A Study on the Physical Layer Performance of GFDM for High Throughput Wireless Communication

Transcription

1 217 25th European Sgnal Processng Conference (EUSIPCO) A Study on the Physcal Layer Performance of GFDM for Hgh Throughput Wreless Communcaton Ahmad Nmr, Dan Zhang, Ana-Belen Martnez and Gerhard Fettwes Vodafone Char Moble Communcaton Systems, Technsche Unverstät Dresden, Germany {frst name.last name}@fn.et.tu-dresden.de Abstract In ths paper, we nvestgate the physcal layer (PHY) performance of generalzed frequency dvson multplexng (GFDM) for hgh throughput wreless communcaton. For comparson purposes, orthogonal frequency dvson multplexng ()-based IEEE 82.11ac PHY s used as a benchmark. Harnessng the flexblty of GFDM, we propose a novel confguraton, beng complant to the IEEE 82.11ac PHY for data transmsson. Wth that confguraton, we can acheve not only lower outof-band (OOB) emsson performance but also hgher spectral effcency. By further dervng the correspondng recever, the overall GFDM-based PHY mplementaton s shown to attan better frame error rates (FERs) under varous modulaton and codng schemes (MCSs). Moreover, at the sgnal to nose ratos (SNRs) where the target FER of 1% s fulflled, GFDM can also provde hgher throughput than. I. INTRODUCTION In the last years, IEEE wreless local area network (WLAN) technologes have been evolvng contnuously. Due to ther flexblty, low cost and easy of deployment compared to wred networks, they become more and more popular for both prvate and busness use n the daly lfe. Therefore, they need to accommodate the ncreasng demand on data traffc for heterogeneous servces. The member IEEE 82.11ac [1] n the WLAN famly targets hgh throughputs. Orthogonal frequency dvson multplexng () [2] s the waveform adopted by the IEEE 82.11ac physcal layer (PHY). Gven ts hgh out-of-band (OOB) [3] emsson, the subcarrers close to the edges of each band have to be dsabled, thereby degradng the spectral effcency. Targetng hgher spectral effcency, ths paper ams at nvestgatng the waveform aspect of the PHY for hgh throughput communcaton. Generalzed frequency dvson multplexng (GFDM) [4] s a new waveform wth hgh spectral effcency and low OOB. Makng use of ts flexblty, t can be confgured to work n complance wth the IEEE 82.11ac. The lower OOB emsson of GFDM allows to reduce the number of guard subcarrers used n. These subcarrers can be used for data transmsson, ncreasng the throughput. Addtonally, GFDM can be confgured to work on a symbol bass, namely, multple data symbols per subcarrer. Usng one cyclc prefx (CP) to protect multple data symbols per subcarrer, we can save tme resources. In ths partcular case, two CP- symbols are combned nto one GFDM symbol. The tme resource correspondng to the saved CP s reused by nsertng a tranng sequence to track the common phase error (CPE) caused by the resdual carrer frequency offset (CFO). To our best knowledge, ths s the frst work n the lterature that nvestgates the waveform aspect of IEEE 82.11ac for an mproved PHY performance. The remnder of the paper s organzed as follows: Secton II provdes a revew of GFDM modulaton. In Secton III, we propose the confguraton and waveform desgn of GFDM for 82.11ac. The recever desgn s presented n Secton IV whle evaluaton and smulaton results are represented n Secton V. Fnally, we conclude the paper n Secton VI. II. GFDM OVERVIEW GFDM s a symbol-based multcarrer modulaton technque that employs crcular flterng [4]. The avalable bandwdth B s dvded nto K subcarrers wth subcarrer spacng Δf = B K. Each subcarrer conssts of equally spaced M subsymbols wth tme duraton T sub = 1 Δf = K B. Therefore, the duraton of one GFDM symbol s equal to T = MT sub = N B, N = MK. Each par of (k, m)-subcarrer and subsymbol can be used to transmt one data symbol d k,m modulated by a crcular pulse shape g k,m (t) gven by g k,m (t) =w T (t)g T (t mt sub )e j2πkδft, (1) where, g T s a perodc pulse shape of perod T, and w T (t) s rectangular wndow, where w T (t) =1, t [, T] and elsewhere. Let K x and M x be the sets of actve subcarrers and subsymbols, respectvely. The sgnal correspondng to the -th GFDM symbol s denoted as x (t) = d k,m, g k,m (t). (2) m M x k K x Then, the sgnal of a frame, whch contans I blocks, can be expressed as x(t) = I 1 x (t T ). GFDM commonly adopts = CP of duraton T cp τ max to tackle the mpact of fadng channel wth maxmum excess delay spread τ max. Then the wndow becomes w T +Tcp (t). The dscrete tme sgnal representaton can be derved from the crtcal samplng of the analogue sgnal wth frequency F s = B. Wth that, we get K, N and N cp samples per ISBN EURASIP

2 217 25th European Sgnal Processng Conference (EUSIPCO) subsymbol, symbol and CP, respectvely. The -th block can be represented n a vector x C N 1, such that, [x ] (n) = d k,m, g[< n mk > N ]e j2π k K n. (3) k K x m M x The block wth CP s represented by copng the last N cp samples to the begnnng of x. The matrx representaton can be wrtten as x = Ad, [d] (k+mk) = d k,m, (k, m) K x M x and elsewhere. A C N N s the modulaton matrx, [A] (n,k+mk) = g[< n mk > N ]e j2π k K n. The set of allocated resources s defned as N x = {n = k + mk, (k, m) K x M x }, (4) then, x = A (x) d (x), (5) where A (x) =[A] (:,Nx) and d(x) =[d] (Nx). III AC BASED GFDM CONFIGURATION In ths work, we consder GFDM as an alternatve waveform for the payload of the 82.11ac frame. The same preamble s used for tme and frequency synchronzaton and channel estmaton, Fg symbols GFDM 1 symbols symbols 4 /2 GFDM symbols Fg. 1: Proposed GFDM vs frame structure. For the confguraton [1], the subcarrer spacng s fxed to Δf = khz, whch corresponds to a useful symbol duraton T =3.2 μs. The CP duraton s one quarter of T,.e. T cp =.8 μs. Thus, the total symbol duraton equals T sym =4μs. By usng K ofdm subcarrers, the number of samples per symbol s equal to K ofdm + N cp. A set of subcarrers K d s used to transmt data symbols d (d), and another set K p s used to transmt plot symbols d (p). In the proposed GFDM confguraton, the GFDM symbol has no CP. Instead an approxmately fxed tal of length N tal = N cp s used to play the role of CP. In ths way, the tal of the ( 1)-th symbols s used as CP for the -th symbol, as llustrated n Fg. 2. However, the fxed tal needs to be added to the begnnng of the frame. Fxed tal CP-lke symbol Fxed tal 1 Fxed tal 2 Fg. 2: Fxed tal approach. By explotng the fact that N cp = K ofdm /4, we set K = K ofdm /4 to have a subsymbol duraton equal to N cp. Accordngly, the subcarrer spacng of GFDM s 4 tmes wder. Consderng a well-localzed prototype pulse shape wthn two subsymbols spacng,.e. g[n], K n N K 1, then for m =1, M 2, g k,m [n] =g[< n mk > N ], n= Fxed tal N K,,N 1. Ths means that the tal of K samples s null, as llustrated n Fg. 3, where a rased-cosne (RC) pulse shape wth roll-off factor α =.5 s used. As a result, Tal GFDM Tal GFDM 1 Tal Fg. 3: GFDM waveform desgn. The frst subsymbol (black curve) s a perodc plot sgnal. the set of subsymbols M d = {1,,M 2} can be used for data transmsson. Furthermore, the frst subsymbol can be exploted to transmt a determnstc perodc plot sgnal. Ths requres that the plot subsymbols are fxed durng the whole frame. Wth ths confguraton, the GFDM symbols have approxmately a fxed tal equal to the last K samples of the plot subsymbol. On the other hand, ths desgn helps n reducng the OOB [4]. Moreover, to ensure smooth transton of the plot sgnal, the frst K samples of the GFDM plot subsymbol are coped to the end of the frame. In order to guarantee the same throughput, t s requred that K M d K ofdm. Hence, we take M =1to keep the GFDM symbol as short as possble. Consequently, the GFDM symbol duraton s twce the one, as shown n Fg. 4. CP CP GFDM symbol symbol Fxed tal Fg. 4: GFDM vs symbol n 82.11ac. Param. GFDM Δf khz 125 khz T sym 4 μs (16 samples) 8 μs (32 samples) K M 1 1 K d { 58,, 58} { 15,, 14}/{} \{, ±1} K p K p {±53, ±25, ±11} { 14,, 13}/{} M d {} {1,, 8} M p {} {} N d N p 6 27 g T (t) 1 Perodc RC (α) TABLE I: 82.11ac confguraton for B =4MHz. In addton to the subsymbols sets M d, and M p = {}, K d and K p denote the subcarrers sets used for data and plot symbols, respectvely. As a result, the sets N d and N p are defned as n (4). Table I summarzes the detaled confguraton for B =4MHz. ISBN EURASIP

