Study on Cross-Layer Retransmission Scheme in Wireless Communication System

Transcription

1 Study on Cross-Layer Retransmission Scheme in Wireless Communication System Supervisor : Professor Jae-Hyun Kim by Sang-Min Choo School of Electrical and Computer Engineering at the AJOU UNIVERSITY August, 2008

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3 Study on Cross-Layer Retransmission Scheme in Wireless Communication System By Sang-Min Choo Submitted to the School of Electrical and Computer Engineering in partial fulfillment of the requirements for the degree of Master of Electrical Engineering at the AJOU UNIVERSITY Approved by Professor Jae-Hyun Kim, Ph.D. (Supervisor) Date Professor Seong-Keun Oh, Ph.D.(Committee) Date Professor Chae-Woo Lee, Ph.D. (Committee) Date

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5 DEDICATION The Lord has blessed me with strength to carry on and a wonderful family To my parents and sister

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7 Acknowledgement First of all, I would like to express my genuine gratitude to my supervisor, Professor Jae-Hyun Kim, for his advice, guidance and encouragement in the development of my research. Without his support, insight and teaching, this work would not have been possible. Besides as an academic advisor, he has been a life-advisor who has been willing to teach important elements in life. He has been also willing to share his knowledge and career experience to support my plans after graduation. Working with him was enjoyable and worth experiencing. I would also like to thank Professor Seong-Keun Oh and Professor Chae-Woo Lee for serving as my advisory committee and providing candid and valuable advice on my research. Special thanks are given to Professor Chae-Woo Lee for advising and encouraging my plans for Ph.D on abroad. I am also very grateful to Professor Seong-Keun Oh for his mentoring not only on my research but especially on my life as Christian. My fellow graduate students, WINNERs, have made my life at Ajou University enjoyable and memorable. In particular, I would like to thank Jae-Ryong Cha, Sung-Min Oh and Hyun-Jin Lee for insightful comments on my research and encouragement to help me see positive way for every obstacle. It is my great pleasure spending

8 time with Choong-Hee Lee, Shin-Hun Kang and Seong-Hwan Oh for late snacks and chat. I also want to thank Sung-Jin Lee, Ju-A Lee, Ji- Su Kim, Kyu-Hwan Lee, Sung-Hyung Lee and Kwang-Chun Ko for being reliable friends and helped me over the years. There are old friends from my youth in the Olympic apartments and Indonesia whom I thank from the bottom of my heart for their encouragement along the way. You know who you are. Without their friendship, my life would have been no fun at all. I want to take this opportunity to thank especially to my beloved, Joo-Yeon Shin, for her constant love, encouragement and support. Most importantly, this thesis is dedicated to my parents and sister for their love, confidence, sacrifice and support. There are no words to express my deepest gratitude for all you have done. I love you all. Finally, the Father in heaven, the reason and purpose of my life, I will live a life worth of your calling. 2

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10 Abstract In this thesis, we develop a cross-layer design scheme which combines adaptive modulation and coding (AMC) with several retransmission schemes known as hybrid automatic repeat request (HARQ) at the physical layer, automatic repeat request (ARQ) at the medium access control (MAC) layer and HARQ combined with ARQ in order to analyze the performance in terms of spectral efficiency and transmission delay. To evaluate the performance of spectral efficiency and transmission delay, we derive equations of the average packet error rate (PER) used in HARQ and ARQ, respectively. Numerical results reveal that maximizing the average spectral efficiency depends on the number of transmissions, not on the type of retransmission implemented. However, a noticeable gain in the average transmission delay has been offered by AMC with HARQ over AMC with ARQ. When retransmission schemes are exploited both at the PHY and MAC layer, HARQ and ARQ scheme respectively, the performance of ARQ relies on the performance of HARQ, which indicates that only HARQ would be desirable as long as it works perfect. i

11 Contents Contents... i List of figures... ii List of tables... iii Abbreviations... 1 Chapter 1. Introduction... 1 Chapter 2. System model System structure Features of HARQ and AMC Channel model... 9 Chapter 3. Cross-Layer design Performance constraints Combination of AMC with HARQ Combination of AMC with ARQ Combination of AMC with HARQ and ARQ Chapter 4. Performance analysis Average spectral efficiency Transmission delay Chapter 5. Numerical results Average spectral efficiency Transmission delay Chapter 6. Conclusion Reference i

