1. V.Bota, Zs.Polgar, M.Varga Communications Department, Technical University Cluj-Napoca Joint Modeling of the Raleigh-Faded Mobile Radio Channel and User-Chunk Allocation

2. TUCN Data Transmissions Laboratory COST 289 - 12-th MCM, Firenze, Italy2 Overview Factors the affect the performances provided by the adaptive use of a set of (non-)coded QAM modulations over a mobile multipath channel within an OFDM transmission scheme governed or not by an H-ARQ protocol: 1. the ODFMA transmission scheme (number of sub carriers, frequency separation, chunk dimensions, payload and service symbols, coherence time and BW) 2. the set of (non-)coded QAM configurations (code +modulation), Coded configurations – LDPC codes, concatenated LDPC-error detection and LDPC-LDPC codes Chunk-error probability Spectral efficiency provided by a configuration Selected set of coded configurations Considerations regarding the SNR thresholds that separate the SNR domains – channel states 3.the user-chunk allocation method (BFP, FH) employ the frequency diversity of the channel and the multi-user diversity 4.channel modeling -  factors 3 and 4 should be considered together (joint modeling of the equivalent channel) and generate the channel states probabilities  these factors are used to compute the average throughput of non/H-ARQ transmission for the adaptive employment of set of QAM configurations on a single channel-carrier– this step requires the computation of the channel state probabilities  factors 3 and 4 could be also used to determine the time evolution of the channel for one user, involving the computation of the state-transition probabilities 5. the frequency-reuse pattern for the group of channel-carriers of one site – this increase the global throughput of the site

3. TUCN Data Transmissions Laboratory COST 289 - 12-th MCM, Firenze, Italy3 1. ODFMA Transmission Scheme N sbc = 416 payload subcarriers with a frequency separation f s = 39.0625 kHz; an user-chunk consisting 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 N usM = N sbc /A = 52. chunk duration E OFDM-symbols Figure 1 OFDMA multiuser access principle and chunk structure. chunk bandwidth A OFDM subcarriers f s subcarrier separation OFDM symbol period time-frequency chunks the chunk rate D ch = f s /[(1+Gi)E]=2983.5 ch/s; a guard-interval Gi=0.125, the user-chunk bandwidth BW ch = 312.5 kHz. [1] the chunk parameters allow for v ≤ 250 km/h and delay-variance of the multipath channel ≤ 6  s for a correlation factor of 0.5.

4. TUCN Data Transmissions Laboratory COST 289 - 12-th MCM, Firenze, Italy4 2. Set of Coded or Non-coded QAM Configurations - Chunk-Error Probability the symbol error probability of a QAM constellation with N k points and the bit- error rate, assuming a Gray mapping of the bits on the symbol: SNR k denotes the S/N ratio (in dB) considered for configuration k SNR k eq (3.c) is increased with the coding gain C Gk of the coded configuration k, referred to the non-coded constellation with the same number of bits/symbol. the coding gains were established by computer simulations, [9]. the probability of an L∙n k -bit chunk, transmitted with configuration k on a channel with SNR k, to be correctly received or decoded is: (2) (1)

5. TUCN Data Transmissions Laboratory COST 289 - 12-th MCM, Firenze, Italy5 2. Set of Coded or Non-coded QAM Configurations Spectral efficiency provided by a configuration the nominal bit rate of a transmission using a configuration with n k bit/symb is: the throughput is obtained by multiplying the nominal bit-rate to the probability of correctly decoded chunks: Θ ck (SNR k ) = C R ·L·n k ·R cfgk  p cchk (SNR k ) the spectral efficiency results by dividing the throughput Θ by the chunk bandwidth BW c : For the particular OFDMA scheme of section II it is : D ck = C R ·L·n k ·R cfgk (bit/s) (3) (4) (5) (6)

6. TUCN Data Transmissions Laboratory COST 289 - 12-th MCM, Firenze, Italy6 2. Set of non-coded QAM configurations- ANCM the ANCM set consists of non- coded QAM modulations with n k = 1,..,11 bits/symb separated by thresholds T k – table 1 the SNR domains where the QAM constellations are employed for n k = 1,…,8 on a AWGN channel are (channel states) – see fig.2 n k bit/sb123456 T k [dB]T 1 -2 T 2 ; 8.3 T 3 13.2 T 4 16.2 T 5 20.2 T 6 23.6 n k bit/sb7891011 T k [dB]T 7 26.6 T 8 29.8 T 9 33 T 10 36.2 T 11 39.4 29.8 26.6 23.6 20.2 16.213.2 8.3 S7 S6 S8 S3 S4 S2 S1 S5

