Robustness of MIMO-OFDM Schemes for Future Digital TV to Carrier Frequency Offset

Robustness of MIMO-OFDM Schemes for Future Digit al TV to Carrier Frequency Offset Youssef Nasser, Jean-François Hélard, Matthieu Crussière Institute of Electronics and Telecommunications of Rennes, UMR CNRS 6164, Rennes, France 20 Avenue des Buttes des Coesmes, 35043 Rennes cedex, France Email : youssef.nasser@insa-rennes.fr Abstract- This paper investigates the impact of carrier frequency offset (CFO) on the performance of different MIMO-OFDM schemes with high spectral efficiency for next generati on of terrestrial digital TV. We show that all studied MIMO-OFDM schemes are sensitive to CFO when it is greater than 1% of inter- carrier spacing. We show also that the Alamouti scheme is the most sensitive MI MO scheme to CFO. Keywords- Modulation & Multiplexing (MIMO-OFDM), Signal Proce ssing for Tr ansmission (Carri er Frequency Offset). I. INTRODUCTION Digital video broadcast is the technology driving fixed, portable and mobile TV. Since its inauguratio n in 1993, digital vide o broadcast (DVB) project for terrestria l (DVB-T) tra nsmission has fully responde d to the objectives of i ts designers, d elivering wirel ess digital TV services in almost every con tinent [1]. The main concern of many researche rs is to support tra nsmission at hi gher data rates with minimum error probability. In 2006, the DVB forum launched a study mission t o investigate what technologies m ight be considered for a futu re DVB-T2 standard. It is expected that a multiple input multip le output (MIM O) system combined with ort hogonal frequency division multiple xing (OFDM) shou ld take place for that target. However, it is well known that OFDM system s suffer considerably from carrier frequency offset (CFO) between transmitter and receiver since CFO includes inter carrier interference (ICI) at the receiving side [2]. This work is carried out within the framework of the European project ‘ Broadcast for the 21 st Century ’ (B 21C) which constitutes a con tribution task force to the reflections engage d by the DVB for um. The main contributi on of this wor k is twofold. Fi rst, a generali zed framework is proposed fo r modelling the eff ect of CFO on MIMO-OFDM systems. Ther efore, we analyze the robustness of differe nt MIMO-OFDM schemes to CFO using a sub-optimal iterativ e receiver. This analysis should give a global view on the best s uitable MIMO- OFDM schem e with respect to CFO. The paper is organi sed as follows. Secti on 2 describes the transmission system model. In section 3, we present the different MIMO schem es considered in this paper. Secti on 4 gives some simulati on results. Conclusi ons are drawn in section 5. II. SYSTEM MODEL We consider in this p aper the downlink co mmunication with two transmit an tennas ( M T =2) at the base station and two receiving antennas ( M R =2) at the terminal. Fi gure 1 depicts the transmitter modules. Info rmation bits b k are first channel encoded with a convolutional enco der of coding rate R . The encode d, interleaved bits are then fed to a quadrature am plitude modulati on (QAM) m odule which assigns B bits for each of the com plex constellation points. The refore, each gr oup s =[ s 1 ,…, s Q ] of Q comple x symbols is encode d through a space time (ST) bl ock code (STBC) encoder and transmitted d uring T symbol durations according to the chosen ST sc he me. The ST coding rate is then defi ned by L = Q / T . With M T transmitting antennas, th e output of the ST encoder is an ( M T , T ) matrix X =[ x i,t ] where x i,t ( i =1,…, M T ; t =1,…, T ) is a function of the input symbols s q ( q =1,…, Q ) depending on STBC encoder type. The resulting symbols are then fe d to OFDM m odulator of N subcar riers. Sou r c e En c oder In te r l ea v e r Mapper ST B C En c oder OF D M Mod . OF D M Mod . Ant. 1 Ant. M T k b S RF Un it F TX RF Un it F TX