Rapid growth of Wireless Interoperability Microwave Access (WiMAX) as a broadband wireless technology is expected due to increasing demand for convenient Internet access and highspeed data access. In order to construct wideband wireless systems such as WiMAX, however, effective modeling must be performed. In this report, wideband modeling was performed on key elements of a WiMAX system, notably the modulator, frequency upconverter, and transmit power amplifier. This modeling included the study of phase-noise effects. Extensive computations were carried out to study the effects of nonlinear effects as well as performance variations due to phase noise.

Wireless transmission of high data rates requires careful modeling of both the transmitter and receiver. A number of reports have addressed this previously. For example, in ref. 1, a multi-band multi-standard receiver architecture for wireless applications, such as IEEE 802.11a/b/g WLAN, and IEEE 802.16a wireless metropolitan-area network (WMAN) is presented. The targeted frequency bands include the licensed bands at 2.3 GHz, 2.5 to 2.7 GHz, and 3.5 to 3.7 GHz, and the unlicensed ISM 2.4- GHz and UNII 5-GHz bands. The main advantage of the proposed receiver include the use of a single frequency synthesizer for wideband frequency translation, with each frequency band sharing the same LNA and mixer for reduced chip area.

Reference 2 explains orthogonal frequency division multiplex (OFDM) and single-carrier (SC) physical layers as two separate and standalone compliant modes for the licensed bands between 2 to 11 GHz. The purpose of this article is to explore the benefits of mixed-mode operation with OFDM downlink and SC with Frequency Domain Equalization (SC-FDE) uplink; each is strictly compatible with currently available OFDM and SCFDE modes. It is not proposed as a new operating mode, but rather an integration of the existing OFDM and the SC modes.

Reference 3 describes equalizer adaptation in time-variant frequency-selective FRA-channels in the presence of oscillator phase noise. This article will explore the complexity of implementing that equalizer and compare it to a set of different equalizers. In addition, this article will examin the effects of a various parameters concerning the WiMAX baseband spectrum, such as the modulation scheme and the number of Fast Fourier Transform (FFT) points, and the effects of phase noise during modulation and frequency upconversion. By studying these parameters, a telecommunication systems designer can better understand how to increase the performance of a given model. Modeling of the telecommunications channels was performed with the aid of the Advanced Design System 2005A^{TM} simulation software from Agilent Technologies (www.agilent.com).

Figure 1 shows the transmitter model, consisting of a baseband modulator unit, and RF modulator and frequency upconverters, and a power-amplifier and phasenoise input. Figure 2 shows the baseband modulator unit, consisting of the input data modulation, the pilot data modulation, their mutual OFDM modulation, and an imported preamble to produce a complete IEEE 802.16 WiMAX baseband signal. Figure 3 shows the RF modulation and signal upconversion process. An amplifier, an in-phase (I)/quadrature (Q) modulator with an external oscillator and Chebyshev bandpass filter are used for this purpose. Figure 4 shows the power amplification and phasenoise input port. This involves the use of an RF gain amplifier, an external noise source (to provide controlled degradation of the external oscillator), and a power splitter for the timed measurements.

A computer-aided-engineering (CAE) software program based on Agilent ADS 2005A was used to develop a simulation program. Two cases were studied: a case free of phase noise and a case with a noisy modulator. For the first case, the focus was on the effects of various baseband parameters on the output baseband signal. These parameters include bandwidth, the number of Fast Fourier Transform (FFT) points, and the modulation scheme. The relationships established in the IEEE 802.16 WiMAX standard were used as the basis for the simulation, including:

Sampling frequency, Fs = floor X 8000

Subcarrier spacing, ?f = Fs/NFFT

Useful OFDM symbol time, Tb = 1/?f

Cyclic prefix time, Tg = G X Tb

OFDM symbol time, Ts = Tb + Tg

Sampling time = Ts = Tb/NFFT

Samples per symbol = bandwidth X OFDM symbol time

Symbols per second = bandwidth/symbols per second or 1/OFDM symbol time

The subcarrier spacing is the sampling frequency divided by the number of the FFT points. Therefore, the useful symbol time is the inverse of the subcarrier spacing. By setting the step that the ADS algorithm will use for timed measurements, TStep, equal to the useful symbol time divided by the number of FFT points (the inverse of the sampling frequency), the algorithm will work properly.

One simulation was set up with a constant modulation scheme (16QAM with a 1/2 coding rate), a constant number of FFT points (256), a constant guard time (0.25 X the symbol time), and bandwidth as the variable. The starting bandwidth was 1.75 MHz and the stopping bandwidth was 28 MHz, using care to select channel bandwidths specified in the IEEE standard. By increasing the bandwidth, the ripple of the signal increased as well, while unwanted sidelobes were suppressed more than -35 dBc than the desired signal level (Fig. 5).

