The baseband receiver, which is simulated in MATLAB, performs numerous operations: find the RF burst and packet edge (starting point) for the burst; estimate and correct the coarse frequency offset; estimate and perform coarse and fine symbol time synchronization; estimate packet (RF burst) end position, and extract useful packet information; perform fine frequency-offset estimation and correction of remaining frequency offset; remove CP and convert time-domain signal to frequency-domain symbols; estimate the channel-frequency response (CFR) and correct symbol rotations due to common and carrier dependent phase offset; employ frequencydomain equalization using the CFR; detect the symbols and obtain soft symbol values to be used by the channel decoder; employ de-interleaver/decoder/ derandomizer; decode the FCH field and check the CRC. In the following subsection, a brief explanation for each block will be provided. Note that some of the blocks are standard signal-processing blocks like De-interleaving/Decoder/ Derandomization, FFT, CP removal, etc. Since information about these blocks is widely available, they will not be explained further here.

Note that in WiMAX (like other wireless-communication systems), training sequences are inserted within the data symbols to help synchronization and channel estimation. The downlink subframe begins with two OFDM symbols used for synchronization and channel estimation at the subscriber station. These two symbols together represent the preamble of the DL subframe and are referred to as the "long preamble." The uplink subframe begins with one OFDM symbol that is used at the base station for synchronization to the individual SS. This single uplink symbol is referred to as the "short preamble." Figure 10 shows the long and short preamble structures. The first symbol in the long preamble is composed of every 4th OFDM carrier (50 out of 200 total). Therefore, the time-domain signal has four repeated parts. While the first symbol in the long preamble is useful for coarse signal acquisition, it is not sufficient for detailed channel measurement and correction. Therefore in the downlink subframes, the first symbol is followed by another of the same length, containing alternate active carriers. The second symbol in time domain has two repeated parts.

Packet detection is employed to see if there is a useful packet or not (and to find the starting point of that packet). The repeating structure of the training sequences is used in this search. Two sliding windows are used. The first window is used to calculate the autocorrelation between the received signal and a delayed version of it. The amount of the delay is equal to the length of the repeating sequence, depending on whether it is downlink or uplink. The second window is used to obtain the received signal power that is used to normalize the decision statistics, so that the decision variable does not depend on the instantaneous power. The size of both windows is same, M. The values of the first and second windows can be expressed as:

and the decision variable is:

where:

y(n) = the received signal,
and
M = the window size.

If the magnitude of d(n) exceeds a threshold, it can be assumed that there is an incoming packet starting at the point at which d(n) exceeds that threshold. The selection the threshold is a design criterion for which there is a trade-off between false alarm and miss rates.

The authors have introduced additional modification to the above method, including the use of different D in the downlink (D = 128) and uplink (D = 64), adaptive threshold (start with high threshold and gradually decrease it). In addition, for calculation of b(n), the authors realized that it is better to employ the following:

Figure 11 presents a sample output of the packet-detection algorithm. It shows the results after autocorrelation and moving average filtering. The output samples are tested against a threshold. Whenever a point is reached where the samples exceed the threshold, it is declared a packet, and that point is assumed as the starting point of the packet. Figure 11 was obtained for a good SNR value (SNR = 80 dB) where the correlation of the noise is close to zero, and the correlation of the repeated parts are close to one. For low SNR values, the peak will decrease. Note also that the correlator output around the peak is not like an impulse (or a narrow pulse), it is a fairly wide pulse. Therefore, the output of the packet detection provides only a rough idea about where the packet starts.

Frequency offset is estimated using the training sequences, such as the Moose method described in ref. 13. The average phase difference between two identical parts of the training sequences is calculated and then normalized to obtain the frequency offset. The average phase difference can be calculated as: