Procedure of Initial Downlink Synchronization

2.2.2.1 Stage I: Symbol Timing Synchronization

In [1], two methods of symbol timing estimation have been considered, both using the cyclic prefix: ML estimation and CP correlation. The method of ML estimation is proposed in [7], which uses the maximum likelihood criterion to estimate time and frequency offsets. Under the assumption that the received samples are jointly Gaussian, the estimated symbol time offset ˆθ is given by

θ = arg max {|Γ(θ)| − ρΦ(θ)} ,ˆ (2.2.1) and ρ = _{SN R+1}^{SN R} with SNR being the signal to noise ratio. It is a one-shot estimator in the sense that the estimates are based on the observation of one OFDM symbol.

To roduce the complexity, the CP correlation method uses only the correlation part to estimate the symbol time, ignoring the part that compensates for the difference in energy in the correlated samples. As the samples of different OFDM symbols are uncorrelated, the peak of the sliding sum of r(k)r^∗(k + N) would occur when the samples r(θ), · · · , r(θ + N + L − 1) are all within the same OFDM symbol. Then, the symbol time offset estimator becomes

θ = arg maxˆ

A comparison of the complexity difference between the two methods is given in [2].

For further reduction of the CP correlation complexity, we can compute the CP correlation at sample time θ by (2.2.2), then the CP correlation at sample time θ+1

samples

Fig. 2.8: Structure of the symbol time and frequency estimator (from [1]).

is given by

Reference [1] shows that although the performance of ML estimator algorithm is better than that of CP correlation algorithm in AWGN channels, neither algo-rithm can estimate the exact symbol time at 100% accuracy. In addition, for fading multipath channels the CP correlation algorithm can outperform the ML estimator algorithm. To estimate the exact symbol time, both algorithms should be assisted by other means to find the symbol time more accurately. Here pilot correlation is used as the auxiliary operation, which is combined in stage IV with frame synchro-nization. Since the complexity of ML estimation is much higher than that of CP correlation, but the benefit is questionable [1], [2], we use CP correlation to estimate the symbol time in stage I. The algorithm structure is as shown in Fig. 2.8.

2.2.2.2 Stage II: Fractional Frequency Synchronization

The ML estimator of the fractional frequency offset ˆ² is given by [7], [8]

ˆ² = −1

2π∠Γ(ˆθ),

whose structure is already shown in Fig. 2.8. It is easy to understand why ² can be estimated by this method. The frequency offset ² results in an exponential

modulation in the time domain, in that the received samples are multiplied by n

1, e^j2π²N , e^j2π²2N , ...

o

. In AWGN channel, the received sample in the guard time is r(k) = s(k)e^j2π²kN + n(k),

and the sample in the last part of the useful time is

r(k + N) = s(k + N)e^{j2π²(k+N )N} + n(k + N),

where s(k) is the transmitted signal, N is the FFT size, and n(k) is the noise. Then the multiplication of r(k) and r^∗(k + N) yields

r(k)r^∗(k + N) = s(k)s^∗(k + N)e^{−j2π(²+N )N} + noise.

Note that e^{−j2π(²+N )N} is the common factor of all the pairwise sample products for r(k) in the guard interval. Hence the sum of these products should reduce the noise effect. The frequency offset ² can be estimated by the phase of the sum of r(k)r^∗(k + N) taken at the symbol start position. Note that the phase contribution of any integer frequency offset is an integer times 2π. Thus this estimator is merely able to detect fractional frequency offset.

2.2.2.3 Stage III: Integer Frequency Synchronization

The integer frequency synchronization stage is performed after FFT by utilizing the guard band and two fixed pilot carriers which are at the edge of the used carriers to correct the frequency offset. There are two reasons to using the guard band to do integer frequency synchronization. First, guard carriers suffer less degradation from by ICI than pilot carriers. Secondly, the complexity of using the guard carriers is much less than that using the pilot carriers as no multiplication is required.

