**3.2. Frequency-domain equalization**

Analyzing the operation principle of OFDM, Frequency domain equalization is illustrated in Figure 4a which shows the baseband equivalent model of a single-carrier system employing this equalization technique. The received signal samples are passed to an N-point DFT, each output sample is multiplied by a complex coefficient Ci , and the output is passed to an IDFT to transform the signal back to the time domain. Now, if we take the system sketched in Figure 4a and place it between an IDFT operator and a DFT operator, we obtain an OFDM system incorporating a frequency domain equalizer. Obviously, the DFT and IDFT operators at the output end cancel each other, and the system simplifies to what we see in Figure 4b. This is precisely the schematic diagram of the equalized OFDM system discussed in the previous. Figures 4a and 4b give evidence of the strong similarities of OFDM signaling and frequency domain equalization in single-carrier systems. In cases, time/ frequency and frequency/ time transformations are made. The difference is that in OFDM systems, both channel equalization and receiver decisions are performed in the frequency domain, whereas in single-carrier systems the receiver decisions are made in the time domain although channel equalization is performed in the frequency domain.

compared with the AWGN only as shown in Figures 11 and 12 for *N*=256 and *N*=512, respec‐

MMSE-SUI 1 MMSE-SUI 3 MMSE-SUI 5

PAPR Reduction in WiMAX System http://dx.doi.org/10.5772/55380 47

MMSE-SUI 1 MMSE-SUI 3 MMSE-SUI 5

0 5 10 15 20 25 30 35 40

SNR [dB]

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**Figure 5.** OFDM BER Performance (*N*=256, 16QAM)

10-4

**Figure 6.** OFDM BER Performance (*N*=256, 64QAM)

10-3

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tively.

In this section we study the performance MMSE equalizer rather than ZF over SUI MultiPath Channels, because the MMSE solution is more efficient [15]-[17], as it makes a trade-off between residual ISI (in the form of gain and phase mismatchs) and noise enhancement.

**Figure 4.** Frequency domain channel equalization. (a) Single carrier (b) OFDM
