2D inear Precoded OFDM for future mobile Digital Video Broadcasting Oudomsack Pierre Pasquero, Matthieu Crussière, Youssef, Joseh Nasser, Jean-François Hélard To cite this version: Oudomsack Pierre Pasquero, Matthieu Crussière, Youssef, Joseh Nasser, Jean-François Hélard. 2D inear Precoded OFDM for future mobile Digital Video Broadcasting. Signal Processing Advances in Wireless Communications, Jul 2008, Recife, Brazil.., 2008. <hal-00325766> HA Id: hal-00325766 htts://hal.archives-ouvertes.fr/hal-00325766 Submitted on 30 Se 2008 HA is a multi-discilinary oen access archive for the deosit and dissemination of scientific research documents, whether they are ublished or not. The documents may come from teaching and research institutions in France or abroad, or from ublic or rivate research centers. archive ouverte luridiscilinaire HA, est destinée au déôt et à la diffusion de documents scientifiques de niveau recherche, ubliés ou non, émanant des établissements d enseignement et de recherche français ou étrangers, des laboratoires ublics ou rivés.
2D INEAR PRECODED OFDM FOR FUTURE MOBIE DIGITA VIDEO BROADCASTING Oudomsack Pierre Pasquero, Matthieu Crussière, Youssef Nasser, Jean-François Hélard Institute of Electronics and Telecommunications in Rennes INSA Rennes, 20, avenue des Buttes de Coesmes, 35043 Rennes, France E-mail: oudomsack.asquero@ens.insa-rennes.fr, first name. last name}@insa-rennes.fr ABSTRACT In this aer, we roose a novel channel estimation technique based on 2D sread ilots. The merits of this technique are its simlicity, its flexibility regarding the transmission scenarios, and the sectral efficiency gain obtained comared to the classical ilot based estimation schemes used in DVB standards. We derive the analytical exression of the mean square error of the estimator and show it is a function of the autocorrelation of the channel in both time and frequency domains. The erformance evaluated over a realistic channel model shows the efficiency of this technique which turns out to be a romising channel estimation for the future mobile video broadcasting systems.. INTRODUCTION Orthogonal frequency division multilexing (OFDM) has been widely adoted in most of the digital video broadcasting standards as DVB-T [], DMB-T, ISDB-T. This success is due to its robustness to frequency selective fading and to the simlicity of the equalization function of the receiver. Indeed, by imlementing inverse fast Fourier transform (IFFT) at the transmitter and FFT at the receiver, OFDM slits the single channel into multile, arallel intersymbol interference (ISI) free subchannels. Therefore, each subchannel, also called subcarrier, can be easily equalized by only one coefficient. To equalize the signal, the receiver needs to estimate the channel frequency resonse for each subcarrier. In the DVB- T standard, some subcarriers are used as ilots and interolating filtering techniques are alied to obtain the channel resonse for any subcarrier. Nevertheless, these ilots reduce the sectral efficiency of the system. To limit this roblem, we roose to add a two dimensions (2D) linear recoding (P) function before the OFDM modulation. The basic idea is to dedicate one of the recoding sequences to transmit a so-called sread ilot [2] that will be used for the channel estimation. The merits of this channel estimation technique are not only due to the resource conservation ossibility, but also to the flexibility offered by the adjustable time and frequency sreading lengths. In addition, note that the recoding comonent can be exloited to reduce the eak-to-average ratio (PAPR) of the OFDM system [3], or to erform the frequency synchronisation. The contribution of this article is twofold. First, a general framework is roosed to describe the 2D recoding technique used for channel estimation. Secondly, exloiting some roerties of random matrix and free robability theories [4] [5], an analytical study of the roosed estimation method is resented. The article is organized as follows. In section 2, we resent the rinciles of 2D P OFDM, and detail the channel estimation technique using the sread ilots. In section 3, we analyse the theoretical erformance of this channel estimation by develoing the analytical exression of its mean square error (MSE). Then, simulation results in terms of MSE and bit error rate (BER) are resented and discussed in section 4. Concluding remarks are given in section 5. 