OFDMA: Synchronization Techniques AMPLIATO, BEAURIN, GUILLEMIN, POVEDA, SOULIER [email protected] [email protected] [email protected] [email protected] [email protected]

Abstract. Orthogonal frequency division multiple access (OFDMA) is a modulation and multiple access method proposed for the 4th generation in cellular mobile communication systems. This document presents the effects of frequency offset in downlink on the performance of OFDMA. The main problem with frequency offset is that it introduces interference among the subcarriers; consequently synchronization errors in reception. The report describes three techniques to estimate frequency offset using repeated data symbol. First estimation is due to maximum likelihood estimation (MLE), second method is a linearization of least squares (LS) and third one is the extended Kalman filter (EKF) algorithm. All three are estimated by supposing an ideal channel. Once the procedures performed well it has been developed a technique in order to estimate the channel by a least mean square (LMS) method. The techniques proposed for OFDMA synchronization are derived and their performance computed and compared with simulation results. It is shown that to maintain a transmission loss of 0.01% it is just necessary a signal-to-interference ratio of 7 dB. Keywords. OFDMA, orthogonal frequency division multiplexing (OFDM), multiple access, multicarrier modulation, inter-carrier interference (ICI), downlink, multipath, Doppler effect, frequency offset, extended Kalman filter, maximum likelihood estimation, least squares method, mean square error.

I. Introduction Nowadays cellular communications are everywhere, supplying free mobility to their users. These communications provide actually voice, but low data rate services as streamed multimedia (video chat, video on demand or mobile TV). There now exists a growing demand of these services and it is expected to continue in the future. A solution proposed at these demands is an efficient modulation scheme known as OFDMA because it provides a high data rate services in a wireless network. In OFDMA, different users simultaneously transmit their own data by modulating an exclusive set of orthogonal subcarriers, thus each user’s signal may be separated easily in the frequency domain at reception [4]. This new technique allows reduced ICI, has a more spectral efficiency and copes with channel distortions [2]. As a drawback, its level of performance is very sensitive to synchronization errors. They are determined by timing and frequency offsets [1]. Especially to frequency offsets, known as carrier frequency offset (CFO). This results from the Doppler shift, due to users’ movement, as well as from the mismatch between the carrier frequencies at the transmitter and receiver [7]. As different users’ signals are mixed together at the receiver, the CFO causes ICI both from the user itself and from all the other users. Three methods are proposed to estimate CFO based on the retransmission of data symbol in downlink transmission. First synchronization technique is based in MLE, second in a linearization of LS algorithm and finally to improve the throughput of these first two procedures it has been performed an EKF method. They have been implemented by supposing an ideal channel. Last part of the project is about channel estimation by LMS technique [8]. This part attempts to implement the channel and the CFO estimation in the receiver to build an OFDMA system able to work in a typical cellular mobile communication channel, like Rayleigh channel. Unfortunately the synthesis results in a low performance system, even though both estimations separately work properly. The document is organized as follows. The OFDMA system description is given in Section II where there is a review both the transmitter and receiver schemes. In Section III is treated the three methods used to CFO estimation. Channel estimation it is introduced in Section IV. Section V shows simulation results to confirm the performance of the proposed methods. Finally, a conclusion is given in Section VI.

II. System Description In an OFDMA transmitter firstly the data stream pass over a symbol mapping, after this data is divided into blocks of length . Fig. 1 illustrates the block diagram of a downlink transmitter, denoting , the block of the user . The carrier allocation system (CAS) unit maps the data symbols of each block into subcarriers to the corresponding user. The result is an -dimensional vector, . After all that, the data is fed to a , . Those vectors are summed resulting a vector conventional OFDM modulator [5] that consists of a -points inverse discrete Fourier transform (IDFT) followed by a Cyclic Prefix of -points to avoid interference between consecutive blocks (IBI). The output block after the Cyclic Prefix in time-domain can be written as (1). 1

1

√ where

1

are the entries of

Fig.1: Block diagram of an OFDMA transmitter The channel modifies the transmitted signal due to multipath; also the mobility of the receiver causes the Doppler effect that produces the CFO. The channel impulse response (CIR) could be denote as (2) where is the channel order related to the duration of the impulse response of shaping filters as well as to the channel delay spread. 0 ,

