V.Bota, Zs.Polgar, M.Varga Communications Department, Technical University Cluj-Napoca

1. V.Bota, Zs.Polgar, M.VargaCommunications Department,Technical University Cluj-Napoca Performance Evaluation of H-ARQ Adaptive Coded QAM Transmissions over Multipath Mobile Channels

2. Overview The computation of the average spectral efficiency provided by the adaptive use of a set of (non-)coded QAM modulations over a mobile Rayleigh-faded multipath channel within an OFDM transmission scheme governed or not by an H-ARQ protocol involves the following steps: • Describe the ODFM transmission scheme • Establish the set of (non-)coded QAM configurations (code +modulation), the SNR domains where each of them is optimum (channel states) and their performances (BER, CER and spectral efficiency) within the domains • Establish the user-chunk allocation method (BFP, FH) • Model the channel and compute the channel state probabilities, i.e. the average probabilities to employ each configuration (code +modulation) • Compute the average efficiency of a non-ARQ transmission and evaluate the average performances for various coding schemes • Compute the average efficiency of a H-ARQ transmission and evaluate the average performances for various coding schemes COST 289 "Spectral and Power Efficient Broadband Communications"

3. 1. ODFM Transmission Scheme • Nsbc = 416 payload subcarriers with a frequency separation fs = 39.0625 kHz; • an user-chunk that consists of A subcarriers x E OFDM symbol periods (A = 8, E = 12) that contains L-QAM payload symbols, L = 81; • the maximum number of users NusM = Nsbc/A = 52. • the chunk rate Dch= 2983.5 ch/s, for a guard-interval Gi =0.125, • the user-chunk bandwidth BWch= 312.5 kHz. [1] COST 289 "Spectral and Power Efficient Broadband Communications"

4. S5 S4 S3 S8 S2 S1 26.6 29.8 20.2 23.6 13.2 16.2 8.3 S7 S6 2. Set of non-coded QAM modulations - ANCM • the ANCM set consists of non-coded QAM modulations with nk = 1,..,11 bits/symb separated by thresholds Tk • figure 1 presents the SNR domains where the QAM constellations are employed (channel states) for nk = 1,…,8 on a AWGN channel COST 289 "Spectral and Power Efficient Broadband Communications"

5. 2. Set of LDPC-coded QAM modulations - ACM • The ACM set consists of 12 LDPC-coded QAM configurations shown in table 2. • The LDPC are L2q codes of girth 6, defined by parameters k, j, p [10]. • The configurations are defined by the numbers of coded and non-coded bits/symbol, by their coding rates and by the coding gains. • The coding gains are referred to the non-coded QAM modulations with the same numbers of bit/symbol, nk. • The thresholds Tk of the SNR domains (channel states – Sk ) where each configuration is optimum are also shown. COST 289 "Spectral and Power Efficient Broadband Communications"

6. 3. User-Chunk Allocation Method • the user-chunk allocation method ensures the frequency diversity, to compensate the variable attenuation of the Rayleigh fade of the mobile multipath channel; • the method employed is Best Frequency Position (BFP), i.e. each user-chunk is allocated the group of Cu sub-carriers that ensure the best average SINR for the bin-period envisaged, [2,3,4]; • involves the state-prediction of all available bins, over a prediction time-horizon, performed by the user mobile station. • the channel prediction is assumed to be perfect COST 289 "Spectral and Power Efficient Broadband Communications"

7. 4. Computation of the channel state probabilities • The computation of the average throughput over a time-varying channelemploys the channel modeling as a Markov chain with S states, each state having an average probability of occurrence wk, k = 1,…S. • The computation of the state probabilities wk requires a detailed description of the particular radio channel analyzed and has two consider the combination of the Rayleigh fading and multipath propagation [6] and the user-chunk allocation algorithm performed by the scheduler of the base-station [4], [7], on the other hand. • This method provides a good accuracy when compared to the simulation results, [3], but it requires a significant amount of computation that should be performed for every average level of the first arrived path. • The probability distribution also depends of the average SNR0 . COST 289 "Spectral and Power Efficient Broadband Communications"

