A Link Quality Model for Generalised Frequency Division Multiplexing
5G systems aim to achieve extremely high data rates, low end-to-end latency and ultra-low power consumption. Recently, there has been considerable interest in the design of 5G physical layer waveforms. One important candidate is Generalised Frequency…
Authors: Ghaith R. Al-Juboori, David Halls, Angela Doufexi
A Link Quality Model for Generalised Frequency Division Multiplexing Ghaith R. Al- Juboori (1) , Dav id Halls (2) , Angela Dou fexi (1) and Andrew R. Nix (1) (1) Communication Syste ms & Networks Group, Department of Electrical and Electronic Engineering University of Bristol , B ristol, United Kingdo m (2) Telecommunicatio n Research Laborator y, Toshiba, Bristol, United Kingdo m Email: {Ghaith. Al-juboori, Angela.Dou fexi, Andy.nix}@bristol.ac. uk, david.halls@ toshiba-trel.co m Abstract − 5G system s aim to achieve extremely high data rates , low end- to -end latency and ultra-low power consumption. Recently , there has been considerable interest in the design of 5 G physical la yer waveforms . One important c andidate is Generalised Frequency Division Multiplexing (GFD M ). In or der to ev aluate its performance and features, system-level studies should be undertaken in a ra nge of scenarios. These st udies, however, require high ly complex compu tations if they are performed using bit-level simulators. In this paper, the Mutual Information (M I) based link quality model (PHY abstrac tion), which has been regularly used to implement sy stem-level studies for Orthogonal Frequency Division M ultiplexin g (OFDM), is applied to GFDM . The performance of the GFDM waveform using this model and the bit-level simulation perfor man ce is measured using different channel types. Moreover, a system-level study for a GFDM based LTE -A syste m i n a realistic scenario, using both a bit-level simulator and this abstraction model, has been st udied and compared. The results reveal the accuracy of this model using realistic channel data. Based on these res ults, the PHY abstraction technique can be applied to ev aluate the performance of GFDM based syste ms in an effective manner with low complexity . The maximum difference in the Packet Error R ate (PER) and throughput results in the abstraction case co mpar ed to bit-le vel simulation does not ex ceed 4% w hilst offering a simulation time saving reduction of around 62 ,000 times. Index Terms − 5G ; GFDM; LTE-A; MI -ba sed link quality model I. I NTRODUCTI ON The require men ts for 5G s ystems vary depending o n t he scenario consider ed, such as I nternet of Thi nks (IoT), Ma chine Type Co mmunication (MT C) and high d ata rate mobile communications. Different te chniques need to be deployed to achieve these req uirements, including Massive MI MO, millimetre wave bands and usin g new p hysical la ye r waveforms. T he selection of the air interface is ke y due to its impacts on the transcei ver co m plexity and th e system le vel performance [1] . Orthogonal Freq uency Divisi on Multiplexin g (OFDM) is successfully used in many wireless standards suc h as Wireless Local Area Network s (WLA Ns) and t he 4G cell ular mobile standards (LTE & LTE -A). This success is due to its desirab le features suc h as ro bustness to Inter-Sy m bol Interference (ISI) and low implementation co mplexity due to the ef ficient use of Inverse Fast Fo urier T ransform/Fast Fourier T ransform (IFFT/FFT ) pro cessing [2]. On the o ther hand, OFDM suffe rs from several disadvanta ges fo r example, its high o ut of b and radiation, high sen sitivity to Carrier Frequency O ffset (CF O) and high peak to average power ratio (PAPR) [3 ]. T hese drawbacks may prevent it fro m bein g used in 5G systems. Recent research looking i nto the selectio n of a new air interface for 5 G has focused mainly i n t wo ar eas. T he first has proposed enhancements an d alternatives to the OFDM