7. TUCN Data Transmissions Laboratory COST 289 - 12-th MCM, Firenze, Italy7 2. Selected Set of Coded Configurations Setting the thresholds the set of coded modulations to be employed adaptively should observe the following requirements: a.each configuration should provide the highest spectral efficiency, on a limited domain of SNR ; the extension of this domain depends of the SNR range that should be covered by the adaptive system and of the number of configurations included in it, which at its turn depends on the processing resources. b.the thresholds separating the SNR states should be set differently for transmission schemes operating under an H-ARQ protocol and for schemes which are not governed by such a protocol, see next slides. c. the variation of the spectral efficiency between a configuration and its neighbours in the set should have a moderate value of about 0.5- 0.8 bps/Hz; such variations would ensure a smaller granularity of the spectral effi­ ciency, which would affect less the average spectral efficiency of the adaptive system, when configurations are used outside their domains of optimality, due to erroneous channel estimation/prediction. This requirement also calls for a large number of configurations in the set.

8. TUCN Data Transmissions Laboratory COST 289 - 12-th MCM, Firenze, Italy8 2. Considerations Regarding the SNR Thresholds that Separate the SNR Domains Two criteria were considered in threshold setting: 1.Imposing a CER = 10 -2 ; the BER required to ensure CER=10 -2 range between 2  10 -5, for 256-QAM, and 1.2  10 -4, for 2-PSK – see figure 4 this constraint ensures practically constant spectral efficiencies for each coded configuration, in its SNR domain, at a value higher than 0.99 of its nominal one. 2. Thresholds determined by the intersections of spectral efficiency curves (CI) These thresholds take the x-axis values of the intersection points of the  (SNR) curves of set ACM – see figure 2, previous slide. Their values are with 1-1.5 dB smaller than the thresholds obtained imposing CER < 10 -2. The spectral efficiencies provided are no longer constant within one interval. the CI thresholds lead to higher spectral efficiencies for low and medium SNR values, compared to the CER = 10 -2 thresholds, but the CERs are higher [16] the CI thresholds might be employed in non-ARQ environ­ments, but in H-ARQ schemes they would lead to significantly poorer performances and to an increase of the latency inserted, due to the higher rate of retransmissions.

9. TUCN Data Transmissions Laboratory COST 289 - 12-th MCM, Firenze, Italy9 3. User-Chunk Allocation Methods A. Best Frequency Position (BFP), i.e. each user- chunk is allocated the group of C u sub-carriers that ensure the best average SINR for the chunk-period envisaged, [2];  involves the state-prediction of all available chunks, over a time-horizon, performed by the user MS. T chun k B chun k time freq. - the user-chunk allocation method ensures the frequency diversity, to compensate the variable attenuation of the Raleigh fade of the mobile multipath channel, and employs the multi-user diversity; - the methods considered are: B. Frequency Hopping (FH), i.e. the Bu available bins are allocated to each user according to a Bu-states pseudo-random sequence; the hopping frequency is the reciprocal of the bin duration.  each user enters the pseudo-random sequence with a different initial value, delivered by the base station at signing-in.  the mobile station performs a prediction of the channel state across the time- horizon evaluated in [2], only for the chunk it will use next.

