Praise for Fundamentals of WiMAX

280 Chapter 8 • PHY Layer of WiMAXbits in the block, and s is M/2, where M is the order of the modulation alphabet (2 for QPSK, 4for 16 QAM, and 6 for 64 QAM), and d is an arbitrary parameter whose value is set to 16:m kkN----- c ⎞ kmod d= ⎛⎝ d ⎠ ( ) + floor⎛ k ⎝d -- ⎞⎠s floor⎛ m k----- ⎞ m⎝ s ⎠ k N c floor d ⋅ m k= ⋅+ ⎛ + – ⎛---------------⎞⎞⎝⎝ ⎠⎠The deinterleaver, which performs the inverse of this operation, also works in two steps.The index of the jth bit after the first and the second steps of the deinterleaver is given byN c.mod( d)(8.1)m j = s ⋅ floor j ⎝⎠⎛⎞ s - + ⎛ j + floor ⎛-----------d ⋅ j ⎞⎞⎝ ⎝ N c⎠⎠k j dm j ( N c – 1) floor d ⋅ m j= – ⎛ ⋅ ⎛---------------⎞⎞ .⎝⎝ ⎠⎠N cmod( d)(8.2)When convolutional turbo codes are used, the interleaver is bypassed, since a subblock interleaveris used within the encoder, as explained in the previous section.8.4 Symbol MappingDuring the symbol mapping stage, the sequence of binary bits is converted to a sequence of complexvalued symbols. The mandatory constellations are QPSK and 16 QAM, with an optional 64QAM constellation also defined in the standard, as shown in Figure 8.7. Although the 64 QAM isoptional, most WiMAX systems will likely implement it, at least for the downlink.Each modulation constellation is scaled by a number c, such that the average transmittedpower is unity, assuming that all symbols are equally likely. The value of c is 1 ⁄ 2, 1 ⁄ 10,and 1 ⁄ 42 for the QPSK, 16 QAM, and 64 QAM modulations, respectively. The symbols arefurther multiplied by a pseudorandom unitary number to provide additional layer 1 encryption:, (8.3)where k is the subcarrier index, and w k is a pseudorandom number generated by a shift registerof memory order 11. Preamble and midamble symbols are further scaled by 2 2,which signifiesan eight fold boost in the power and allows for more accurate synchronization and variousparameter estimations, such as channel response and noise variance.8.5 OFDM Symbol Structures k = 2⎛1 2 -- –⎝w k ⎠As discussed in Chapter 4, in an OFDM system, a high-data-rate sequence of symbols is splitinto multiple parallel low-data rate-sequences, each of which is used to modulate an orthogonaltone, or subcarrier. The transmitted baseband signal, which is an ensemble of the signals in allthe subcarriers, can be represented as⎞ sk