waveform, in order to improve many of its feat ures such as the spectral containment and the s ensitivity to CFO, as in [4]. The second area is looking at alternative waveforms to OFDM. Many ca ndidates have been proposed such as Ge neralised Frequency Division Multiplex ing ( GFDM), Filter Ban k M ulti- Carrier ( FBMC) [5] and Universal Filtered Multi -Carrier (UFMC) [6]. In this paper , we focus on the GFDM waveform. System-level p erformance stud ies are necessary to accurate ly evaluate the per formance of a system using a GFDM waveform, however, these studies have high computation al co mplexity if they are implemented using bit-level simulator s. In this paper, the link quality model, which is often used to evaluate the system-le vel perfor mance f or OFDM [7], in a simple and lo w complexity manner, is investi gated for GFD M. To the best of o ur k nowledge, thi s subject is not investigated yet. The Mutual Information (MI ) b ased link quali ty model is used because it outperforms other models, as illustrated in section III. The rem ainder of this paper is organised as follows: in section II, a brief descriptio n of the GF DM air inter face, its features and a low complexity transceiver model are given . In section III, general descriptio ns of t he link quality model a nd the MI -based link q uality model (for OFDM & GFDM) are presented. The si mulation para meters which have been used in this pap er are listed in sectio n IV. The results are sho wn and discussed in section V. Finally; the conclusio ns are given in section VI. II. GFDM SYSTEM MODEL A. GFDM Overview GFDM is a d igital multicarrier modulation sc heme, and its flexibility helps it to address the different req uirements of 5G ; the basic structure for the GFDM tran smitter i s ill ustrated in Fig. 1. The GFDM block consists of K subcarrier s and M sub - symbols per subcarrier, unlike OFDM whic h h as only one symbol per subcarrier. A pulse shape filtering proce ss is used on each subcarrier to reduce the Out- Of -Band (OOB) radiation. Different types o f filters (orthogonal and non -orthogonal) c an be used as a pr ototype filter, an d this in creases the flexibility of the GFDM w avefor m [8 ] . An u p-conversio n p rocess is perform ed before adding the sub-carriers signals together to form the final GFDM signal. The GFDM signal ca n be express ed as: where is t he complex data symbol which is transmitted on the sub-carrier k and the s ub-symbol m . represents the time and frequenc y shift ed version of the impulse respo nse of the prototype filter, it can be written as: where n is t he sampling index ( n =0 ,……., N -1) and N is eq ual to K by M . + S/P X(n) d 0,0 , … , d 0,M-1 UP CONVERSION UP SAMPLING FILTERING X X Exp(0) X X Exp(j2 π ((K-1)/K)n) d K-1,0 , … , d K-1,M-1 MAPPING BINARY DATA g Tx [n] N N Fig. 1: The Basic GF DM Transmitter [9] . Direct implementation of th e two above equations (1 and 2 ) requires a number of complex multiplications which is equal to NKM 2 . Ho w ever, in t his paper, the method used in [3] and implied a significant reduction in the computation co m plexit y by r eformulating the GFDM trans mitter in a similar fashion to that used in OFDM (e mploying an IFFT/FFT), is applied . After th e GFDM m o dulator, the cy c lic prefix (N CP samples) is added to the GFDM signal. One of the important reasons for this addition is in order to be able to perform the equalisatio n process at the receiver s ide in the frequency domain . After that, the signal is transmitted thro ugh the channel. Assuming perfect synchronisation a nd channel estimation processe s, t he reverse steps are applied to get the estimated d ata sequence at the receiver. Several m et hods can be used to im ple ment th e GFDM demodulator such as a match ed filter, zero forcing a nd Minimum Mean Square Err or (MMSE); for more details, plea se see [1] . The zer o forcing method is applied in the