulation and Coding Scheme for Truncated Hybrid ARQ Chung G. Kang Si H. Park Jin W. Kim Springer Science+Business Media, LLC Abstract It has been known that adaptive modulation and coding (AMC) at the physical layer can be combined with a truncated automatic repeat request (ARQ) at the data link layer so as to maximize the spectral efficiency under prescribed delay and error performance constraint. In this paper, we consider the same joint design approach when incremental redundancy-based hybrid ARQ (IR-HARQ) is associated with an AMC design at the physical layer. The extensive simulation studies for predicting the progressive combining gain with each retransmission enables to evaluate the bandwidth efficiency that can be achieved by selecting a more aggressive modulation and coding rate set (MCS) at the expense of packet error rate in earlier transmissions. It has been demonstrated that the aggressive AMC design approach in association with IR-based truncated HARQ can improve bandwidth efficiency by 5.8 and 3.3 db, as compared to the conservative AMC design approach with truncated HARQ and aggressive AMC design approach with truncated ARQ (i.e., without taking the progressive combining gain in HARQ into account), respectively. Keywords Truncated hybrid ARQ Adaptive modulation and coding Link adaptation Bandwidth efficiency 1 Introduction It is well known that adapting transmission parameters to the varying channel conditions in a wireless system can bring benefits. For example, adaptive modulation and coding (AMC) is one particular example of the typical link adaptation techniques, widely adopted in emerging broadband wireless access systems, e.g., IEEE e Wireless MAN and 3GPP HSDPA, compensating for the variation in channel conditions. A level of the modulation and coding set (MCS) is dynamically selected for AMC subject to the channel quality that is periodically reported by the receiver [1,2]. C. G. Kang (B) S. H. Park J. W. Kim School of Electrical Engineering, Korea University, Seoul, Korea ccgkang@korea.ac.kr

2 C. G. Kang et al. Meanwhile, the forward error correction (FEC) and automatic repeat request (ARQ) are two basic categories of error control techniques. In order to overcome their individual drawbacks, a combination of these two basic schemes, called hybrid ARQ (HARQ), has been developed, where unsuccessful attempts are used in FEC decoding instead of being discarded. HARQ is a variation of the ARQ error control scheme, with the objective of reducing the number of transmission by adding FEC bits to the existing error detection bits. In other words, HARQ can be considered as another type of link adaptation technique with ACK/NACK signaling for determining retransmission. Due to its fast retransmissions and combining features in the physical layer, an error-prone wireless link can be turned into a robust link from the upper-layer viewpoint. In order to minimize delays and buffer sizes in practice, the maximum number of retransmissions is limited for ARQ or HARQ protocol, which is commonly referred to as a truncated ARQ or HARQ protocol [3,4]. Since error-free delivery cannot be warranted under a truncated ARQ or HARQ protocol, the corresponding packet can be declared to be a loss for the real-time service or to reattempt the end-to-end retransmission between source and destination nodes, e.g., according to TCP protocol. Instead of considering AMC and truncated ARQ schemes as separate design entities for link adaptation, they can be combined to maximize spectral efficiency under the prescribed delay and error performance constraints [5]. TheAMC scheme can bedesigned to guarantee the required performance in association with the error-correcting capability of the truncated ARQ that depends on the maximum allowable number of retransmissions. The proposed joint approach relies on an aggressive MCS selection strategy, which can increase the overall spectral efficiency by allowing for a less tight constraint in the packet error rate at the earlier transmission opportunities. Such an aggressive AMC design has been demonstrated to be effective for improving the spectral efficiency in [5]. In this paper, we consider the same design approach when hybrid ARQ (HARQ) is associated with an AMC design at the physical layer. We intend to evaluate the bandwidth efficiency achieved by the aggressive AMC design approach with respect to the progressive combining gain in HARQ, more specifically, for incremental redundancy-based HARQ (IR-HARQ). Toward this end, it is essential to predict the progressive combining gain with each retransmission in HARQ. Our main contribution is to evaluate a performance improvement in bandwidth efficiency with a joint AMC design with HARQ over that without the progressive combining gain taken into account. We note that another AMC design approaches for HARQ are also considered by [6 9], in which the Chase combining gain is taken into account merely by taking the sum of signal-to-noise ratios (SNRs) for the multiple transmissions. More specifically, works in [8,9] attempt to maximize the link-level throughput merely, without taking into account the QoS constraints that a target PER must be achieved within the pre-specified maximum number of retransmissions. Furthermore, the current work is different from them in the sense that our joint AMC design considers the IR-based combining gain, which has been successfully given in a closed form of packet error rate (PER) by curve-fitting the link-level simulation results. The subsequent sections of this paper are organized as follows. In Sect. 2, the system model for AMC design is explained. Various types of AMC design approaches are considered, including the proposed one with truncated HARQ, and described in Sect. 3. Furthermore, the spectral efficiency analysis for the different design approaches is presented in Sect. 4. Finally, conclusions are drawn in Sect. 5.

