The mean phase value is then used to calculate the frequency offset as:

In the downlink, for coarse frequencyoffset estimation, the two length-64 blocks are used in the middle of the first symbol (M = D = 64). There are two advantages to doing this:

1. By using only shorter blocks of 64, larger frequency offsets can be compensated.
2. Using middle blocks, the effect of inaccuracy for coarse timing on frequency-offset estimation can be reduced. In the uplink, we don't have a choice other than using short preamble (where M = D = 128).

For fine frequency-offset estimation (both in the uplink and downlink), the second symbol is used where better noise averaging can be obtained by using a block of 128 (i.e, M = D = 128). In the uplink, there isn't any other choice than in using this symbol anyway.

Once the frequency offset is calculated, the received time samples can be rotated in the opposite direction of the estimated frequency offset to compensate the effect of the frequency offset, i.e.,

Timing synchronization refers to finding the exact timing instant of the beginning of each OFDM symbol. Unless the correct timing is known, the receiver cannot remove the cyclic prefixes at the right timing instant of the symbol and separate individual symbols correctly before computing the FFT of their samples. Timing synchronization algorithm basically fine-tunes the rough symbol timing obtained by the packet detection algorithm. Fine symbol timing is calculated by using the short training sequence. Cross-correlation between the received signal and known reference is calculated. In this case, we obtain the optimum timing position when the cross-correlation is maximum. However, due to multipath components, it is possible to observe multiple peaks. Also, the largest peak might not correspond to the first multipath component. Therefore, an additional fine tuning of the symbol timing is needed for multipath channels. We use joint channel estimation and symbol timing estimation for fine tuning of the symbol timing estimate.

Figure 12 shows the cross-correlation between received signal and known reference. The peak, where maximum occurs, clearly shows the correct timing point for a flat fading channel (a single multipath component). However, when the channel is frequency selective, multiple peaks can be observed. Figure 13 shows the cross-correlator output for frequencyselective channels.

The packet-end detection and packet-extraction block detects the end of a packet, specifically important for measurement purposes (not an integral part of a regular receiver). If FCH information content is not available, this is an important block that detects when the useful information in the RF burst ends. If FCH content is available, or some side information about the RF burst is given as an input, we can turn off the packet end detection calculation. Otherwise, we need to turn it on so that we don't decode and measure the noise part in the received signal.

The algorithm takes advantage of the gaps before and after the RF burst to determine the end of the RF burst. Before the RF burst is turned on, a short gap that is purely noise is used to calculate the noise power. Since we have detected the beginning of the RF burst, we can also calculate the signalplusnoise-power after the starting point of the RF burst (note we use the data after the preamble for this purpose, i.e., skip the preamble). A short period (one OFDM symbol length of data) is enough for calculation of signalplusnoise-power. Using these two calculated pieces of data, it was possible to develop a decision metric to find the end of the packet.

The first step is to determine the signal-to-interference-power ratio (SNR) using the noise power measured before the packet start and signal power after the packet start (the noise power is ignored during the packet transmission assuming that signal power is much larger than the noise power):

where:

W = a window of samples (which in our case is the number of samples for one OFDM symbol length namely 256).

The SNR is monitored over nonoverlapping block of samples for all the receive samples. (For computational complexity reduction, nonoverlapping blocks are used; however, sliding windowing is also possible). Then, the SNR values are compared for each block with respect to the SNR value given above. When the SNR drops below a threshold value, it is declared as the end of the package. The choice of threshold is a design criterion.

Channel estimation is an integral part of many coherent wireless-communication receivers. There are many advanced channel-estimation techniques available in the literature. A very simple channel estimator was employed here. In this work, the channel is assumed to be almost constant during a data packet as explained earlier. A simple least-squares (LS) channel estimator with a sliding window noise averaging is used for channel-frequency estimation. The LS estimates can be given as:

where:

X_pilot = the known carrier symbols in the preamble.