paper . III. LINK QUALITY MODEL Recently, the link quality m odel ( a PHY ab straction method) has bee n effectively employed for evaluating s ystem performance and in predicting li nk ad aptation p recisely ba sed on the Sign al to Interference an d Noise Ratio (SINR) measured by the receiver [10 ]. The link quality m odel co mprises a vector of received SINR, t he post processing SIN R across the cod ed block at the input o f the decod er for certai n channel realisati on is mapped into a single value which is called t he Effective SI NR (ESINR). Using this val ue, the model can predict the Blo ck Error Rate (B LER), i.e, the P acket Error Rate (PER) , for a gi ven channel snaps hot across the OFDM subcarriers which are used to transmit the coded block. Fig. 2 illustrates t he basic concepts of the abstrac tion ap proach which is explai n ed in detail in the following. First ly, the po st processing SINR per sub -carrier n (frequency sample) for a certain user i is calc ulated as [11] : where q rep resents the interferer, N I is the total number of interferers, P tx is the transmitted power and P loss is the path loss including shado wing. Secondly, the abstraction transforms the vector of SINR for a certain block (OFDM block) u sing a mapping function Ф (SINR) to another domain , w hich is r elated to the mapping function . After that, the transformed values are linearly a veraged over the block before the average value is returned back to the SINR domain to get the ESINR (γ eff ) usin g Ф -1 as shown in the follo wing equation: where J is t he n umber of s ub-carriers and is the SINR for t he sub-carrier i . Different methods for mapping have been discussed in the literature, namely the Expo nential Effective SINR m apping, where Ф is replaced by the neg ative exponential fu nction and Mut ual Information Effective SI NR Mapping (MI ESM). In this p aper, the MIESM method is proposed due to its simple structure and hi gh accuracy compared to the other methods [10]. T he details of this approach will be given in th e next sub -section. Finall y, the ESINR (γ eff ) will be used to calcu late the B LER based SNR vers us B LER curves in t he Additi ve White Gaus sian Noise (AWGN) case. This technique has b een widely validated for OFDM wavefor m in di fferent works, for example [10, 11]. System Level Link Level -Generate Frequency selective channel H(f). -Determine the received SINR of each sub-carrier. Link Adaptation ,Scheduling,ARQ ,etc Mapping Function e.g. MIESM,EESM BLER AWGN (PHY Abstraction Mapping) Throughput, Packet Error Rate(PER), etc. BLER SINR =[SINR 1 , …… ..SINR J ] Fig. 2: PHY l ink- to -sy stem mapping procedure. A. Mutual Information Based Link Quality Model As mentioned in [10], the MI -based PHY abstraction technique can be separated in to m odulation and coding models. According ly , Fi g. 3 sho ws t he MI -based link quality model structure, and a brief description for each m odel is given below: 1-Modulation Model In this model, the descriptio n of the maximum channel capacity of a spec ific modulation scheme is given based on a symbol- by -symbol b asis without considering the decod ing information loss. The Symbo l I nformation (SI) of the channel symbol, for a given SN R value (γ) , is expressed as: where is the exp ected value, is the co mplex value cha nnel output symbol with SNR equa l to γ , m is the mod ulation order, is the AWGN channel transition probability densit y conditioned o n the noiseless channel symbol , and is assumed. Mod. Model Coding Model Collection & correction Stage MI-metric Quaility Mapping Stage SINR 1 SINR 2 SINR J SI 1 SI 2 SI J SI SINR BPSK QPSK 16QAM 64QAM BLER Eff-SINR Cr=r n Cr=r 1 MI To Eff-SINR Mapping BLER Multi-state Channel Quality of one coding block Mapping Function Fig. 3: MI -based q uality model struct ure. 2-Coding Model. This model con tains two stage s; the SI collect ion /correction