N7615C Signal Studio for Mobile WiMAX 2018 software calculates one OFDM symbol at a time, using an IFFT of the size specified by the FFT Size parameter in the Carrier Setup node. To create the guard interval at the front of the symbol, it appends a cyclic prefix to the front of the symbol. The cyclic prefix length is specified by the Guard Period parameter in the Waveform Properties node, which is expressed as the ratio of the cyclic prefix to the useful symbol length. For mobile WiMAX, this value is 1/8, so for a 1024 FFT size, the last 128 samples of the IFFT will be copied and appended to the symbol, creating a composite symbol that is 1152 samples long. (Refer to Figure 1, below.) Using the last 128 samples has the effect of making the composite symbol appear continuous in time; that is, the 1024 point FFT of the symbol will be identical regardless of which 1024 samples we choose out of the 1152 available. These 128 additional samples are what produce multipath fading immunity since we can slide in time by up to 11.4 ms without causing a decoding error.
We need a means of assembling consecutive symbols without causing spectral regrowth, which arises from the fact that a given symbol rarely begins with the same amplitude and phase with which the previous symbol ended. To avoid spectral regrowth, we must create a smooth transition between the last sample of one symbol and the first sample of the next symbol. We do this with a combination of two tools: a cyclic suffix, and windowing.
The windowing function is controlled by the Symbol Rolloff [%] parameter in the Waveform Properties node, which is expressed as the percentage of the window length to the length of one symbol. To illustrate this, assume we have selected a Symbol Rolloff of 5%, which is a window length of 51 samples for a 10 MHz signal (5% of the 1024 FFT). To create the cyclic suffix, we copy and append the first 51samples of a given symbol to the end of that symbol, so that now the symbol is effectively 1203 samples long. This has the desired effect of making the symbol appear continuous going into the transition. However, if we are to comply with the standard, we cannot arbitrarily lengthen the symbol in this way. Instead, this cyclic suffix overlaps in time (and is effectively summed) with the cyclic prefix of the next symbol. This overlapped segment is where windowing is applied. In fact, two windows are applied, one being the mathematical inverse of the other. The first cosine window is applied to the cyclic suffix of symbol 1, and rolls off from 1 to 0 over its duration. The second cosine window is applied to the cyclic prefix of symbol 2, and rolls on from 0 to1 over its duration. This gives the desired smooth transition from one symbol to the next.
There is one more variable in the equation: the window length. In this example we used a window length of 51, so the cyclic suffix was 51 samples long. However, the length of the cyclic suffix is adjusted along with the window length setting, which is determined by the Symbol Rolloff [%], so any suffix length between 0 and 10% of the total symbol length may be set. The effect of windowing is that it improves spectral regrowth and adjacent channel power ratio (ACPR), but at the expense of multipath fading immunity and possibly less desirable error vector magnitude (EVM) characteristics. This occurs because redundancy in the guard band is reduced due to the fact that the guard band sample values are compromised by the smoothing.
The following figures display the application of cosine windowing:
Figure 1. Cosine windowing
Figure 2. Spectrum plot of I/Q waveform with Symbol Rolloff = 0% (no windowing)
Figure 3. Spectrum plot of I/Q waveform with Symbol Rolloff = 5% (default)