10. TUCN Data Transmissions Laboratory COST 289 - 12-th MCM, Firenze, Italy10 4. Multipath Raleigh Channel Model -a multipath Raleigh faded channel with W paths is considered – see figure -W paths with relative attenuations 0, a 2,…, a w and relative delays 0, τ 2,…, τ w. - the first path has a level of r 1 -the BW of a sub carrier is constant B and the SNR on each path has the same distribution - the SNRs of paths 2,…, W are relative to the SNR 0 of path 1 (7) (8)

11. TUCN Data Transmissions Laboratory COST 289 - 12-th MCM, Firenze, Italy11 the p.d.f. of the Raleigh-faded rated level x = r/σ N on sub carrier k and path i is: for a signal composed of W Raleigh-faded waves with relative attenuations a i, and delays τ i the p.d.f. of rated level of the received signal transmitted on the k-th sub-carrier should be computed taking into account the phase differences Ω kij between two waves, i and j: p.d.f. of the received multipath-Raleigh faded rated level r/σ is computed by: Joint modeling of the Raleigh channel and user-chunk allocation method – p.d.f. of the received SNR p k (x k ) – probability of the level of the SNR received on sub-carrier k to have the value x k U – probability of the level on the last path to take a value so that, given the other w-1 levels and delays, the composed level equals the rated level x k ; (9) (10) (11) (12)

12. TUCN Data Transmissions Laboratory COST 289 - 12-th MCM, Firenze, Italy12 Joint modeling of the Raleigh channel and user-chunk allocation method – state probabilities for FH allocation Frequency Hopping allocation We need to compute the probability of the rated level to lie between a pair of threshold T l (dB) and T l+1 (dB) (J l and J l+1 the linear values corresponding to T l, T l+1 ) where configuration l should be used; This probability is obtained by averaging p k (x) between the J l and J l+1 thresholds : The probability of a user to employ the configuration l is obtained by averaging, over all N u sub carriers, the probability of the rated level of the signal, received on a subcarrier k, to lie between thresholds, J l, J l+1 : For FH bin-allocation method, the probability of a bin to be assigned to one user is 1/B u. the BFP method is affected by the number of connected users - carrier loading Two multipath channels are considered:  CH – 4 paths with 0, 3, 6, 9 dB relative attenuations and 0, 200, 400, 600 ns relative delays  CH 1 – 18 paths according to the WP5 Urban Macro [13] (13)

13. TUCN Data Transmissions Laboratory COST 289 - 12-th MCM, Firenze, Italy13 Joint modeling – state probabilities for FH allocation Theoretical and simulation results Const. No 12345678 P FH -computed0.07450.12280.13410.23620.20660.14880.06630.0107 N FH /10000 - simulated0.07340.12150.13380.23810.20620.15150.05810.0174 Measured and computed probabilities to employ the specified non-coded configurations (SNR 0 =16 dB, FH method) – on CH – Lc=2% the differences between the computed and simulated results are below 1% non-coded nbnb SNR thr. (dB) 1 -- 28.3 313.2 416.2 520.2 623.6 726.6 829.8 Non-coded configurations and corresponding SNR thresholds Measured and computed probabilities to employ the specified non-coded configurations (SNR 0 =16 dB); FH chunk allocation method – on CH – Lc=2% 12345678 0 0.05 0.1 0.15 0.2 0.25 P FH Constellation No. Simulated Computed

14. TUCN Data Transmissions Laboratory COST 289 - 12-th MCM, Firenze, Italy14 Joint modeling of the Raleigh channel and user-chunk allocation method – state probabilities for BFP Best Frequency Position – allocation  The probability p BFP (J l, J l+1 ) that the maximum rated level lies between thresholds J l, J l+1, requires the computation of the probability of the average rated level of bin m to lie in this domain, p am, multiplied with the probability that the average rated levels of all other bins, Q mj to be smaller than the average rated level of bin m; mCU +q – the index of sub carrier q in bin m the BFP method is affected by the carrier loading (14) (15)

15. TUCN Data Transmissions Laboratory COST 289 - 12-th MCM, Firenze, Italy15 Joint modeling – state probabilities for BFP allocation Theoretical and simulation results Measured and computed probabilities to employ the specified non-coded configurations (SNR 0 =16 dB); - BFP – on CH – 1 user the differences between the theoretical evaluation and the simulation results are small enough (<2%). this approach requires a large amount of computation and should be performed for every SNR 0 value; for the BFP allocation, it should also be performed for every cell-carrier loading (L c ). 12345678 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 P OA Constellation No. Simulated Compute d Const. No12345678 P BFP – computed0.00120.00130.00760.07560.29100.39360.21580.0139 N BFP /10000 – simulated0.00500.00250.00650.06750.27850.41650.21050.0130