stage and the quality mapp ing stage. In the first stage, the SI of J symbols in each block are collected/corrected and added together to get the Recei ved cod ed Bit Information (RB I) . These s ymbols ha ve SIN R values of and modulation orders of and the R BI’s calculation is expressed as: (6 ) The Received Bit Information Rate (RB IR), which is eq uivalent to the sample average o f the normalised SI over t he rec eived block for code blo cks for a given modulatio n, with a value in the range [0,1], can be evaluated as: (7 ) To take the practical coding loss from t he Shannon limit into consideration (the correc tion pr ocess in the first sta ge) , the SI values ca n be multiplied by ) befor e they are combined . As stated in [10], is close to 1 for T urbo and convolutional codes. Finally, the RBIR value is then mapped again to the SINR domain to get the ESI NR which will be used to get the BLER val ue based on t he AWGN lo ok-up table . The coding model only relate s to the p erformance of the coding s ystem in AWGN, decoding algorith m and blo ck size. B. Mutual In formation Based Link Quality Mod el for GFDM According to the method which is used to implement the GFDM tran sceiver in this stu dy [3] , the M data sub-symb ols are firstly converted to the freq uency domain by taking t he FFT. Since this process distributes the M sub-symbols on M frequency samples, there fore, the SI distribution is ass umed to be uniform over t he frequenc y samples. Based o n thi s assumption, the same steps can b e used for ca lculating MI in the GFDM case as ar e used for OFDM waveforms [10 ]. IV. SIMULATION PARAMETERS A. A WGN and Rayleigh channel mod els Here, a co mparison between the si mulation result s and th e PHY ab straction results in the case of AWGN and narro wband Rayleigh is shown. A cyclic prefix is used to prevent I SI. The parameters that are u sed in this case ar e listed in Table I. TABLE I: SIMULATI ON PARAMETERS Parameter Value No. of sub-carrier s 64 No. of sub-symbol s 9 Filter types Dirichlet, RC -0.1, RC -0. 9 Channel ty pes AWGN , Narrow band Rayleigh Channel coding Turbo code MCS modes QPSK-1/3, 16QA M-1/3 B. S ystem level parameters A compar ison bet ween the syste m-level re sults for LT E- A based on the GFDM waveform using the b it-level si mulator , which is alread y done by the authors as a part of a previous study [9], and the PHY abstraction m ethod is also presented . A 3GPP macro-cellular deplo yment w ith a frequency reuse factor of one is used. There are three sectors in each cell, and the cell radius, cell diameter and Inter- Site Distance (ISD) are R , 2 R a nd 3 R r espectively [12]. T he User Equipment (UEs) locations w ere randomly dis tributed at th e s treet level in t he cell and at a distance bet ween 50 - 100 0 m from the main Base Station ( BS ) . The 3D extended 3GP P-ITU channel m odel h as bee n u sed , where the e ffect of the ele vation is also taken into consideration [13]. Table II summarises t he system level par ameters that have been used in th is case. One thousand cha nnel s napshots have been produced for each link (betw een each UE and the main BS and each UE and each o ne of the other six first-tier inter fering BS s) to get statis tical ly relevant perfor mance results. T he GFDM para meters for this case are listed in Tab le III. TABLE II : SYSTEM-LEV EL PARAMETERS Parameter Value Channel mode l Ex tended 3D 3G PP -ITU (SI SO) PDSCH simulatio n models Bit level Simulator & PHY A bstract Bandwidth 20 MHz Carrier Fr equency 2.6 GHz Environment Urban-Macro Cell Radius 500 m BS transmit pow er 43 dBm No. of users per cell 900 BS antenna heig ht 25 m Antennas Measured patch BS & UE handse t as in [14] BS down tilt 10 º Minimum user se nsitivity -120 dBm Link direction Downlink (fr om BS to UE) Noise F igure 9 dB TABLE III : GFDM PARA M ETERS Parameter Value Sub-frame duratio n 1ms or 30,720 sa mples GFDM symbo