1 ,…,

1

2

It is assumed that there is no time offset, then after pass the down-conversion, the received signal in presence of frequency synchronization errors takes the form /

3

/ where contains the frequency offset, noted as . , is the CIR and is complex-valued 2 additive white Gaussian noise (AWGN), with variance σ . The OFDMA downlink receiver block diagram is shown in Fig.2. The stream is divided into adjacent segments of , each corresponding to a transmitted OFDMA block. Next, data pass through a removing Cyclic Prefix; the length remaining samples are collected in a vector

0 ,

1 ,…,

1

4

and passed to an -point discrete Fourier transform (DFT) [1]. Following level consist in the estimation of the frequency error and its later correction to obtain the desired signal in reception.

2 of 7

Fig. 2: Block diagram of an OFDMA receiver

III. CFO Estimation There are two situations depending on whether the frequency offset is an integer multiple of the subcarrier spacing or not. If it is an integer the DFT output signal takes the form |

|

|

| |

(5)

(A)

⁄ . Therefore first case only results in a shift of the subcarriers by ε positions as shows portion (A). where 2 Thus orthogonality among subcarriers is preserved and no ICI is produced. In the second case the situation is drastically different. After Fourier transform is applied and several simplifications too, the signal results in sin / , 6 sin / (C)

(B)

(D)

where portion (B) includes data symbols modified by the channel transfer function, portion (C) is the term that destroys orthogonality and finally, portion (D) is AWGN. Therefore when ε is not integer multiple of subcarrier spacing, the subcarriers are no longer orthogonal. So they interfere with each other, producing ICI [1]. Thus it is important to estimate the frequency offset in order to eliminate or at least minimize its impact. A. Maximum Likelihood Estimation The use of MLE to estimate CFO has been proposed by Moose [3]. The technique consists in the transmission of two identical blocks. Supposing they remain identical after passing through downlink transmission channel except for a phase shift (E) proportional to the frequency offset. The phase shift between two successive blocks is measured at the DFT output n

⁄

7 n

(E)

where is the signal component. Observe that between the first and second DFTs, both the ICI and the signal are altered in exactly the same way, by the phase shift. Therefore if is estimated ( ̂) it is possible to revere this signal damage in reception. The observation equations for the estimation algorithm are 8 where MLE estimates

2

and 9

After minimize the conditional joint density function of the observations

3 of 7

10

min the estimation is the result of the equation ∑ ∑

1 2 ̂

11

B. Linear Least Squares Another procedure to estimate CFO is proposed using the LS algorithm. The principle of two identical blocks transmission is followed as well. Furthermore the observation equations are the same as in MLE. However it is necessary to linearize the equation before applying the algorithm. The linearization consists in a first order Taylor series decomposition, as follows 12 where

is initialised to zero for the first iteration and 13

Observation equation could be writing after linearization as 14 where

is AWGN. Hence, as the observation equation is linear, the estimation is the result of the equation ̂

1 2

15

C. Extended Kalman Filter The algorithm EKF is carried out to improve the throughput of the system, because with this method it takes one data block in order to find a proper ̂. Firstly is has been considered a state-space model so as to estimate the CFO. The state equation is represented as follows ̂

̂

1

16

The measurement equation is 17 / where . Consequently, as the measurement equation is non-linear for , therefore it is necessary to linearize the expression around . The linear expression yields

2

18

The calculation of Kalman Gain is as follows 1

1

4 of 7

19

2

20

Furthermore the estimation of CFO is as shown below ̂

̂

1

21

It is then necessary to calculate the estimate variance

as 1

22

IV. Channel Estimation Channel estimation is performed via LMS algorithm [8]. To begin with, let see what parameters the receiver knows in order to determine the channel. First one and the simpler is output signal . The noise variance is generally well approximated so that the general form of the noise is known. To finish, the last known parameters is the input signal . In fact we could assume that we are in a learning state: the receiver knows exactly what the sender has sent. The same OFDMA frame that enables EKF frequency offset estimation is taken to estimate the channel.

Fig. 3: Adaptive LMS filter [8] LMS implies to seek the vector

that minimizes the square error 23

where is at a minimum of the square error function. Its derivation gives the best filter expression over the the signal.

elements of 24

It is clear that the more the learning signal is long the more the estimation is accurate. In here, over a 1024 OFDMA frame, the estimated channel coefficients are very close from the real channel, i.e. MSE , 10

V.

