All Digital Baseband Sampling Cloc Frequency Synchronization for WiMAX Communication Chun-Hung Chou and Jen-Ming Wu Institute of Communications Engineering National Tsing Hua University Hsinchu, Taiwan, 30013 ROC jmwu@ee.nthu.edu.tw Abstract This paper presents an efficient low complexity algorithm of sampling cloc offset estimation and compensation for WiMAX (IEEE 802.16-2004) OFDM mode. The effects caused by sampling cloc offset are symbol window drift in time domain and subcarrier phase rotation in frequency domain. Both of them will introduce inter-carrier interference in the demodulation. Furthermore, the first effect will lead to irreducible inter-symbol interference especially for long pacet transmission. Our proposed sampling cloc frequency synchronization algorithm will solve the effect in time domain with symbol re-timing and the effect in frequency domain with phase tracing. The phase tracing is done by the least-square algorithm and the complex conjugate multiplication. Simulation results show that our proposed algorithm provides very efficient compensation for sampling cloc offset. Moreover, our proposed algorithm is very suitable for VLSI implementation. I. INTRODUCTION Orthogonal frequency division multiplexing (OFDM) is a parallel transmission system with a special set of orthogonal carrier frequencies. It most effective scheme to combat the problems caused by multipath fading environment and achieve high data rate transmission. The channel equalizer of OFDM is simpler than single carrier system due to the near flat fading per subcarriers, and the modulator/demodulator can easily implement by Fast Fourier Transform (FFT). Furthermore, it has the high spectral efficiency because the spectra of the sub-carriers are overlapped. So OFDM has been adopted in several standards of wireless communication such as DVB-T, IEEE802.11a/g, and WiMAX. However, the performance of OFDM system very sensitive to the carrier frequency offset and the timing offset. In other words, the advantages of OFDM very much rely on the well synchronization. There are several synchronization issues to be dealt within an OFDM receiver such as carrier offset (CFO), symbol timing offset (STO), and sampling cloc frequency offset (SFO). In this paper, we focus on the sampling cloc frequency synchronization. It critical part of the synchronization because of its time variant property. This problem is especially serious for long pacet transmission. For example, if the SFO is 16 parts per million (ppm) of the sampling instant, the FFT length is 256, and the cyclic prefix (CP) length is 64 in WiMAX, then the received time-domain signal sample will drift 320 16ppm samples per OFDM symbol. In other words, it will drift one received time-domain complex-valued sample after 195.3125 OFDM symbols. This leads to irreducible inter-symbol interference (ISI). Moreover, the phase rotation caused by SFO in frequency domain is especially serious for high order QAM modulation. So the sampling cloc frequency synchronization is necessary for a practical OFDM system. In [1] and [2], the sampling cloc frequency synchronization is based on closed-loop synchronization. It needs the loop filter, the Numerically Controlled Oscillator (NCO), and the interpolator. The implementation complexity of closed-loop synchronization is very high. Moreover, it needs the time of convergence. In [3] and [4], the open-loop synchronization is adopted. It can reduce the hardware cost of closed-loop synchronization structure. However, they only deal with the problem of SFO in frequency domain. In other words, the irreducible ISI will occur for long pacet transmission. In our proposed synchronization scheme, we adopt the open-loop synchronization with symbol re-timing. In the frequency domain, we use the 8 pilot tones to estimate the phase rotation of each data subcarrier with least square algorithm and compensate it with complex conjugate multiplication. In the time domain, we perform symbol re-timing to cancel the ISI according to the observation of phase rotation of specific subcarrier. The remainder of this paper is organized as follows. In section II, we will introduce the pacet format and symbol description specified in WiMAX. In section Ⅲ, the effects of synchronization errors of an OFDM receiver in time domain and frequency domain are introduced respectively. The proposed SFO synchronization algorithm will be introduced in section Ⅳ. The simulation results will be shown in section Ⅴ. The conclusion is given in section Ⅵ. II. SYMBOL DESCRIPTION AND PACKET FORMAT In the time domain of an OFDM symbo the useful symbol time is T b (=256). A copy of the last T g of the useful symbol period, termed cyclic prefix (CP), is used to combat multipath. The CP length can be configured to 1/32, 1/16, 1/8, or 1/4 of the period T b. The OFDM symbol frequency domain description in WiMAX is illustrated in Fig. 1 [5]. There are 192 subcarriers for data transmission, 8 subcarriers for pilot, 52 subcarriers for guard bands, and 1 subcarrier for DC in every OFDM symbol. The data modulation type can be BPSK, QPSK, 16-QAM, and 64-QAM. The constellations shall be normalized by multiplying the constellation point with the indicated factor to achieve equal average power. The pilots are generated by Pseudo Random Binary Sequence (PRBS) and modulated by BPSK. These pilots are used for phase tracing and symbol re-timing estimation in our proposed synchronization algorithm. The pacet format is shown in Fig.
