**7. Symbol mapping and structure**

When a symbol is mapped, the sequence of binary bits is converted to a sequence of complex valued symbols. The mandatory constellations are QPSK and 16 QAM, with an optional 64QAM constellation also defined in the IEEE 802.16e standard. Assuming all symbols are equo-probable each modulation constellation is scaled by a factor <; such that the average transmitted power is unity. Where<; is given by /½\_,.J½a,.J¾ *<sup>2</sup>*for QPSK, 16QAm and 64QAM modulations shown in Fig. 11. If convolution coding is applied for PHY encryption then we have an output given by

$$S\_k = 2(\bigvee\_2 - w\_k)S\_k$$

By scaling the preamble and midamble symbols by a factor 2../2 we we amplify the power by a factor 8 and allow for more accurate synchronization and various parameter estimations, such as channel response and noise variance .

A high-data-rate sequence of symbols can be split into multiple parallel low-data ratesequences, each of which is used to modulate an orthogonal tone, or subcarrier. The resulting baseband signal, which is an ensemble of the signals in all the subcarriers, can be represented as

Fig. 11. QPSK, 16QAM and 64QAM Modulation Constellations

#### **8. References**