Source Encoder Interleaver Mapper STBC Encoder OFDM Mod. OFDM Mod. Ant. 1 Ant. M T k b S RF Unit F TX RF Unit F TX Figure 1- Block diagram of the transmitter After D/A conversion, the signal is transposed to the transmitter carrier frequency F TX by the RF unit, and transmitted through the ch annel. At the receiver (Figur e 2), it is transposed to base band with the receiver carrier frequency F RX and sampled at sam p ling freque ncy F s =1/ T s . In this work, we assume equ al carrier frequencies F TX for all transmitting antennas and equal carrier frequencies F RX for all receiving antennas. The carrier frequency o ffset is therefore given by Δ F= F RX - F TX . After OFDM demodulatio n, the signal recei ved by the j th antenna at each time sample t on t he n th subcarrie r could be written as: () 1 1 , 00 1 [, ] [ , ] [ ] , [, ] T M N ji j i j mp T yn t xp t h p n p w n t M ϕ − − == =+ ∑∑ (1) where h j,i [ p ] is the frequency channel coeffi cient on the p th subcarrier assum ed constant during T OFDM sym bols, W j [ n ] is the additive white Gau ssian noise (AWGN) with zero mean and N 0 /2 variance. φ ( n , p ) is a function of th e CFO, given by : () ( ) ( ) () () N p n FT N p n FT N N e p n s s p n FT N N N j s / ) ( sin ) ( sin 1 ) , ( ) ( 1 − + Δ − + Δ = − + Δ − π π φ π (2) The signal received by the M R antennas on sub-carrier n are gathered in a matrix Y [ n ] of dim ension ( M R , T ). It can be deduced from (1) by: 1 [] (, ) [] [] (, ) [ ] [ ] [] N p pn nn n n n n p p p n ϕϕ = ≠ =+ + ∑ YH X H X W 1 [] [] (, ) [ ] [ ] [] N p pn nn n p p p n ϕ = ≠ =+ + ∑ eq HX H X W (3) In (3), the first term repres ents useful signal, the second term indicates the ICI and the last one is the AWGN. φ ( n , n ) can be seen as a phase rotation and an amplitude distortion o f the useful signal due to CF O. The ICI co uld be seen as an additiv e noise to the useful signal. It will be neglected in the equalization process. H [ n ] is a ( M R , M T ) matrix whose com ponents are the channel coeffi cients h j,i [ n ], X [ n ] is a ( M T , T ) matrix whos e components are t he transmitted symbols on the M T antennas during T OFD M symbols on the n th subcarrier and W [ n ] is the AWGN. PI C de t e c t o r Ant. 1 Ant. M R D e m a pper ( L LR comp .) De I n te r l e a v e r SI SO De c o d e r In te r l e a v er So f t Gray M a pper ) ( ˆ l S ) 1 ( ˆ − l S b ˆ Estimated bits RF U n it F RX RF U n it F RX PIC det ecto r Ant. 1 Ant. M R Demapper (LLR comp .) DeInterl eaver SISO Decoder Interl eaver Soft Gray Mapper ) ( ˆ l S ) 1 ( ˆ − l S b ˆ Estimated bits RF Unit F RX RF Unit F RX Figure 2- Iterative receive r structure with parallel interference cancellation detector Let us now describe t he transmissi on link with a ge neral model indepe ndently of the ST codi ng scheme. We separate the real and imaginary parts of the complex symbols input vector s { s q : q =1,…, Q }, of the outputs X of the double layer ST encoder as well as those of t he channel matrix H, and the received signal Y . Let s q,R and s q,I be the real and im aginary parts of s q . The main parameters of the double code are given by i ts dispersion matrices U q and V q correspondi ng (not equal) to the real and imaginary parts of X respectively. With these notations, X is given by: () ,, 1 Q qq q sj s ℜℑ = =+ ∑ qq XU V (4) We separate the real and imaginary parts of S , Y and X and stack them row- wise in vectors of dimensions ( 2 Q ,1), (2 M R T ,1) and ( 2 M T T ,1) respectively. W e obtain: 1, 1, , , 1, 1, , , , , ( 1,1 ) , ( 1,1 ) , ( 2 , ) , ( 2 , ) , , , ..., , , , ..., , , ..., , , , ..., , RR TT tr QQ tr T T MT MT tr MT MT ss s s yy y y y y xx x x ℜℑ ℜ ℑ ℜℑ ℜ ℑ ℜ ℑ ℜℑ ℜ ℑ ⎡⎤ = ⎣⎦ ⎡ ⎤ = ⎣ ⎦ ⎡⎤ = ⎣⎦ s y x (5) where tr holds for matrix transpose. Since, we use linear ST c oding, the vector x can be written as: . = xF s (6) where F has the dimensions (2 M T T , 2 Q ) and is obtained through the