12 List of figures Figure 1. Cross-layer structure of the system... 4 Figure 2. Functional block of the system... 6 Figure 3. PER of MCS level vs. average SNR Figure 4. Delay components Figure 5. Average spectral efficiency vs. average SNR Figure 6. Probability of MCS selection for the 1st transmission Figure 7. Probability of MCS selection for the 2nd transmission Figure 8. Probability of MCS selection for the 3rd transmission Figure 9. Average spectral efficiency for ARQ vs. average SNR Figure 10. Average spectral efficiency for HARQ+ARQ vs. average SNR Figure 11. Average spectral efficiency for HARQ and ARQ vs. average SNR Figure 12. Average transmission delay of retransmission schemes. 31 ii

13 List of tables Table 1. MCS levels and parameters of BER expression for HARQ 8 Table 2, MCS levels and parameters of PER expression for ARQ... 8 Table 3. Delay analysis iii

14 Abbreviations AMC : Adaptive modulation and coding ARQ : Automatic repeat request BER : Bit error rate CSI : Channel state information FEC : Forward error correction HARQ : Hybrid automatic repeat request MAC : Medium access control MCS : Modulation and coding scheme PDU : Protocol data unit PER : Packet error rate QoS : Quality of service RCPC : Rate-compatible punctured convolutional RTT : Round-trip time SNR : Signal-to-noise ratio

15 Chapter 1. Introduction In wireless communication systems, the demand of high data rates and quality of service (QoS) is growing rapidly. Therefore, enhancing channel utilization and throughput in future wireless communication systems is a very important and challenging issue. In order to provide a solution, adaptive modulation and coding (AMC) scheme has been studied and defined as one of key functions at the physical layer by many wireless communication standards, such as 3GPP/3GPP2 and IEEE /16[1]-[4]. The basic concept of AMC is to match the modulation and coding rate to channel conditions[5]. To perform AMC, the signal-to-noise ratio (SNR) range is divided into several regions and different modulation and coding scheme (MCS) levels are assigned to different SNR regions. However, AMC cannot keep up with the dynamic change of the instantaneous SNR value due to the limited number of MCS levels. Moreover, the accuracy of channel estimations and measurements may be changed and affected by time-varying characteristics of wireless channel. Therefore, to provide high reliability of transmission, one has to set lower MCS level than the assigned that corresponds to SNR region. An alternative way to mitigate channel fading and provide more 1

16 reliable wireless channels is to exploit retransmission schemes. There have been two different retransmission schemes, automatic repeat request (ARQ) and hybrid automatic repeat request (HARQ), which are defined at the physical (PHY) layer and medium access control (MAC) layer, respectively[1],[2],[4]. ARQ is a scheme by which the receiver can request the retransmission of a packet that has been received with errors. In ARQ scheme, only error-detection is used and the erroneous packets are discarded. On the other hand, HARQ scheme combines forward error correction (FEC) and ARQ together and generally offers much better performance than ARQ scheme. Both error-detection and error-correction are performed in HARQ scheme. Some studies have presented a cross-layer design which combines AMC with HARQ[6] and AMC with ARQ[7] to maximize spectral efficiency. However, they have not shown a comparison of the performance of each cross-layer design and analyzed the case where two-layer ARQ, HARQ at the PHY layer and ARQ at the MAC layer, is applied in the system. Moreover, the performance analysis of delay is not evaluated. In this thesis, based on the works that have shown a cross-layer design for AMC with HARQ or AMC with ARQ, we develop a cross- 2

17 layer design scheme to analyze the performance in terms of spectral efficiency and transmission delay. The rest of this thesis is organized as follows. We introduce system model in chapter 2. In chapter 3, we present the cross-layer design. Chapter 4 explains the performance analysis of the cross-layer design scheme. We present numerical results in chapter 5 and finally draw concluding remarks in chapter 6. 3

