On the Influence of Carrier Frequency Offset and Sampling Frequency Offset in MIMO-OFDM Systems for Future Digital TV

On the Influence of Carrier Frequency Offset and Sampling Frequency Offset in MIMO-OFDM Systems for Future Digit al TV Youssef Nasser member IEEE , Jean-François Hélard Senior member IEEE , Mat thieu 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) and sampling frequency offset (SFO) on the p erformance of different MIMO-OFDM schemes with high spectral efficiency for next generation of terrestrial digital TV. We analyze particularly orthogon al Alamouti scheme, and non- orthogonal (NO) scheme s like VBLAST, linear dispersion (LD) code and Golden code. This analysis gives a glob al view on the b est suitable MIMO-OFD M scheme with respect to CFO and SFO. We show that for high spectral efficiency , Alamouti is more sensitive to CFO and SFO. M oreover, w e show that all studied MIMO-OFDM schemes are sensitive to CFO when it is greater than 1% of inter-c arrier spacing. Their sensitivity due to SFO is le ss than that due to CFO. Keywords - MIMO-OFDM, Carrier Frequency Offset, Sampling Frequency Offset, Iterative rec eiver. I. INTRODUCTION Building a next generation dig ital TV which enables new services such a s video cont ribution for medi a companies, mobile TV di stribution , IPTV distri bution be comes a new challenge for broadcasters. Since its inaugu ration in 1993, digital video broadcast (DVB) project for terrestrial (DVB-T) tra nsmission ha s fully resp onded to the objectives of its designers [1]. I n 2006, D VB forum launches a st udy missi on to inaugurat e original a nd high defined services fo r digital TV. During this mi ssion, researches are asked t o investigate which technologies could be consi dered for a second gener ation terrestri al digital TV call ed DVB-T2. T he main concern of researchers is to support tran smission at higher data rates with minimum error probability. It is expected th at a multipl e input mult iple output (MIMO) system combined with orthogonal frequency d ivision multiplexing (OFDM) should take place for that ta rget. However, it is well known that OFDM sy stems suffer co nsiderably from carrier freque ncy offset (CF O) and sampling fre quency offset (SFO) between transm itter and receiver since CFO and SFO include inter ca rrier 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 co ntribution task force to the consideration engaged by the DVB forum . The main contributi on of this wor k is twofol d. First, a gene ralized framework is proposed for modelli ng the effect of CFO and SFO on MIMO-OFDM syste ms. Therefore, we analyze the robustness of different MIMO-O FDM schemes to CFO and SFO using a sub-optimal iterativ e receiver. II. SYSTEM MODEL We consider in this paper the downlink communication with with two transmit antennas ( M T =2) at the base station and two two receiving antennas ( M R =2) at the terminal. Figure 1 depic ts the transmitte r modules. After c hannel encoding of inf ormation bit s b k with a co nvolutio n encoder of co ding rate R , the enc oded bits are m apped according to a Gray quadra ture amplitude m odulation (QAM) schem e. The Gray m apper assig ns B bits for each of the complex constellation points. Using M T transmitting antennas, a sp ace time (ST) bloc k code (STBC) encoder assigns a ( M T , T ) matrix X =[ x i,t ] to each group of Q c omplex sym bols S =[ s 1 ,…, s Q ] from the input