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**Chapter 3. Simulation Approach**

In the previous we laid out a mathematical model for CDMA communications. In this chapter we present the implementation details of a simulation based on that mathematical model.

Generation of AWGN

When transmitted signals arrive at a receiver, thermal noise is added to transmitted signals at the front end of the receiver. We model the thermal noise as the additive white Gaussian noise (AWGN). This section explains how the noise term of the received signal representation is modeled in the simulation. s k (t) in Equation (2-3) is the complex baseband representation of the transmitted signal and the corresponding signal constellations is illustrated in Figure 3-1.

Pk is the power of one bit and 2Pk is the magnitude of one symbol since the QPSK

modulation scheme is used. They can be expressed as

r : rate of error control code;

SF : spreading factor;

m : samples per symbol,

and A is magnitude of the modulation symbol. In simulation, Eb is assumed to be one,

and noise is scaled to produce the desired Eb N0 . The noise samples to be added are

written as

n = x + jy

where x is in-phase part and y is quadrature part of noise sample. Gaussian random variables with the same variance which is where Es is energy per QPSK modulated symbol.

**Channel Model**

For simulation of frequency selective and slow fading channels, the modified Jakes’ model in [13] is used. This modified channel model generates time-uncorrelated Rayleigh fading waveforms while the Jakes’ deterministic fading model is for simulating time-correlated waveforms [13].

“The advantage of the modified Jakes’ model over other forms of fading simulator lies in its greatly reduced executing time and capability for simultaneous generation of multiple uncorrelated fading signals [13].” The fading waveform for the lth path is represented by In Equation (3-4), the random variables are deterministic with time and path. This random process is ergodic and the fading waveforms are uncorrelated to each other. Therefore, one Rayleigh distributed and the other uniform distributed random variable can be obtained from the magnitude and phase of Equation (3-4).

Figure 3-2 shows the distributions of 80000 samples of a waveform from the modified Jakes’ model. The Gaussian distributions of X c , l (t) and X s , l (t) in Equation (3-4) are presented in Figure 3-2 (a). The Rayleigh distribution of αk , l is shown in Figure 3-2 (b). The uniform distribution of e jψ k ,l is shown in Figure 3-2 (c).

For the simulation, the values of channel parameters are set arbitrarily, according to Table 3-1. These parameters are intended to model on urban microcell environment, which is among the most challenging environments from a capacity perspective.

The choice of the delay and attenuation parameters is according to a power delay profile of a specific channel environment. Indoor or outdoor, urban or rural, and macrocell or microcell channel environment each leads to a different power delay profile. Since the number of multipath is three, the number of the fingers of the Rake receiver is less or equal to three. For simulations in frequency selective fading channel environment, chip duration should be less than delay.

**Orthogonal Variable Spreading Factor (OVSF) codes**

In WCDMA system, the Hadamard codes called OVSF codes are used for spreading message signals. In general, the OVSF code of length 2n+1 is generated through the procedure described in Figure 3-3 [10].

The notation CSF , k means the k th code with the spreading factor SF . The spreading factor should be a power of 2, and for a given SF , there are SF orthogonal codes which differ from each other in exactly SF2 positions. Also, orthogonality is preserved even between some two codes with different SF s. However, if one code is one of the mother codes of the other one, they are not orthogonal to each other and can not be used for spreading codes simultaneously. Therefore, the spreading factor of one user restricts the number of available codes for the other users.

In Figure 3-4, C4,2 is the mother code of C8,4 and C8,5 . The auto-correlation of the OVSF codes is quite poor even though they are orthogonal to each other. In Figure 3-5, auto and cross-correlation properties of OVSF codes are presented.

**Simulation Assumptions**

Some assumption should be made for simulation of the CDMA system described in the previous chapter. First, the simulation is based on a baseband signal. Thus, symbols, noise, and multipath fading are represented in complex baseband form instead of multiplying by a high-frequency sinusoidal carrier. For an analytical description of the simulation condition, it is assumed that the carrier frequency is 2 GHz and the chip rate is 3.84 Mcps. This assumption is in accordance with the WCDMA standards. However, the simulation results cannot be compared with the performance of a commercial WCDMA system since the simulation condition does not satisfy with the other WCDMA standards.

Short spreading codes are used for simulation. In Figure 3-6, SF denotes the length of spreading code and is the abbreviation for spreading factor. The data rate is variable according to the value of SF . Therefore, the general expression for the data rate is ( 2 × 3.84) SF Mbps. The first null bandwidth is 3.84 MHz since the rectangular pulse shaping is used in this simulation. The WCDMA standard employs raised cosine pulse shaping with a roll-off factor of 0.22. While pulse shape plays a significant role in determining the spectral characteristics of the signal, and may play a factor in performance if timing offset is an issue, it dose not heavily influence the performance of the system in multipath and multiple access interference. In order to reduce simulation complexity, we use rectangular pulse shapes in this thesis. The values of the carrier frequency and chip duration are required to generating the Rayleigh fading channel waveforms using the modified Jakes’ model.

**Gaussian Approximation for QPSK**

In this section, the Gaussian approximation for the performance of DS-CDMA system using QPSK modulation scheme is derived in the AWGN channel environment. The well-known Gaussian approximation for BPSK is extended to the case of QPSK.

Assuming the phase of carrier signal φ1 and the delay τ1 for 1st user are equal to zero, the transmitted signal of 1st user can be expressed as Including the other K −1 concurrent users’ signals, the received signal can be represented by At the output of the correlators, the decision statistics of in-phase and quadrature component are expressed as where the random phase θk is uniformly distributed on the range between 0 and 2π . The first and second term of Ik ,Re and Ik ,Im has zero mean and the same variance as the interference of DS-CDMA using a BPSK modulation scheme. Therefore, the average power of interference for QPSK is double that of BPSK.