l duration 66.67µs or 2048 sam ples Sub-symbol dur ation 4.17µs or 128 sam p les Subcarrier spac ing 240 kHz Sampling fre quency 30.72 MHz Total No . of sub-carrier ( K ) 128 No. of active subcarriers ( K on ) 75 No. of s ub -sy mbols per GF DM symbol ( M ) 15 No. of GF DM per sub-frame 15 Cyclic prefix le n gth 4.17µs or 128 sam p les Prototy pe filter Dirichlet Channel coding Turbo code MCS modes QPSK 1/3, 16 QA M1/2, 64QA M2/3 V. RESULTS A. Comparison using AWGN and Rayleigh channel models. Fig. 4 shows the BE R vers us SNR per formance for two Modulation & Coding Schemes (MC Ss) and three t ypes of filters for th e bit-level and PHY abstraction methods in an AWGN c hannel. As we ca n see , the P HY ab straction results closely match t he si mulation results . In this case, the channel frequency samples are equal to o ne (AWGN channel) , and the S NR per each frequency sa mple will be equal (no interference between the UEs is assumed) . T his means t hat t he mapping, averaging and quality mapping processes (look -up tab le) ar e working p roperly b ased on the frequency s ampling. Moreover, we see a difference depend ing on t he filter t ype used at ea ch MCS. Fo r example, the Dirichlet filter h as the best performance compared to the RC filters due to the absence of Inter- Carrier Interference (ICI). Additional ly , there is a de gradation in the RC filter ’ s perfor mance due to ICI . This degradation d epends on the roll-off fac tor of the filter , f or example, the difference is fairly negligible in the case o f a roll-off factor of 0. 1 when compared to the orthogonal fi lter, whil st it becomes ar ound 2 dB in the case of a ro ll-off factor of 0.9. Fig. 4: Per formance of the two approaches in A WGN . Fig. 5 illustrates the performance of GFDM in a narrowband Rayleigh chan nel. The channel frequenc y respon se, in t his case, is flat, this means that t he S NR p er frequency sa m ple in ea ch block will be equal. As can be seen, results sho w a very go od match between the two approaches. Further more, a di fference in performance d epending on the filter t ype is also seen. Fig. 5: Per formance Comparison in narrow band Rayleigh B . System-level a nalysis In order to represent realistic channel scenarios for system- level analysis , the 3 D-3GPP ITU channel model is used here. Both PER and t hroughput metrics ar e sho wn in the perfor mance evaluation since they are common metrics used in system-level studies. Fig . 6 illustrates the perfor m ance of the two appr oaches (the bit-level simulation and the P HY ab straction) , PER vers us the SN R at a certai n U E lo cation. As mentioned i n [1 0], the accuracy ter m, which is used to measure the acc uracy o f the PHY ab straction method, is d efined as the maximum S INR difference between the simul ated and the pred icted results at BLERs from 1 % to 10 %. Table IV lists the accuracy term for different MCSs. It can be seen that the ma ximum di fference is around 0. 6 dB in the 64QAM-2/3 MCS. The above results are for a unity ad justing factor (γ code ). Ho wever, we found that in this case, the best va lue of γ code depend s on t he channel ty pe , i .e. it is not the same value for different channel t ypes. TABLE IV : Accuracy for differe nt MCSs MCSs Accuracy 1~1 0% BLER QPSK-1/3 0.5 dB 16QAM-1/2 0.5 dB 64QAM-2/3 0.62 dB Fig. 6: Per formance Comparison for certain UE. Fig. 7 represents the C umulative Distributio n Functio n (CDF) of the PER for the UEs in i nterference -free (SNR) and 0 2 4 6 8 10 12 10 -4 10 -3 10 -2 10 -1 10 0 SNR(dB) BER RB IR-R C0.1-1 6 QA M RB IR-R C0.1-QPSK RB IR-R C0.9-1 6 QA M RB IR-R C0.9-QPSK RB IR-Dir i-16Q A M RB IR-Dir iQ PSK Sim-RC 0.1-16QAM Sim-RC 0.1-QPSK Sim-RC 0.9-16QAM Sim-RC 0.9-QPSK Sim-Diri -16QA M Sim-Diri -Q PSK Di fference due to ICI RC-0. 9 16QAM Di fference due to ICI RC-0. 9 QPSK 0 5 10 15 20 25 30 35 40 10 -4 10 -3 10 -2 10 -1 10 0 SNR(dB) BER RBI R-RC0 . 