### Page Title

**Changes in Bandwidth **

Changes in bandwidth resulted in changes in data transfer rate. The bandwidth is clearly affected by the number of available symbols. By increasing the bandwidth, the sampling frequency also increases, as does the subcarrier spacing. By the increase of the bandwidth, the sampling frequency also increases, and so does the subcarrier spacing. However, the symbol time is constantly decreasing, as is the sampling time. Therefore, while the bandwidth is increased, more data is also sampled, resulting in greater signal ripple.

The number of samples per symbol is constant and equal to 280 in the IEEE standard. What is changing is the number of symbols that are finally being sampled. For a 1.75- MHz bandwidth, for example, there are 6250 symbols; for a 20-MHz bandwidth, there are 71429 symbols; and for a 28-MHz bandwidth, there are 100,000 symbols. While the bandwidth increases, the number of symbols, resulting in the increased ripple.

Another simulation was set up with constant modulation scheme (16QAM with a 1/2 coding rate), constant guard time (0.25 X symbol time), constant bandwidth (20 MHz), and using the number of the FFT points as a variable. The starting value was 256 FFT points and the finishing value was 4096 FFT points. The results of this simulation show that as the number of FFT points increases, the ripple of the output spectrum signal diminishes and the sidelobes are suppressed, reaching -55 dBc relative to the desired signal level. This sidelobe suppression helps to reduce intersymbol interference (ISI). This occurs because of the precision possible with a large number of FFT points, minimizing amplitude ripple effects. More data is being multiplexed in the same OFDM symbol so that large variations in the complex FFT amplitude value are eliminated.

When the number of the FFT points increases, there is a substantial decrease in the subcarrier spacing . In contrast, there is an increase in the symbol time, while the sampling time remains the same, allowing more samples to be received per symbol. This explains the stretching of symbols in the frequency domain. In the case of 256 FFT points, there are 280 samples per symbol and in the case of 4096 FFT points, there are 4480 samples per symbol.

When sampling a large number of FFT points, a great deal of computing power and adequate spectrum space for the spectral representation are required. However, it is obvious that many samples per symbol lead to few symbols per second. That is because of the relation between them . Thus, in a 20-MHz bandwidth, for 280 samples per symbol, there are 71,429 symbols per second, whereas for 4480 samples per symbol, there are 4464 symbols per second. Using a large number of FFT points doesn't lead to increased transfer rate, but to signal oversampling. This may diminish the effects of ripple but may cause spreading in the frequency domain, which leads to ISI (Fig. 6).

For another simulation, the number of FFT points was kept constant (256), with constant guard time (0.25 Xsymbol time), constant bandwidth (20 MHz), and a variable modulation scheme. The initial modulation scheme was BPSK with 1/2-rate coding, progressing to a final modulation scheme of 64QAM with 3/4-rate coding. The table shows the different modulation schemes used in the simulations. The results reveal that signal ripple increases with the increasing complexity of the modulation scheme. This occurs because as the points in the constellation increase, an increase in the transferring symbols also exists, but the points are so close (and multiple carriers are used to represent them), that signal rippling is created and also probable errors arise during their representation in the frequency domain.

For the simulation with BPSK modulation, 1 b per carrier was used. For QPSK, 2 b per carrier was used. For 16QAM, 4 b per carrier was used, and for 64QAM, 6 b per carrier was used. This was expected to create problems during demodulation and lead to increased bit-error rate (BER) upon reception. Figure 7 shows the results of the simulations performed with varying modulation schemes.

For these simulations, the number of FFT points was kept constant (256), the guard time was a constant (0.25 X symbol time), the bandwidth was a constant (20 MHz), and the modulation scheme was varied from BPSK to QPSK to QAM (see table). The simple equation of Data rate = Number of Data Carriers X Bits per Carrier X Coding Rate X Number of Transferred Symbols per second was applied in the simulation.

As the modulation scheme becomes more complex, the data transmission rate increases. As the modulation scheme becomes more complex, the symbols entering the constellation during the modulation increase as well. As a result, more symbols are transferred to the same frame. The amount of transmitted data is much greater for the 64QAM modulation scheme than for BPSK. The possibility of errors occurring is much greater in the QAM case (because the symbols entering the constellation are very close with each other and there may be symbol confusion during the demodulation) and that is its disadvantage. More data may be transmitted in the same time using QAM, but the probability of errors occurring is much greater. The maximum transmit rate which is achieved is approximately 86 Mb/s for a 28- MHz bandwidth, which is quite acceptable for the new IEEE standard.

In one simulation, phase noise was used as the variable, imported into the modeled transmitter chain. The noise enters during the modulation, which is also affected by an external oscillator. A typical set of values for the simulations was phase noise of -70 dBc/Hz offset 10 kHz from the carrier, -90 dBc/Hz offset 100 kHz from the carrier, -105 dBc/Hz offset 1 MHz from the carrier, and -120 dBc/Hz offset 10 MHz from the carrier (Fig. 8).

