IJEECE 5(2) July-December 2013; pp. 149-158
Estimation of Time Offset in OFDM Systems in the Presence of CFO Melkeri Vidyadhar S., Yamuna B. J. and Chetna Singhal Das Sri Krishna Institute of Technology, Visvesvaraya Technological University, Bangalore
Abstract: Orthogonal frequency-division multiplexing (OFDM) has been adopted by many broadband wireless communication systems for the simplicity of the receiver design to support high data rates and user mobility. However, studies also show that the advantage of OFDM over the single-carrier modulation schemes could be substantially compromised by timing or frequency estimation errors at the receiver. The time synchronization problem for OFDM systems is most common in the downlink of wireless communication systems, in this paper a novel timing synchronization algorithm which minimizes false alarm probability and indirectly improves correct detection probability. We then introduce a universal fractional carrier frequency offset (CFO) estimator that outperforms conventional methods at low signal to noise ratio with lower complexity. More accurate timing and frequency estimates can be obtained by our proposed algorithms, presenting a successive timing estimation algorithm to solve the timing ambiguity. Both analytical and simulation results are presented to confirm the performance of the proposed methods in various realistic channel conditions. Keywords: OFDM, Cyclic prefix, Correlation, AWGN channel, Synchronization.
I.
INTRODUCTION
In order to keep its technology competitive, 3rd Generation Partnership Project (3GPP) is considering long term evolution (LTE) [16], in which evolution of both radio interface and network architecture is necessary. 3GPP LTE systems will provide higher data rate services with better quality of service than the current 3G systems. This will require reliable and highrate communications over time-dispersive (frequency-selective) channels with limited spectrum and inter-symbol interference (ISI) caused by multi-path fading. Orthogonal frequency division multiple accesses (OFDMA) [16] [22] provide several advantages, such as high spectral efficiency, simple receiver design, and robustness in a multi-path environment. Due to these advantages, OFDMA was chosen as the downlink air interface of 3GPP LTE systems. II. CYCLIC PREFIX The cyclic prefix (CP) protects the OFDM symbols from ISI. The name of cyclic prefix indicates what it is and how it is generated. Firstly, as a prefix, it needs to be placed in the beginning of an OFDM symbol. Secondly, being a cyclic extension to the original signal, the signal within *
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the CP needs to be the same as the last portion of the OFDM symbol. Although the use of the CP prolongs the duration of OFDM symbols and results in a loss in data throughput, it has become a common practice in most commercial OFDM systems because of the effectiveness in ISI mitigation.The benefit of the CP with an exemplary received waveform of one subcarrier in an OFDM signal. [16] [22], Without CP, it is inevitable for the FFT window to contain the signals from two OFDM symbols. As a result, the sudden phase change on the subcarrier spreads its spectrum into others after FFT and causes inter-carrier interference (ICI) that could significantly degrade the system performance. With the insertion of CP, which is assumed to be longer than the time interval between the first and last channel paths, the phase discontinuity can be avoided by a properly located FFT window. III. TIME DISPERSION An uncorrupted OFDM signal can be demodulated without any interference between subcarriers. One way to understand this subcarrier orthogonality is to recognize that a modulated subcarrier xk(t) consists of an integer number of periods of complex exponentials during the demodulator integration interval Tu = 1/�f However, in case of a time-dispersive channel the orthogonality between the subcarriers will, at least partly, be lost. The reason for this loss of subcarrier orthogonality in case of a time-dispersive channel is that, in this case, the demodulator correlation interval for one path will overlap with the symbol boundary of a different path, as illustrated in Figure 1. Thus, the integration interval will not necessarily correspond to an integer number of periods of complex exponentials of that path as the modulation symbols ak may differ between consecutive symbol intervals. As a consequence, in case of a time-dispersive channel there will not only be inter-symbol interference within a subcarrier but also interference between subcarriers [16]. If the correlation at the receiver side is still only carried out over a time interval Tu = 1/�f, subcarrier orthogonality will then be preserved also in case of a time-dispersive channel, as long as the span of the time dispersion is shorter than the cyclic-prefix length. In practice, cyclic-prefix insertion is carried out on the time-discrete output of the transmitter IFFT. Cyclic-prefix insertion then implies that the last samples of the IFFT output block of length N is copied and inserted at the beginning of the block, increasing the block length from N to N + Np at the receiver side Fig. 1. The cyclic-prefix insertion is beneficial in the sense that it makes an OFDM signal insensitive to time dispersion as long as the span of the time dispersion does not exceed the length of the cyclic prefix. IV. PERFECTLY SYNCHRONIZED SYSTEM The perfectly synchronized system is said to be so, when there is no effect of CFO and TO in the signal and the system is assumed to be free of inter-carrier interference (ICI) and intersymbol interference (ISI). There is no block included to remove the effect of ICI or ISI, which are mainly included due to the multipath fading of the OFDM signal. V. NEED FOR SYNCHRONIZATION If the Analog to Digital (AD) and Digital to Analog (DA) converters have different sampling clocks, then the mismatch in the clock speed between these two would lead to either an additional
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Figure 1: Time Dispersion and Corresponding Received Signal
sample or loss of sample depending upon the relative speed between the two clocks. Also the receiver side PC does not know where exactly the first sample of the first OFDM symbol occurs. This is where, time synchronization comes into play. Normally besides time synchronization, we need to undertake frequency synchronization when there is a mismatch between the transmitter and receiver local oscillators. But in our case, as we use the same local oscillator in the transmitter and the receiver side, the frequency offset is zero.The need of the Frequency and Time synchronizations is a major part of the OFDM system which is needed for the perfect reception of the transmitted signal. In OFDM, symbol-timing errors may cause inter-symbol interference (ISI). Since FFT windows can include adjacent OFDM symbol components, this also leads to inter-channel interference (ICI) which causes essential degradation in channel estimation needed by coherent systems [16]. The synchronization issues in OFDM systems. •
The symbol timing synchronization, determinant of the correct symbol start position, i.e., the FFT window position before the FFT demodulation at the receiver end.
