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

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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 Digital TV Youssef Nasser member IEEE, Jean-François Hélard Senior member IEEE, 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 : [email protected] Abstract- This paper investigates the impact of carrier This work is carried out within the framework of the frequency offset (CFO) and sampling frequency offset European project ‘Broadcast for the 21st Century’ (B21C) (SFO) on the performance of different MIMO-OFDM which constitutes a contribution task force to the schemes with high spectral efficiency for next consideration engaged by the DVB forum. The main generation of terrestrial digital TV. We analyze contribution of this work is twofold. First, a generalized particularly orthogonal Alamouti scheme, and non- framework is proposed for modelling the effect of CFO orthogonal (NO) schemes like VBLAST, linear and SFO on MIMO-OFDM systems. Therefore, we dispersion (LD) code and Golden code. This analysis analyze the robustness of different MIMO-OFDM gives a global view on the best suitable MIMO-OFDM schemes to CFO and SFO using a sub-optimal iterative scheme with respect to CFO and SFO. We show that receiver. for high spectral efficiency, Alamouti is more sensitive to CFO and SFO. Moreover, we show that all studied II. SYSTEM MODEL MIMO-OFDM schemes are sensitive to CFO when it We consider in this paper the downlink communication with is greater than 1% of inter-carrier spacing. Their with two transmit antennas (MT=2) at the base station and two sensitivity due to SFO is less than that due to CFO. two receiving antennas (MR=2) at the terminal. Keywords- MIMO-OFDM, Carrier Frequency Offset, Figure 1 depicts the transmitter modules. After channel Sampling Frequency Offset, Iterative receiver. encoding of information bits bk with a convolution encoder of coding rate R, the encoded bits are mapped I. INTRODUCTION according to a Gray quadrature amplitude modulation (QAM) scheme. The Gray mapper assigns B bits for each Building a next generation digital TV which enables new of the complex constellation points. Using MT services such as video contribution for media companies, transmitting antennas, a space time (ST) block code mobile TV distribution, IPTV distribution becomes a new (STBC) encoder assigns a (M ,T) matrix X=[x ] to each challenge for broadcasters. Since its inauguration in 1993, T i,t group of Q complex symbols S=[s1,…,sQ] from the input digital video broadcast (DVB) project for terrestrial of ST module. The ST coding rate is then defined by (DVB-T) transmission has fully responded to the L=Q/T. The output matrix is transmitted over MT antennas objectives of its designers [1]. In 2006, DVB forum during T symbol durations i.e. each column is transmitted launches a study mission to inaugurate original and high once during one symbol duration. The different elements defined services for digital TV. During this mission, x (i=1,…,M ; t=1,…,T) are functions of the input researches are asked to investigate which technologies i,t T symbols sq (q=1,…,Q) depending on STBC encoder type. could be considered for a second generation terrestrial Ant. 1 digital TV called DVB-T2. The main concern of OFDM RF Unit researchers is to support transmission at higher data rates DAC Mod. FTX b S Ant. M with minimum error probability. It is expected that a k STBC T Source Encoder Interleaver Mapper multiple input multiple output (MIMO) system combined Encoder OFDM RF Unit DAC F with orthogonal frequency division multiplexing (OFDM) Mod. TX should take place for that target. However, it is well known that OFDM systems suffer considerably from Figure 1- Block diagram of the transmitter. carrier frequency offset (CFO) and sampling frequency The symbols at the output of STBC are fed to OFDM offset (SFO) between transmitter and receiver since CFO modulators of N subcarriers. The output at each OFDM and SFO include inter carrier interference (ICI) at the modulator is a sequence of samples having a rate Fe=1/Te. receiving side [2]. After digital to analogue conversion (DAC), the signal is transposed to the transmitter carrier frequency FTX by the In order to describe the transmission link with a general RF unit, and transmitted through the channel. At the model independently of the ST scheme, we introduce the receiver (Figure 2), it