18 Chapter 2. System model 2.1. System structure The cross-layer structure of the system is shown in Figure 1. It consists of AMC and HARQ scheme at the PHY layer and ARQ scheme at the MAC layer. Transmitting unit at the MAC layer is a MAC protocol data unit (PDU) and a HARQ packet is a basic transmission unit at the PHY layer. Even though a HARQ packet may comprise one or more MAC PDUs or fragments of a MAC PDU, in this thesis, we assume one MAC PDU corresponds to one HARQ packet and overhead between MAC PDU and HARQ packet is negligible. Figure 2 shows the functional blocks of the system for the PHY and MAC layers. Figure 1. Cross-layer structure of the system 4

19 At the PHY layer, HARQ generator, HARQ controller, MCS level selector, channel estimator, transmitter and receiver blocks are defined. For the retransmission protocol, the stop-and-wait protocol is implemented. If an error of a HARQ packet still remains after error correcting, a retransmission request is generated by the HARQ controller and is transmitted to the HARQ generator at the transmitting side. The HARQ generator forms a MAC PDU into a HARQ packet and delivers to the transmitter. Upon receiving a retransmission request, the HARQ generator arranges retransmission of the requested packet. The HARQ generator stores a HARQ packet until the transmission of a packet is successful or the number of the retransmission exceeds the maximum number. The channel estimator measures and estimates the channel quality and the channel state information (CSI) is sent to the MCS level selector through feedback channels. Based on the received CSI, the MCS level selector determines a MCS level that corresponds to the CSI. The updated MCS level information is sent by transmitter along with a HARQ packet. The MAC layer consists of the ARQ generator and the ARQ controller. Like the HARQ controller, a retransmission request is generated by the ARQ controller. The ARQ generator arranges 5

20 retransmission of the requested packet. When an ARQ scheme is only implemented in the system, a MAC PDU is directly delivered to the transmitter. Figure 2. Functional block of the system 2.2. Features of HARQ and AMC In this thesis, rate-compatible punctured convolutional (RCPC) codes are used as the FEC codes of HARQ type-ii. The features and usages in HARQ type-ii are well presented in [6], thus we follow the outline of HARQ analysis explained in [6]. RCPC codes are known as one of the most appropriate alternatives for providing channel 6

21 coding applied in HARQ type-ii. RCPC offers different code rates obtained from the same low rate by puncturing technique. As a result, only one single decoder is needed to decode all the codewords at different code rates. In this thesis, we let C i denote i rates provided by a RCPC low rate. After receiving a block, a Viterbi decoder is used for error detection and correction. If an error is detected after error correction, a receiver requests retransmission of a block. For the first retransmission, incremental redundancy bits from C 2 code with information bits are sent and decoding is performed using C 2 by combining the first and second block. This process is continued until no error is detected after decoding or the number of the retransmission exceeds the maximum number. For AMC scheme, several MCS levels are considered in this thesis. We adopt the group of MCS levels, consisting of BPSK, QPSK QAM modulations with convolutional codes as defined in [3]. These MCS levels are listed in Table 1and Table 2 for HARQ and ARQ, respectively. 7

22 Table 1. MCS levels and parameters of BER expression for HARQ Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Modulation BPSK QPSK QPSK 16QAM 16QAM 64QAM Coding rate 1/2 1/2 3/4 9/16 3/4 3/4 Rates(bits/sym.) a n b n γ n (1) (db) γ n (2) (db) γ n (3) (db) Table 2, MCS levels and parameters of PER expression for ARQ Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Modulation BPSK QPSK QPSK 16QAM 16QAM 64QAM Coding rate 1/2 1/2 3/4 9/16 3/4 3/4 Rates(bits/sym.) a n g n γ n (3) (db)

23 2.3. Channel model In this thesis, we assume that it is possible to capture the channel quality by a single parameter, namely the received SNR. For multipath fading channel model, Nakagami-m channel model is widely considered. However, for the simplicity of analysis, we adopt Rayleigh channel model to describe the received SNR statistically. Equation (1) shows the Rayleigh random variable with probability density function. 1 γ P( γ ) = exp( ) γ γ γ (1) γ : Average received SNR The following is our assumptions adopted in this thesis. (a) The channel varies only from packet to packet. (b) Perfect CSI is available at the receiver. CSI is fed back to the transmitter without error and delay. (c) Error detection by CRC is perfect. (d) The channel quality is described by the received SNR (e) It is a one-to-one mapping between A MAC PDU and a HARQ packet. (f) HARQ and ARQ scheme operate as a stop-and-wait protocol. 9