Simulation

The simulation of the CFO estimation is shown in figure 4. The graph presents in terms of Bit Error Rate (BER) the system performance. It is calculated over the noise introduced into the communication chain. The curves are close to the theoretical BPSK curve. It involves that the frequency estimation error has no impact at the receiver level. Here, another interesting point is: how many OFDMA frame are considered to estimate the frequency offset? What the system capacity is decreased? The frame used for frequency estimation cannot carry information at the same time: they decrease the data rate. It has been seen previously that 2 frames are needed for MLE and LS estimation whereas only one for EKF. Thus, regarding the BER curve, EKF seems to be the best method to evaluate the frequency offset. Another point is how long the frequency offset keeps constant. The assumption chosen is that it remains constant during 1 ms. In fact, even if the user drive his car and accelerate suddenly, it could be considered that the offset would not change during that given period. 1 ms, it is the time needed to send 12000 bits ( =12 Mhz). So, regarding a 1024 OFDMA frame,

5 of 7

there are around 22 frames which has the same frequency offset. It seems logical that the offset estimation has to be carrying out every 22 frames. Furthermore, over 22 frames, the throughput decreased by 2/22 for the MLE and LS estimation and 1/22 for EKF estimation. The later shows all its interest in that kind of system. It requires only one frame, and it is enough to estimate the offset as regarding the BER.

Fig. 4: Performance comparison of the three methods Simulation for channel correction is shown in figure 5. The adaptive algorithm LMS is quiet effective even if the BER is far from the one without channel regarding frequency estimation. One could pretend that the LMS estimation is not accurate. In fact, it has been noticed that BER with channel model is always higher than BER without channel model. Even if the exact channel is used to cancel channel effect, the same BER results are obtains. In fact, the OFDMA techniques enable to correct the channel effect in the frequency area. The hypothesis assumed is the following: in temporal domain, the length of the Rayleigh channel is =7. As its Fourier transform is carried out, it size is 1024 (to fit with the OFDMA frame); during that transformation, some errors might occurs.

Fig. 5: Channel estimation performance

6 of 7

VI. Conclusion It has been seen that frequency offset in OFDMA causes serious loss of SNR due primarily to ICI. Synchronization techniques minimize quite well the restriction. However it is required a frequency offset as well as a channel impulse response constant, for a period of two blocks of symbols for MLE, LS and for a period of one block in EKF. The channel estimation has been achieved in the simulation. Although the implementation of frequency and channel estimation set do not perform well. The OFDMA system communication chain has been simulated entirely, that means transmitter, channel and receiver. It has been obtained a close simulation of the desired modulation and multiple access technique. As a future work it is proposed to solve the drawback in the frequency and channel estimation set by the implementation of a particle filter as a solution. Also an implementation of a dynamic carrier allocation system could increase the performance of the simulated OFDMA system.

References [1] M. Morelli, C.C. Jay Kuo and Man-On Pun, "Synchronization Techniques for Orthogonal Frequency Divison Multiple Access (OFDMA): A Tutorial Review", Proceedings of the IEEE, vol. 95, no. 7, July 2007 [2] O. Olukayode Isaac, Y. Zhang, P. Shirisha, "OFDM Carrier Frequency Offset Estimation", PhD Thesis, Karlstad University, Sweden, June 2006 [3] Paul H. Moose, "A Technique for Orthogonal Frequency Division Multiplexing Frequency Offset Correction", IEEE Transactions on communications, vol. 42, no. 10, October 1994 [4] P. Zhao, L. Kuang, J. Lu, "Carrier Frequency Offset Estimation Using Extended Kalman Filter in Uplink OFDMA Systems", Proceedings of the IEEE, Tsinghua University, China, 2006 [5] M. Debbah, "OFDM", Mobile Communications Group, Eurecom [7] Bor-Sen Chen, Chang-Lan Tsai, "Frequency Offset Estimation in an OFDM System", Proceedings of the IEEE, National Tsing Hua University, Taiwan, 2001 [8] M. Najim, A. Giremus, J. Grolleau "Filtrage Optimal niveau I et II", Cours troisième année, Ecole Nationale Supérieure d'Electronique, Informatique et Radiocommunication de Bordeaux, Septembre 2007

7 of 7