A Novel Link Error Prediction Model for OFDM Systems with HARQ

Transcription

1 A Novel Link Error Prediction Model for OFDM Systes with HARQ Josep Colo Ikuno, Christian Mehlführer, Markus Rupp Institute of Counications and Radio-Frequency Engineering Vienna University of Technology, Austria Gusshausstrasse 2/389, A-14 Vienna, Austria Eail: {jcolo, chehl, Web: Abstract This paper presents a link error prediction odel capable of accurately predicting the block error ratio in OFDM systes with hybrid ARQ. The joint odeling of the channel coding and the retransissions solves any of the issues with present odels. Our odel is based on accuulated conditional utual inforation, utual inforation effective SNR averaging, and siulated AWGN perforance curves. As a consequence, our odel is fading-insensitive and takes into account the nonideality of rate atching. The odel can be applied to any OFDM syste that utilizes rate atching as a eans to achieve adaptive odulation and coding and HARQ. We deonstrate the application of our odel in exeplarily LTE and validate its accuracy by siulation. The whole siulation environent together with the results of this paper are ade available for download fro our hoepage. I. INTRODUCTION Modern counication systes use Hybrid Autoatic Repeat Request HARQ on top of the Physical PHY layer to copensate for incorrectly decoded packets. In HARQ systes, an incorrectly received packet is retransitted and all transissions of this packet are jointly decoded. Depending on how the retransitted packets are generated, we distinguish between: i Chase Cobining CC, in which each retransission is a repetition of the original transission, and ii Increental Redundancy IR, in which each retransission adds new bits [2, 3]. In order to siulate coplete networks with any links between base stations and obile terinals, Link Error Prediction LEP odels that accurately abstract the PHY procedures at low coplexity are required [4]. Such odels predict the link perforance for each individual link and enable i the assessent of perforance at syste level at reduced coputational coplexity and ii at the obile terinal, the design of better link adaption algoriths. While LEP odels that incorporate HARQ do already exist, the odel proposed here addresses issues that are currently not considered by both analytical odels i-v and odels based on fitting of siulation results vi: i Bit repetition due to low coding rates being obtained fro a higher rate other code is currently not considered in analytical odels [, 6]. Since odern systes eploy Effective Code Rates ECRs uch lower than that of the other code 4.3 ties lower than the other code rate in the case of LTE, the predicted perforance significantly deviates fro the real perforance. ii It has been entioned in [7, 8] that a packet could be separated in CC and IR parts. However, since the transitted bits are interleaved and IR cobining is done at bit level, there is no siple way of differentiating the two parts, which is why this is currently not done in odels. By utilizing repetition ratios in our odel, the need of identifying overlapping bits in the signal and calculating their individual SNRs is eliinated. iii In analytical odels, OFDM is either typically not accurately odeled or just flat fading is considered [, 9, 1]. Since OFDM systes exploit frequency diversity by eans of channel coding, a odel taking the OFDM signal structure into account is required for actual systes. iv Results fro odels for odulation orders higher than and retransission nubers higher than one are not provided [ 1]. Since odern systes, such as LTE, support odulations up to and up to three retransissions, a good LEP odel has to be validated also for these cases. v Exponential Effective Signal to Interference and Noise Ratio Mapping EESM-based ethods, such as [6], require extensive calibration. In our odel we instead apply Mutual Inforation Effective SNR Mapping MIESM as SINR averaging ethod. MIESM has the advantage of not requiring calibration at all and additionally being fading-insensitive [11 13]. vi In contrast to our odel, in siulation-based odels, such as [9], the coplexity of tuning the odel paraeters increases exponentially with the nuber of retransissions. Addressing the above issues, this paper presents a unified LEP odel for HARQ that is based on Accuulated Conditional Mutual Inforation ACMI and MIESM. Although the nuerical results are presented for LTE, our odel can accurately predict the Block Error Ratio BLER of any OFDM syste that applies rate-atching to adjust the channel coding rate and to ipleent HARQ. The reainder of this paper is organized as follows. In Section II we present the inforation-theoretic view of the different types of HARQ and how these types are applied in a syste that uses a one-step rate atching process to both adapt the ECR and generate data packets with different redundancy fro the sae data. Section III describes how the BLER is