24 Chapter 3. Cross-Layer design 3.1. Performance constraints In this section, we define following constraints to satisfy QoS requirements. (1) The maximum number of transmissions per packet is N t (2) The probability of packet loss after N t transmissions is no greater than P loss. Constraints mentioned above can be extracted from QoS requirements of service class. In general, N t can be specified by dividing the maximum allowed delay between two communicating nodes over the round-trip delay for each transmission. P loss should be defined differently for each service class[8]. Considering constraints, the following inequality should be satisfied. P P P P P N t 1/ Nt loss loss = target (2) where P is the average packet error rate (PER) and a packet is considered as loss if it is not correctly received after N t transmissions. From equation (2), when P loss and N t are given, P target can be obtained. P target is a target PER to achieve for each transmission. 10

25 3.2. Combination of AMC with HARQ Performance requirements HARQ type-ii uses incremental redundant bits for retransmissions. Thus, different calculation of PER and bit error rate (BER) according to the transmission number are needed to be considered. In the following, we discuss the BER requirement by P target in cases for the initial transmission and retransmissions. (1) Case 1 For the initial transmission, only transmitted bits are considered when computing PER. Therefore, the PER can be easily obtained from (3). PER = 1 (1 BER ) (1) (1) L (3) where PER (1) and BER (1) denote the PER and BER of the initial transmission, respectively. L is the packet size in bits. If we let PER (1) = P target, we can obtain the target BER for the initial transmission. Then, (3) can be expressed in terms of target BER, which results in (4). L BER = 1 (1 P ) (4) (1) target target 1 11

26 (2) Case 2 For retransmissions, since PER and BER of each transmission are not independent, it is difficult to obtain the exact relationship between PER and BER after ith retransmission. Therefore, we use a PER upper bound in [9] under assumption that convolutional code with hard-decision Viterbi decoding is used. The PER upper bound is written as (5). PER = 1 (1 P ) L P (1) (1) u upper (5) where PER (i) is the PER after ith retransmission and P u (i) is the union bound of the first-event error probability for the ith retransmission. Since the convolutional code is used, P u (i) can be given by (6). ( i) ( i) ( i) u = d d ( i ) d = d f P a p (6) where d f is the free distance of the convolutional code and a d is the total number of error events with weight d. P d is the probability of error at distance d. When the hard-decision Viterbi decoding is applied, P (i) d can be approximately expressed as (7) given in [10]. d ( i) ( i) ( i) 2 d (4 (1 ) p ρ ρ (7) where ρ (i) is bit error rate for the ith retransmission. When ρ (i) is very small and generally (6) is dominated by the 12

27 first part where d=d f, (6) can be simplified as (8). ( i ) d f ( i) ( i) d f ( i) ( i) 2 u d 2 ( ) f P a ρ (8) If we let PER (1) = P target and ρ (i) =target BER and insert (8) into (5), we can obtain the target BER for retransmissions as (9). BER = 1 L 1 (1 P ) ( i ) target target ( i ) d ( ) f i a d 2 f 2 ( i ) d f (9) MCS level selection For MCS level selection, we divide SNR range into N continuous and non-overlapping regions, where N is the total number of MCS level. For each transmission, when the received SNR γ falls into [γ n, γ n+1 ], MCS level n is chosen. The minimum SNR boundaries are determined by the target BER in (4) and (9). To simplify the MCS level selection, we will rely on the following approximate BER expression as in [11]. BER ( γ ) a exp( b γ ) (10) n n n where n is the MCS level index and γ is the received SNR. Parameters a n, b n are MCS level-dependent and are obtained by fitting (10) to the exact BER. From (4), (9) and (10), we can set the minimum SNR required to achieve target BER for each transmission as (11). 13

