chapter 3

CHAPTER 3

SIMULATION ANALYSIS

OF BER PERFORMANCE

Introduction

Simulation Models

Simulation Results and Analysis

Conclusion

SIMULATION ANALYSIS OF

BER PERFORMANCE

1. Introduction

• OFDM

Orthogonal Frequency Division Multiplexing (OFDM) is a modulation scheme that is especially suited for high-data-rate transmission in delay-dispersive environments. It converts a high-rate data stream into a number of low-rate streams that are transmitted over parallel, narrowband channels that can be easily equalized. Traditional modulation methods become problematic at very high data rates. As the required data rate increases, the symbol duration Ts has to become very small in order to achieve the required data rate, and the system bandwidth becomes very large. As delay dispersion of a wireless channel is given by nature, its values depend on the environment, but not on the transmission system. Thus, if the symbol duration becomes very small, then the impulse response (and thus the required length of the equalizer) becomes very long in terms of symbol durations. The computational effort for such a long equalizer is very large and the probability of instabilities increases. For example, the Global System for Mobile communications (GSM) system which is designed for peak data rates up to 200 kbit/s, uses 200 kHz bandwidth, while the IEEE 802.11 system with data rates of up to 55Mbit/s uses 20MHz bandwidth. In a channel with 1 μs maximum excess delay, the former needs a two-tap equalizer, while the latter needs 20 taps. OFDM, on the other hand, increases the symbol duration on each of its carriers compared to a single-carrier system, and can thus have a very simple equalizer for each subcarrier.

• MIMO

In radio, multiple-input and multiple-output (MIMO) is the use of multiple antennas at both the transmitter and receiver to improve communication performance. MIMO technology offers significant increases in data throughput and link range without additional bandwidth or increased transmit power. It achieves this goal by spreading the same total transmit power over the antennas to achieve an array gain that improves the spectral efficiency (more bits per second per hertz of bandwidth) and to achieve a diversity gain that improves the link reliability (reduced fading). Diversity coding is one of the forms of MIMO.

For Additive White Gaussian Noise (AWGN) channels, the Bit Error Rate (BER) decreases exponentially as the Signal-to-Noise Ratio (SNR) increases, and a 10-dB SNR leads to BERs on the order of 10−4. However, in Rayleigh fading, BER decreases linearly with the SNR. We thus would need an SNR on the order of 40 dB in order to achieve a 10−4 BER, which is clearly unpractical. The reason for this different performance is the fading of the channel: the BER is mostly determined by the probability of channel attenuation being large, and thus of the instantaneous SNR being low. A way to improve the BER is thus to change the effective channel statistics – i.e., to make sure that the SNR has a smaller probability of being low. Diversity is a way to achieve this. The principle of diversity is to ensure that the same information reaches the receiver (RX) on statistically independent channels. Consider the simple case of an RX with two antennas. The antennas are assumed to be far enough from each other that small-scale fading is independent at the two antennas. The RX always chooses the antenna that has instantaneously larger receive power. As the signals are statistically independent, the probability that both antennas are in a fading dip simultaneously is low – certainly lower than the probability that one antenna is in a fading dip. The diversity thus changes the SNR statistics at the detector input.

• MIMO-OFDM

The MIMO-OFDM system uses two independent space-time codes for two sets of two transmit antennas to mitigate inter-symbol interference (ISI) and enhance system capacity.

2. Simulations

Baseband and Passband Simulation

For a given modulation technique, two ways to simulate modulation techniques are called baseband and passband. Baseband simulation, also known as the lowpass equivalent method, requires less computation.

Baseband Modulated Signals Defined.  If we use baseband modulation to produce the complex envelope y of the modulation of a message signal x, then y is a complex-valued signal that is related to the output of a passband modulator. If the modulated signal has the waveform

1. Comparison of BER Performances for Various Modulation Types in AWGN Channel

Fig. 3.1 Block Diagram of Transceiver used for Simulation over AWGN Channel

Simulation Models

Fig. 3.2 Simulation Model of BPSK Transceiver over AWGN Channel Fig. 3.3 Simulation Model of QPSK Transceiver over AWGN Channel Fig. 3.4 Simulation Model of OQPSK Transceiver over AWGN Channel Fig. 3.5 Simulation Model of M-PSK Transceiver over AWGN Channel Fig. 3.6 Simulation Model of DBPSK Transceiver over AWGN Channel Fig. 3.7 Simulation Model of MSK Transceiver over AWGN Channel Fig. 3.8 Simulation Model of M-PAM Transceiver over AWGN Channel Fig. 3.9 Simulation Model of M-QAM Transceiver over AWGN Channel Fig. 3.10 Simulation Model of M-FSK Transceiver over AWGN Channel Fig. 3.11 Simulation Model of CPFSK Transceiver over AWGN Channel

Simulation Code:

EbNo = 0:2:30;

ber = berawgn(0:2:30, 'psk',2, 'nondiff');

ber2 = berawgn(0:2:30, 'dpsk',2);

ber3 = berawgn(0:2:30, 'psk',4, 'nondiff');

ber4 = berawgn(0:2:30,'oqpsk','n');

ber5 = berawgn(0:2:30, 'psk',16, 'nondiff');

ber6 = berawgn(0:2:30, 'dpsk',16);

ber7 = berawgn(0:2:30, 'pam',2);

ber8 = berawgn(0:2:30, 'pam',16);

ber9 = berawgn(0:2:30, 'qam',16);

ber10 = berawgn(0:2:30,'msk','off');

ber11 = berawgn(0:2:30,'cpfsk',2,0.5,1);

ber12 = berawgn(0:2:30,'fsk',2,'coherent' );

ber13 = berawgn(0:2:30,'fsk',16,'coherent' );

