**3.3. Simulation results**

To compare the performance of OFDM systems in frequency selective fading channel, we consider OFDM block transmission over SUI channel model which is multipahs channel adopted by IEEE 802.16a task group for evaluating Broadband wireless system in 2-11 GHz bands. The sampling rate was assumed 20 Ms/sec.

This simulated system employs an OFDM signal with *N* =256, and 512 sub carriers using QPSK, 16 QAM, and 64 QAM, respectively.

In this simulation, SUI 1 from train type C(Flat/Light tree density), SUI3 from train type B(Hilly/ Light tree density or Flat/moderate tree density), and SUI 5 from train type A(Hilly/moderate to heavy tree density) are assumed for simplicity.

BER performance of OFDM system using MMES equalizer will be investigated in Figures 5, 6, 7, 8, 9,and 10 over SUI 1,3,5 channel models and AWGN for *N*=256 and 512 at 16QAM, 64 QAM and QPSK, respectively. Moreover, the performance of OFDM over SUI channel will be compared with the AWGN only as shown in Figures 11 and 12 for *N*=256 and *N*=512, respec‐ tively.

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

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

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.

To compare the performance of OFDM systems in frequency selective fading channel, we consider OFDM block transmission over SUI channel model which is multipahs channel adopted by IEEE 802.16a task group for evaluating Broadband wireless system in 2-11 GHz

This simulated system employs an OFDM signal with *N* =256, and 512 sub carriers using QPSK,

In this simulation, SUI 1 from train type C(Flat/Light tree density), SUI3 from train type B(Hilly/ Light tree density or Flat/moderate tree density), and SUI 5 from train type A(Hilly/moderate

BER performance of OFDM system using MMES equalizer will be investigated in Figures 5, 6, 7, 8, 9,and 10 over SUI 1,3,5 channel models and AWGN for *N*=256 and 512 at 16QAM, 64 QAM and QPSK, respectively. Moreover, the performance of OFDM over SUI channel will be

performed in the frequency domain.

46 Selected Topics in WiMAX

**3.3. Simulation results**

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

bands. The sampling rate was assumed 20 Ms/sec.

to heavy tree density) are assumed for simplicity.

16 QAM, and 64 QAM, respectively.

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

0 5 10 15 20 25 30 35 40

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

PAPR Reduction in WiMAX System http://dx.doi.org/10.5772/55380 49

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

SNR [dB]

0 5 10 15 20 25 30 35 40

SNR [dB]

10-4

10-4

**Figure 10.** OFDM BER Performance (*N*=512, QPSK)

10-3

10-2

BER

10-1

100

**Figure 9.** OFDM BER Performance (*N*=512, 64QAM)

10-3

10-2

BER

10-1

100

**Figure 7.** OFDM BER Performance (*N*=256, QPSK)

**Figure 8.** OFDM BER Performance (*N*=512, 16QAM)

**Figure 9.** OFDM BER Performance (*N*=512, 64QAM)

0 5 10 15 20 25 30 35 40

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

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

SNR [dB]

0 5 10 15 20 25 30 35 40

SNR [dB]

10-4

10-4

**Figure 8.** OFDM BER Performance (*N*=512, 16QAM)

10-3

10-2

BER

10-1

100

**Figure 7.** OFDM BER Performance (*N*=256, QPSK)

10-3

10-2

BER

10-1

100

48 Selected Topics in WiMAX

**Figure 10.** OFDM BER Performance (*N*=512, QPSK)

**4. WiMAX with compander for PAPR reduction**

**Figure 13.** Simulation model of WiMAX system.

amount of compression.

**5. Simulation results**

reasons of standard compliance.

The system will be used in this work is shown in Figure 13. The transmitter section maps a random data bit sequence, into a sequence of QAM symbols. The QAM symbols are partitioned into N-length blocks and modulated onto the sub-carriers of an OFDM modulator via the inverse Fast Fourier Transform (IFFT). Before guard interval insertion, prior to transmission, the signal is companded with µ-law compander. The companded signal is then passed through the amplifier at the transmitter, which distorts the signal according to nonlinear solid state power amplifier models. After transmission, the signal is passed through SUI channels and

PAPR Reduction in WiMAX System http://dx.doi.org/10.5772/55380 51

corrupted with AWGN, compensation, µ-law expansion, and OFDM demodulation.

Compander (µ) was described in detail in chapter 3 where µ is the parameter controls the

The performance of proposed WiMAX is evaluated using computer simulation. In this study, the channel is assumed to be known perfectly at the receiver. The simulated system employs an OFDM signal with *N = 256* subcarriers, among which *192* data carriers (*QPSK, 16QAM or 64QAM* signal mapping), *8* pilots, the others are nulls, guard interval *Tg = (1/4)Tb*, where *Tb* is the useful symbol time, and sampling frequency=9.12 *MHz*. For simplicity, uncoded OFDM will be employed. When applying the compander/expander, we must take into account some system constraints: Neither the pilots nor the guard intervals are allowed to be modified, for

**Figure 11.** BER Performance comparison (16QAM, *N*=256).

**Figure 12.** BER Performance comparison (16QAM, *N*=512).