28 γ ( i ) n 1 a = ln( ), n = 1, 2,..., N b BER n n ( i ) target (11) where γ n (i) is the SNR boundary for the ith transmission attempt of MCS level n. The fitting parameters for (11) are shown in Table Combination of AMC with ARQ Performance requirements For ARQ scheme, since each transmission is independent from the previous transmission, there is no combining gain after retransmission. Unlike HARQ case, we do not need to consider different approach for the initial transmission and retransmissions to obtain target BER. For every transmission, only target PER is required to be achieved. Therefore, target PER can be easily obtained from (2) when P loss and N t are given MCS level selection Identical to the approach used in HARQ case, we divide SNR range into N continuous and non-overlapping regions, where N is the total number of MCS level. For each transmission, when the received SNR γ falls into [γ n, γ n+1 ], MCS level n is chosen. The only difference 14

29 from HARQ case is that in ARQ scheme the minimum SNR boundaries are determined by the target PER instead of the target BER. To simplify choosing MCS levels, we will rely on the following approximate PER expression. PER ( γ ) a exp( g γ ) (12) n n n When a n, and b n for the approximate BER expression in (10) and packet size L are given, we can derive a n, and g n for the approximate PER expression in (12) by simulation. Using (2) and (12), we can obtain the minimum SNR required to achieve target PER. γ ( i ) 1 a n = ln( ), n = 1, 2,..., g PER N (13) n n ( i ) target where γ n is the SNR boundary for the transmission of MCS level n. The fitting parameters for (12) are provided in Table 2. Figure 3 shows PER for each MCS level. Given the packet size and using (3) and (10), we can obtain PER for each MCS level which is plotted as solid line and the approximate PER given in (12) is represented as stars. From Figure 3, we can deduce that the fitting parameters listed in Table 2 for PER expression are well fitted. 15

30 PER MCS-2 MCS-4 MCS MCS-1 MCS-3 MCS Average SNR (db) Figure 3. PER of MCS level vs. average SNR (solid lines denote PER from (10) and stars are fitting curves from (12)) 3.4. Combination of AMC with HARQ and ARQ Performance requirements When both HARQ and ARQ are implemented in the system, ARQ scheme operates only if an error of a packet still remains after HARQ process. HARQ scheme alone can overcome the packet error rate up to the P loss defined at the PHY layer. Therefore, if P loss is defined as a probability that a packet is dropped if it is not correctly 16

31 received after N t transmissions, the probability of ARQ scheme operation can be expressed as (14). N +1 P t = PER ARQ (14) MCS level selection When two-layered ARQ protocol, HARQ at the PHY layer and ARQ at the MAC layer, is applied to the system, AMC scheme works with HARQ only. Therefore, the procedure of selecting MCS level is identical to the mentioned in HARQ case. 17

32 Chapter 4. Performance analysis This thesis focuses on the performance analysis of cross-layer design of AMC with retransmission schemes such as HARQ, ARQ and HARQ combined with ARQ in terms of average spectral efficiency and transmission delay Average spectral efficiency To evaluate the average spectral efficiency, we first need to obtain the average PER. Since the calculation of PER for HARQ and ARQ is different, we will apply different approach to each case. (1) Calculation of PER in HARQ case To find out the PER of HARQ scheme, we will follow the outline of analysis from [6, eq.(17)-(23)]. We will let (15) denote the probability of an error event after ith transmission using MCS level n 1,...,n i under SNR values equal to γ (1),, γ (i), respectively. ( i ) (1 ) ( i ) { (,..., ) n 1,..., n i } P F γ γ (15) As stated before, a packet error occurs when the number of transmissions reaches the maximum value N t. The probability of this under channel [γ (1),, γ (i) ] with MCS levels {n 1,...,n i } is expressed as (16). 18