8. 4. Computation of the channel state probabilitiesApproximate method • an approximate method to compute the p.d.f. of the received signal level (and the SNR at the receiver), for any given average SNR0 of the first arrived path, which could be applied for any SNR0 and Nus. • it requires a smaller amount of computation and consists of three steps: • determine the probabilities of the receiver’s SNR to vary between an imposed set of thresholds Tk, for a given SNR0 of the first arrived path and Nus, either by the approach [3] or by computer simulations; • find an interpolation function f(x) that approximates the distribution of the SNR on the channel, fulfilling the conditions imposed by step a. • translate and scale the f(x) around the desired SNR of the first arrived wave, SNRa. COST 289 "Spectral and Power Efficient Broadband Communications"

9. 4. Computation of the channel state probabilitiesApproximate method • the interpolation function f(x) should fulfill conditions (1); condition (1.b) includes an additional upper threshold Tk+1 which insures the solvability of the system of equations (2). • f(x) should also 0 < f(x) <1, it should have only one maximum across the whole range of x considered. • by choosing f(x) to be a polynomial function of order S, (2.a) and using the state probabilities wk, the coefficients of f(x) are computed by solving the system of equations defined by (2.b) and (2.c). (1) (2) (2) COST 289 "Spectral and Power Efficient Broadband Communications"

10. 4. Computation of the channel state probabilitiesApproximate method - example • the WP5 Urban Macro channel model (18 paths) [9], for SNR0 =16 dB, [3]; • the SNR values were split into 11 domains (channel states), separated by thresholds Tk, table 3, ANCM. The user- chunk allocation is BFP. • the state probabilities wk of the total SNR to lay within each domain are shown in table 3 (obtained by simulations), for Nus = 1, 25 and 50. • for a simpler computation only • the states with high probability were retained, see table 4 COST 289 "Spectral and Power Efficient Broadband Communications"

11. 1 us 25 us 50 us 0.06 f(x) 0.05 0.04 0.03 0.02 0.01 SNR(dB) 0 15 20 25 30 35 40 Computation of the channel state probabilitiesApproximate method - example • the graphs f(SNR) vs. SNR obtained for SNR0 = 16 dB and Nus= 1, 25 and 50 are shown in fig. 2 • the probabilities of the SNR to lie within each interval are obtained by integrating f(x) between the corresponding thresholds (2.a). • the values obtained (C )are shown for SNR0 = 16 dB in table 5 and compared to the values obtained by computer simulation (S), for Nus = 1. • Comparisons between the computed and simulated values performed for Nus = 25 and 50 also indicated good matching between the two sets of values. COST 289 "Spectral and Power Efficient Broadband Communications"

12. Computation of the channel state probabilitiesApproximate method - example • the probabilities of the SNR to lie between the given thresholds can be computed, using the function f(x), for different values of the SNR0. • denoting by SNRref the value of SNR0 for which the f(x) was derived(16 dB), for the desired value of Nus, and by SNRa the actual SNR of the first arrived path, the interpolating function fa (SNR) can be computed by translating and scaling the fr(x), on the x-axis (in dB) which is equivalent to: (3) • the state probabilities wk to lie between the imposed thresholds were computed by integrating the fa (x) between pairs of thresholds (Tk, Tk+1) . • the values of wk for SNRa= 4 dB and 1 dB are presented in table 5 together with the values obtained by computer simulations, for Nus= 1. • additional comparisons performed by the authors for different values of SNRa and Nus show that the errors of the approximate method are of about the same range as those of table 5. • therefore, this approximate method may be employed to compute the probabilities wk of the multipath Rayleigh channel to be in state Sk with areasonable accuracy, which would not affect the throughput evaluation. COST 289 "Spectral and Power Efficient Broadband Communications"