16. TUCN Data Transmissions Laboratory COST 289 - 12-th MCM, Firenze, Italy16 Approximate computation of the received SNR p.d.f. based on computed/simulated data an approximate method to compute the p.d.f. of the received SNR, for any desired average SNR 0 of the first arrived path consists of three steps:  compute or simulate the probabilities of the receiver’s SNR to lay between an imposed set of thresholds T k, for a given SNR 0, named SNR ref, of the first arrived path. Computation can be done using the using the method described above;  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, SNR 0. this method requires a smaller amount of computation and ensures a good accuracy of the obtained p.d.f. if f(x) is the function which interpolates the SNR p.d.f. and w k is the probability of the current SNR to lay within the k-th domain, the interpolation function should fulfill the conditions, J 1 – min. thr. J S – max. thr.: (16)

17. TUCN Data Transmissions Laboratory COST 289 - 12-th MCM, Firenze, Italy17 Approximate computation of the received SNR p.d.f. based on computed/simulated data the interpolation function f(x) should also be positive and it should have only one maximum across the whole range of x variable considered; to simplify the computation of f(x), the number of SNR domains are reduced by suppressing those who exhibit a w k below an imposed value, e.g. w k < 1∙10 -3, and adjusting the lowest and highest thresholds, to Tk m and Tk M. the f(x) was chosen to be a polynomial function of order S=k M -k m +1, (a); Using the probabilities w k of the SNR to lay within the k-th interval, the coefficients of f(x) are computed using (b) - (c). Scaling of the f(x), to the (f a (x)) function for other desired SNR 0 (SNR 0-a ) of the reference path: the state probabilities for the two allocation methods are computed by integrating f a (c,x) between each pair of thresholds J l, J l+1. (17) (18)

18. TUCN Data Transmissions Laboratory COST 289 - 12-th MCM, Firenze, Italy18 Approximate computation of the received SNR p.d.f. based on computed/simulated data- some results as an example, the WP5 Urban Macro channel model (18 propagation paths)- CH 1, for a given average SNR 0 =16 dB of the first path and L c (cell load) = 2%, 50%, 75%, 100% with both the BFP and FH chunk allocation methods were considered – see table and figures T k [dB]T 1 =-2T 2 =8.3T 3 =13.2T 4 =16.2T 5 =20.2 T 6 =23.6 L c =2%0002∙10 -5 1.4∙10 -3 3.9∙10 -2 L c =50%0005∙10 -5 3.2∙10 -3 5.5∙10 -2 L c =75%0008∙10 -5 8.5 10 -3 7.3∙10 -2 L c =100 % 003.1∙10 -4 6.8∙10 -3 2.6∙10 -2 8.8∙10 -2 L c =x%5∙10 -4 1.1∙10 -2 3.7∙10 -2 1.47∙10 -1 2.4∙10 -1 2.510 -1 T k [dB]T 7 =26.6T 8 = 29.8T 9 =33T 10 = 36.2T 11 = 39.4 L c =2%3.4∙10 -1 5.3∙10 -1 8.7∙10 -2 7.8∙10 -4 0 L c =50%3.5∙10 -1 5.0∙10 -1 8.8∙10 -2 7.9∙10 -4 0 L c =75%3.4∙10 -1 4.8∙10 -1 8.7∙10 -2 8.2∙10 -4 0 L c =100 % 3.1∙10 -1 4.8∙10 -1 8.9∙10 -2 1.0∙10 -3 0 L c =x% 2.2∙10 -1 7∙10 -2 4.5∙10 -3 2∙10 -5 0 SNR domains and state probabilities for BFP and FH; SNR 0 =16dB; L c =x% corresponds to the FH chunk allocation 152025303540 0 0.01 0.02 0.03 0.04 0.05 0.06 SNR (dB) cell load < 2% cell load = 50% cell load = 75% cell load = 100% Interpolation functions of the channel SNR p.d.f. for L c =2%, 50%, 75%, 100% - BFP – CH1. p.d.f. (SNR) the BFP allocation is affected by the carrier loading because of the possible conflicts between users which should be allocated the same chunk