33 PER n, n,.., n 1 1 N t (1) ( N ) t ( γ,..., γ ) (1) (1) (2) (1) (2) ( N ) (1) (2) ( N ) { ( γ ), ( γ, γ ),.., ( γ, γ,.., γ ) n n, n n, n,.., n } = P F F F t N t t (16) By considering all possible MCS levels selected for each transmission attempt, we can obtain the average PER by integrating (16) over all SNR values for each transmission trial as N N N { } (1) (1) ( N ) (1) (2) ( N ) γ γ γ γ n1 n1, n2,.., n (1) (2) ( N ) γ γ γ t n n n N + 1 t t t (1) (2) ( N t ) γ γ γ N t n n n 1 2 Nt PER = P F ( ),.., F (,,.., ) n1 = 1 n2= 1 Nt = 1 (17) t p( γ ) p( γ ) dγ dγ (1) ( N ) (1) ( N ) However, it is difficult to calculate the average PER directly from (17) since the joint probability of PER at each transmission shown in (16) is hard to be computed. Therefore, we use the bounded equation for (16) shown in [12]. t N t i= 1 ( i) (1) (2) ( i) { ( γ, γ,.., γ ) n, n,.., n } P F 1 2 i { } (1) (1) (2) (1) (2) ( N ) (1) (2) ( N ) ( γ ), ( γ, γ ),.., ( γ, γ,.., γ ) n n, n n, n,.., n ( N ) ( ) { ( } (1), (2) N γ γ,.., γ ) n, n,.., n P F F F t t P F N t t N t t (18) In this thesis, we use the upper bound equation because it reflects the worst case of the average PER. To compute the upper bound, the following equations are used. P ( i) (1) (2) ( i) { F ( γ, γ,.., γ ) n } 1, n2,.., ni ( i) (1) (2) ( i) 1 { 1 P,.., [ γ, γ,.., γ ] u n n } 1 i L (19) 19

34 P,.., [ γ, γ,.., γ ] ( i) (1) (2) ( i) u n1 ni a d i i ( BER γ γ γ, ) n.. ( i ) ( ) ( i) d f (1) (2) ( ) ( i ) d f 2 (,,.., ) 1 n i ( i ) f 2 (20) BER ( i ) (1) ( 2 ) ( i ) ( γ, γ,.., γ ) n, 1.. n i i ( j ) ( j ) L BER ( j = 1 j n j i j = 1 L j γ ) (21) BER ( γ ) a exp( b γ ) n n n (22) where () i (1) (2) () i P u n 1 n i,.., [ γ, γ,.., γ ] is the union bound of the first-event error probability after ith transmission with MCS level {n 1,...,n i } under channel [γ (1),, γ (i) ], respectively. ( i ) (1) (2) ( i) BER (,,.., ), n1.. n i γ γ γ is the approximate total BER of the combined for ith packets. (2) Calculation of PER in ARQ case Before, evaluating the average PER, we first find the probability of MCS level n is chosen as γ n+ 1 Pr(n) = p ( γ) dγ γ n γ γ n+ 11 γ = exp( ) dγ γ n γ γ γ γ = γ γ n n+ 1 exp( ) exp( ) (23) where P γ (γ) is Rayleigh channel model and γ is the average SNR. If we let PERn be the average packet error rate for MCS level n, 20

35 using (1), (12) and (23) we can derive PERn as PER n 1 = Pr(n),where n+ 1 n ( c γ c γ ) n n 1 γ n+ 1 1 γ = exp( ) exp( ) n Pr(n) a b γ dγ n γ n γ γ 1 a 1 n = exp( n n ) exp( n n+ 1 ) Pr(n) γ c c n γ γ PER ( γ) p ( γ) dγ n 1 = + b γ γ (24) From (23) and (24), the average PER can be computed as the ratio of the average number of incorrectly received packets over the total average number of transmitted packets as in (25). PER = N n n= 1 N R Pr( nper ) n= 1 R Pr( n) n n (25) where R n denotes the transmitted information bits per symbol for MCS level n. When the average PER for each HARQ and ARQ case is computed, the average number of transmissions per packet can be expressed as (26). N p N p p p p p N p p 2 Nt 1 (, ) = (1 ) + 2( )(1 ) + 3( )(1 ) ( )(1 ) t t N t = i p i= 1 i 1 ( )(1 p) (26) where P presents the average PER and N t indicates the maximum 21