13. 5. Spectral efficiency of non-ARQ transmissions • the transmission scheme uses a M-chunk long packet in a system that employs adaptively the ANCM set of S = 8 non-coded modulations; it uses the BFP method and assumes perfect channel state prediction. • to evaluate the average throughput we consider the QAM-symbol and bit error rates, pek and BERk, of configuration k, on a channel in state k, k = 1,…S, i.e. the SNRk = 10lg (Ps/Pn)k values range from Tk-1 to Tk. • since the pek of a QAM constellation is expressed by (4.a) and that, due to the Gray mapping, the BERk is expressed by (4.b) [2], the probability of an L∙nk-bit chunk, transmitted with configuration k on a channel in state k to be correct after decoding is given by (5). • for the coded configurations, the SNRkeq are increased with their coding gains CGk referred to the non-coded constella­tions with the same numbers of bit/symbol. (4) (5) COST 289 "Spectral and Power Efficient Broadband Communications"

14. 5. Spectral efficiency of non-ARQ transmissions • the average probability of a chunk to be correctly decoded, considering all possible channel states, is expressed by (6); • the average probability of an M-chunk long packet to be correctible received and the average probability of retransmission for such a packet are expressed by (7.a, 7.b) (6) (7) • in an application not governed by an ARQ protocol, the nominal average bit rate Dnav, the average throughput Θn and the average spectral efficiency ηav are shown in (8), where Rec denotes the rate of an external code applied to the whole M-chunk packet. (9) (8) • the average time required for the transmission of an U-bit long packet (U not an integer multiple of the average chunk length) is given by (9). COST 289 "Spectral and Power Efficient Broadband Communications"

15. 5. Spectral efficiency of non-ARQ transmissions • the average spectral efficiency of the described transmission scheme in a non-ARQ environment is computed on a WP5 Macro channel for v=30 km/h. • M = 8-chunk packets were considered [1]. • the configurations adaptively employed at the chunk level are either non-coded, nk bits/symbol, slide 4, or LDPC-coded, nc+nn bits/symbol, slide 5, with coding gain Cgk and configuration rate Rck. • the spectral efficiency and packet error rates vs. SNR0 curves are shown in figures 3 and, 4 for the following coding schemes: • non-coded, using adaptively configurations of table of slide 4; • coded at chunk-level, using adaptively the configurations of slide 5; • coded at frame-level with an external LDPC code, Rce=0.86, CGe=6.5 – 7 dB, using adaptively configurations of slide 4; • same as above, but the external LDPC code has, Rc= 0.91,CGe=6 – 6.5 dB. • the average numbers of bits mapped/QAM symbol for the coding schemes employed are shown in table 6, for several values of the SNR0. It also includes the lengths of the external codes employed (1 code­word/ packet). COST 289 "Spectral and Power Efficient Broadband Communications"

16. 0 lg(1-Pcpav) non-coded -0.5 chunk level coded Slide 5 -1 -1.5 -2 packet level coded Rce=0.92 -2.5 packet level coded Rce=0.86 -3 SNR0 (dB) -3.5 8 10 12 14 16 18 20 4 2 6 0 6 η-av (bps/Hz) 5 chunk level coded slide 5 4 3 packet level coded Rce=0.92 2 packet level coded Rce=0.86 1 non-coded SNR(dB) 0 0 2 4 6 10 12 14 16 18 20 8 5. Spectral efficiency of non-ARQ transmissions • Figure 3 Packet error probabilities vs. SNR0 for Figure 4 Average spectral efficiency vs. SNR0 for • different coding schemes – 8 chunks/packet, different coding schemes – 8 chunks/packet Table 6 Average no. of bits/symbol and external codeword lengths for M = 8 chunk/packet COST 289 "Spectral and Power Efficient Broadband Communications"

17. 5. Spectral efficiency of non-ARQ transmissionsComments • the spectral efficiency of the non-ARQ transmissions is affected by two contradicting factors: • the average number of bits mapped adaptively/symbol; as seen from columns 2 and 3 of table 6, this number is significantly higher for the chunk-coded scheme because the set of configurations is larger, i.e. smaller granularity, and because of the non-coded bits mapped, which increase the configuration rate and the first factor of (8.c). • the packet-error probability, which is dependant on the packet length and of the correction capability of the code, and decreases the second factor of (8.c). • the 1- Pcpav for the chunk level coding is higher than the one of the packet level coding, see fig. 2. This can be explained two facts: • the SNR thresholds of the coded set of slide 5 were imposed so that CER ≤ 10-2; • the non-coded bits, which increase Rcfg, also increase the chunk and packet error rates. COST 289 "Spectral and Power Efficient Broadband Communications"