Fig.;

semilogy(0:2:30, ber,0:2:30, ber2,0:2:30, ber3,0:2:30,ber4,0:2:30,...

   ber5,0:2:30, ber6,0:2:30, ber7,0:2:30,ber8,0:2:30, ber9,0:2:30,...

   ber10,0:2:30,ber11,0:2:30,ber12,0:2:30,ber13);

legend('BPSK','DBPSK','QPSK', 'OQPSK','16 PSK','16 DPSK','BASK',...

   '16 PAM','16 QAM','MSK','CPFSK','BFSK','16 FSK' );

2. Comparison of BER Performances for Various Channel Codes

Fig. 3.12 Simulation Model of Transceiver with Coded AWGN Channel

3. Comparison of BER Performances for Various Modulation Types in Rayleigh Fading Channel

Fig. 3.13 Simulation Model of Transceiver with Rayleigh Channel

4. Improve the BER performance of  Rayleigh Fading Channel

1. Reed-Solomon Coding

Fig. 3.14 Simulation Model of RS coding with 16-PAM and AWGN channel

2. Convolution Coding

Fig. 3.15 Simulation Model of Convolution coding and Viterbi decoding with QPSK and Rayleigh channel

3. Frequency Diversity using OFDM- Based Equalization

Fig. 3.16 Simulation Model of OFDM based equalization

4. Space Diversity using MIMO-Based Equalization

Fig. 3.17 Simulation Model of MIMO

5. MIMO with TCM

Fig. 3.18 Simulation Model of MIMO with TCM

6. OFDM + MIMO-Based Equalization

Fig. 3.19 Simulation Model of OFDM with MIMO

3. Simulation Results

Fig. 3.20 BER performance of BPSK, QPSK, 8-PSK, 16-PSK

Fig. 3.21 BER performance of DBPSK, DQPSK, 8-DPSK, 16-DPSK

Fig. 3.22 BER performance of M-ary PAM

Fig. 3.23 BER performance of M-ary QAM

Fig. 3.24 BER performance of BFSK, 4-FSK, 8-FSK, 16-FSK

Fig. 3.25 BER performance of 2-CPFSK, 4-CPFSK, 8-CPFSK, 16-CPFSK

Fig. 3.26 Theoretical BER performance of various Modulation Schemes in AWGN Channel using BERTool

Fig. 3.27 Simulated BER performance of various Modulation Schemes in AWGN Channel using Simulink

Fig. 3.28 BER performance of various Modulation Schemes in AWGN Channel using Matlab Coding

Fig. 3.29 Comparison of Block Codes based on BER using BERTool

Fig. 3.30 Theoretical BER performance of various Modulation Schemes in Multipath Rayleigh Channel using BERTool

Fig. 3.31 Simulated BER performance of various Modulation Schemes in Multipath Rayleigh Channel using Simulink

Fig. 3.32 Comparison of Simulated BER performance of RS coding, Convolution coding, OFDM, MIMO, MIMO with TCM, OFDM with MIMO in Multipath Rayleigh Channel using Simulink

4. Conclusion

In this chapter, the simulation models of various transceiver systems are implemented using Matlab Toolbox package. BER performance analysis for both AWGN and Rayleigh fading channel model are demonstrated. In First section, the effect of modulation order M is observed on various modulation methods such as M-PSK, M-PAM etc with AWGN Channel. Additionally, comparison of these modulation methods based on BER performance is presented. In second section, effect of various channel codes is observed in AWGN channel.  In third section, comparison of various modulation methods with Rayleigh channel is done. In last section, effect on OFDM, MIMO and TCM techniques are performed using simulation.

In first section, it is concluded from Fig. 3.20 to Fig. 3.23 that for spectrum efficient modulation techniques (or linear modulation) such as M-PSK, M-PAM, M-DPSK, M-QAM BER performance degrades with increase in modulation order (M) whereas from Figures 3.24, 3.25 for power efficient modulation techniques (or constant-amplitude modulation) such as M-FSK, M-CPFSK, BER performance improves with increase in modulation order (M) . Figures 3.26-28 shows the comparison of BER performances of various modulation techniques. In second section, from Fig. 3.29, it is observed that Reed Solomon code have better code gain than others for 32-QAM.

Table 3.1 Code Gain of channel codes at BER of 10-6 wrt uncoded 32-QAM

Channel Codes	Code Gain
Hamming Code	1.85
Golay Code	2.64
Reed-Solomon Code	3.67

In third section, from Fig. 3.30 and 3.31, it is concluded that BER performance is linear for Rayleigh channel unlike waterfall type in AWGN channel.

In fourth section from Fig. 3.32, it is concluded that BER remains linear by using of convolutional code and RS code. Diversity techniques: MIMO, MIMO with TCM, OFDM and OFDM with MIMO change the linear relation into a dip in BER plot which is desired. For low value of Eb/No (<5dB), OFDM’s BER is better than others but thereafter BER remain constant. For Eb/No >6dB, OFDM with MIMO results is better than others.