3 Design of Adaptive Modulation and Coding Scheme for Truncated Hybrid ARQ Fig. 1 Aggressive design of MCS boundary points for HARQ: illustrative example 2 System Model for AMC Design 2.1 Aggressive AMC Design: Overview The terminology, Aggressive AMC, comes from the fact that a higher level of modulation and coding can be employed by allowing for a less tight constraint in the packet error rate at the earlier transmission opportunities. The basic idea of the aggressive design with truncated HARQ can be explained with the PER curves presented in Fig. 1, one for the first transmission and the other for the second transmission with the same modulation and coding rate. It is important to note that it demonstrates the improvement in PER with the combining gain in HARQ. Herein, P loss denotes the target packet loss rate, which is defined as the probability that a packet is dropped when it is not successfully transmitted with the maximum allowable number of retransmissions. Meanwhile, P n,0 and P n,1 denote the target packet error rate for the initial transmission and retransmission, respectively. A possible yet typical approach is to set the target PER for each transmission to P loss, which requires the target SNR of γ con in Fig. 1, regardless of how many retransmissions were made earlier. It is a conservative design approach in the sense that it attempts to meet the target packet loss rate in first transmission, without taking the combining gain of HARQ into account. As opposed to the conservative approach, the different target PER can be set in each transmission, in order to meet the packet loss performance constraint. In other words, the target SNR γ agg can be set such that P n,0 (γ agg ) P n,1 (γ agg ) = P loss.as illustrated in Fig. 1, itisalwaystruethatγ agg <γ con, allowing for adoption of higher order modulation with the same SNR, i.e., boosting the data rate in an aggressive manner from the beginning. In this paper, the spectral efficiency of AMC design is analyzed for truncated HARQ and its spectral efficiency is compared with existing AMC design approaches. 2.2 System Model for AMC Design In general, the channel quality can be captured by a single parameter, namely the received signal-to-noise ratio (SNR), denoted by γ. Since the Rayleigh fading channel is considered, the received SNR is exponentially distributed, i.e., its PDF is given as follows:

4 C. G. Kang et al Mode Mode 2 PER PER SNR (db) SNR (db) 10 0 Mode Mode 4 PER PER SNR (db) SNR (db) 1st Tx 2nd Tx 3rd Tx Fig. 2 Packet error rate for different AMC modes: simulated versus curve-fitted (solid lines for the simulated PER and dashed lines for the curve-fitted PER) p γ (γ ) = 1 ( γ exp γ ) γ (1) where γ is the average received SNR. Let N denote the total number of transmission modes available for AMC. Assuming constant power transmission, the overall SNR range is partitioned into (N + 1) non-overlapping consecutive intervals, with boundary points denoted as {γ n } N+1 n=0, i.e., mode n is chosen when γ [ γ n,γ n ). (2) In order to avoid the deep channel fades, no payload bits will be transmitted when γ 0 γ γ 1. In the course of AMC design, the boundary points {γ n } n=0 N+1 must be determined. In general, exact closed-form expressions for PER with the different channel coding rates are not readily available when forward error correction coding, e.g., Turbo coding, is employed. Therefore, we rely on Monte Carlo simulations to evaluate the PER subject to channel coding. Furthermore, it becomes more complicated as PER depends on the number of retransmissions in the HARQ system. We have evaluated the PER using simulation for four different AMC modes with a different number of retransmissions, assuming the incremental redundancy (IR)-HARQ scheme is adopted. The results are presented in Fig. 2. Inorderto simplify the AMC design, the following approximate PER expression is considered [5]:

5 Design of Adaptive Modulation and Coding Scheme for Truncated Hybrid ARQ Table 1 Parameters for PER approximation Mode 1 Mode 2 Mode 3 Mode 4 Modulation QPSK QPSK 16QAM 16QAM Code rate 1/2 2/3 1/2 2/3 R n 1 4/3 2 8/3 a n, a n, a n, g n, g n, g n, t n, t n, t n, P n,i (γ ) { 1, if 0 <γ <tn,i a n,i exp ( g n,i γ ), if γ t n,i (3) where n denotes mode index (n = 1, 2,...,N) and i denotes retransmission index (i = 0, 1, 2,...,N max, with i = 0 for initial transmission). Equation 3 is justified by the fact that a typical PER performance improves exponentially in a moderate SNR region, while any packet cannot be decoded correctly when the SNR is less that a certain level. Parameters a n,i, g n,i,andt n,i in (3) can be obtained by fitting the PERs obtained by simulation. Based on the simulation results presented in Fig. 2, the fitting parameters a n,i, g n,i,andt n,i are listed in Table 1. It is important to note that the PERs in (3) accurately approximate the PERs that are obtained by simulation. 3 AMC Design Approaches with HARQ In this section, the different AMC design approaches are considered for conservative and aggressive situations with ARQ and HARQ. The boundary points are determined for the different AMC design approaches. The average spectral efficiencies for the different approaches are computed and compared in the subsequent sections. 3.1 Conservative AMC Design with Truncated HARQ In the conventional AMC design, it is assumed that the packet loss constraint must be satisfied only at the first transmission, even if it can endure the certain delay imposed by N max, the maximum allowed number of retransmissions. In other words, it implies the following constraint: P n,0 (γ ) P loss. (4)

6 C. G. Kang et al. Table 2 Boundary points conservative AMC with truncated HARQ Mode 1 Mode 2 Mode 3 Mode 4 γ n (db) Table 3 Boundary points aggressive AMC with truncated ARQ Mode 1 Mode 2 Mode 3 Mode 4 N max = N max = From (3), the boundary points are found as 0, ( ) n = 0 1 γ n = g n,0 ln Ploss a n,0, 0 < n < N , n = N + 1 (5) Using the curve-fitting results in Fig. 2, the boundary points {γ n } n=0 N+1 (db) for the conventional AMC design are summarized in Table Aggressive AMC Design for Truncated ARQ The same target PER must be maintained for each transmission in the truncated ARQ, i.e., P n,0 (γ ) = P n,1 (γ ) = = P n,nmax (γ ). As the probability of packet loss must be no larger that P loss only after N max retransmissions, the PER in each transmission must satisfy the following constraint: { Pn,0 (γ ) } N max +1 Ploss. (6) Inverting the PER expression in (3), the boundary points for truncated ARQ are found as follows: 0, ( ) n = 0 1 P γ n = g n,0 ln 1/Nmax+1 loss an,0, 0 < n < N + 1. (7) +, n = N + 1 It is important to note that the boundary points {γ n } n=0 N+1 for aggressive AMC design for truncated ARQ are different for varying N max.table3 summarizes the corresponding boundary points {γ n } n=0 N+1 (db) for N max = 1andN max = Aggressive AMC Design for Truncated HARQ As opposed to the truncated ARQ scheme in which the same target PER is maintained for each transmission, the target PER is reduced by taking the combining gain into account in the truncated HARQ scheme. In order to satisfy the delay and performance constraint, the following objective is imposed: N max i=0 P n,i (γ ) P loss (8)

7 Design of Adaptive Modulation and Coding Scheme for Truncated Hybrid ARQ Table 4 Boundary points aggressive AMC with truncated HARQ Mode 1 Mode 2 Mode 3 Mode 4 N max = N max = where P n,i (γ ) is a target PER for the ith transmission when mode n is chosen. From (3), the following boundary points are now obtained: 0, n = 0 1 γ n = ln P loss, 0 < n < N + 1. Nmax g n,i Nmax a n,i i=0 i=0 +, n = N + 1 Table 4 summarizes the corresponding boundary points { γn th } N+1 n=0 (db) for N max = 1and N max = 2. (9) 4 Performance Analysis and Numerical Results 4.1 Performance Analysis In this section, the expression of the average spectral efficiency is presented for the different AMC design approaches. It follows the same line as in [5]. Based on (1) and (2), mode n for AMC operation will be chosen with the following probability: Pr (n) = γ n+1 γ n = exp p γ (γ ) dγ ( γ ) ( n exp γ ) n+1. (10) γ γ Let P n,i denote the average PER corresponding to ith retransmission of mode n. It can be obtained by the following closed-form: P n,i = γ n ( a n,i exp gn,i γ ) p γ (γ ) dγ γ n = a n,i γ b n,i { exp ( bn,i γ n ) exp ( bn,i γ n )} (11) where b n,i g n,i + 1/γ. In the truncated ARQ system, however, sub-index i is not required because all transmissions have the same packet error rate. The average PER of ith retransmission can be computed as the ratio of the average number of packets in error over the total average number of transmitted packets, i.e.,