The well-known bit error probability of BPSK is expressed where N is the processing gain and equal to W Rb . To calculate the error probability of QPSK, two parameters in Equation (3-23) should be changed. One is pJ substituted by 2× pJ since the interference level of QPSK increases by a factor of 2. The other is due to the reduction of information data bandwidth. For QPSK, Rb decreases by a factor of 2. As a result, the Gaussian approximation of QPSK is the same as that of BPSK, and expressed as

**Simulation Results**

In this section, computer simulation results are shown to verify how the channel environment and various parameters affect the performance of a CDMA system. The computer programming for simulation is based on the previous mathematical description and assumptions. All simulation results are for the performance on the uplink from mobile handsets to a base station.

Figure 3-7 compares the performance in three cases of one, three and five users in an AWGN channel. There is no multipath. The spreading factor is 16 in Figure 3-7(a), and 8 in Figure 3-7(b). The Gaussian approximation (GA) provides some validation of the simulation results. Comparing between Figures 3-7 (a) and (b), it is apparent that as the SF decreases, the mean interference between users increases, resulting in corresponding degradation in BER performance.

In Figure 3-8, the simulation result in Figure 3-7 shows the Frame Error Rate (FER) for the situation corresponding to Figure 3-7. One frame consists of 2560 chips, so 160 information bits are transmitted in each frame since the spreading factor is 16. In the case of three users, more erroneous frames are expected at the receiver due to the increase of interference.

The effect of Rayleigh fading is represented in Figure 3-9. It is assumed that there is only one path, and one finger for a Rake receiver. As the speed of user is increased, performance is poorer. As expected, Rayleigh fading severely impacts performance.

In Figure 3-10, the effect of Rayleigh fading is represented in terms of FER. The frame length is the same as the length of 2560 chips. Since the performance in the Rayleigh fading channel poorer, the FER is higher.

For Figure 3-11, the number of Rake fingers is only one and the results explore the effect of multipath. Since only one finger is used, the receiver cannot resolve the signal components for the 2nd or 3rd path. Therefore, the more paths that exist, the more interference is caused. However, since the attenuation on 3rd path is severe according to Table 3-1, the 3rd-path signal almost does not cause interference.

The more fingers of a Rake receiver that are used, the better the performance that can be expected since the additional fingers resolve multipath signal components. Figure 3-12 shows the performance changing according to various numbers of fingers. From Table 3-1, there are three paths which signals pass along with different time delays. As shown in Figure 3-12, the incremental performance improvement diminishes as the number of Rake fingers increases, owing the fact that less power is contained in additional multipath.

Figure 3-13 compares the performances at 16, 32 and 64 of spreading factor. The higher spreading factor is applied, the greater spreading gain can be guaranteed. However, since the increase of spreading factor is accompanied with the decrease of data rate, the choice of spreading factor is in accordance with a target BER or desired data rate.

As described in Chapter 2, the other users’ signals cause interference to a desired user. Therefore, there is an acceptable number of users to meet a desired QoS. As shown in Figure 3-14, when the number of users is 10, increasing the power of signal does not decrease the probability of bit error, creating on irreducible error floor. In order to preserve a desired QoS in the practical environment of changing number of users, some management processes should be performed: for example, increasing processing gain or blocking new users.

Increasing the power of a desired user’s signal improves the performance of the desired user at the expense of other users experiencing more interference. In Figure 3-15, when the power of desired signal is 3dB higher than that of the other users’ signals, the performance for desired user becomes better than the case of equal power. Conversely, when the power of desired signal is 3dB lower than that of the other users’ signals, the performance for desired user becomes poorer than the case of equal power.

Chapter Summary

In this chapter, the implementation details of a simulation and simulation results are presented. The simulation model of AWGN and multipath fading channel, the property of OVSF codes, and the assumed data rate and bandwidth are described in Chapter 3. The simulation results show the effects of AWGN and multipath fading, and how the number of fingers or users, spreading factor, and signal power affect the performance.

**Hybrid coding with ARQ and FEC**

This chapter presents the theoretical description of ARQ protocol, FEC scheme and hybrid coding. The purpose of this chapter is to represent the performance improvement with hybrid coding in theory and simulation.

**Coding Scheme**

In real wireless channel environment, noise and signal interference cause the desired signal to be easily harmed. Therefore, it is necessary to reduce the probability of bit error in order to meet quality of service requirements. Channel coding is one method for error detection and correction by means of adding redundant bits to information bits. In this section, the performance of block coding and convolution coding is investigated.

**Block Codes**

A block code is able to detect and correct error bits. In general, k information bits are represented as an n -bit code word through the encoding process. In other words, n − k redundancy bits are added to obtain coding gain.

Contents

**Acknowlegements **

**Chapter 1. Introduction **

1.1 Multiple Access Scheme

1.2 Purpose of Research

1.3 Outline of Thesis

**Chapter 2. DS-CDMA transceiver **

2.1. Transmitter

2.2. Multipath Channel

2.3. Receiver

2.4. Chapter Summary

**Chapter 3. Simulation Approach **

3.1. Generation of AWGN

3.2. Channel Model

3.3. Orthogonal Variable Spreading Factor (OVSF) codes

3.4. Simulation Assumptions

3.5. Gaussian Approximation for QPSK

3.6. Simulation Results

3.7. Chapter Summary

**Chapter 4. Hybrid coding with ARQ and FEC **

4.1. Coding Scheme

4.2 Simultaneous Use of Both of ARQ and FEC

4.3. Chapter Summary

**Chapter 5. Conclusion and Future Work **

5.1. Conclusion

5.2 Future Work

References

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