The first step in integer frequency offset estimation is for SS to check whether the received OFDM symbol is from the BS rather than another SS. In 802.16a [3], the definition of the guard bands and pilots are different for DL and UL. The indices

Fig. 2.9: DL/UL symbol identification (from [2]).

of the DL guard carriers are from −1024 to −852 and from 852 to 1023, while for UL they are from −1024 to −849 and from 849 to 1023. A threshold can be set and if any of the carriers {−849, −850, −851, 849, 850, 851} is larger than the threshold, the SS will regard the symbol as a DL symbol, as shown in Fig. 2.9.

For the DL, the standard defines that carriers −851 and 851 are fixed location pilots which are modulated to ±⁴₃ in amplitude. If there is no integer frequency offset, the FFT outputs of all the guard carriers will be small. So, all the guard carriers are checked to see if any of them exceeds the threshold. The direction of checking is from 1023 to 852, and then from −1024 to −852. If a carrier k is detected to be larger than the threshold, the ±851st fixed pilots are assumed to have shifted k − 851 carrier spacings due to the frequency offset. Thus the checking is stopped and the frequency is corrected by k − 851 carrier spacings.

In a fading channel, ICI may cause serious distortion. Thus, if the ±851st pilots

Fig. 2.10: State diagram of the frame synchronizer.

are distorted to be less than the threshold, the frequency offset will not be detected by the method. An additional check is added to see whether both of the ±851st pilot carriers are larger than the threshold. After these three checks, the integer synchronization finishes. The threshold is chosen to be 0.55 in our simulation. This value is derived from the simulation results in [1].

2.2.2.4 Stage IV: Frame Synchronization

In stage I, the OFDMA symbol start time have been roughly estimated, but the SS has to know exactly where the frame starts. The frame start time estimation proposed in [1] uses the pilot correlation method. In the 802.16a standard [3], the varible location pilots change their locations from symbol to symbol depending on the symbol index L. The modulation of pilots is decided by the PRBS generator, and the initialization vector of the PRBS generator is different in the preamble

symbol than in a non-preamble symbol. Therefore, there are 7 possible kinds of pilot structure as shown in Table 2.3. If the received symbol has the same pilot locations and the same initial vector of modulation PRBS with the reference data, the correlation of them will be larger than the other 6 cases. A frame is determined to start if there are three successive DL symbols with the maximum correlation corresponding to the preamble.

Table 2.3: Possible Pilot Structures in Frame Synchronization

DL preamble DL normal symbol

L = 0, P RBS = 01010101010 L = 0, P RBS = 11111111111 L = 2, P RBS = 01010101010 L = 2, P RBS = 11111111111 L = 1, P RBS = 01010101010 L = 1, P RBS = 11111111111 L = 3, P RBS = 11111111111

The proposed frame synchronization algorithm is illustrated in Fig. 2.10. In order to build connection, we have to find the starting point of a frame in initial synchronization. After finding the third preamble symbol, we can turn the operation to normal synchronization as shown in Fig. 2.10. The method presented in [2]

declares frame synchronization failure when there is one unexpected symbol in pilot correlation. But we find that one unexpected symbol does not mean that it cannot find correct pilot correlation in the next symbol. So we modify the method to declaring frame synchronization failure with the detection of 6 unexpected symbols within one DL subframe.

From [2], because of the use of pilot correlation, we may need to do FFT at each sample location for a range of 65 samples (from −32 to +32, as shown in Fig. 2.11(b) and (c) [1]) in order not to miss the true symbol start time. In order to reduce the computational complexity, the conventional FFT is only applied at location −32.

At the subsequent sample locations, the FFT may be computed recursively as X_n(k) = [X_n−1(k) − x_n−N + x_n] e^j2πkN (2.2.6)

x

Fig. 2.11: Multiple FFTs are needed for a consecutive range of sample locations to ensure finding the true symbol start time. (a) Symbol location detected in stage I, where the gray region is the useful samples which are applied FFT. (b), (c) Leftmost and rightmost ranges of correlation, respectively. (From [1].)

where N is the FFT size, k is the carrier index, n is sample number, and x_n is the new sample location.