36 number of transmissions. The average spectral efficiency for ith transmission attempt without considering retransmission can be obtained as (27). N ( i ) S = Rn ( i ) Pr ( n ) (27) n = 1 where R n denotes transmitted information bits per symbol that are provided in Table 1and Table 2 for each MCS level. When the average PER is given as P, from (26) we can derive the probability of each transmission will occur. In case where N t equals to 3, the probability of the first, the second and the third transmission would be 1-P, P (1-P) and P P (1-P), respectively. Therefore, the overall average spectral efficiency can be expressed as (28). N ( ) = t i S P overall i S (28) i= Transmission delay To evaluate the transmission delay, reference delay values are listed in Table 3 given from [13]. Figure 4 shows delay components in the system and we can derive the round-trip time (RTT) for each retransmission scheme. 22

37 HARQ RTT = 5ms ARQ RTT (without HARQ) = 17ms ARQ RTT (with HARQ) =( HARQ RTT N) +10ms Table 3. Delay analysis Description Duration (ms) Processing delay(intra-layer) 1 Processing delay(inter-layer) 4 Transmission Time Interval (TTI) 1 Frame Alignment 0.5 Figure 4. Delay components 23

38 Chapter 5. Numerical results In this chapter, we present numerical results, where each retransmission scheme is considered. We set the packet length L to be 1000 bits with the approximate PER shown in Figure 3. For every retransmission scheme, we let N t =3 and P loss = For HARQ analysis, we choose a (2) d =2, a (3) d =5, d (2) f =7 and d (3) f =12 given from [14] Average spectral efficiency Figure 5 shows the average spectral efficiency of AMC combined with HARQ. We can observe that even the average SNR is 30dB, the average spectral efficiency is not at the highest. This implies that even the average SNR is around 30dB, a packet error can still occur and the highest MCS level may not always be selected. From Figure 6 to 8, we observe that as the number of the transmission increases, the probability of selecting MCS level 6 increases, which increases the spectral efficiency. However, there is still a small probability that other than MCS level 6 can be chosen. It explains why the average spectral efficiency does not reach to the maximum value when the average SNR is 30dB. 24

39 Average Spectral Efficiency (bits/symbol) HARQ + AMC, Nt= Average SNR (db) Figure 5. Average spectral efficiency vs. average SNR Probability of MCS level selection MCS-1 MCS-2 MCS-3 MCS-4 MCS-5 MCS Average SNR (db) Figure 6. Probability of MCS selection for the 1st transmission 25

40 Probability of MCS level selection MCS-1 MCS-2 MCS-3 MCS-4 MCS-5 MCS Average SNR (db) Figure 7. Probability of MCS selection for the 2nd transmission Probability of MCS level selection MCS-1 MCS-2 MCS-3 MCS-4 MCS-5 MCS Average SNR (db) Figure 8. Probability of MCS selection for the 3rd transmission 26

41 Figure 9 shows the average spectral efficiency of AMC combined with ARQ. It is observed that the average spectral efficiency improves with increasing N t. This is because as N t increases, the target PER increases as shown in (2), which results in larger region for high MCS levels. However, the increment degrades quickly. From the figure, the average spectral efficiency of N t =3 is slightly better than that of N t =2. This implies that the maximum number of transmission does not need to be large for any given P loss and small number of transmission can achieve sufficient spectral efficiency gain while satisfying smaller delay. Average Spectral Efficiency (bits/symbol) ARQ + AMC, Nt=1 ARQ + AMC, Nt=2 ARQ + AMC, Nt= Average SNR (db) Figure 9. Average spectral efficiency for ARQ vs. average SNR 27

42 The average spectral efficiencies of AMC combined with HARQ+ARQ for P loss =0.1 and P loss =0.01 at the PHY layer are plotted in Figure 10. From the figure, we can recognize that the average spectral efficiency of HARQ+ARQ follows the trend of that of HARQ and if P loss is set to higher value at the PHY layer, the average spectral efficiencies both at the PHY and MAC layers are smaller. This is because when P loss is higher, the probability of retransmission occurrence is higher, which degrades the average spectral efficiency. This indicates that overall performance of HARQ+ARQ highly depends on the performance of HARQ. Average Spectral Efficiency (bits/symbol) HARQ HARQ HARQ+ARQ HARQ+ARQ Average SNR (db) Figure 10. Average spectral efficiency for HARQ+ARQ vs. average SNR 28