2.. 2D P OFDM 2. SYSTEM DESCRIPTION Fig. exhibits the roosed 2D P OFDM system exloiting the sread ilot channel estimation technique. First of all, data bits are encoded, interleaved and converted to comlex symbols x [i]. These data symbols are assumed to have zero mean and unit variance. They are interleaved before being recoded by a Walsh-Hadamard (WH) sequence c i of chis, with 0 i = 2 n and n N. The chis obtained are maed over a subset of = t. f subcarriers, with t and f the time and frequency sreading factors resectively. The first t chis are allocated in the time direction. The next blocks of t chis are allocated identically on adjacent subcarriers as illustrated in Fig. 2. Therefore, the 2D chi maing follows a zigzag in time. et us define a frame as a set of t adjacent OFDM symbols, and a sub-band as a set of f adjacent subcarriers. In order to distinguish the different subsets of subcarriers, we define m and s the indexes referring to the frame and the sub-band resectively, with 0 s S. Given these notations, each chi y [n, q] reresents the comlex symbol transmitted on the nth subcarrier during the qth OFDM symbol of the subset of subcarriers [m, s], with 0 n f and 0 q t. Hence, the transmitted
Fig.. 2D P OFDM transmitter and receiver based on sread ilot channel estimation technique Fig. 2. 2D chi maing scheme signal on a subset of subcarriers [m, s] writes: Y = CPx () where x = [x [0]... x [i]... x [ ]] T is the [ ] comlex symbol vector, P = diag P 0... P i... } P is a [ ] diagonal matrix where P i is the ower assigned to symbol x [i], and C = [c 0... c i... c ] is the WH recoding matrix whose ith column corresonds to ith recoding sequence c i = [c i [0,0]... c i [n, q]... c i[ f, t ]] T. We assume normalized recoding sequences, i.e. c i [n, q] = ±. Since the 2D chi maing alied follows a zigzag in time, c i [n, q] is the (n t + q)th chi of the ith recoding sequence c i. 2.2. Sread ilot channel estimation rinciles Insired by ilot embedded techniques [6], channel estimation based on sread ilots consists of transmitting low level ilot-sequences concurrently with the data. In order to reduce the cross-interferences between ilots and data, the idea is to select a ilot sequence which is orthogonal with the data sequences. This is obtained by allocating one of the WH orthogonal sequences c to the ilots on every subset of subcarriers. et H be the [ ] diagonal matrix of the channel coefficients associated to a given subset of subcarriers [m, s]. After OFDM demodulation and 2D chi de-maing, the received signal can be exressed as: Z = H Y + w (2) where w = [w [0, 0]...w [n, q]... w [ f, t ]] T is the additive white Gaussian noise (AWGN) vector having zero mean and variance σw 2 = E w [n, q] 2}. At the recetion, the de-recoding function is rocessed before equalization. Therefore, an average channel coefficient Ĥ avg [m, s] is estimated by subset of subcarriers. It is obtained by de-recoding the signal received Z by the ilot recoding sequence c H and then dividing by the ilot symbol x () = P x [] known by the receiver: Ĥ avg [m, s] = x () c H Z = c H x () [H CPx + w ] (3) et us define C u = [c 0... c i... c ] the [ ( )] data recoding matrix, P u = diag P 0... P i... } P the [( ) ( )] diagonal matrix which entries are the owers assigned to the data symbols, and x (u) = [x [0]... x [i ]... x [ ]] T the [( ) ] data symbols vector. Given these notations, (3) can be rewritten as: Ĥ avg [m, s] = x () = [ c H H c x () + c H H C up ux (u) + c H w ] tr H} + x () [ c H H C up ux (u) + c H w ] = H avg [m, s] + SI[m, s] + w (4) The first term H avg [m, s] is the average channel resonse globally exerienced by the subset of subcarriers [m, s]. The second term reresents the self-interference (SI). It results from the loss of orthogonality between the recoding sequences caused by the variance of the channel coefficients over the subset of subcarriers. In the sequel, we roose to analyse its variance. 3. THEORETICA PERFORMANCE OF THE ESTIMATOR In order to analyse the theoretical erformance of the roosed estimator, we evaluate its MSE under the assumtion