1 -16QA M RBI R-RC0 . 1 -QPS K RBI R-RC0 . 9 -16QA M RBI R-RC0 . 9 -QPS K RBI R-Di ri-16Q AM RBI R-Di ri-QPS K S im-RC0.1-16 QAM S im-RC0.9-16 QAM S im-D iri-16QA M S im-RC0.1-QPS K S im-RC0.9-QPS K S im-D iri-QPS K 0 5 10 15 20 25 30 35 40 10 -3 10 -2 10 -1 10 0 SNR(dB) PER Sim-GFDM-Q PSK-1/3 Sim-GFDM-16 QAM- 1/2 Sim-GFDM-64 QAM- 2/3 RBIR-G FDM-QPS K-1/3 RBIR-G FDM-16Q AM- 1/2 RBIR-G FDM-64Q AM- 2/3 interference present ( SINR) c ases in both methods. The effect of takin g the interference into cons ideration w hich leads to increase PER is clearly seen in this fig ure. Moreo ver, the resul ts of the two methods are close, and the maximum d ifference between them is around 4%. a: SNR case b: SI NR case Fig. 7: CDF of UEs PER in SNR and SIN R cases Fig. 8 sho ws the CD F fo r the throughput for bo th approaches in i nterference -free and inter ference-included cases; gi ven the use of adaptive MCS selection , i.e. for each user the best MCS mode is selected. It can be observed that the simulation and PHY abstracti on results are very s imilar. The throughput for both approaches is clearly much better i n the interference-free case. It can be seen that 6 5% of the UEs ha ve a throughput greater than 2 0 Mb ps in the inter ference-free case; while just 20% of the UE s achieve this rate when interference is consider ed in the simulator. However, the difference bet w een the t wo methods is less in th e interference-included case, which is the more realistic case. Additionally, t he maximum difference in t he t hroughput’s CDF values in bo th cas es, interference-free a nd included, d oes not exceed 4 %. Finally, t he total time req uired to r un the system-level simulation using the PHY abstraction on a PC was 1.59 hour s. The expected ti me required to r un the full bit -level si mulation on a PC -based is around 98, 000 hours (although the simulati on was actually e xecuted on the High- Perfor mance Computing platform at the University of B ristol) . This means that ar ound 62 ,000 times saving in ti me can be obtained. Fig. 8: CDF of UEs Throughput i n SNR and SI NR cases. VI. CONCLUSION This pap er has proposed an MI -based link q uality model for the GFDM wavefor m . As t he simulation resu lts sho w, the results of the bit-level simulato r and the PHY abstractio n model are very closel y m atched. Moreover, a system-level study in a realistic channel sce nario was p resented for GFDM. These results demonstrate that the MI -based link quality model (PHY abstract ion) can be used effectively in the implementation o f GFDM b ased system syste m-level studies and can lead to a significant reduction in t he computatio n al complexity. This will sa ve ti me and resources requir ed to measure a nd stud y GFDM performance a nd to a nalyse its suitability as a ne w waveform for 5G s ystems. A CKNOWL E DGMENTS Ghaith Al -Jubo ori would li ke to thank the Higher Co mmittee for Education Develop ment (HCED) in Iraq, Ministry of Oil and the University of Bag hdad for sponsoring his PhD st udies . REFERENCE [1] N. Michailow, M. Matthe, I. S. Gaspar, A. N. Calde villa, L. L . Mendes, A. Festag , et al. , "Ge neralized Fr equency Division Multiplexing for 5th Generation Cellular Networ ks," Communications, IEEE Transa ctions on, vol. 62, pp. 3045-3061, 2014. [2] L. L. Hanzo, Y. Akhtman, L. 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N ix, "Exploiting the e levation dimension of M IMO system for boo sting handset capacity," in 2015 IEEE I nternational Conf erence on Communication Workshop (ICCW) , 2015, pp. 1281-12 85. 0 0.2 0.4 0.6 0 .8 1 0 0.2 0.4 0.6 0.8 1 P ER Probability (PER < a bsc issa) RB IR-MCS-1(QPSK-1/3)) RB IR-MCS-4(16QA M- 1/2)) RB IR-MCS-7(64QA M- 2/3)) Sim.-MCS-1(QPSK-1/3)) Sim.-MCS-4(QPSK-1/3)) Sim-M CS-7( 64Q A M - 2/3)) 0 0 .2 0.4 0 .6 0.8 1 0 0.2 0.4 0.6 0.8 1 PER Probability (PER
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