is transposed to base band with the dispersion matrix F such that X=FS. Then, we separate receiver carrier frequency FRX and sampled at sampling the real and imaginary parts of X[n] and Y[n], and we frequency Fs=1/Ts using analogue to digital converter stack them row-wise as done in [3]. We obtain the vector (ADC). In this work, we assume equal carrier frequencies V[n] given by: FTX (respectively equal sampling frequencies Fe) for all N transmitting antennas and equal carrier frequencies FRX V[n] = G[n]FS[n] + ∑φ(n, p)G[ p]FS[ p] +W[n] (equal sampling frequencies Fs) for all receiving p=1 p≠n antennas. The CFO is therefore given by ΔF=FRX-FTX and N the SFO is defined by 1/ΔT=1/(Ts-Te). After OFDM (4) demodulation, the signal received by the jth antenna at = Geq [n]S[n] + ∑φ(n, p)Geq [ p]S[ p] +W[n] th p=1 each time sample t on the n subcarrier could be written p≠n as: with Geq [n] = G[n].F MT −1 N −1 1 Y j [n,t] = ∑∑X i [ p,t]h j,i [ p]φ()n, p +W j [n,t] (1) where G[n] is composed of blocks Gj,i (j=1,…,MR; M T m=0 p=0 i=1,…,MT) each having (2T,2T) elements [3]. where hj,i[p] is the frequency channel coefficient on the In this work, we use an iterative receiver for NO schemes. th p subcarrier assumed constant during T OFDM symbols, (1) The estimated symbols Sˆ at the first iteration are W [n] is the additive white Gaussian noise (AWGN) with j obtained via minimum mean square error (MMSE) zero mean and N /2 variance. φ(n,p) is a function of the 0 filtering as: CFO and SFO, given by: −1 N −1⎛ ΔT ⎞ (1) tr tr 2 ⎜ ⎟ (5) jπ ⎜ NΔFTs + e(n)+e(n− p) ⎟ sˆu [n] = gu [n](Geq [n].Geq [n] + σ w I ) V[n] φ(n, p) = e N ⎝ Ts ⎠ × tr th ⎛ ⎛ ΔT ⎞⎞ where g [n] of dimension (1, 2M T) is the u column sin⎜π ⎜ NΔFT + e(n) + e(n − p)⎟⎟ u R ⎜ ⎜ s ⎟⎟ 1 ⎝ ⎝ Ts ⎠⎠ (1) of Geq (1≤u≤2Q). sˆu is the estimation of the real part (u N ⎛ ⎛ ΔT ⎞ ⎞ (2) sin⎜π ⎜ NΔFT + e(n) + e(n − p)⎟ N ⎟ odd) or imaginary part (u even) of sq (1≤q≤Q) at the first ⎜ ⎜ s T ⎟ ⎟ ⎝ ⎝ s ⎠ ⎠ iteration. At each iteration, the demapper provides soft information about transmitted coded bits. The soft ⎧n if n ≤ N / 2 with e(n) = ⎨ information is represented by log likelihood ratios (LLR). n − N elsewhere ⎩ After deinterleaving, it is fed to the outer decoder which computes the a posteriori extrinsic information of the Ant. 1 RF Unit ADC coded bits. After interleaving, this information will be FRX bˆ PIC Sˆ (l) Demapper SISO used by the soft mapper to produce estimation of DeInterleaver Estimated bits detector (LLR comp.) Decoder Ant. M R RF Unit transmitted QAM symbols. From the second iteration ADC FRX Sˆ (l−1) (l>1), we perform parallel interference cancellation (PIC) Soft Interleaver Gray Mapper followed by a simple inverse filtering: Figure 2- Iterative receiver structure with parallel interference ˆ (l) ~ (l−1) cancellation detector. Vu = Y − Geq,u Su The signal received by the MR antennas on subcarrier n (6) (l) 1 tr (l) are gathered in a matrix Y[n] of dimension (MR,T). It can ˆ ˆ su = tr gu Vu be deduced from (1) by: gu gu N The exchange of information between detector and Y[n] = φ(n,n)H[n]X[n] + ∑φ(n, p)H[ p]X[ p] +W[n] p=1 decoder runs until the process converges. p≠n N (3) III. SIMULATION RESULTS = H eq [n]X[n] + ∑φ(n, p)H[ p]X[ p] + W[n] p=1 In this section, we present a comparative study of four p≠n MIMO coding schemes: Alamouti, and NO schemes like In (3), the first term represents useful signal, the second VBLAST [4], Linear Dispersion (LD) code of Hassibi [5] term indicates ICI and the last one is AWGN. φ(n,n) and Golden code [6]. We use a frequency non selective could be seen as phase rotation and amplitude distortion channel per subcarrier with independent Gaussian of the useful signal due to CFO and SFO. The ICI could distributed coefficients. The performance is computed in be seen as an additive noise to the useful signal. It will be terms of bit error rate (BER) versus Eb/N0 ratio for different values of CFO and SFO. CFO is expressed as a neglected in the equalization process. H[n] is a (MR,MT) matrix whose components are the channel coefficients function of inter-carrier spacing 1/NTs and SFO is expressed as a function of N and T in such a way to hj,i[n]. X[n] is a (MT,T) matrix whose components are the s guarantee that the SFO does not exceed one sample in transmitted symbols on the MT antennas during T OFDM symbols on the nth subcarrier and W[n] is the AWGN.
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