2. The first two consecutive OFDM symbols are short preamble and long preamble respectively. The short preamble uses only subcarriers the indices of which are a multiple of 4. As a result, the time domain waveform of the first symbol consists of four repetitions of 64-sample fragment, preceded by a CP. The long preamble utilizes only even subcarriers, resulting in time domain structure composed of two repetitions of a 128-sample fragment, preceded by a CP. The data symbols follow the long preamble. The short preamble is used for pacet detection and coarse CFO estimation. The long preamble is used for symbol boundary detection, fine CFO estimation, and channel estimation. Fig. 1. OFDM frequency domain description Fig. 2. Pacet format in time domain III. EFFECTS OF SYNCHRONIZATION ERROR In this section, we will introduce the effects of synchronization error [6]. The synchronization errors include SFO and residual carrier frequency offset (RCFO). The RCFO is caused by non-exact CFO correction using preamble in time domain. It will also cause the phase rotation in frequency domain, so we combine it to the problems which need to be solved. Now we define SFO as and RCFO as. The SFO is defined through T T T(1 ) T, where Tis the receiver ADC sampling instant and T transmitter DAC sampling instant. The RCFO is defined through frx ftx, where ftx and frx are the local oscillator frequencies at the transmitter and the receiver respectively and implies the residual error after CFO correction using preamble in time domain. A. Effect In Time Domain In the absence of sampling cloc frequency synchronization, the OFDM symbol blocs observed in the receiver window slowly wander away form lns, l 1 Ns to lns lns, l 1 Ns l1 Ns, where NsN Ng length of complete OFDM symbo N length of FFT, N length of CP, and l symbol index. A g positive/negative SFO (i.e. sampling period slightly too slow/fast) leads to a left/right drift of ln s samples. According to IEEE 802.16-2004 standard, the maximum SFO is 16ppm ( 8ppm ). If the FFT length is 256 and the CP length is 64 in WiMAX, the received time-domain complex-valued sample will drift 320 16ppm samples per OFDM symbol. In another word, it will drift one received time-domain complex-valued sample after 195.3125 OFDM symbols. Moreover, this will lead to irreducible ISI. This phenomenon can be solved by robbing (if z >0 ) or stuffing (if z <0 ) samples from the cyclic prefix. B. Effect in Frequency Domain The effect in frequency domain can be seen by demodulating the l th received OFDM symbol via FFT. The demodulated signal can be expressed as ln s N g f 1 Z exp j2p A H s pf exp jp 1 f I V N N ln sf exp j 2p exp j j A H s pf expj j I V N 2 3 expj j expj j A H s pf expj j I V 1 2 3 where f 1 z e z ; e x T b x NT normalized RCFO (NRCFO); Al, constellation point for IFFT input at th subcarrier of l th OFDM symbol; H channel complex response at th subcarrier of l th OFDM symbol; I ISI at th subcarrier of l th OFDM symbol; Vl, AWGN at th subcarrier of l th OFDM symbol. In (3), the Al, is rotated by expj 1 expj 2 expj 3 and attenuated by s. However, the term are usually small enough so that the attenuation factor s is very close to 1 and can therefore be neglected. The time-invariant terms (irrelevant to OFDM symbol index l ) expj 2 and expj 3 can t be distinguished form the channel gain factor H and may thus be incorporated into H. Then, Z can be rewritten as ln N s Z exp j2 A H I V From Eq.(4), the demodulated symbols are seen to be rotated by a time-variant phasor exp j l, where 2 Ns / N. The relation between f and is shown in Fig. 3. Because of the time index l (symbol index), the rotated phase function of time and different between subcarriers (see Fig. 4). So the receiver has to trac and compensate the rotated phase continuously in time. Fig. 3. The relation between f and
