Initial DL Synchronization

As mentioned, we have to estimate the symbol timing offset, CFO, and preamble index during initial DL synchronization. We achieve the task of initial DL synchronization in several stages after considering the complexity for DSP implementation. Fig. 5.2 depicts the overall structure of the proposed initial DL synchronization. It is a two-stage organization where stage1 operates in the time domain to estimate the OFDMA symbol timing and the fractional CFO, and stage 2 operates in the frequency domain to detect the integer CFO and the preamble index jointly.

Below we use the parameters of the 1024-FFT system as an example to describe the synchronization techniques.

5.1.1.1 Timing Offset and Fractional Carrier Frequency Offset

A number of CFO estimation approaches have been proposed. One is the data-aided ap-proach [23], [24], applicable when the preamble consists of known signal (or when a reliable decision on the preamble contents can be made). In the case of IEEE 802.16e OFDMA, it is not suitable because in DL, the preamble can be one of 114 choices, and in UL, the a prior known signal (i.e., the pilots) only consists of one-third of the received signal. The second approach is based on subspace analysis, e.g., via the ESPRIT

algo-rithm [25], [26]. While the resolution in CFO estimation of these methods can be high, the computational complexity can also be high. The third approach is completely blind estimation relying solely on the repetitive signal structure of OFDMA symbols, e.g., the presence of CP. This appears simplest and suitable for use in IEEE 802.16e OFDMA.

Similarly, there are several approaches to symbol timing estimation, for example, an ap-proach utilizing the quasi-periodic time-domain structure of the preamble is introduced in [27]. But, again, one simplest and appropriate for IEEE 802.16e OFDMA is blind estimation based on CP structure.

By taking advantage of CP, an algorithm proposed in [28] can estimate the symbol timing instance and frequency offset relatively accurately in AWGN, blindly with no as-sistance from pilot symbols. Nevertheless, it suffers considerable performance degrada-tion in multipath propagadegrada-tion or Rayleigh fading [21]. A modified technique proposed in [29] is shown to have better performance in fast Rayleigh fading.

Let N be the FFT size and L be the CP length in number of samples. Figure 5.3 il-lustrates the algorithm structure proposed in [29]. Under the assumption that the received samples are jointly Gaussian, symbol time offset ˆτ and fractional CFO ˆθ are given by

ˆ

Figure 5.3: Structure of J.-C. Lin’s symbol timing and fractional carrier frequency syn-chronization method [29].

and c is set to a constant 1/L.

As mentioned, one most important task needed to be done during initial DL synchro-nization is to find the preamble index. Consequently, we may sacrifice the signal in the first DL subframe in order to estimate the preamble index more accurately. As a result, we use all the information in the DL subframe to attempt a more accurate estimate of timing offset and fractional CFO, and then find the preamble index by using the preamble symbol compensated by the estimated timing offset and CFO. We accumulate the real part and the imaginary part of λ(τ ) of all symbols in the first DL subframe to get Re{A(τ )}

and Im{A(τ )}. After that, we estimate the timing offset and fractional CFO in the last symbol of the DL subframe with

ˆ

τ = arg max{c|A(τ )|²}, (5.3)

θ = −ˆ 1

2πtan⁻¹(Im{A(ˆτ )}

Re{A(ˆτ )}). (5.4)

5.1.1.2 Integer CFO Estimation and Preamble Index Identification

Since the preamble index must be estimated by using the preamble, we keep the received preamble signal in a buffer and compensate it with the fractional CFO and timing offset estimated in the last symbol of the first DL subframe. Then we estimate the integer CFO and identify the preamble index using the compensated preamble in the frequency domain.

Note that there are three types of preamble carrier-sets and each segment uses only one carrier-set. Carrier-set 0 uses subcarrier indexes 86, 89, 92, ..., 932, 935. The subcarrier indexes used by carrier-set 1 are those used by carrier-set 0 adding 1, and carrier-set 2, adding 2. Because of this, we cannot find the exact integer CFO until we find the correct preamble index which contains the information about the used carrier-sets. Here we consider several methods to find the preamble index and integer CFO jointly.

A. Correlation Method [30]

First, we exploit some signal structure to find the coarse integer CFO. In IEEE 802.16e OFDMA, the pilot subcarriers in a preamble are limited to the central part of the band and there are guard bands at both bandedges. The pilot subcarriers are BPSK modulated.

Hence, we may look for the lower and upper ends (in frequency) of the pilot subcarri-ers by examining the subcarrier amplitudes. Since the pilot subcarrisubcarri-ers in a preamble sequence are spaced three subcarriers apart, we may add up the power of every third sub-carrier starting from the lower-end subsub-carrier as identified above up to the number of pilot subcarriers in the preamble. To account for the possible mis-identification of the lower or upper end of nonzero subcarriers, we may repeat the above power sum computation starting from several subcarrier locations around the assumed lower end. Actually, there are many terms repeated in each sums, so we can discard those repeated terms without affecting the performance. Finially, all the power sums may be compared, and we can find the coarse integer CFO from the one with the largest sum.

Since the preamble carrier-set can be one of three possibilities, the estimated inte-ger CFO, say f_I, through the above method does not necessarily give the actual integer CFO, but could be ±1 away from it. The exact value will have to be determined after identification of the preamble index.

After that, we conduct an exhaustive search to identify the preamble index by correlat-ing each of the 114 candidates with the received signal in the frequency domain and find the one with the largest magnitude of correlation. From the identified preamble index, we also obtain the corresponding segment and carrier-set as well as the actual integer CFO.