2 data bits Channel code: code rate Puncturing: coded bits data bits Channel code: Repetition code: coded bits Fig. 1. Rate atching structure: + 1 outputs are cobined and then decoded at the receiver. The turbo-encoded bits, which are coded with a fixed rate r c, are then rate-atched to an arbitrary rate r eff. odeled. In Section IV we apply our odel to LTE, for which we show perforance results in Section V. We conclude the paper in Section VI. II. HARQ In this section, the concept of ACMI is presented for the different HARQ schees. We find that we can odel the rateatching process as a concatenation of an inner code and an outer repetition code. In this section we assue that all sybols transitted in one frae experience the sae SNR. This assuption will not be required in the next section. Depending on the type of HARQ being eployed, the ACMI I of the cobination of several HARQ blocks is calculated differently [14]. In the case of CC, in which the sae bits are retransitted M ties, the effective receive SNR is increased with every retransission. Thus, the ACMI I can be expressed as M I CC γ = I γ, 1 where γ denotes the SNR of the -th retransission = {, 1,..., M} with = corresponding to the initial transission and I is the BICM capacity [1], calculated as explained in 6 below. For IR, if a parity-priority IR-PP schee is used, only new parity bits are sent in subsequent retransissions, thereby directly increasing the ACMI I I IR-PP γ = M I γ. 2 If systeatic priority IR-SP is applied, each retransission contains the systeatic bits of the original essage as well as new parity bits. In this case I results in a cobination of 1 and 2 I IR-SP γ = D M C I γ + 1 D M I γ, 3 C where D is the nuber of data systeatic bits and C the total nuber of bits sent in each transission. A. HARQ by eans of rate-atching In a one-stage rate-atching process such as the one applied in LTE the generation of the different data block versions for the IR HARQ is copletely integrated. For a specific target ECR r eff, different values of result in different bit selections, that is, different HARQ retransissions Figure 1. Fig. 2. Model of the received block after the -th retransission has been received and cobined. Because of the finite length of the other code rate r c, it is necessary that for C > D/r c, bits are repeated, where D is the nuber of data bits and C the resulting nuber of coded bits Figures 1 and 2. In order to apply our ACMI-based odel, we represent the cobined received block as a concatenation of IR represented by a channel code with variable rate r and CC represented by a repetition code with rate 1/Nrep, as shown in Figure 2. Thus, after the -th retransission, the original D bits are coded into C + 1 bits, which coprise CU unique bits fro the other code and CR repeated bits: C + 1 = C U + C R ; C U = D/r, C R. 4 The nueric values of CU and C R depend on the specific rate atching process. An exaple for LTE is given in Section IV. III. OUTAGE PROBABILITY AND PERFORMANCE METRIC In this section, the concepts presented in Section II are applied to derive the outage probabilities for AWGN and frequency selective channels. A. AWGN odel If a capacity-approaching channel code with suitably long blocklength is used, it is well known that the BLER can be approxiated by the Mutual Inforation MI outage probability [16 18]. In the case of a syste with HARQ, equivalent expressions can be derived by using ACMI. Under this assuption, the outage probability ε is the probability P that I < D. Thus, in the AWGN case we obtain: [ C ε γ,, D, C, n = P U n I n N rep γ ] < D, where n is the nuber of bits per sybol of the applied Modulation and Coding Schee MCS, and I n is the BICM capacity for that odulation, expressed as [1]: I n γ = n E Y [Γ] Γ = 1 2 n n i=1 b= z A i b 1 ˆα A log 2 α A i b exp Y γ ˆα z 2 exp Y γ α z 2 A... the set of 2 n sybols the coplete sybol alphabet A i b... the set of sybols for which bit i equals b Y... CN, 1, 6 where ˆα cycles through the whole sybol alphabet and α just through the set of sybols for which bit i equals b.