19. TUCN Data Transmissions Laboratory COST 289 - 12-th MCM, Firenze, Italy19 Approximate computation of the received SNR p.d.f. based on computed/simulated data- some results T k [dB]T 1 =-2T 2 =8.3T 3 =13.2T 4 =16.2T 5 =20.2T 6 =23.6 L c =x%5∙10 -4 1.1∙10 -2 3.7∙10 -2 1.47∙10 -1 2.38∙10 -1 2.67∙10 -1 T k [dB]T 7 =26.6T 8 =29.8T 9 =33T 10 =36.2T 11 =39.4 L c =x%2.2∙10 -1 7∙10 -2 4.5∙10 -3 2∙10 -5 0 5 10 15 2025 30 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 SNR (dB) p.d.f. (SNR) Interpolation functions of the channel SNR p.d.f. - FH – CH1 Simplified SNR domains and state probabilities for FH- CH1 ; the interpolating function derived for SNR ref = 16 dB was translated and scaled to SNR 0 = 1and 4 dB; the state probabilities obtained by integrating the two translated interpolation functions between the thresholds, C, were compared to the state probabilities obtained by computer simulations, S – see table for BFP – on CH1 T k [dB]T 1 -2 T 2 8.3 T 3 13.2 T 4 16.2 T 5 20.2 T 6 23.6 T 7 26.6 T 8 29.8 S. 16 dB0002∙10 -5 1.4∙10 -3 0.0390.340.62 C.16 dB0001∙10 -5 1.4∙10 -3 0.0390.340.62 S. 4 dB00.00950.1380.670.1810.002000 C. 4 dB00.00770.1440.6650.1760.006700 S. 1 dB8.7∙10 -4 0.1460.5020.3483.5∙10 -3 000 C. 1 dB0.00140.1500.4940.3411.5∙10 -2 000

20. TUCN Data Transmissions Laboratory COST 289 - 12-th MCM, Firenze, Italy20 Approximate computation of the received SNR p.d.f. based on computed/simulated data- some results both the analytical and the approximate method, ensure good accuracies of the wk SNR state probabilities. the w k SNR state probabilities delivered by the analytical method are differing with less than 1% and 2% from the ones obtained by computer simulations. the approximate method provides the probabilities w k, with a slightly greater error, about 3%, but requires a significantly smaller amount of computation than the analytical approach.

21. TUCN Data Transmissions Laboratory COST 289 - 12-th MCM, Firenze, Italy21 Performances of chunk allocation methods the BFP method ensures great state probabilities only for a limited number of channel states, 3 max.4, the rest of the states being employed quite seldom. the SNR average value of these states is 8-10 dB higher than the SNR 0 level - this is because the BFP method allocates (with high probability) the chunk with the highest SNR for each user, taking advantage of the frequency diversity of the multipath Raleigh channel, in a very efficient way. for FH method the cell-carrier loading does no longer affect the p.d.f, because the user chunks are allocated independently according to a pseudo­random sequence. the FH allocation employs with significant probabilities w k more channel states, 5 or 6, because it does not place the user on the particular chunk that ensures the best SNR. the average SNRs of these states are smaller with even 8 dB, or greater with up to 14 dB, than the SNR of the firstly arrived wave, SNR 0. the most employed states have an average SNR higher with 0-10 dB than SNR 0. the FH method takes advantage of the channel frequency diversity in a less efficient manner - it performs an averaging over the whole available BW.

22. TUCN Data Transmissions Laboratory COST 289 - 12-th MCM, Firenze, Italy22 Joint modeling of the multipath channel and chunk allocation using a Markov chain the p.d.f. of the total SNR is independent of the mobile speed  the total SNR p.d.f. only allows for the average channel state-probabilities  it only allows the computation of average performances, e.g. throughput or spectral efficiency, over a relatively long time interval. if the transmission analysis requires the probability distributions of the studied performances, distributions that are dependent on the mobile speed, a Markov-chain modeling of the channel and multiuser access method should be elaborated. this would require the computation of the state-transition probabilities. they could be obtained by using the crossing-level rates and fading statistics of the composed multipath Raleigh-faded signal, using its p.d.f. in a manner similar to the one applied to the single path Raleigh-faded channel, see [Rap]. different chains should be derived for different cell-carrier loadings (for BFP) and mobile speeds.