3 217 25th European Sgnal Processng Conference (EUSIPCO) The useful bt rate R depends on the payload sze N p and the modulaton and codng schemes (MCSs). Besdes the overhead of the preamble, another factor s the zero paddng, whch s requred to ft the coded payload n an nteger number of symbols. The overhead s larger for hgh MCSs, smaller payload and longer symbol, as llustrated n Fg. 5. It can also be shown that, for a gven MCS and suffcently bg N p, R becomes constant, R E[NP ] E[T f (N. Here, T p)] f (N p ) denotes the frame duraton. As lsted n Table. II, wthn the selected ranges of N p, the GFDM gan s hgher for lower MCSs, as well as when the payload s large Fg. 5: PHY nformaton bt rate vs payload sze. M R c N P range R G [Mpbs] GFDM QAM [Byte] GFDM gan 4 1/2 [5, 1] % 16 3/4 [1, 15] % 256 5/6 [15, 2] % TABLE II: MCSs settngs. IV. TRANSCEIVER DESIGN As depcted n Fg. 7, the transmtted sgnal of the payload s a superposton of data and plot sgnals, whch are allocated accordng to the sets N d and N p 1. Therefore, the -th block can be wrtten, followng (5) as x = A (d) d (d) + A (p) d (p). (6) The payload sgnal x[n] s multplexed wth a preamble, to generate the transmtted sgnal x t [n], Fg. 1. The sgnal s transmtted va a fadng channel wth equvalent mpulse response h[l] of length L taps. The overall CFO of transmtter and recever s denoted as f o. Addtve whte nose CN (,N ) s added at the recever. On the receved sgnal y t [n], tme and frequency synchronzaton s performed explotng the preamble tranng frames, Fg 6, the legacy short tranng feld (L-STF) [5], [6] and the legacy long tranng feld (L-LTF) [7]. Frst, the frame s detected, the CFO s estmated and compensated and the reference symbol tmng s found wth resdual tme offset (TO) denoted as T o. Afterwards, zero forcng channel estmaton [8] s performed usng L-LTF and 1 Ths sgnal model can be used to descrbe both GFDM block and symbol. Thereby, the later dervatons are applcable for both cases. L-STF L-LTF L-SIG VHT-SIGA VHT-STF Fg. 6: based preamble. VHT-LTF VHT-SIGB symbols the very hgh throughput (VHT)-LTF. Assumng T o and T o + L 1 N cp, the estmated channel s equvalent to ĥ[l T o ]. A resdual phase nose φ n remans after synchronzaton. Therefore, the payload receved sgnal can be expressed as y[n] =e jφn h[n T o ] x[n]+v[n], (7) where, v[n] s the addtve nose. The receved block y s generated as [y ] (n) = y[n+n cp +N]. Under the assumpton T o +L 1 N cp, the lnear convoluton becomes crcular [9]. However, n the case of the proposed fxed tal confguraton, f the tal of the symbols are not exactly equal, addtonal nterference appears. Therefore, y can be expressed as, y = Φ H c x + z (tal) + v. (8) where, Φ s a dagonal matrx generated from the phase nose, H c the crcular channel matrx, z (tal) the nterference due to tal msmatch and v addtve nose vectors. Takng N-DFT of (8) and replacng (6), we get ỹ = e jφ Λ (ˆ h) (Ã(d) ) d (d) + Ã(p) d (p) + z (tal) + z (ICI) + ṽ. } (9) Here, x = N-DFT(x) and Λ ( h) = dag{ h. The terms, z (ICI) and e jφ denote the nter-carrer-nterference (ICI) and CPE due to phase nose. As represented n [1], when φ n s small, the phase nose effect after DFT transformaton can be approxmated by phase rotaton, whch s equal [Ã(p) on all subcarrers, and addtonal ICI. Defnng Ã(p,d) = Ã (d) ], z = z (tal) we get + z (ICI) +ṽ, d(p) = e jφ d (p), and ] [ d(p) ỹ = Λ (ˆ h) Ã (p,d) d (d) d (d) = e jφ d (d) + z. (1) Assumng that z s domnated by the Gaussan nose vector ṽ, wth varance N, and the data symbols and plots are..d. wth varance E s, the lnear mnmum mean square error (LMMSE) [11] equalzaton matrx B can be expressed as ( B = Ã (p,d)h Λ (ˆ h)h Λ (ˆ h) Ã (p,d) + N ) 1 I E Ã(p,d)H Λ (ˆ h)h. s (11) The estmator of the rotated plots and data symbols can then be found as, [ ] [ ] ˆ d(p) B (p) ˆ d (d) = B (d) ỹ, (12) where B (p) C Np N and B (d) C N d N are the LMMSE flter matrces correspondng to the plot and data symbols, respectvely. Ths estmator can be mplemented wth low complexty, as proposed n [12]. By usng the plot knowledge, ISBN EURASIP

4 217 25th European Sgnal Processng Conference (EUSIPCO) Info bts Encoder QAM mapper Plots ( ) ( ) GFDM Modulator ( ) ( ) + [ ] MUX [ ] [ ] (, ) [ ] based Sync. and channel estmaton [ ] = + [ ] LMMSE equalzer and CPE estmaton Decoder Fg. 7: Baseband transcever block dagram. we can estmate the phase rotaton from the model, ˆ d (p) = e jφ d (p) + ɛ. (13) The addtve nose ɛ s characterzed by the mean vector [ˆ d(p) ] E [ɛ ]=E e jφ d (p) = b, (14) where, b s the bas ) of the LMMSE estmator, b = B (Λ (p) (ˆ h) Ã (p) I d (p) e jφ + B (p) Λ (ˆ h) Ã (d) d (d) e jφ. The covarance matrx of ɛ s gven by (ˆ d(p) ) R ɛ =cov = N B (p) B (p)h. (15) By usng the best lnear unbased estmator (BLUE) [11], we get (ˆ d(p) ) d (p)h Rɛ 1 b ˆθ = d (p)h Rɛ 1. (16) d (p) Afterwards, the estmate of CPE can be acheved by ˆφ = (ˆθ). Fnally, the estmated data symbols ˆd are rotated by ˆφ and fed to the decoder. Next, we evaluate the FER, and throughput wth respect to the sgnal to nose rato (SNR) defned by 2 ( ) E[ x t[n] SNR =1log 2 ] 1 N [db]. (17) Unform power allocaton s used among all actve subcarrers and subsymbols. The channel under nvestgaton follows the TGn Channel Model B [13], that has 9 Raylegh delay taps, Table III, and Doppler shft f d = 3 Hz. f o s a random varable wth unform dstrbuton n [ 233, 233] Khz. Ths range corresponds to an oscllator accuracy of 2 ppm at transmtter and recever, wth a maxmum carrer frequency of GHz. Synchronzaton, channel and CPE estmaton are performed as dscussed n Secton IV. N p s randomly selected wth unform dstrbuton on the ranges gven n Table II. Wthn the selected payload sze range, the throughput can be calculated as Th = R (1 FER) V. SIMULATION RESULTS We consder an 82.11ac based PHY n 4 MHz operaton mode, Table I. We am to compare ts performance wth our proposed GFDM based PHY. The PHY performance metrcs of nterest nclude: 1) power spectral densty (PSD), 2) frame error rate (FER) and 3) throughput. Frst, the OOB emsson s evaluated and demonstrated n Fg. 8 whch depcts the PSD of the data sgnal P x (d). As shown n the fgure, GFDM ( =.5) GFDM ( =.5) Fg. 9: FER vs SNR Fg. 8: PSD of data sgnal. GFDM acheves ultra low OOB emsson wth the proposed confguraton. Fg. 1: PHY throughput vs SNR. Fg. 9 and Fg. 1 llustrate the FER and the achevable throughput, respectvely. GFDM outperforms sgnfcantly at hgher SNRs and lower MCS, n terms of FER. 2 Note, here our SNR represents the rato between the power of the transmtted sgnal and nose. It s not equal to energy per symbol to nose rato. ISBN EURASIP

5 217 25th European Sgnal Processng Conference (EUSIPCO) Tap ndex Excess delay [ns] Power [db] TABLE III: TGn channel model B delay taps and gan. Doppler shft f d = 3 Hz. Ths allows GFDM to provde better throughput when the FER s above the threshold of 1%. Wth ths condton, the throughput gan of GFDM ranges between 2 5%. For nstance, wth MCS 16- QAM and code rate 3/4, the operatng SNR to delver FER below 1% s beyond 3dB, see Fg. 9. Accordngly, Fg. 1 shows that GFDM can delver hgher throughput than when SNR s larger than 3 db. It s worth notng that both fgures use the SNR as the channel qualty measure. For GFDM, each GFDM symbol carres more