disper sion matrices of the real and imaginary parts of X . We obtain the vector y [ n ] given by : 1 [] [] [] (, ) [ ] [ ] [] N p pn nn n n p p p n ϕ = ≠ =+ + ∑ yG F s G F sw 1 [] [] (, ) [ ] [ ] [] N p pn nn n p pp n ϕ = ≠ =+ + ∑ eq eq Gs G s w with [] [] . nn = eq GG F (7) where G [ n ] is composed of blocks G j,i ( j =1,…, M R ; i =1,…, M T ) each having (2 T ,2 T ) elem ents [3] given by: () () () () () () () () () () () () () T T j i j i j i j i j i j i j i j i j i j i j i j i j i h h h h h h h h h h h h G 2 , 2 , , , , , , , , , , , , , , , , , , , , , , , , , 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ − − − = ℜ ℑ ℑ ℜ ℜ ℑ ℑ ℜ ℜ ℑ ℑ ℜ L L O L O L L L L L (8) In this work, we use an iterative receiver for non- orthogonal (N O) schemes whe re the ST detector and channel decoder exchange ex trinsic information in an iterative way until the algori thm converges. The iterative detection and deco ding expl oits the error correction capabilities of the chann el code to provide improved performance.The estim ated symbols (1) ˆ s at the first iteration are obtained via minimum mean square error (MMSE) filtering as: ( ) 1 (1) 2 ˆ [] [] [] . [] [] uw sn n n n n σ − =+ tr tr ue q e q g GG I y (9) where [] n tr u g of dim ension (1, 2 M R T ) is the u th colum n of G eq (1 ≤ u ≤ 2 Q ). ) 1 ( ˆ u s is the estimation of the real p art ( u odd) or imaginary p art ( u even) of s q (1 ≤ q ≤ Q ) at the first iteration. At each iteration, the demapper provide s soft information about transmitted coded b its. The soft information is represented by log likelihood ratios (LLR). After de-interleaving, it is fed to the outer decod er which computes the ‘ a posteriori’ extrinsic information of th e coded bits. After interleaving, this extrinsic info rmation will be used by the soft mapp er to produce estimation of transmitted QAM symbols. From the second iteration ( l >1), we perform parallel interference cancellation (PIC ) followed by a simple inverse filtering: () ( 1 ) () () ˆ [] [] [] [] 1 ˆˆ [] [] [] [] [] ll u ll u nn n n sn n n nn − =− = eq, u tr u tr uu yy G s gy gg % (10) where [] n eq,u G of dimensio n (2 M R T , 2 Q -1) is the matrix [] n eq G with its u th column rem oved, (1 ) l u s − % of dim ension (2 Q -1, 1) is the vector (1 ) [] l sn − % estimated at the previou s iteration by the soft mapper with its u th entry remov ed. The exchange of inform ation between detector and decoder runs until the process con verges. III. CONSI DERED ST CODING SC HEMES First, we consider the simplest ortho gonal ST coding scheme proposed by Alamouti [ 4] as a reference of comparison. Since M T =2, we have Q = T =2 and the ST coding rate L =1 . This code is given by the matrix: ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − = * 1 * 2 2 1 s s s s X (11) For non-orthogonal schemes, we consider in th is work the well-known multiplex ing scheme i.e. the V-BLAST [5]. VBLAST is designed to maximize the rate by transmitting symbols sequ entially on different a ntennas. Its coding scheme is gi ven for T =1, Q =2 and L =2 b y: [] tr s s X 2 1 = (12) We also consi der the LD code pro posed by Hassibi [6] for which we have Q =4, T =2 an d L =2. It is d esigned to maximize the mutual information between transmitter and receiver. It is defined by: ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − + − + = 3 1 4 2 4 2 3 1 2 1 s s s s s s s s X (13) Finally, we consider the optimi zed Golden code [7] denoted herea fter by GC . The Golde n code is designed to maximize the rate such that the diversity gain is preserved for an increased signal constellation size. It is defined for Q =4, T =2 and L =2 by: ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + + + + = ) ( ) ( ) ( ) ( 5 1 2 1 4 3 4 3 2 1 s s s s s s s s X θ β θ β μ θ β θ β (14) where 2 5 1 + = θ , θ θ − = 1 , ) 1 ( 1 θ β − + = j , ) 1 ( 1 θ β − + = j , j = μ and 1 − = j . IV. SIMULATION RESULTS In this