23. TUCN Data Transmissions Laboratory COST 289 - 12-th MCM, Firenze, Italy23 Joint modeling of the multipath channel and chunk allocation using a Markov chain we present some Markov chains obtained by computer simulations for some significant values of the OFDMA access-scheme considered out of the set of non-coded QAM modulations only the first 8 are used adaptively in each chunk, i.e from 2-PSK to 256-QAM. the complete Markov-chain assigned to the channel SNR states has 8 possible states, one assigned to each SNR domain the Markov chains can be simplified by dropping some states with very low associated probabilities, i.e. smaller than 0.01, to allow a simpler and still accurate performance evaluation since the w k probabilities depend of the carrier-loading for the BFP allocation, we developed separate Markov chains for L c = 2, 50 and 100%. because the state-variability, for BFP, is dependent of the user speed, we analyzed the Markov chain for v=4 and 120 km/h. A Markov chain was also developed for the FH allocation All chains consider the WP5 Urban Macro channel model - CH1 SNR state no.12345678 SNR thr (dB) -- 8.313.216.220.223.626.629.8

24. TUCN Data Transmissions Laboratory COST 289 - 12-th MCM, Firenze, Italy24 Markov chain for BFP – L c = 2%, 50%, v = 4 or 120 km/h Final state - speed Tab.a BFP allocation, L c =2%State probab. 678 6120 km/h0.08390.05540.02690.03775 4 km/k0.97130.00180.00077 7120 km/h0.4640.39720.11280.33888 4 km/k0.01580.98070.0095 8120 km/h0.44840.5450.35630.62305 4 km/k0.01270.01740.9897 Initial state Final state – speed Tab. b BFP allocation, L c =50%State probab. 678 6120 km/h 0.551770.03750.020380.05652 4 km/k0.9720.002430.001235 7120 km/h 0.224130.69990.15320.34746 4 km/k0.0140.981480.00937 8120 km/h 0.22030.26030.825460.59292 4 km/k0.01350.0160.98938 - the increase of the cell-carrier loading from L c =2% to 50% leads to increased probabilities of the lower states S6, S7. - for v = 4 km/h, the transition probabilities w lj are very small and the transition probabilities w ll are close to 1. - for v = 120 km/h, the transition probabilities w lj increase significantly and the w ll probabilities decrease significantly. Initial state BFP – L c = 2% and 50%;speed 4km/h and 120km/h SNR 0 = 16 dB St.6 w(6) w(6-6) w(8-8) St.7 w(7) w(7-7) w7-6) w(6-7) w(8-7) w(6-8) St.8 w(8) w(7-8) W(8-6)

25. TUCN Data Transmissions Laboratory COST 289 - 12-th MCM, Firenze, Italy25 Markov chain for BFP – L c =100%, v = 4 or 120 km/h L c =100% - BFP; CH1 v= 4km/h and120km/h – SNR 0 = 16 dB St.6 w(6) w(6-6) w(8-8) St.7 w(7) w(7-7) w(7-6) w(6-7) w(8-7) w(7-8) w(8-6) w(6-8) St.5 w(5) w(5-5) w(8-5) w(6-5) w(5-8) w(5-7) w(7-5) St.8 w(8) w(5-6) Initial state Final state - speed Tab. c BFP allocation, L c =100% 5678 5120 km/h 0.05240.04630.03620.0206 4 km/k 0.970.0014 2 0.00110.0006 6120 km/h 0.14750.13360.11280.0718 4 km/k 0.00040.97290.00350.0021 7120 km/h 0.38820.37860.35630.2868 4 km/k 0.01190.01160.97970.0088 8120 km/h 0.41170.44120.49440.6163 4 km/k 0.0130.01360.01530.9882 State probab. 0.02910.09170.31960.5565 -the increase of Lc to 100% leads to an greater number of states to be considered, from 3 to 4, and to greater values of w k of the lower states S6 and S7. - the increase of the user speed increases the state-transition probabilities w lj and decreases the w ll ones, giving more variability to the channel.