data symbols than the symbol. Therefore, for a gven SNR, the effectve energy per data symbol n the GFDM case s smaller than that n the case. For ths reason, the benefts of usng GFDM are expected to be enlarged when energy per symbol to nose rato s the channel qualty measure. In Fg. 11, we compare the effect of tal msmatch on the performance. For bgger α, RC becomes more localzed n tme. Therefore, the tal msmatch nterference decreases. As can be seen from the fgure, the effect appears only at hgher SNRs and MCS, where the nterference due to tal msmatch s domnant over the nose. Nevertheless, the error floor only takes place when the FER s already below 1% GFDM ( =.5) GFDM ( =.9) Fg. 11: FER acheved by GFDM wth dfferent roll-off factors. VI. CONCLUSION The specfcatons mposed by the new generatons of wreless communcatons drve the research of nnovatve solutons whch can cope wth the current unresolved ssues. In partcular, the hgh OOB emsson obtaned wth has to be reduced. GFDM appears as a flexble waveform that fulflls the requrements whch cannot satsfy. In ths paper, GFDM s confgured and evaluated under the IEEE 82.11ac framework. By means of smulaton, t s shown that GFDM presents a substantally lower OOB emsson than. Smulatons results ndcate that, for the low, medum and hgh MCSs consdered n ths work, GFDM can acheve up to 5% gan n terms of throughput. Whereas the frame error rate (FER) s smlar wth hgh MCS for both waveforms, GFDM acheves a consderable lower FER for the other two cases, especally at hgher SNRs. The acheved gan of GFDM comes at the cost of ncreased complexty compared to based PHY. Nevertheless, the well-localzaton property n tme and frequency of the pulse shapng allows effcent mplementaton of GFDM modem and advanced recever algorthms. ACKNOWLEDGMENT Ths work was partly funded by the German Federal Mnstry of Educaton and Research (BMBF) under grant 16KIS25 (project: prowlan). The authors would lke to thank the Horzon 22 project ICT ewine for partally fundng the works. We also thank the revewers for ther constructve comments and remarks. REFERENCES [1] Part 11: Wreless LAN Medum Access Control (MAC) and Physcal Layer (PHY) Specfcatons. Amendment 4: Enhancements for Very Hgh Throughput for Operaton n Bands below 6 GHz. IEEE Std 82.11ac-213, Dec 213. [2] J. A. Bngham, Multcarrer modulaton for data transmsson: An dea whose tme has come, IEEE Commun. Mag., vol. 28, no. 5, pp. 5 14, 199. [3] J. Van de Beek and F. Berggren, Out-of-band suppressson n, IEEE Commun. Lett., vol. 55, no. 9, pp , Sep 214. [4] N. Mchalow et al., Generalzed frequency dvson multplexng for 5th generaton cellular networks, IEEE Trans. Commun., vol. 62, no. 9, pp , Sep 214. [5] M. J. Canet et al., FPGA mplementaton of an based WLAN recever, Mcroprocess. Mcrosyst., vol. 36, no. 3, pp , May 212. [Onlne]. Avalable: [6] H. Song et al., Frequency-Offset Synchronzaton and Channel Estmaton for -Based Transmsson, IEEE Communcatons Letters, vol. 45, no. 4, pp , Mar 2. [7] A. B. Awoseyla et al., Robust tme-doman tmng and frequency synchronzaton for systems, IEEE Transactons on Consumer Electroncs, vol. 55, no. 2, pp , May 29. [8] V. D. Beek et al., On channel estmaton n systems, n Vehcular Technology Conference, 1995 IEEE 45th, vol. 2. IEEE, 1995, pp [9] J. Heskala and J. Terry Ph D, wreless LANs: A theoretcal and practcal gude. Sams, 21. [1] A. G. Armada, Understandng the effects of phase nose n orthogonal frequency dvson multplexng (), IEEE Trans. Broadcast., vol. 47, no. 2, pp , 21. [11] S. M. Kay, Statstcal sgnal processng, Estmaton Theory, vol. 1, [12] D. Zhang, M. Matthé, and G. Fettwes, A study on the lnk level performance of advanced multcarrer waveforms under MIMO wreless communcaton channels, accepted for publcaton n IEEE Trans. Wreless Commun. [13] G. Bret et al., IEEE P82.11 Wreless LANs. TGac Channel Model Addendum, Mar 29. ISBN EURASIP