•
The carrier frequency synchronization (i.e., carrier frequency recovery technique), utilized to eliminate the carrier frequency offset caused by the mismatch of the local oscillators between the transmitter and the receiver, nonlinear characteristic of the wireless channel as well as the Doppler shift.
•
The sampling clock synchronization, which is to mitigate the sampling clock errors due to the mismatch of the crystal oscillators.
In most of the papers, the major disadvantage of compensation to the estimation of the offset is when the presence of carrier frequency offset in the received signal due to the multipath fading of the received signal. Whereas in some of the papers the CFO effect is taken as constant which means the signal is perfectly synchronized which is not possible in the practical systems, and the estimation of the timing offset is calculated using different methods as listed
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• • • •
Offset estimation using cyclic prefix Pilot assisted estimation ML estimation Hybrid estimation etc.
VI. PROBLEM DEFINITION In this paper a deep study about the algorithms proposed for calculating the timing synchronization is done and considering the disadvantages of the above systems we have come up with the novel time offset estimation method which has less effect of CFO and works in low SNR, here we make use of the cyclic prefix for the estimation of the offset; the process for which is given in the second chapter. Our major problem statement is to estimate the exact time offset in the received signal and provide the offset to the receiver, so that the FFT window is placed at the starting point of the data received. This is carried out by considering the effect of CFO which mainly causes the failure of most of the estimation algorithms. Hence in our problem statement we consider the effect of the CFO in the received signal and estimate the timing offset, the performance analysis is made for different CFO values. VII. SYNCHRONIZATION USING CYCLIC PREFIX This is one of the blind synchronization method in which correlation is performed between cyclic prefix (CP) and the last part of the OFDM symbol. Cyclic prefix (CP) which is a copy of final piece of each subcarrier is inserted at the beginning of OFDM symbol. Length of the cyclic prefix should be long enough to ensure orthogonality of the system. However, the performance of this method is seriously reduced in the time-variant multipath channel. Due to the multipath components, the signals from different paths have different delays which might prone a problem, as they do not arrive simultaneously. The orthogonality between different subcarriers will be destroyed when integration is done over entire symbol duration. The cyclic prefix based correlation technique is effective, when large number of subcarriers is used. For frequency offset estimation, once the symbol timing is known, the correlation output can be used to estimate the frequency offset. Initially, phase of the correlation output between the two samples is estimated and is divided by 2ðT, where T is the time interval between the corresponding samples [4]. VIII. TIME-INVARIANCE PROPERTY OF RECEIVER A system is called time-invariant or shift invariant, if its input-output characteristics do not change with time. Let y(n) have system response T to the input signal x(n), represented as, y(n) = T[x(n)] Then if the same input signal is shifted by T units of time to yield, x(n – T) and applied to the system (time invariant system), the response of the system should also be delayed by T units to yield. y(n – T). That is, T[x(n–T)] = y(n–T) (2.10)
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For the system to be time invariant, the equation should hold for all possible values of, T. If it does not hold even for one value of T, then the system is time variant. The first uncertainty is modeled as the delay in the channel impulse response which is modeled as �(k – T) where T is the integer valued unknown arrival time of the received symbol the complete OFDM symbol received at the receiver is delayed by the value T hence it’s of major importance to calculate the value of T and give it to the receiver to perform the correct FFT processing. In OFDM systems, it is important to maintain the orthogonality between the subcarriers to avoid ICI. Though in our laboratory system we use the same local oscillators at the transmitter offset on the autocorrelation property of the sequence just for completeness. Considering we have a frequency offset of � in our system, sequence input to the correlate k
will look like, e j 2 �� N where � denotes the difference in the transmitter and receiver oscillators as s fraction of the inter-carrier spacing in normalized frequency, all the subcarriers experience the same shifts these two uncertainties and the AWGN thus yields to the received symbol. Receiver symbols can be modeled with both the uncertainties as given with the effect timing effect T and the frequency effect � is given as y ( k ) � x ( k � T )e
j 2 ��
k N
w(k ) for 0 � k � N � 1
The received signal y (k) is given as after removing the tap effects from the received frame y(k ) �
N �1� P
�
x( n) h( k � n ) � w(n ) for 0 � k � N � 1
n �0
The output of the transmitter is received by the receiver and the symbols received are corrupted by both channel and AWGN noise showing uncertainty of time or frequency offset. Presently considering frequency offset as constant, let us calculate the timing offset as shown in the block diagram. The received symbols are correlated within the frame for the cyclic prefix with the copy of cyclic prefix in the same frame, which gives the peak value among the correlation. This is done for the complete block of symbols which is sent and the offset value T is calculated as explained in the later sections. After getting the offset value of the symbol frame, the FFT window is moved to the starting position of the frame and the FFT process is done to get back the signal. Using the correlation values which is obtained by moving window correlation of CP to CP these values have the highest peak value when the data is correlated, by making use of these c( k ) �
p � L �1
� { y(k ) y (k � N )} *
k �0
Correlation values c(k) the peak position is calculated and FFT window is moved to the peak position, hence providing the correct demodulation of the received signal. Many of the algorithms are provided to find the Time offset and the Carrier frequency offset in the received frame which are given in the literature survey [17].