26. TUCN Data Transmissions Laboratory COST 289 - 12-th MCM, Firenze, Italy26 Markov chain for FH Final st. → ↓ Init. st 2345678 20.01110.01350.01190.01220.01250.01110.0077 30.05720.04400.03820.03870.03700.03610.0338 40.16390.15770.15320.15390.15100.14080.1358 50.25530.24740.24860.24360.23630.23410.2160 60.25270.26120.27200.26520.26400.26490.2583 70.19810.21740.20970.21870.22580.22790.2469 80.06140.05780.06550.06830.07250.08430.100 wkwk 0.01170.03760.14900.23850.26490.22290.0745 -the Markov-chain for the FH would not be affected by the cell-loading and mobile velocity, due to the predefined order of allocating chunks to one user. - it employs a larger number of states, mostly the ones around SNR 0 State and state transition probabilities for FH user chunk – SNR 0 =16 dB

27. TUCN Data Transmissions Laboratory COST 289 - 12-th MCM, Firenze, Italy27 non-ARQ environment the average probability of a chunk to be correctly decoded, considering all possible channel states, is: the average probability of an M-chunk long packet to be correctible received and the average probability of retransmission for such a packet are; Applications of state probabilities Computation of average throughput and spectral efficiency in an application not governed by an ARQ protocol, the nominal average bit rate D nav, the average throughput Θ n and the average spectral efficiency η av are shown in (11), where R ec denotes the rate of an external code applied to the whole M-chunk packet. (19) (20) (21) (22)

28. TUCN Data Transmissions Laboratory COST 289 - 12-th MCM, Firenze, Italy28 Applications of state probabilities Computation of average throughput and spectral efficiency SW H-ARQ environment [] the protocol efficiency, i.e. the ratio between the N u av and the N t av is: the average throughput and spectral efficiency of the transmission governed by an H-ARQ protocol are: (23) (24)

29. TUCN Data Transmissions Laboratory COST 289 - 12-th MCM, Firenze, Italy29 References (selected) [ 1] IST-2003-507581 WINNER, “Final report on identified RI key technologies, system concept, and their assessment”, Report D2.10 v1.0, December 2005. [2] M. Sternad, T. Ottosson, A. Ahlen, A. Svensson, “Attaining both Coverage and High Spectral Efficiency with Adaptive OFDM Downlinks”, Proc. of VTC 2003, Orlando, Florida. [3] 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. [4] D.J.C. McKay, “Good error-correcting codes based on very sparse matrices,” IEEE Trans. on Information Theory, vol. 45, March, 1999. [5] ITU-T, “LDPC codes for G.dmt.bis and G.lite.bis,” Temporary Document CF-060. [6] V. Bota, Zs. Polgar, M. Varga,,”Performances of LDPC-Coded OFDM Transmissions and Applications on Fixed and Mobile Radio Channels”, Proceedings of COST 289 Seminar on Spectrum and Power Efficient Broadband Communications, Barcelona, October 2004. [7] G.Ungerboeck, “ Trellis-Coded Modulation with Redundant Signal Sets, Part I and Part II”, IEEE Communications Magazine, vol.25, No.2, February 1987. [8] Th. S. Rappaport, Wireless Communications, New Jersey: Prentice Hall PTR, 2001. [9] V. Bota, M. Varga, Zs. Polgar, “Performances of the LDPC-Coded Adaptive Modulation Schemes in Multi-Carrier Transmissions”, Proceedings of COST 289 Seminar on Spectrum and Power Efficient Broadband Communications, July, 2004, Budapest, Hungary. [10] V. Bota, M. Varga, Zs. Polgar, “Convolutional vs. LDPC Coding for Coded Adaptive-QAM Modulations on Mobile Radio Channels”, Proceedings of COST 289 Seminar on Spectrum and Power Efficient Broadband Communications, October 2005. [13] IST-2003-507581 WINNER, “Assessment of Radio-link technologies”, Report D2.3 ver 1.0, Feb. 2005. [14] Zs. Polgar, V. Bota, M. Varga, “Modeling the Raleigh-Faded Mobile Radio Channel”, WETTIT 2006, October 2006, Cluj-Napoca, Romania. [15] H. Tanembaum, “Computer Networks”, Prentice Hall, 1989. [16] V.Bota, Zs.Polgar, M.Varga, “Performance Evaluation of H-ARQ Adaptive Coded QAM Transmissions over Multipath Mobile Channels” 3 rd Workshop of COST 289, July 2006, Aveiro, Portugal