of ST module . The ST codi ng rate is then defi ned by L = Q / T . The output matrix is transmitted over M T antennas during T symbol durations i.e. each column is transmitted once during one symbol duration. The different elements x i,t ( i =1,…, M T ; t =1,…, T ) are functions of the input symbols s q ( q =1, …, Q ) depending on STBC enco der type. So ur ce E n c ode r Interl e a v e r M a ppe r ST BC Enc o der OF D M Mod. OF D M Mod. Ant. 1 Ant. M T k b S RF Uni t F TX RF Uni t F TX DA C DA C 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 DAC DAC Figure 1- Block diagram of the transmitter. The symbols at the output of STBC are fed to OFDM modulators of N subca rriers. The output at each OFDM modulator is a sequence of sa mples having a rate F e =1/ T e . After digital to analogue conversion (DAC), the signal is transposed to the transmitter carrier fre quency F TX by the RF unit, and transmitted through the channel. At the receiver (Figure 2), it is trans posed to base band with the receiver carrier frequency F RX and sampled at sam p ling frequency F s =1/ T s using analog ue to digi tal converter (ADC). In this work , we assume equal carri er frequencies F TX (respectively equal samplin g frequencies F e ) for all transmitti ng antennas and e qual carrier frequencies F RX (equal sampling frequencies F s ) for all receiving antennas. The CFO is therefore given by Δ F=F RX -F TX and the SFO is define d by 1/ Δ T =1/( T s -T e ). After OFDM demodulatio n, the signal re ceived by the j th antenna at each time sample t on the n th subcarrier could be written as: () ] , [ , ] [ ] , [ 1 ] , [ 1 0 1 0 , t n W p n p h t p X M t n Y j M m N p i j i T j T ∑∑ − = − = + = φ (1) where h j,i [ p ] is the frequency chan nel coefficient on the p th subcarrier assum ed constant during T OFDM sym bols, W j [ n ] is the additive white Gaussian noise (AWGN) with zero mean and N 0 /2 variance. φ ( n , p ) is a function of th e CFO and SF O, given by: ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − + Δ + Δ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − + Δ + Δ × = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − + Δ + Δ − N p n e n e T T FT N p n e n e T T FT N N e p n s s s s p n e n e T T FT N N N j s s ) ( ) ( sin ) ( ) ( sin 1 ) , ( ) ( ) ( 1 π π φ π with ⎩ ⎨ ⎧ − ≤ = elsewhere N n N n if n n e 2 / ) ( (2) PI C det e c to r Ant. 1 Ant. M R D e mappe r (L LR c o mp .) De In t e r l ea v e r SISO D e code r Inte rl e a v e r So f t G r ay M a pp er ) ( ˆ l S ) 1 ( ˆ − l S b ˆ Estimated bi ts RF U n i t F RX RF U n i t F RX AD C AD C PIC detector Ant. 1 Ant. M R Demapper (LLR comp.) DeInter leaver SISO Decoder Interleave r Soft Gray Mapp er ) ( ˆ l S ) 1 ( ˆ − l S b ˆ Estimated bi ts RF Unit F RX RF Unit F RX ADC ADC Figure 2- Iterative re ceiver structure wi th parallel interfer ence cancellation dete ctor. The signal received by the M R antennas on su bcarrier n are gathered in a matrix Y [ n ] of dime nsion ( M R , T ). It can be deduced from (1) by: ] [ ] [ ] [ ) , ( ] [ ] [ ) , ( ] [ 1 n W p X p H p n n X n H n n n Y N n p p + + = ∑ ≠ = φ φ ] [ ] [ ] [ ) , ( ] [ ] [ 1 n W p X p H p n n X n H N n p p eq + + = ∑ ≠ = φ (3) In (3), the first term repres ents useful signal, the second term indicates ICI and the last one is AWGN. φ ( n , n ) could be seen as phase rotation a nd ampli tude distortio n of the useful s ignal due t o CFO and SFO. The ICI c ould be seen as an