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IX. PROPOSED TIME OFFSET ESTIMATION ALGORITHM The proposed time offset estimation algorithm consists of three steps: Moving window correlation, Peak detection, Offset estimation Fig. 2. (A) Moving Window Correlation In the algorithm which is proposed the received symbols from the transmitter after passing through the channel it contains the uncertainties � which are added in the received symbol frame of y(k) y(k) = s(k – �) Moving window correlation is performed on the received frame of data correlated; we select the data for the moving window correlation in such way that the overlapped part of the data due to multipath fading of the channel is eliminated i.e. since we are using 3 taps channel the last part of the received frame is over lapped with the multiple paths of the data so eliminating the part the window for the correlation is selected.
Figure 2: Block Diagram of Proposed Algorithm
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(B) Peak Detection and Averaging After performing the correlation using moving window, we obtain the graph of random peaks, in this process the average sum of the peak data of the frame from graph is calculated by shifting the selection of the position by the frame length and are averaged to get the maximum value, i.e. using 1st symbol of first frame and first symbol of second frame is added in this way jump is performed for length of frame, so that we obtain N number of the values added among which the perfectly correlated symbols will be having the highest peak average value by which we can give the starting position of the frame, here the complete data is correlated using moving window with the length of cyclic prefix but removing the taps effect from the correlating data, (C) Time Offset Estimation The offset estimation of the symbols is carried out as follows, the received symbols are delayed for the integral value assuming the integer value � is the offset in the received symbols, which delays the received symbols then the received symbols are correlated, Fig 3.1 but in this correlation the length of data used is only for the one frame length, the correlation process is same as explained in the section A Fig. 3.2. The obtained correlation results are used to get the peak position within the frame; the selected received frame for the correlation will be having the peak position of the second frame. Using this position it’s compared with the length of the frame and the estimated offset is obtained this offset value is given to receiver to correctthe starting position of the receiver frame for the processing of the FFT to obtain the received data. X. RESULT ANALYSIS
Figure 3.1: SNR = 5, CP=64, N=1024 before Offset
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Figure 3.2: SNR=5, CP=64, N=1024 after Offset
The below simulation results gives the offset estimation of algorithm for different SNR values the offset given is 10 and SNR ranges from 0db-30db Fig. 4.
Figure 4: CP=32, N=1024, TAPS=3, DIFFERENT SNR
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XI. CONCLUSION OFDM is an emerging modulation technique to handle impairments of frequency selective fading channel. Hence, OFDM is a prime candidate for future wireless communication techniques. One of the major drawbacks of OFDM system is the shift or the uncertainty in the timing of the symbols i.e. time offset in the system which is due to the data rotation and due to multipath fading of the channel as the channel involved is air. XII. SCOPE FOR FUTURE WORK As we have seen in the above proposed method, there is a lot of scope for future work which gives the platform for further development of the system. Time synchronization in the OFDM system is the major issue which needs to be corrected before further processing blocks in the receiver systems. The program complexity can be further reduced for the faster calculation in estimating the offset in the system. In most of the proposed algorithm the offset estimation is mainly dependent on following issues. 1. System should be perfectly synchronized. 2. The effect off carrier frequency offset should be neglected. 3. The effect of SNR is more random. 4. Noise variance of the system. 5. Threshold dependent. In most of the proposed algorithms the effect of carrier frequency offset is neglected but where as in the proposed algorithm it is been checked for the correctness of the estimation for the different Doppler effects the system works correct up to 0.1 Doppler effect in the transmitted data symbols, hear further work can be done to improve the estimation for Doppler effect which is more then 0.1, for the high performance in the system. Acknowledgment The joy of accomplishing a task on hand will last a lifetime only if we humbly acknowledge the people who have played a significant part in its fulfillment. This, we feel a genuine way of expressing our gratitude and feelings in the simplest manner. I express my deep sense of gratitude to Dr. Raghunath K, and Dr. Vijay krishna for his inspiring guidance, encouragement, and continuous supervision throughout the paper work till the completion of the paper. Last but certainly not the least; I would like to thank the almighty, my family and dear friends, who blessed, supported and helped me during the entire length of my paper work.
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