Correlation of the received preamble with a possible preamble sequence does not nec-essarily give a good indicator to their degree of match, because for it to be a good indica-tor, the preamble cannot span a frequency range much beyond the coherence bandwidth–

but unfortunately this can be very far from the truth under the IEEE 802.16e OFDMA DL system parameters discussed previously.

Towards a solution, note that since the coherence bandwidth may cover several subcar-rier spacings, we may employ a technique resembling differential detection but working in the frequency domain [31] prior to the cross-correlation in order to mitigate the cor-ruption of either frequency selective fading or nonzero OFDM symbol timing offset. We introduce the differential method and a number of variations to simplify the computational complexity in the following. More details can be found in [32].

B. Differential Method [32]

First, we find the maximum power of all the subcarriers in the 3 possible carrier-sets which start from the (86 − f_max)th subcarrier, the (87 − f_max)th subcarrier, and the (88 − f_max)th subcarrier of the received preamble, respectively, and determine the carrier-set used for estimation, where f_max is the maximum CFO search range. Note that the carrier-set we use here has length 284 + int(f_max/3) × 2 + 1, where 284 is the number of pilots in the DL preamble. Second, we derive the differential sequence from this carrier-set by

D_R[k] = Re{r_kr_k+1^∗ } = r_re,kr_re,k+1+ r_im,kr_im,k+1 (5.5) where k = 0, 1, ..., 282 + int(f_max/3) × 2 + 1.

In writing the above, we have slightly abused the index k to let it indicate the kth nonzero preamble subcarrier rather than the kth OFDMA subcarrier. This is because in IEEE 802.16e OFDMA, the nonzero preamble subcarriers are not contiguous but are spaced three subcarriers apart.

Then we derive 114 possible differential sequences from the known preamble se-quences by

D_j[k] = 1 − 2 × q_j[k] ⊕ q_j[k + 1] (5.6) where j = 0, 1, ..., 113, k = 0, 1, ..., 282, q_j[k] ∈ {0, 1} is the jth binary preamble sequence, and ⊕ denotes the “exclusive or” operation. In the end, we compute 114 × (int(f_max/3) × 2 + 1) possible metrics by using of D_R, and the length of this sequence is 283 . Then we can find the preamble index ˆj and ˆn by

(ˆn, ˆj) = arg max

n,j M_n,j. (5.8)

Note that ˆn denotes the lower-end subcarrier in the carrier-set and the estimated preamble index ˆj determines the lower-end subcarrier of the preamble symbol in the transmitter.

Therefore, we can derive the integer CFO using ˆn and ˆj.

C. Early Dropping of Bad Candidates by Dynamic Metric Thresholding [32]

This method is used to reduce the computational complexity by dropping the bad candi-dates early on. We divide the summation over 283 subcarriers in the metric computation into a number of fixed-length windows. Rather than finish computing the metric for each (n, j) pair over the total number of 283 subcarriers and then compare for the best, we may set a threshold after each window. The (n, j) pairs that perform below the threshold are dropped. This continues until only one (n, j) pair remains or until we come to the end of the last window when all the surviving (n, j) pairs are compared.

There are several parameters that can be designed in this method. We can design the length of the window size and the threshold for each window. In our design, we set the threshold to a fraction of the largest metric of all the retained (n, j) pairs. It goes without saying that the detection performance depends on the window size and the threshold, and so is the computational complexity. In the end, considering that the channel may be subject to multipath fading, it may not be good to let each window consist of contiguous preamble subcarriers. Rather, the windows should be interleaved, with the subcarriers in each window spaced, for example, beyond the coherence bandwidth.

D. Reduction of Search Range Through Coarse Estimation of Integer CFO [32]

In this method, we use the guard bands to reduce the number of candidates for integer CFO. First, we use the same approach as the first step of the correlation method to find the coarse integer CFO. This estimated coarse integer CFO may not be the true integer CFO, but may be near the true value. Then we can apply the differential method discussed previously around this coarse integer CFO for a more accurate result, but now the search range can be more restricted than without the above coarse search. Furthermore, we may apply the early dropping method around the coarse integer CFO to further reduce the computational complexity.

E. Hardlimiting of the Differential Signal [32]

Here, we consider hardlimiting the “differential signal” to simplify the differential method.

First, we still need to find the carrier-set used for estimation as the first step of the

differ-Figure 5.4: Structure of normal DL synchronization.

ential method. Then we derive the hardlimited differential sequence from this carrier-set by

DR[k] =





1, sgn{Re[r_kr^∗_k+1]} < 0,

0, sgn{Re[r_kr^∗_k+1]} > 0, (5.9) where k = 0, 1, ..., 282 + int(f_max/3) × 2 + 1. Then, we derive 114 possible differential sequences from known preamble sequences by

D_j[k] = q_j[k] ⊕ q_j[k + 1] (5.10) where j = 0, 1, ..., 113, k = 0, 1, ..., 282, and qj[k] ∈ {0, 1}. In the end, we compute the Hamming distance between the D_j[k] and D_Rn[k] by

M_n,j⁰ = X282 k=0

DRn[k] ⊕ Dj[k] (5.11)

where n = 0, 1, ..., int(f_max/3) × 2 + 1. Then we can find the preamble index ˆj and ˆn by (ˆn, ˆj) = arg min

n,j M_n,j⁰ . (5.12)

Again, we can derive the integer CFO through the preamble index ˆj and ˆn as we do in the differential method. This method is particularly useful for reducing the complexity of hardware implementation.