18. 5. Spectral efficiency of non-ARQ transmissionsComments • the average spectral efficiency is a trade-off, see (8.c), between the average nk (including itsgranularity and the coding rates) and Pcpav (depending of the CGk). • the global computation of (8) presented in figure 2, shows that the chunk-coded scheme has a higher spectral efficiency, than the packet-coded scheme, though it exhibits higher packet error rates. • this is because the first factor of (8.c) is larger for this coding scheme and compensates the smaller value of the second factor. • for a longer packets, e.g. 4 times longer, making M = 32 chunks, the packet-level coding and the chunk-level coding ensure about the same spectral efficiency, because of the higher packet error probability of the chunk level coding, compared to M = 8 chunks. • by imposing the thresholds at higher values, so that CER < 10-3, (1-Pcpav) is decreased but the spectral efficiency is also decreased • the thresholds settings may be adapted to the application to ensure the desired trade-off between packet-error rate and spectral efficiency COST 289 "Spectral and Power Efficient Broadband Communications"

19. 6. SW H-ARQ average spectral efficiency • the throughput and spectral efficiency performances of the proposed transmission scheme are now analyzed within an Stop & Wait Hybrid ARQ (SW H-ARQ) protocol [4] which employs adaptively a set of (non)coded modula­tions. • the SW–ARQ employs an M-chunk long packet, performing one transmission and q retransmissions of the whole packet before count time-out. • The count timeout lasts for TT seconds and the protocol resumes the transmission, after the count timeout, with the packet that generated the count time-out (Z-type protocol). • A perfect (N)ACK transmission across the uplink connection is also assumed. • for application governed by the H-ARQ protocol defined above, the average probability of an M-chunk long packet to be correctible received and acknowledged after its transmission (first attempt) P0av and the average probability of retransmission are: (10) COST 289 "Spectral and Power Efficient Broadband Communications"

20. 6. SW H-ARQ average spectral efficiency • the average probability of such a packet to be positively acknowledged after the i-th retransmission, i.e. one transmission and i retransmissions, Piavand the average probability to reach the count time-out state, i.e. to fail the transmission and the q retransmissions, PTav are: (11) • the impact of the TT is equivalated by the average number of bits that could have been transmitted during this state, expressed by a multiple dav of the average number of bits of a packet: (12) • the average total number of payload bits that are successfully acknowledged, after the (q+1) attempts, is: (13) • the average total number of transmitted bits Ntav required to successfully acknowledge the Nuav bits after the q+1 attempts (including the count time-out). COST 289 "Spectral and Power Efficient Broadband Communications"

21. 6. SW H-ARQ average spectral efficiency • the protocol efficiency, i.e. the ratio between the Nuav and the Ntav is then expressed by: (15) • the average throughput and spectral efficiency of the transmission governed by an H-ARQ protocol are: (16) • Comments: • if we remove the protocol requirements, no count timeout (dav= 0) and no retransmissions (q = 0), the ςp= Pcpav, see (13) and (15), and the spectral efficiency is the one of the non-protocol schemes, see (11). • for q > 0, the ςp is smaller than Pcpav and increases with the increase of q; for an infinite number of retransmissions (q →) the ςp→ Pcpav and the spectral efficiency of the protocol scheme tends to the one of the non-protocol scheme. • the average time required to transmit an M-chunk packet under the H-ARQ protocol is: (17) COST 289 "Spectral and Power Efficient Broadband Communications"

22. 6 spec_ef(bps/Hz) 5 chunk level coded table 4.b 4 packet level coded Rce=0.92 coded 3 2 packet level coded Rce=0.86 coded 1 non-coded SNR(dB) 0 4 10 12 14 16 18 20 2 6 8 6. SW H-ARQ average spectral efficiency • the two contradictory factors that affect the av, slide 18, (8.c), also affect pav in a similar manner, but Pcpav is replaced by the second factor of ςp, (15). • the performances of configurations from sets ANCM and ACM, slides 4 and 5 were evaluated for an H-ARQ protocol in the transmission scheme and channel, described before. • the H-ARQ parameters are: q=3 retrs. dav= 5, M = 8 chunk/packet. • the average spectral efficiencies provided by the coding schemes of table 5 are presented in figure 5. • the chunk-level coded scheme provides • a higher spectral efficiency than the • packet-level coding schemes as in • the non-protocol scheme, due to the same reasons, for frames of 1 packet. • for longer packets, the two coding schemes have about the same pav. • the values of pave are smaller than in the non-protocol case due the count time-out interval TT, term dav in (15). The increase of TT, compared to the packet duration, leads to a significant decrease of the spectral efficiency. COST 289 "Spectral and Power Efficient Broadband Communications"