additiv e noise to the useful sign al. It will be neglected in th e equalization pr ocess. H [ n ] is a ( M R , M T ) matrix whose com ponents are the channel coefficients h j,i [ n ]. X [ n ] is a ( M T , T ) matrix whose c omponent s are the transmitted sy mbols on the M T antennas duri ng T OFDM symbols on the n th subcarrier and W [ n ] is the AWGN. In order to describe t he transmission li nk with a general model independen tly of the ST scheme, we introdu ce the dispersion matrix F such that X = FS . Then, we separate the real and imaginary parts of X [ n ] and Y [ n ], and we stack them row-wise as done in [3]. We obtain the vector V [ n ] given by: ] [ ] [ ] [ ) , ( ] [ ] [ ] [ 1 n W p FS p G p n n FS n G n V N n p p + + = ∑ ≠ = φ ] [ ] [ ] [ ) , ( ] [ ] [ 1 n W p S p G p n n S n G N n p p eq eq + + = ∑ ≠ = φ with F n G n G eq ]. [ ] [ = (4) where G [ n ] is com posed of blocks G j,i ( j =1,…, M R ; i =1,…, M T ) each having (2 T ,2 T ) elem ents [3]. In this work, we use an iterative receiver for NO sc hemes. The estimated sym bols ) 1 ( ˆ S at the first iteration are obtained via minim u m mean squ are err or (MMSE) filtering as: ( ) ] [ ] [ ]. [ ] [ ] [ ˆ 1 2 ) 1 ( n V I n G n G n g n s w tr eq eq tr u u − + = σ (5) where ] [ n g tr u of dimensio n (1, 2 M R T ) is the u th column of G eq (1 ≤ u ≤ 2 Q ). ) 1 ( ˆ u s is the estimation of the real part ( u odd) or imaginary part ( u even) of s q (1 ≤ q ≤ Q ) at the first iteration. At each iteration, the demapper provides soft information about tran smitted coded bits. The soft information is represented by log likelihood ratios (LLR). After deinterleaving, it is fed to the outer decoder which computes the a post eriori extrinsic information of the coded bits. After interleaving, this information will be used by the soft mapper to produce est imation o f transmitted QAM symbols. From the second iteration ( l >1), we perform parallel interference cancellation (PIC ) followed by a simple inverse filtering: ) ( ) ( ) 1 ( , ) ( ˆ 1 ˆ ~ ˆ l u tr u u tr u l u l u u eq l u V g g g s S G Y V = − = − (6) The exchange of i nformat ion between det ector and decoder runs until the process con verges. III. SIMULATION RE SULTS In this section, we present a comparative study of four MIMO coding schemes: Alam outi, and NO schemes like VBLAST [4], Linear Di spersion (L D) code of Hassi bi [5] and Golden code [6] . We use a frequency no n selective channel per subca rrier with i ndependent Ga ussian distributed coefficients. The performance is computed in terms of bit error rate (B ER) versus E b /N 0 ratio for different values of CFO a nd SFO. C FO is expresse d as a function of i nter-carrie r spacing 1/ NT s and SFO is expressed as a fun ction of N and T s in such a way to guarantee that the SFO does not exceed one sample in one OFDM sym bol. The simul ations param eters are chosen from those of DVB -T. Figure 3 show s that the sensitivity of Alamouti scheme to CFO for a spectral efficiency η = 6[b/s/Hz] becomes noticeable for a relative CFO N Δ FT s ≥ 1% i.e. Δ F ≥ 0.01/ NT s which is equival ent to 5ppm for 2K m ode in DVB-T. Figure 4 shows that SFO introduc es degradatio n for a rel ative value N Δ T / T s ≥ 5%. Figure 5 gives the E b /N 0 required to reach a BER=10 -3 when a CFO occurs at the receiver. Figure 6 shows the effect of SFO at a BER=10 -4 i.e. it shows the E b /N 0 required to reach a BER=10 -4 . For CFO, we are limited