Finally, a set of simulations was performed to evaluate the amplifier in the modeled transmitter chain. A number of characteristics were studied, including noise figure, 1- dB compression, and saturation point. The saturation point power was set to +31 dBm, so the 1-dB compression point power was used as a variable with values from +21 to +29 dBm and variable values from 3 to 7 for the noise figure.

As could be seen from the simulation results, as the 1-dB compression point increased, the level of the signal (useful and noisy without discrimination) increased noticeably. For 1-dB compression at +21 dBm, the waveform peak was below 0 dBm, while for 1-dB compression at +29 dBm, the peak exceeds 0 dBm, reaching +5 dBm. During this increase, unwanted sidelobes began to diminish, which helps to minimize ISI.

### Page Title

As the noise figure increased, the interference of noise in the signal also increased, raising the level of the signal as a whole. Noisy signals are clearly not desirable, and the IEEE standards for the spectrum mask can be applied to determine which set of values (1-dB compression or noise figure) in order to achieve operation within the spectral mask. As Fig. 8 shows, the simulation process come down to the sets {27,5} or {29,3}. If choice between these 2 sets needs to be made, the final choice will be the set {29,3}, which results in small signal rippling more depressed sidelobes.

The results of these simulations show the effects of changes in different parameters on IEEE 802.16 WiMAX system performance. Because changes in different parameters affect the overall performance differently, system-level engineers have some flexibility in optimizing the system performance. Even in the case of different levels of phase noise, these simulations show how the overall system- level performance can be optimized in the WiMAX case.

**Acknowledgments **Special regards are owed to the primary author's supervisor, Professor Nicolaos Uzunoglu for his special attention and interest in the successful completion of this thesis, and to Dr. Yorgos Stratakos for his willingness to help and share his experience on wireless systems.

**References **1. Chao-Shiun Wang, Wei-Chang Li, and Chorng-Kuang Wang, "A Multi-Band Multi-Standard RF Front End For IEEE 802.16a and IEEE 802.11a/b/g Applications," Graduate Institute of Electronics Engineering & Department of Electrical Engineering, National Taiwan University, Taipei, Taiwan.

2. Moshe Ran, David Falconer, and Anader Benjamin Seeyar, "A Mixed OFDM Downlink and Single Carrier Uplink for the 2-11 GHz Licensed Bands," unpublished.

3. Ralph Hasholzner, Christian Drewes, and Joachim S. Hammerschmidt, "The effects of multiple access schemes on equalization for broadband wireless local loop systems," unpublished.

4. Techteam.gr Wiki,' 2006, http://www.techteam.gr/wiki/WiMAX

5. Todor Cooklev, Wireless Communication Standards: A study of IEEE 802.1^{TM}, 802.15^{TM}, and 802.16^{TM}, Artech House, Norwood, MA, 2002

6. "Exploitation of Broadband in Western Greece," White Paper, 2006, http://ru6.cti.gr/broadband/el/wimax.php

7. Westech Communications, Inc. on behalf of the WiMAX Forum, "Can WiMAX Address Your Applications?" WiMAX Forum, 2005.

8. Wikipedia, "WiMAX Technology" 2005.

9. Edward Grabianowski and Marshall Brain, "How WiMAX Works," http://computer.howstuffworks.com/wimax5.htm

10. SR Telecom White Paper 033-100596-001, Issue 1, "WiMAX Technology, LOS and NLOS Environments," August 2004.

11. Advanced Design System 2005A Documentation, WMAN IEEE 802.16^{TM} Specifications,' 2005.

12. IEEE Computer Society and the IEEE Microwave Theory and Techniques Society Sponsored by the LAN/MAN Standards Committee, 802.16^{TM} IEEE Standard for Local and metropolitan area networks Part 16: Air Interface for Fixed Broadband Wireless Access Systems,' October 1, 2004.

13. Shinsuke Hara, Ramjee Prasad, Multicarrier Techniques for 4G Mobile Communications, Artech House, Norwood, MA, 2003.

14. Dusan Matiae, "OFDM as a possible modulation technique for multimedia applications in the range of mm waves," October 30, 1998.

15. Anibal Luis Intini, "Orthogonal Frequency Division Multiplexing for Wireless Networks," University of California, Santa Barbara, CA, December 2000

16. Charal Langton, "Intuitive Guide to Principles of Communications, Orthogonal Frequency Division Multiplexing (OFDM) Tutorial," http://www.complextoreal.com

17. Applied Radio Labs, "Phase Noise Reference," April 25, 2003, http://www.radiolab.com.au/DesignFile/PNRef/PNRef.htm