43 Figure 11 depicts the comparison of the average spectral efficiency between HARQ and ARQ scheme. Since both schemes are based on the same performance constraints and experience the same channel, this yields no difference in terms of the average spectral efficiency. This implies that to achieve the highest spectral efficiency, the type of retransmission scheme implemented does not affect. Average Spectral Efficiency (bits/symbol) ARQ + AMC HARQ + AMC Average SNR (db) Figure 11. Average spectral efficiency for HARQ and ARQ vs. average SNR 5.2. Transmission delay In this section, we evaluate the transmission delay of each retransmission scheme. The transmission delay is defined as the 29

44 instance between the initial transmission of a packet at the sender and the correct reception of a packet at the receiver. For fairness in the number of total transmission, we set N t =3 for all cases, which indicates one retransmission in HARQ and ARQ for HARQ+ARQ scheme. To evaluate the average transmission delay, we first compute the average number of transmission per packet in each case, and then multiply the results by RTT. The average transmission delay of retransmission scheme is depicted in Figure 12. The figure shows that HARQ scheme experiences the smallest average transmission delay around 5ms. This is because while HARQ scheme operates at the PHY layer, ARQ scheme operates at the MAC layer, which yields an additional delay between layers. HARQ+ARQ scheme experiences the smaller average transmission delay than ARQ scheme because HARQ+ARQ scheme operates only for one retransmission at the MAC layer, which would decrease total transmission delay. 30

45 Figure 12. Average transmission delay of retransmission schemes 31

46 Chapter 6. Conclusion In this thesis, we developed a cross-layer design scheme that combines AMC with several retransmission schemes, such as HARQ, ARQ and HARQ+ARQ to analyze the performance in terms of spectral efficiency and transmission delay. We derived equations for packet error rate of HARQ and ARQ and the average spectral efficiency over Rayleigh fading channel. Numerical results show that AMC with HARQ scheme does not have a significant gain on the average spectral efficiency over AMC with ARQ scheme and yet has a great improvement on the average transmission delay. However, to implement HARQ schemes, larger buffers would be needed for combining transmitted and retransmitted packets together. This will yield to a trade-off between system overhead and transmission delay. When both HARQ and ARQ schemes are implemented in the system, the performance of ARQ scheme relies on the performance of HARQ scheme, which suggests that it may not be necessary to exploit ARQ scheme if HARQ scheme works perfect. Even though the performance of each retransmission scheme is shown in this thesis, it is evaluated under the several assumptions which may not be true in practical. One possible extension of this 32

47 work is to analyze the performance when there exists a packet error of feedback message for CSI and ACK/NACK. Another possible future work would be considering not only small-scale fading such as Rayleigh or Nakagami-m fading channel but also large-scale fading such as path-loss and shadowing. Although our approach and the concept of a cross-layer design scheme are based on several assumptions, which makes our work concentrated on specific cases, it is expected that the analysis presented in this thesis may be beneficial and would give directions to the practical wireless communication system design. 33

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49 Wireless Links, IEEE Trans. Commun., vol.3, pp , Sept [8] R. Srinivasan, J. Zhuang, L. Jalloul, R. Novak, and J. H. Park, Draft IEEE m Evaluation Methodology Document, Apr. 17, [9] M. Pursley and D. Taipale, Error Probabilities for Spread- Spectrum Packet Radio with Convolutional Codes and Viterbi Decoding, IEEE Trans.Commun., vol. 35,pp1 12,Jan [10] J. Proakis, Digital Communications, New York: McGraw-Hill, [11] M.-S. Alouini and A. J. Goldsmith, Adaptive modulation over Nakagami fading channels, Kluwer J. Wireless Commun., vol. 13, no. 1 2, pp , May [12] S. Kallel and D. Haccoun, Generalized Type II Hybrid ARQ Scheme Using Punctured Convolutional Coding, IEEE Trans. Commun., vol.38, pp , Nov [13] 3GPP TSG-RAN WG2 #58, LTE Performance verification U-plane and C-plane latencies, R ( ). [14] D. Haccoun and G. Begin, High-Rate Punctured Convolutional Codes for Viterbi and Sequential Decoding, IEEE Trans. Commun., vol. 37, pp , Nov