nce we assume that the pilot sub-carriers have unity magnitude. An alternative approach to pilot-based channel estimation is Minimum Mean Squared Error (MMSE) method. The MMSE channel estimator exploits the second-order statistics of the channel CHAPTER 9 The IEEE 802. 16m Physical Layer (Part I) LS Estimation OFDMA SC-FDMA Estimation SNR (dB) FIGURE 9-40 An example comparison of the LS and MMSE channel estimation algorithms transfer function to minimize the mean-square error. Let RHH = E(HHH), and o2 denote the auto- correlation matrix of the channel vector H and the AWGN noise variance, respectively. The MMSE estimate of the channel transfer function is given as: HMMSE = RHH[RHH + (XX ) - 1 - 1 HLS = XX H I I (9-30) The MMSE estimator performs much better than LS estimators, especially under low SNR conditions. A major drawback of the MMSE estimator is its high computational complexity, particularly if matrix inversion is necessary every time the input data changes. Figure 9-40 shows an example where the performance of the LS and MMSE channel estimation algorithms has been compared. In this example NFFT = 64, and the channel is modeled as a two-tap delay line filter. The superiority of MMSE over LS estimation in low SNR conditions can be seen in Figure 9-40. 9.12 CHANNEL CODING AND MODULATION Forward-Error-Correction (FEC) channel coding schemes are commonly used to improve the effi- ciency and robustness of wireless digital communication systems. On the transmitter side, an FEC encoder adds redundancy to the input data in the form of parity bits, while at the receiver, the redundancy is utilized by the FEC decoder to correct a number of channel errors. The use of FEC schemes would allow tolerance of more channel errors that otherwise can be tolerated without forward error correction. The use of FEC schemes enables wireless communication systems to operate with a lower transmit-power, to transmit over longer distances, to tolerate more interference, and to transmit at a higher data rate. A binary FEC encoder re