8 P i = N R n P n,i n=1 N R n Pr(n) i=1 C. G. Kang et al. where R n is the rate (bits/symbol) of mode n [10]. Thus, the average number of transmissions per packet can be found as N = 1 + N max 1 i=0 (12) i P k. (13) Hence, the overall average spectral efficiency, as a function of N max, is given as follows: S e (N max ) = 1 N R n Pr(n). (14) N n=1 Note that the average PER for HARQ is also given by (12), now with the different parameters a n,i and g n,i for (3), which are obtained by curve-fitting the link-level simulation results as discussed in Sect Numerical Results In this section, the average spectral efficiencies are compared for the different AMC design approaches, so as to illustrate how much additional gain can be achieved by aggressive AMC design with truncated HARQ. It is assumed that the target packet loss rate is given by P loss = and the number of maximum allowed retransmission is limited to N max = 1or 2. In the following presentation, it is important to note that the performance of the conservative AMC design does not depend on N max. The average spectral efficiencies are presented in Fig. 3. As expected, the conservative AMC design for truncated HARQ presents worst performance in spectral efficiency. It is due to the fact that the lower rate mode tends to be selected so as to meet the target packet loss rate at the first transmission and furthermore, the corresponding target PER is applied to each retransmission if necessary. It is obvious from observation that the boundaries points k=0 Fig. 3 Average spectral efficiency (solid lines for N max = 1anddashed lines for N max = 2) Average Spectral Effficiency (bits/symbol) AMC+HARQ - Conservative AMC+ARQ - Aggressive AMC+HARQ - Aggressive Average SNR

9 Design of Adaptive Modulation and Coding Scheme for Truncated Hybrid ARQ Fig. 4 Packet loss probability (solid lines for N max = 1and dashed lines for N max = 2) Actual P loss AMC+HARQ - Conservative AMC+ARQ - Aggressive AMC+HARQ - Aggressive Average SNR Fig. 5 Probability of mode 4 selection (solid lines for N max = 1anddashed lines for N max = 2) Probability of mode 4 Selection AMC+HARQ - Conservative AMC+ARQ - Aggressive AMC+HARQ - Aggressive Average SNR for the same AMC mode in Table 2 are greater than those from aggressive design in Tables 3 and 4. Referring to Fig. 4, in which actual packet loss rates are presented for the different approaches, it is important to note that the packet loss performance is over-satisfied, resulting in a tremendous waste of the bandwidth efficiency. Meanwhile, the proposed aggressive AMC design with truncated HARQ provides 5.8 db gain over the conservative one with truncated HARQ and 3.3 db gain over the aggressive one with truncated ARQ. It is important to note that the performance of the truncated HARQ improves with increasing N max, e.g., approximately 2 db gain with N max = 2 over that with N max = 1. It implies that further throughput improvement is expected at the sacrifice of delay performance. However, it demonstrates that additional gain diminishes as N max increases. Figures 5 and 6 present the probability that mode 4 and mode 1 are selected, respectively, as SNR varies. In the proposed design, it is clear that the probability that a high rate mode is selected is larger than that of other approaches while the probability that a low rate mode is selected is smaller than that of other approaches. The overall improvement in average throughput is accompanied with the average number of retransmissions as presented in Fig.7. It confirms that the delay performance can be properly traded with system capacity in

10 C. G. Kang et al. Fig. 6 Probability of mode 1 selection (solid lines for N max = 1anddashed lines for N max = 2) Probability of mode 1 Selection AMC+HARQ - Conservative AMC+ARQ - Aggressive AMC+HARQ - Aggressive Average SNR Fig. 7 Average number of transmissions (solid lines for N max = 1anddashed lines for N max = 2) The Average Number of Transmissions AMC+HARQ - Conservative AMC+ARQ - Aggressive AMC+HARQ - Aggressive Average SNR the truncated retransmission scheme. To summarize, the truncated HARQ almost completely takes advantage of the gain achieved by the aggressive design approach. 5 Conclusions In this paper, an aggressive AMC design approach has been reconsidered in association with IR-based truncated HARQ. It aims at maximizing the spectral efficiency by fully exploiting the progressive combining gain in HARQ, especially when a target level of packet loss rate is prescribed. Unlike the existing works, the extensive simulation studies for predicting the IRbased combining gain with each retransmission enables to evaluate the bandwidth efficiency that can be achieved by selecting a more aggressive modulation and coding rate set (MCS) at the expense of packet error rate in earlier transmissions. In fact, it aims at maximizing the spectral efficiency by fully exploiting the progressive combining gain in HARQ. As opposed to the current assumption, it is not always true that the channel quality indication (CQI) is perfectly matched (i.e., the feedback channel has zero delay, is error-free, and