Fig. 4: Subcarrier symbol rotation due to SFO and NRCFO IV. PROPOSED SYNCHRONIZATION ALGORITHM In this section, we will introduce the proposed SFO and RCFO synchronization algorithm. The bloc diagram of proposed WiMAX receiver is shown in Fig. 5. We use the open-loop synchronization method to compensate the phase rotation and feedbac the add/drop control signal to adjust the length of CP. where T 88 63 38 13 13 38 63 88 A 1 1 1 1 1 1 1 1 l, 88 l, 63 l, 38 l, 13 l,13 l,38 l,63 l,88 where l, time-variant phase l of (4); m subcarrier index of pilot tone; l slope of the phase rotation with symbol index l (see Fig. 4); bl intercept of the phase rotation with symbol index l (see Fig. ' 4); z data symbol after compensation; OFDM symbol time index l start from 2 due to short-preamble ( l 0 ) and long-preamble ( l 1 ). Equation (6) least square algorithm. It is to be noted that the matrix A is constant. This maes it easy for circuit implementation. However, the phase ambiguity will occur if the estimated phase rotation of the pilot tones is over the decision region ~. To combat this problem, we use the pre-compensation method to ensure the estimated phase rotation of the pilot tones won t exceed the decision region. It is to be noted that the compensated phase of data tones need to be accumulated before each pre-compensation procedure (see Fig. 6). Fig. 7 shows the 16QAM constellation before and after the phase tracing. Fig. 6. The behavior of pre-compensation procedure Fig. 5. Bloc diagram of proposed WiMAX receiver A. Phase Tracing After the frequency domain equalizer, the nown 8 pilot tones are extracted into SFO/RCFO estimator. The pilot tones are allocated at subcarrier index 88, 63, 38, 13 in WiMAX. First, we calculate the phase rotation caused by SFO and RCFO of each pilot tone. Then, we interpolate these estimated phase rotation of pilot tones with least square algorithm to calculate the phase rotation of each data tone. The phase tracing algorithm is as follows: For each instant of time l2,3,4... ( z P ) m m m l 1 ( H A A) A H bl y b l l End z z exp jy ' Fig. 7: The 16QAM constellation before and after phase tracing (SFO=16ppm, RCFO=0) B. Symbol Re-Timing In order to solve the effect in time domain, we need to now when the window will drift, i.e. missing one sample or oversample one sample in time domain. We find that the received OFDM symbol miss/oversample one sample in time domain is equivalent to the subcarrier with maximum index (-128) rotate (if no RCFO) in frequency domain. However, the maximum subcarrier index is used for guard band. So we observe when the data at subcarrier index 64 or -64 will rotate /2 to determine when the OFDM symbol will drift. Then, we can add or drop one sample (i.e. decrease
the length of CP d to d1 or increase the length of CP d to d) 1 to solve this effect. The algorithm is as follows: For each instant of time l2,3,4... Ify 64 b l or y 64 b l, then CP length dd 1 2 2 If y64 b l or y 64 b l, then CP length dd 1 2 2 End It is to be noted that y 64 and bl are the accumulated value due to pre-compensation procedure. Fig. 8 shows the phase variation of y 64b l andy 64 bl. It can be seen clearly the opportunity of add/drop. Fig. 9: RMS error of SFO estimation in AWGN channel with different SFO and RCFO Fig. 8. The phase rotation of subcarrier index +64 and -64 V. SIMULATION RESULTS The simulation parameters are based on WiMAX standard. The number of used subcarriers N used = 200, the FFT length N = 256, and the CP length N g = 64. The number of used subcarriers includes 8 pilot tones, 55 guard tones, and 1 DC tone. The bandwidth is set at 20MHz, the sampling frequency is 23.04MHz, and the carrier frequency is 3.5GHz. The receiver non-idealities, i.e. CFO and SFO, are set at 28ppm (± 14ppm) and 16ppm (±8ppm) respectively. Modulation type is chosen as 16QAM. The CFO synchronization in time domain is done by maximum-lielihood estimator with short and long preamble [7]. To display the utility of symbol re-timing, the STO synchronization is assumed perfect in the following simulation. The frequency domain channel equalizer (FEQ) is a one-tap equalizer. Its training data long preamble. First, we show the Root Mean Squared (RMS) error of the SFO estimation with LS algorithm and pre-compensation procedure. Then, we simulate the BER with different conditions to show the robustness of our proposed synchronization algorithm. Finally, we show the performance of our proposed WiMAX receiver in AWGN channel and multipath fading channel. 