the first OFDM symbol. The interferences and their causes in different OFDM symbols are summarized in Table 2.2. It is shown that RSSs’ CFOs cause ICI to all the symbols in the ranging time slot, while only the first OFDM symbol suffers from the extra ISI and ICI introduced by RSSs with large timing offsets.
Table 2.2: Interference in OFDM symbols of a ranging opportunity.
Symbol CFO Range of Timing Offset
(−τmax, Ng−τmax] (Ng−τmax, N + 2Ng−τmax]
1 ICI - ICI + ISI
{2,3, . . . , Ir} ICI - -
2.4
Summary
In this chapter, we have described the mathematical modeling of the wireless chan- nel and the OFDM system of interest. The classic methods to model the propa- gation loss and shadowing effect of wireless channels have been briefly reviewed. These models suggested a large dynamic range of SNR in outdoor wireless commu- nication environments.
We modeled the multipath fading channel with a tapped delay line, and emu- lated the taps’ time-varying Rayleigh fading by the Jakes’ model [116] and the SUI model [113] respectively for mobile and stationary wireless channels. Two channel models were selected for the simulations in this thesis. Their parameters followed the recommendation of the standards and were representative for deep-fading and time-frequency-selective characteristics of wireless communication channels respec- tively.
The mathematical expressions of OFDM signals were given, followed by the generalized definition of the training symbols. It was shown that the generalized training symbols did not necessarily consist of identical segments in the time do- main in spite of the high correlation between them.
The OFDMA signal observed at the receiver in the ranging time slot was de- scribed mathematically. The timing positions of FFT windows were suggested to minimize ISI and ICI. It was observed that the RSSs were more likely to incur ICI and ISI on the first OFDM symbol in the ranging opportunity, and thanks to the continuous phase of the ranging signal over the whole ranging opportunity, the following OFDM symbols were much less affected by the large timing offsets.
Chapter 3
Coarse Timing Estimation
3.1
Introduction
An OFDM signal contains multiple OFDM symbols concatenated in the time do- main. At the receiver, the boundaries between the OFDM symbols need to be determined before the signal can be translated to the frequency domain using an FFT function. In this chapter, we present a novel algorithm to take advantage of the special structure in the training symbols and locate the start positions of OFDM bursts.
In realistic wireless communication environments, the boundaries between the OFDM symbols are often blurred by multipath channels, so the ideal start of the FFT window at the receiver is usually difficult to locate in the time domain. We know that as long as the samples in the FFT window belong to the same OFDM symbol, the ISI and ICI are avoided. Therefore, it suffices for the coarse timing estimator to find the ISI-free FFT window of the training symbol, then the residual timing offset can be estimated from the frequency domain signal using a refined joint channel and timing estimator discussed in Chapter 5. For instance, in an AWGN channel, all the timing positions from sample 0 to (Ng−1) are good coarse
timing estimates, and we leave the accurate timing estimation to a latter signal processing stage.
A coarse timing estimator needs to detect the arrival of a new OFDM burst, and then give an estimate where the burst starts. Comparing the two steps of timing estimation, the former is much more challenging than the latter, therefore, the discussion on coarse timing estimation actually is mainly about OFDM burst detection. Nevertheless, detection is only an integral step of estimation, and the purpose of the coarse timing estimator is to locate the position where the burst
starts rather than determining whether a burst has started or not.
For the generalized training symbols we introduced in Chapter 2, the high correlation between the segments in the training symbol differentiates the preamble from the noise and other OFDM symbols in the burst. It means that the timing can be estimated by a correlator whose output is expected to be high when the samples are highly correlated, which indicates a good chance to be a training symbol. Once the training symbol is located, the timing for the whole burst can be derived. Although it is possible to use only one correlator for timing estimation, when there are multiple highly correlated segments in the training symbols, one would intuitively want to use a number of correlators and combine the outputs for enhanced performance. These basic ideas lay down the main procedures of our timing estimation method.
In this chapter, we propose to construct a series of component timing metrics, one for each pair of highly correlated segments in the training symbol. Then we linearly combine them to minimize the false alarm probability under the constraints on correct detection performance. The component timing metrics only require the correlation between the segments to be high, so the proposed method is applica- ble to generalized training symbols including those specified by the IEEE 802.16 OFDMA (WiMAX) standard which have three highly correlated but not identical segments. Moreover, the proposed method takes advantage of multiple training symbols for further performance improvement. It is also worth noting that the data symbols in one OFDM burst can have different power levels to reach the users at different distances. We take that into account and yield more realistic results yet found in the existing literature.
The performance of the proposed method is analyzed in three scenarios general- ized from the IEEE 802.11 and IEEE 802.16 standards. When there is one training symbol with two and four identical segments, the proposed method is equivalent to that in [10] and [42] respectively. Our analytical results show that using more identical segments in the training symbol only reduces false alarms and has little impact on the missed detection probability. This justifies our false alarm probabil- ity based optimization criterion, and contradicts the existing timing metric design approach which is based on the detection probability. Simulations agree with our analytical results reasonably well and confirm the performance of the proposed method in various channel conditions.