23. 7. Conclusions • the average spectral efficiency of such transmissions is significantly affected by the number of configurations adaptively used for both non-ARQ and H-ARQ schemes. • the coding rates of the employed configurations affect in two contradictory ways the av: • by decreasing the number of payload bits transmitted • by increasing their probability of correct decoding. • the trade-off between these trends is accomplished within a limited range of SNR, where the respective coded configuration should be employed. • in both transmission modes, the chunk-level coding scheme ensures higher spectral efficiencies for small packets, because it allows the adaptive employment of more coded QAM configurations, while for long packets (more chunks) the two coding schemes provide close spectral efficiencies. • this conclusion holds for coding schemes that employ only one correcting code, either at the chunk-level or at the M-chunk packet level. COST 289 "Spectral and Power Efficient Broadband Communications"

24. Questions for Further Study • the trade-off between the average spectral efficiency and packet-error rate might be balanced, for chunk-level coding which uses adaptively a set of coded modulations, to meet the service requirements, by modifying the thresholds that separate the SNR domains where the modulations are employed. This trade-off could also be modified by changing the number of configurations of the set that is employed adaptively according to the service requirements • the effects of errors in channel state prediction upon the average performances and the possibility to increase the number of adaptively used configurations, as a countermeasure to these effects, should be considered • a significant increase of the average spectral efficiency might be brought by the employment of concatenated codes, the outer code at the packet-level and the inner code at the chunk-level. • the derivation of the average spectral efficiency presented in this paper may be applied for the coding scheme employing concatenated codes, both for non-ARQ and for H-ARQ transmissions. • the employment of erasure codes at the packet-level coding could also improve the reliability of non-ARQ schemes COST 289 "Spectral and Power Efficient Broadband Communications"

25. References (selected) 1] IST-2003-507581 WINNER, “Final report on identified RI key technologies, system concept, and their assessment”, Report D2.10 v1.0,23 Dec. 2005. [2] M. Sternad and S. Falahati, “Maximizing throughput with adaptive M-QAM based on imperfect channel prediction,” Proc. of IEEE PIMRC, Barcelona, Sept. 2004. [3] M. Varga, V. Bota, Zs. Polgar, “User-Bin Allocation Methods for Adaptive-OFDM Downlinks of Mobile Transmissions”, Proc. of “ECUMICT 2006”, 2006, Gent, Belgium. [4] M. Sternad, T. Ottosson, A. Ahlen, A. Svensson, “Attaining both Coverage and High Spectral Efficiency with Adaptive OFDM Downlinks”, Proc. of VTC 2003, 2003, Orlando, Florida. [5] H. Tanembaum, Computer Network, Prentice Hall, 1989. [6] Th. S. Rappaport, Wireless Communications, New Jersey, Prentice Hall, 2001. [7] M. Sternad, “TheWireless IP Project”, Proc. of radioVetenskap och Kommunikation, RVK 02, 2002, Stockholm [8] E. Chiavaccini, G. M. Vitetta, “GQR Models for Multipath Rayleigh Fading Channels”, IEEE J. Select. Areas Comm., vol.19, no.6, pp. 1009-1018, June 2001. [9] IST-2003-507581 WINNER, “Assessment of Radio-link technologies”,Report D2.3 ver 1.0, 28 Feb. 2005 [10] E. Eleftheriou, S. Olcer, “G.gen:G.dmt.bis:G.lite.bis: Efficient Encoding of LDPC Codes for ADSL”, ITU-T, Temporary Document SC-064, 2002. COST 289 "Spectral and Power Efficient Broadband Communications"