11 Design of Adaptive Modulation and Coding Scheme for Truncated Hybrid ARQ there is not much change in channel condition in the course of retransmissions after receiving the CQI). In practice, a channel mismatch problem exists, which may make current design less reliable. A possible extension of this work is to design and analyze a robust approach under the channel mismatch problem and imperfect CSI at the transmitter. References 1. Goeckel, D. L. (1999). Adaptive coding for time-varying channels using outdated fading estimates. IEEE Transactions on Communications, 47, Goldsmith, A. J., & Chua, S.-G. (1998). Adaptive coded modulation for fading channels. IEEE Transactions on Communications, 46, Malkamaki, E. & Leib, H. (2000). Performance of truncated type-ii hybrid ARQ schemes with noisy feedback over block fading channels. IEEE Transactions on Communications, 48, Yang, Q., & Bhargava, V. K. (1993). Delay and coding gain analysis of a truncated type-ii hybrid ARQ protocol. IEEE Transactions on Vehicular Technology, 42, Liu, Q., Zhou, S., & Giannakis, G. B. (2004). Cross-layer combining of adaptive modulation and coding with truncated ARQ over wireless links. IEEE Transactions on Wireless Communication, 3, Chen, F., Su, L., Chen, M., & Yang, D. (2006). A Markov based method for modulation and coding scheme (MCS) with hybrid ARQ retransmission. In IFIP international conference on wireless and optical communications networks. 7. Huaping, F., Chen, F., & Tingjie, T. (2006). A threshold optimizing method based on Markov in AMC combined with HARQ. In International conference on wireless communications, networking and mobile computing. 8. Peng, X., Song, M., & Song, J. (2007). Cross-layer design for adaptive modulation and coding with hybrid ARQ. In International symposium on microwave, antenna, propagation and EMC technologies for wireless communications. 9. Kim, D., Jung, B. C., Lee, H., Sung, D. K., & Yoon, H. (2008). Optimal modulation and coding scheme selection in cellular networks with hybrid-arq error control. IEEE Transactions on Wireless Communications, 7(12, Part 2), Alouini, M.-S. & Goldsmith, A. J. (2000). Adaptive modulation over Nakagami fading channels. Kluwer Journal on Wireless Communication, 13(1 2), Author Biographies Chung G. Kang received the B.S. Degree in Electrical Engineering from the University of California, San Diego in 1987 and the M.S. and Ph.D. Degrees both in Electrical and Computer Engineering from the University of California, Irvine, in 1989 and 1993, respectively. While working on his Ph.D. dissertation from June 1991 to May 1992, he was also with the Aerospace Corporation in El Segundo, California, as a part-time member of technical staff (MTS). In 1993, he joined Rockwell International Inc. in Anaheim, California, where he worked on the signaling system no. 7 and other telecommunication systems development. Since March 1994, he has been with the department of radio communication & engineering at the Korea University, Seoul, Republic of Korea, where he is currently a full professor. In the academic year , he was a visiting associate professor at the University of California, San Diego, where he was also affiliated with the Center for Wireless Communications. His research interests include next generation mobile radio communication system and mobile WiMAX (WiBro) networks, with special emphasis on physical layer/medium access control layer design and performance analysis. His recent research is focused on the cross layer design issues for MIMO/multiple access schemes for mobile broadband wireless access systems and MAC/routing protocols for mobile ad hoc networks. He has over 100 refereed publications in international journals and conference proceedings in the areas of communications network, CDMA cellular systems, OFDM systems, and wireless local area/personal area networks. He has been a consultant to wireless industries, including cellular service and content providers.

12 C. G. Kang et al. He is currently serving as an editor of Journal of Communication and Network (JCN) and a technical program committee member of various international conferences. He is also a vice-chair of 2.3 GHz Portable Internet Project Group (PG302) and a chair of PG302-WG2 service & network working group in Telecommunications Technology Association (TTA) of Korea. He is a member of IEEE COMSOC, IT, and VT, and KICS, having served as a chair of KICS Mobile Communication Technical Activity Group. Si H. Park received the B.S. and M.S. degrees in Electrical Engineering from Korea University, Seoul, Korea, in 2004 and 2006, respectively. He has been with Samsung Electronics as an Research Engineer from 2006 to 2009, contributing to the development of next-generation wireless systems based on Mobile WiMax System. Since 2008, he has been in charge of m standardization. His current research interests include 4G mobile and wireless communication systems, Hybrid ARQ, and radio resource management. Jin W. Kim received the B.S. and M.S. degrees in Electrical Engineering from Korea University, Seoul, Korea in 2005 and 2007, respectively, where he is currently working toward the Ph.D. degree in the School of Electrical Engineering. His research interests include signal processing techniques for multiple antenna systems.