section, we present a comparative study of the four MIMO codin g schemes.. T he perform ance comparison is made for a frequency non s elective channel with independent Gaussian distri buted coeffi cients. It is computed in terms of bit error rate (BER ) versus Eb/N0 ratio for di fferent val ues of CFO expressed in terms of inter-carrier spacing 1/ NT s . The simulations parameters are chosen fr om those of DVB-T as sho wn in Table 1. Table 1- Simulations Parameters Number of s ubcarriers 2K mode Rate R c of convolutional code 1/2, 3/4 Polynomial code genera tor (133 ,171) o Channel estimation perfect Constellation 64-QAM, 256-QAM Spectral Efficiency 6 [b/s/Hz] Figure 3 shows that the sens itivity of Alamouti sche me to CFO for a spectral efficiency η = 6 [b/s/Hz] becomes noticeable for a CFO such that N Δ FT s ≥ 1% i.e. Δ F ≥ 0.01/ NT s (equival ent to 5ppm ). Figure 4 (respecti vely Figure 5) gives t he Eb/N0 requi red to reach a BER=10 -4 (BER=10 -3 ) for a spectral efficiency η = 2 [b/s/Hz] ( η = 6 [b/s/Hz]) and the different MIMO sc hemes. These fi gures show that for low spectral efficiency, Alamouti scheme outperform s other schemes. However, Gol den code offers the best performance for high spectral e fficiency. 6 8 10 12 14 16 18 20 22 24 10 -4 10 -3 10 -2 10 -1 10 0 E b /N 0 [dB] BER Effect of CFO, A lamout i s c hem e, E ff= 6 ND FT s = 0.001 NDFTs= 0. 01 NDFTs= 0. 05 Figure 3- Effec t of CFO, Alamouti schem e, Spectral efficiency η =6 [b/s/Hz] (256-QAM, R=3/4). Moreover, Fi gure 5 shows t hat Alamouti scheme presents the worst results when η increases. Indeed, the Eb/N0 required to obtain a BER=10 -3 is abou t 22.8dB for N Δ FT s =0.05 (equi valent to 25ppm onl y for N=20 48) where it is only about 13.7dB for N Δ FT s =0.01. This is due to the orthogonality loss of Alamouti scheme for higher constellation size. As a conclusion, the choice of a given MIMO-OFDM scheme is not confident for all spectral efficiencies when it is based on CFO. That is, for t h e second gene ration of digital TV trans mission, other parameters sh ould be take n into account for the best choice of a MIMO-OFDM schem e. 0.001 0.01 0.1 0.2 2 3 4 5 6 7 8 9 10 11 12 NDFTs E b /N 0 [d B] Required E b /N 0 to obt ain a B E R=1e-4, Eff= 2 Al amout i (16-QAM , R=1/ 2) LD (Q PSK, R=1 /2) VBLAST (QPSK, R =1/2 ) Go lde n ( QPSK, R =1/2) Figure 4- Re quired Eb/N 0 to obtain a BER=10- 4, Spectral efficiency η =2 [b/s/Hz], results obtained after 3 iterations for LD, VBLA ST and Golden co de. 0.001 0.01 0.05 10 12 14 16 18 20 22 24 NDF Ts E b /N 0 [dB] Requi red E b /N 0 to ob tai n a BER =1e -3 , Ef f = 6 Al amout i (256-QAM, R= 3/4) LD (64-QA M , R= 1/ 2) VB LA ST (64- Q AM , R=1/ 2) Gol den (64-QA M , R= 1/ 2) Figure 5- Re quired Eb/N 0 to obtain a BER=10- 4, Spectral efficiency η =6 [b/s/Hz], results obtained after 3 iterations for LD, VBLA ST and Golden co de. V. CONCLUSION In this paper, we have invest igated the effect of CFO on different MIMO-OF DM schemes for the secon d generation o f terrestrial digital vi deo broad casting (DVB - T2). We showed that, for hi gh spectral efficiency, t h e Alamouti scheme is more sensitive to CFO when compared wit h other NO schem es and the Golden code presents the best results. ACKNOWLEDGME NTS The authors would like to thank the European CELTIC project “B21C” for its support of th is work. REFERENCES [1] http://www.dvb .org [2] Y. Nasser, M. des Noes, L. Ros, and G. Jourdain, "Sensitivity of OFDM-CDMA to carrier frequency offset", International Co nference on Communications ICC 2006, June 2006 , Istanbul Turkey [3] M. A. Khalighi, a nd J.-F. Helard, “Shoul d MIMO orthogonal space-time codi ng be preferred to non orthogonal coding with iterative detection?” IEEE International Symposium on Signal Proc essing and Informat ion Technology, pp.3 40-345, Dec. 20 05, Athens Greece. [4] S.M. 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