1) RMS error of SFO estimation error: The results are shown in Fig. 9 and Fig. 10 with AWGN channel and multipath fading channel respectively. The channel model is the modified Stanford University Interim (SUI) channel models [8]. The SUI3 is adopted in Fig 10. Fig. 10: RMS error of SFO estimation in SUI-3 with various SFO and RCFO 2) Different SFO conditions: In Fig. 11, we show the BER at AWGN channel with different SFO (4ppm to 16ppm). It can be seen that the performance of our proposed synchronization algorithm is very stable for different SFO. Fig. 11: Error-rate performance with different SFO in AWGN channel (CFO=28ppm)
3) Different RCFO conditions: In Fig. 12, we show the BER at AWGN channel with different RCFO (0.005subcarrier spacing to 0.05subcarrier spacing). It can be seen that the performance of our proposed synchronization algorithm is still perform well even with large RCFO. Fig. 14. Error-rate performance of proposed WiMAX receiver in SUI channel (SFO=16ppm, CFO=28ppm) Fig. 12: Error-rate performance with different RCFO in AWGN channel (SFO=16ppm) 4) Proposed WiMAX receiver performance in AWGN channel : In Fig. 13, we show the BER of our proposed WiMAX receiver at AWGN channel. Moreover, we also show the performance without symbol re-timing. If the symbol re-timing is not adopted, the error rate floor will occur at high SNR due to irreducible ISI. Fig. 13: Error-rate performance of proposed WiMAX receiver in AWGN channel (SFO=16ppm, CFO=28ppm) 5) Proposed WiMAX receiver performance in multipath fading channel: In Fig. 14, we show the BER of our proposed WiMAX receiver at multipath fading channel. The SUI1~3 are adopted in our simulation. The simulation results show that our proposed WiMAX receiver performs well even in multipath fading channel. VI. CONCLUSION In this paper, an efficient low complexity algorithm of sampling cloc offset synchronization for WiMAX OFDM communication is proposed. We not only deal with the phase rotation caused by SFO and RCFO in the frequency domain but also the symbol window drift caused by SFO in the time domain. Simulation results show that our proposed algorithm still performs well even in the multipath fading channel. Furthermore, our proposed algorithm is very suitable for VLSI design. ACKNOWLEDGEMENTS The authors would lie to acnowledge the support in parts of this wor by National Science Council (Taiwan) (NSC-94-2220-E-007-025, and NSC-94-2752-E-007-002- PAE), and Intel Corporation (94A0330EA). REFERENCES [1] M. Speth, S.A. Fechte G. Foc & H. Meyr, Optimum Receiver Design for Wireless Broad-Band Systems Using OFDM - Part II: A case study, IEEE Trans. on Comm., vol. 49, no. 4, April 2001. [2] K. Shi, E.Serpedin, and P. Ciblat, Decision-Directed Fine Synchronization For Coded OFDM Systems, IEEE Int l Conf.on Acoustics, Speech, and Signal Processing, vol. 4, 17-21, May 2004. [3] Yi-Hsin Yu, Hsuan-Yu Liu, Terng-Yin Hsu, Chen-Yi Lee, A joint scheme of decision-directed channel estimation and weighted-average phase error tracing for OFDM WLAN systems, IEEE Asia-Pacific Conference on Circuits and Systems, vol. 2, 6-9, Dec. 2004. [4] Suvra S Das, Ratnam V. Rajaumar, Muhammad I.Rahman, Arpan PaFran H.P.Fitze, Ole Olsen,Ramjee Prasad, Low Complexity Residual Phase Tracing Algorithm for OFDM-based WLAN Systems, CSNDSP Symposium, 20-22, July 2004. [5] IEEE Std 802.16-2004 (Revision of IEEE Std 802.16-2001), IEEE Standard for Local and metropolitan area networs, 3 Par Avenue, New Yor, NY 10016-5997, USA [6] M. Speth, S.A. Fechte G. Foc & H. Meyr, Optimum Receiver Design for Wireless Broad-Band Systems Using OFDM - Part I, IEEE Transactions on Communications, vol. 47, no. 11, Nov. 1999. [7] John Terry and Juha Heisala, ODFM Wireless LANs: A Theoretical and Practical Guide, 2002, ISBN 0-672-32157-2. [8] V. Erceg, K.V.S. Hari, M.S. Smith, D.S. Baum et a Channel Models for Fixed Wireless Applications, IEEE 802.16.3 Tas Group Contributions 2001, Feb. 01.