3 1.9 =2 = =2 = Fig. 3. Turbo encoder ECR r of the cobined received data block for each retransission index. Modulation and Coding Schees using,, and odulations shown grouped Fig. 4. Repetition coding gain Nrep in decibels for each retransission index. Modulation and Coding Schees using,, and odulations shown grouped. B. Frequency selective odel By applying the MIESM ethod it is possible to copress a vector γ of SNR values into an AWGN-equivalent effective SNR. This is accoplished in a ore robust anner than with other ethods, such as EESM, which require a uch ore precise calibration [11, 19]. The AWGN-equivalent SNR is obtained by stacking the subcarrier SNR row vectors of each transission in a vector γ 7, which is then non-linearly averaged using MIESM 8: γ = [ γ, γ 1,... γ M, ] 7 γ eff γ = I 1 n 1 N SCs γ i γ I n γ i. 8 Here, N SCs is the total nuber of subcarriers and γ eff is the resulting AWGN-equivalent SNR. As in, the outage probability ε can be calculated as: ε γ,, D, C, n [ C = P U n C. Non-ideality of rate atching ] I n N rep γ eff < D. 9 In order to consider the non-ideal behaviour of the channel coding and the loss in perforance due to the rate atching process, we perfor BLER siulations in Additive White Gaussian Noise AWGN channels. The thereby obtained AWGN BLER curves are used as an approxiation for the outage probability ε: ε γ,, D, C, n BLER AWGN r, n, γ AWGN. 1 Here, γ AWGN are appropriate SNR values to obtain a BLER curve in the range of approxiately 1 3 to 1. The AWGN SNR γ AWGN = N repγ eff is given by the SNR gain N rep due to the repetition coding and the MIESM averaging of the frequency selective SNR distribution γ in 8 to obtain γ eff. Note that for applying the approxiation 1 we have to precalculate one BLER curve for each cobination of odulation order n and outer channel coding rate r. The actual nuber of necessary curves depends on the nuber of MCSs and the rate atching algorith of the specific syste. IV. APPLICATION TO LTE In this section, we show how to apply our LEP odel in LTE. Equivalently, the sae ethod can be used to apply our odel to other OFDM systes. The 3GPP LTE standard [2] defines which MCSs, naed Channel Quality Indicators CQIs, can be used by the LTE syste Table I. In LTE, the values for r cannot be directly calculated fro the definition of the rate-atcher [21]. However, by using the ipleentation of the rate atching process in our LTE link level siulator [22], equivalent puncturing atrices applied to the other code of rate r c = 1/3 can be obtained for each of the HARQ retransissions. The outer turbo coding rate r and the inner repetition coding rate 1/N rep are then easily calculated fro the puncturing atrices. For LTE, r and N rep are shown in Figures 3 and 4. In Figure 3, we see that the outer turbo coding rate drops as ore retransissions are available at the receiver increases. Furtherore, we see that for CQIs saller than TABLE I LTE MODULATION AND CODING SCHEMES [2] CQI Modulation 1/ECR bits/syb

4 BLER =2 =3, odel, odel =2, odel =3, odel Fig.. CQI 6 BLER, ITU Pedestrian-B k/h. Solid line: siulation, Dashed line: LEP odel. Marked: BLER=1% points =2 = Fig. 6. AWGN BLER=1% points, = {, 1, 2, 3}. Solid line: LEP odel, Dashed line: siulations results. TABLE II AVERAGE DEVIATION OF THE MODELED 1% BLER POINTS [DB]. AWGN PedB four and for higher retransission nubers, the outer turbo coding rate saturates at the other code rate r c = 1/3. An ECR lower than 1/3 is achieved in our odel by decreasing the inner repetition code rate, thereby increasing the SNR gain N rep of the repetition code see Figure 4. V. PERFORMANCE We evaluated the accuracy of our odel in extensive single-user link level siulations utilizing our open source Vienna LTE siulator [22]. AWGN and tie-correlated ITU Pedestrian-B [23 2] channel odels were eployed and the siulated BLER was copared to the one predicted by our odel. For each of the 1 LTE MCSs, the BLER curves fro the siulation and fro our odel are copared at 1% BLER, which is the target for the link adaptation. This