of a wide-sense stationary uncorrelated scattering (WSSUS) channel. MSE [m, s] = E Ĥ avg [m, s] H avg [m, s] 2} = E SI[m, s] 2} + E w 2} (5) First, let us comute the SI variance: E SI [m, s] 2} = } E c H P H C u P u CH u HH c where P u = P up H u = diag P 0...P i... P }. Actually, (6) cannot be analyzed ractically due to its comlexity. Alying some roerties of random matrix and free robability theories [4] [5] which is stated in Aendix, a new SI variance formula can be derived: E SI [m, s] 2} = E c H P H ( I c c H ) } H H c = E c H H H H P c c H H c c H H H } c = E P tr ( H H H ) }} 2 tr (H )tr ( H H ) }} A B (7) The exectation of A is the average ower of the channel coefficients on the subset of subcarriers [m, s]. Assuming that the channel coefficients are normalized, its value is one: E tr ( H H H )} = f t (6) E H [n, q] 2} = (8) The exectation of B is a function of the autocorrelation of the channel R HH ( n, q) whose exression is develoed in Aendix. Indeed, it can be written: ( )} E tr (H ) tr H H = f t f t n =0 q =0 R HH ( n, q) (9) where n = n n and q = q q. Note that the autocorrelation function of the channel does not deend on the subset of subcarriers since the channel is WSSUS. By combining (8) and (9), the SI variance exression (7) can be exressed as: E SI 2} = f 2 P t f t n =0 q =0 R HH ( n, q) (0) Now, let us comute the noise variance: E w 2} = E c H P w w H c } = P σ 2 w () Finally, by combining the exressions of the SI variance (0) and the noise variance (), the MSE (5) writes: MSE = f t f t R P 2 HH ( n, q) + σw 2 n =0 q =0 (2) The analytical exression of the MSE of our estimator deends on the ilot ower, the autocorrelation function of the channel and the noise variance. The autocorrelation of the channel (8) is a function of both the coherence bandwidth and the coherence time. We can then exect that the roosed estimator will be all the more efficient than the channel coefficients will be highly correlated within each subset of subcarriers. One can actually check that if the channel is flat over a subset of subcarriers, then the SI (0) is null. Therefore, it is imortant to otimize the time and frequency sreading lengths, t and f, according to the transmission scenario. 4. SIMUATION RESUTS In this section, we analyse the erformance of the roosed 2D P OFDM system comared to the DVB-T standard under the COST207 Tyical Urban 6 aths (TU6) channel model deicted in Table with different mobile seeds. We define the arameter β as the roduct between the maximum Doler frequency f D and the total OFDM symbol duration T OFDM. Table 2 gives the simulation arameters and the useful bit rates of the DVB-T system and the roosed system. In the roosed system, only one sread ilot symbol is used over 6, whereas the DVB-T system uses one ilot subcarrier over twelve. Therefore, a gain in terms of sectral efficiency and useful bit rates are obtained comared to the DVB-T system. These gains are all the higher than the sreading factor is high. Nevertheless, an increase of the sreading length roduces a higher SI value. Consequently, a trade-off has to be made between the gain in term of sectral efficiency and the erformance of the channel estimation. Fig. 3 deicts the estimator erformance in term of MSE for QPSK data symbols, different mobile seeds and different sreading factors. The curves reresent the MSE obtained with the analytical exression (2), and the markers those obtained by simulation. We note that the MSE measured by simulation are really closed to those redicted with the MSE formula. This validates the analytical develoment made in section 3. We note that beyond a given ratio of the energy er bit to the noise sectral density ( Eb No ), the MSE reaches a floor which is easily interreted as being due to the SI (5).