to a measure at a BER=10 -3 since for Alamout i scheme, a BER floor i s obtained. Figu res 5 and 6 are given for a spectral efficiency η = 6[b/s/Hz]. The results for NO schemes are obtained after 3 it erations. These figures show again that all studied MIMO-OFD M schemes are sensitive to CFO for a relative value N Δ FT s ≥ 1% and to SFO for a relative value N Δ T / T s ≥ 5%. Moreover, we can conclude from these figures t hat the E b /N 0 loss due to CFO is greater than that due to SFO. Indeed, for Al amout i scheme, it is of 9dB f or CFO and a BER=10 -3 and, only 4dB for SFO and a BER=10 -4 . For NO scheme s, it is of 2 to 3dB for CFO and 1dB for SFO. Eventually, these figures show th at Alamouti scheme is more sensitive to CFO and SFO. This is d ue to the higher effect of orthogonality loss of Alamouti scheme for higher constellation size. As a conclusion, when it is based on CFO and SFO, the choice of a giv en MIMO-OF DM schem e for high spect ral efficiency allows us to su pport non-Alamouti schemes for the second generation of digital TV transmission. However, these scheme s require an iterative receiver which is more complex to implement. Moreover, other parameters shoul d be ta ken into account f or the best choice of a MIMO-OFDM schem e. Eventually, we note that additional analysi s, results and discussions wi ll be avai lable in t he final v ersion of t he paper. 6 8 10 12 14 16 18 20 22 24 10 -4 10 -3 10 -2 10 -1 10 0 E b /N 0 [d B] BER Effect of CFO, A lam outi s c heme, E ff = 6 NDFTs= 0 .00 1 NDFTs= 0 .01 NDFTs= 0 .05 Figure 3- Effect of CF O, Alamouti schem e, Spectral effi ciency η =6 [b/s/Hz] (256-QAM, R=3/4). 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", Interna tional Confe rence on Communi cations Vol. 10, pp.: 4577- 4582, June 2006, Is tanbul Turkey. [3] M. A. Khalighi, a nd J.-F. Helard, “Shoul d MIMO orthogonal space-time coding be preferred to non orthogonal coding with iterative detection? ” IEEE International Symposium on Signal Proc essing and Informat ion Technology , pp.340-3 45, Dec. 2005, Athens Greece. [4] G. J. Foschini, “Layered sp ace-time archit ecture for wireless comm unication in a fading envir onment when using multi-element antenn a,” Bell Labs Tech. J., vol. 1, no. 2, pp . 41–59, 1996. [5] B. Hassibi, and B. Hochwal d, “High-rate code s that are linear in space and ti me,” IEEE Trans. in Information Theory, vol. 48, no. 7 , pp. 1804–1824, July 2002. [6] J.-C. Belfiore, G. Rekaya, and E. Viterbo, “The golden code: a 2 × 2 full-rate space-time code with nonvanishing determinants,” IEEE Trans. in Information Theory, vol. 51, no. 4 , pp. 1432–1436, Apr. 2005 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 Ef fe c t of SFO , Ala mou ti sche me , Ef f= 6 NDT / Ts= 0. 001 NDT / Ts= 0. 01 NDT / Ts= 0. 05 NDT / Ts= 0. 1 NDT / Ts= 0. 2 Figure 4- Effect of SFO, Alamouti scheme. 0.001 0. 01 0.0 5 10 12 14 16 18 20 22 24 NDFTs E b /N 0 [d B] Required E b /N 0 t o obt ain a B E R= 1e-3, E ff= 6 Al amouti (256-QAM, R=3/ 4) LD (6 4-QAM, R=1/ 2) VB LAS T ( 64-QAM, R=1/2) Gol den (64-QA M, R= 1/ 2) Figure 5- Effect of CFO, Requi red Eb/N0 to ob tain a BER=10 -3 . 10 -3 10 -2 10 -1 10 11 12 13 14 15 16 17 18 19 20 NDT/Ts E b /N 0 [dB ] Required E b /N 0 to obt ain a B E R=1e-4, Eff= 6 Al amout i (256-QA M, R=3/ 4) LD (64-QAM, R= 1/2) VB LA ST (64-QAM, R=1/ 2) Golden (64-QA M, R= 1/2) Figure 6- Effect of SFO, Required Eb/N0 to obtain a BER=10 -4 .