target is known to lead to near-optial perforance [17]. Figure shows a coparison for CQI 6, with the 1% BLER points arked by a dot. The SNR values of the 1% BLER points for different retransission nubers are shown for AWGN and ITU Pedestrian-B channels in Figures 6 and 7. In the case of and transissions, our odeled perforance is very close to the siulated perforance. Only in the case of transission with ore than one retransission, a deviation is observed. Table II shows the average deviation between odel and siulation. In order to quantify the ipact of the lower accuracy in the case of 64- QAM and ore than one retransission, we have to quantify the probability of these cases occurring in a real syste. For doing so, we generated an SINR distribution of a cell shown in Figure 8 by considering the acroscopic pathloss and antenna gain paraeters listed in Table III =2 = Fig. 7. ITU Pedestrian-B BLER=1% points, = {, 1, 2, 3}. Solid line: LEP odel, Dashed line: siulations results. In such a cell, our siulations show that odulation is only used in approxiately 11% of all transissions. In.4% of all transissions, odulation is eployed and one retransission is required for correct decoding. In none of the total of siulated transissions, odulated packets required ore than one retransission to be decoded correctly. We thus conclude that the deviation of our odel will have a negligible ipact on the link error prediction. Note that our LEP odel does not consider the following two specific aspects of LTE: i At very sall codeblock sizes the perforance of the LTE channel code degrades. Thus the BLER perforance becoes dependent on the codeblock size. In our siulations we always used the longest possible codeblock length that fits in a axiu bandwidth of MHz, as the well-established ITU power delay profiles show a periodicity in their frequency correlation properties for larger bandwidths [27]. ii In LTE, the axiu codeblock length is bits. Larger codeblocks are segented prior to turbo encoding. This effect could be easily odeled by calculating an effective BLER eff s = BLER s, where s is the nuber of codeblock segents. Since we did not consider codeblock segentation

5 1 y pos [] x pos [] 1 1 SINR [db] - cdfsinr SINR [db] Fig. 8. SINR distribution used for link level siulation. Only non-distorted central sectors used. TABLE III SIMULATION PARAMETERS. acroscopic pathloss log 1 R, R in k antenna gain pattern 6 3dB bea [26] channel odel tie-correlated ITU Pedestrian-B [23, 24] SNR points Fraes per SNR point 1 Adaptive Modulation and Coding Yes Target BLER 1% Nuber of users 1 in our odel, we chose for our siulations the largest possible bandwidth B MHz that results in a codeblock size VI. CONCLUSIONS We introduced a odel that is capable of predicting the BLER of OFDM transissions with HARQ. Our odel is based on accuulated conditional utual inforation, utual inforation effective SNR apping, and link level siulations to adjust for the non-ideality of the rate-atching process. The odel does not require calibration and is fading-insensitive. Coplexity-wise, it requires the precalculation of AWGN BLER curves for each accuulated effective code rate and BICM curves for each odulation order. Both can be achieved offline and do not influence runtie coplexity. In LTE, this corresponds to the calculation of 26 BLER curves and three BICM curves for the 1 odulation and coding schees and allows BLER prediction for up to three retransissions. The accuracy of our proposed link error prediction odel is validated in AWGN/ITU Pedestrian-B channels and an SINR distribution atching that of a cell. All data, tools and scripts are available online in order to allow other researchers to reproduce our results [1]. ACKNOWLEDGMENTS The authors would like to thank the LTE research group for continuous support and lively discussions. This work has been funded by the Christian Doppler Laboratory for Wireless Technologies for Sustainable Mobility, KATHREIN- Werke KG, and A1 Teleko Austria AG. 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