Table. Profile of TU6 channel Ta Ta2 Ta3 Ta4 Ta5 Ta6 unit Delay 0 0.2 0.5.6 2.3 5 µs Power -3 0-5 -6-8 -0 db 5 Analytical ; Seed 20 km/h ; P = 7 ; t = 8 and f = 8 Simulation ; Seed 20 km/h ; P = 7 ; t = 8 and f = 8 Analytical ; Seed 20 km/h ; P = 5 ; t = 4 and f = 8 Simulation ; Seed 20 km/h ; P = 5 ; t = 4 and f = 8 Table 2. Simulation Parameters and Useful Bit Rates Bandwidth 8 MHz FFT size (N FFT) 2048 samles Guard Interval size 52 samles (64 µs) OFDM symbol duration (T OFDM) 280 µs Rate of convolutional code /2 using (33, 7) o Constellations QPSK and 6QAM Carrier frequency 500 MHz Mobile Seeds 20 km/h and 20 km/h Maximum Doler frequencies (f D) 9.3 Hz and 55.6 Hz β = f D T OFDM 0.003 and 0.08 Useful bit rates of DVB-T system 4.98 Mbits/s for QPSK 9.95 Mbits/s for 6QAM Useful bit rates of 2D P OFDM 5.33 Mbits/s for = 6 for QPSK 5.5 Mbits/s for = 32 5.60 Mbits/s for = 64 Useful bit rates of 2D P OFDM 0.66 Mbits/s for = 6 for 6QAM.02 Mbits/s for = 32.20 Mbits/s for = 64 Fig. 4 and Fig. 5 give the BER measured at the outut of the Viterbi decoder for a mobile seed of 20 km/h and 20 km/h resectively. Note that the value of the ilot ower P has been otimized through simulation search in order to obtain the lowest BER for a given signal to noise ratio (SNR). The erformance of the DVB-T system is given with erfect channel estimation, taking into account the ower loss due to the amount of energy sent for the ilot subcarriers. It aears in Fig. 4, for low-seed scenario, that the system erformance is similar to that of the DVB-T system with erfect channel estimation. This is due to the ower loss due to the ilot which is lower with the roosed system. In Fig. 5, for high-seed scenario and QPSK, by choosing the sreading lengths offering the best erformance, there is a loss of less than db for a BER = 0 4, comaring to erfect channel estimation case. For 6QAM, the loss is less than 2.5 db which is really satisfying given that β = 0.08, corresonding to a mobile seed of 20 km/h. 5. CONCUSION In this aer, we roose a novel and very simle channel estimation for DVB-T. This technique, referred to as sread ilot channel estimation, allows to reduce the overhead art MSE (db) 0 5 20 25 0 2 4 6 8 0 2 4 6 8 20 22 24 26 28 30 Eb/No (db) Fig. 3. MSE erformance obtained with the analytical exression and by simulation ; QPSK ; Seeds: 20 km/h and 20 km/h ; β = 0.003 and 0.08 dedicated to channel estimation. An analytical exression of its MSE, which is a function of the autocorrelation of the channel, is given. It allows to highlight and understand that the choice of the sreading factors has to be made according to the channel characteristics. More generally, this estimation aroach rovides a good flexibility since it can be otimized for different mobility scenarios by choosing adequate time and frequency sreading factors. This work was suorted by the Euroean roject CETIC B2C ( Broadcast for the 2st Century ). APPENDIX In this section, a roerty from the random matrix and free robability theories is defined for the comutation of the SI variance (6). Furthermore, the comutation of the autocorrelation function of the channel R HH is carried out. Random matrix and free robability theories roerty et C be a Haar distributed unitary matrix [5] of size [ ]. C = (c, C u ) can be decomosed into a vector c of size [ ] and a matrix C u of size [ ( )]. Given these assumtions, it is roven in [7] that: C u P u CH ( u αp u I c c H ) (3) where α = is the system load and P u = is the ower of the interfering users. Autocorrelation function of the channel The autocorrelation function of the channel writes: R HH ( n, q) = E H [n, q]h [n n, q q] } (4)
0 0 0 QPSK ; DVB T system with erfect. chan. est. QPSK ; Sread Pilot f=4 and t=6 QPSK ; Sread Pilot f=8 and t=8 6QAM ; DVB T system with erfect. chan. est. 6QAM ; Sread Pilot f=4 and t=6 6QAM ; Sread Pilot f=8 and t=8 0 0 0 QPSK ; DVB T system with erfect. chan. est. QPSK ; Sread Pilot: f=8 and t=4 ; P=5 QPSK ; Sread Pilot: f=8 and t=8 ; P=7 QPSK ; Sread Pilot: f=6 and t=4 ; P=7 6QAM ; DVB T system with erfect. chan. est. 6QAM ; Sread Pilot: f=4 and t=4 ; P=3 6QAM ; Sread Pilot: f=8 and t=2 ; P=3 0 2 0 2 BER BER 0 3 0 3 0 4 0 4 3 4 5 6 7 8 9 0 2 3 4 Eb/No (db) Fig. 4. Performance comarison between the DVB-T system with erfect channel estimation and the roosed 2D P OFDM ; Seed: 20 km/h ; β = 0.003 ; = 64 ; P = 7 3 4 5 6 7 8 9 0 2 3 4 5 6 7 Eb/No (db) Fig. 5. Performance comarison between the DVB-T system with erfect channel estimation and the roosed 2D P OFDM ; Seed: 20 km/h ; β = 0.08 ; = 6, 32 and 64 We can exress the frequency channel coefficients H [n, q] as a function of the channel imulse resonse (CIR): H [n, q] = N FFT γ m,q [k]e 2jπ( s f+n) N k FFT (5) where γ m,q [k] is the comlex amlitude of the kth samle of the CIR during the qth OFDM symbol of the mth frame, and N FFT is the FFT size. Therefore, by injecting (5) in (4), the autocorrelation function of the channel can be rewritten as: R HH ( n, q) = N FFT N FFT N FFT k =0 E [ γ m,q [k] γ ]} m,q q k 2jπ n k N e FFT Since different tas of the CIR are uncorrelated, it comes: R HH ( n, q) = N FFT N FFT E γ m,q [k] γm,q q [k]} n 2jπ N k e FFT (6) According to Jake s model [8], the correlation of the kth samle of the CIR is: E γ m,q [k] γ m,q q [k] } = ρ k J 0 (2πf D qt OFDM ) (7) where ρ k is the ower of the kth samle of the CIR, J 0 (.) the zeroth-order Bessel function of the first kind, f D the maximum Doler frequency and T OFDM the total OFDM symbol duration. Finally, the autocorrelation function of the channel (7) can be exressed as: R HH ( n, q) = N FFT N FFT n 2jπ N ρ k e k FFT J 0 (2πf D qt OFDM ) (8) 6. REFERENCES [] ETSI EN 300 744, Digital Video Broadcasting (DVB) ; Framining structure channel coding and modulation for digital terrestrial television, Tech. Re., Nov. 2004. [2]. Cariou, J.F. Hélard, Efficient MIMO channel estimation for linear recoded OFDMA ulink systems, IEE Electron. ett., vol. 43, no. 8,. 986-988, Aug. 2007. [3] S. Nobilet, J.F. Hélard and D. Mottier, Sreading sequences for ulink and downlink MC-CDMA systems: PAPR and MAI minimization, Euroean Trans. on Telecommun., vol. 3, no. 5,. 465-474, Oct. 2002. [4] J. Evans and D.N.C Tse, arge system erformance of linear multiuser receivers in multiath fading channels, IEEE Trans. on Inf. Th., vol. 46, Issue 6, Set. 2000. [5] M. Debbah, W. Hachem, P. oubaton and M. de Courville, MMSE analysis of Certain arge Isometric Random Precoded Systems, IEEE Trans. on Inf. Th., vol. 43, May 2003. [6] C.K. Ho, B. Farhang-Boroujeny and F. Chin, Added ilot semi-blind channel estimation scheme for OFDM in fading channels, Proc. of IEEE GOBECOM, Nov. 200. [7] J.M. Chauffray, W. Hachem and P. oubaton, Asymtotical Analysis of Otimum and Sub-Otimum CDMA Downlink MMSE Receivers, IEEE Trans. on Inf. Th., vol. 50, Issue, : 2620-2638, Nov. 2004. [8] W.C. Jakes (ed), Microwave Mobile Communications, IEEE Press, New York, 994.