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CHAPTER 5 5 BER PERFORMANCE OF AWGN, RAYLEIGH AND RICIAN CHANNEL
5.1
INTRODUCTION In the previous chapters, channel estimation of MIMO-OFDM
systems are analysed and pilot design using particle swarm optimization method discussed. There are different kinds of channel estimation methods commonly used such as Least Square (LS), Least Square-Modified (LS-Mod) and Minimum Mean Square Error (MMSE). In this chapter, Additive White Gaussian Noise (AWGN), Rayleigh and Rician channel models are examined using LS, LS-Modified and MMSE algorithms. In LS estimation, the procedure is simple but it has high mean square error while in low signal to noise ratio, MMSE is better than that of LS, but its main problem is its high computational complexity, and so LS-Modified is considered to be the best among the three channel estimation methods. Larsson & Li (2001) have examined the channel with two transmit and more than two receiver antennas. In this research, 2x2 MIMO-OFDM system is proposed. Naganjaneyulu & Satya (2009) have estimated the channel in OFDM system using kalman method and the system is simulated in MATLAB and analysed in terms of bit error rate according to various values of signal to noise ratio. The simulation parameters are given in Table 5.1.
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Table 5.1 Simulation parameters Parameter Description
Specification
Number of sub carrier
64
FFT size
64
Modulation Channel Model
BPSK AWGN, Rayleigh and Rician
Number of Pilots
8
Guard Interval
16
Encoder
Trellis
Decoder
Viterbi
5.2
FADING CHANNELS In this chapter, the types of fading channels and their estimation is
discussed. Fading channel is a channel that fades due to obstacle in the transmission path. Multiple signals are received by the receiver because of the multipath component. The originally received signal is the vector sum of the individual signals and they get faded owing to various factors such as reflection, diffraction and scattering. Fading is classified into large scale fading and small scale fading based on the distance. When the distance between the transmitter and receiver is long, then it is known as large scale fading channel. Similarly, when the distance between the transmitter and the receiver is short, it is called small scale fading that has three types namely, Additive White Gaussian Noise, Rayleigh and Rician channel. Bolcskei et al (2002) have demonstrated blind
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channel estimation in OFDM systems. In this work, pilot based channel estimation is proposed for the small scale fading channel. 5.2.1
Additive White Gaussian Noise Channel Additive White Gaussian Noise (AWGN) is a channel model that
has a linear addition of wideband or white noise with a constant spectral density and a Gaussian distribution of amplitude and it does not depend on multipath fading, frequency selectivity, interference and non-linearity or dispersion. AWGN is a basic channel model to every communication channel that has statistically random radio noise characterized by a wide frequency range with regard to a signal in a communication channel. This noise has additive, white and noise samples with a Gaussian distribution. It is a simplest wireless communication system employed at additive white Gaussian noise environment, and the signals are generated and some amount of background noise is added in the channel. Mathematical expression for the received signal in additive white Gaussian noise channel is r(t) = s(t) + n(t)
(5.1)
where, s(t) – Transmitted signal r(t) – Received signal n(t) – Background noise AWGN channel model is the basic and standard channel model. White Gaussian noise is added with the transmitted signal in AWGN channel is shown in Figure 5.1.
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Transmitted Signals s(t)
Channel
Received Signals r(t) = s (t)+n(t)
+
Noise Signal n(t)
Figure 5.1Block diagram of AWGN channel model 5.2.2
Rayleigh Channel Model In mobile radio channels, the Rayleigh channel is a commonly used
model to describe the statistical time varying nature of the envelope of the flat fading signal or envelope of an individual multipath component. The transmitted signals are scattered because of the obstacles in the environment before they reach the receiver. If there is no scattering, they will have zero mean and phase angle between 0 and 2π radians. The gain characteristic is defined by Rayleigh distribution in Rayleigh fading channel, when there is no line of sight between the transmitter and the receiver. Rayleigh fading channel model is used as there are many scatters between transmitter and receiver. It is used in large areas where there is no line of sight and many buildings and other obstacles reflect, diffract and attenuate the signal between the transmitter and the receiver. The block diagram of an OFDM transceiver system over Rayleigh channel is given in Figure 5.2.
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Figure 5.2
5.2.3
Block diagram of an OFDM transceiver system over Rayleigh channel
Rician Channel Model Rician fading channel model is the same as the Rayleigh fading
channel model and it has strong dominant component in the Rician fading channel model that has non fading signal or stationary signal known as line of sight. When there is a stationary signal dominant component present in the line of sight, propagation path with envelope distribution in small scale fading is called Rician. Stationary dominant signal is superimposed with multipath components arriving at random and this random multipath component is added with the dc component and detected at the output of the envelope detector. Rician fading is a channel model to propagate the signal with partial cancellation of radio frequency signal so that the signal reaches the receiver with different multipath interference. The line of sight signal is stronger than the other signals that occur in Rician fading. The gain is characterized by the Rician distribution and the block diagram of an OFDM transceiver system over Rician channel is shown in Figure 5.3.
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Figure 5.3
5.3
Block diagram of an OFDM transceiver system over Rician multipath channel
CHANNEL ESTIMATION ALGORITHMS Li et al (2006) have proposed to estimate the channel using Linear
Programming (LP) algorithm. In this chapter, to estimate the AWGN, Rayleigh and Rician channels least square, minimum mean square error and modified least square algorithms are used and their performance discussed. The signals are distorted in the channel owing to fading, and there is a need to estimate the channel at the receiver to recover the original signal. Shin et al (2004) have proposed comb type training structure for channel estimation of MIMO-OFDM system. To do so, data signals and training signals are needed. The expected performance, calculation complexity and variation in time period are the parameters to be considered. Ozdemir & Arslan (2007) have proposed Linear Minimum Mean Square Error (LMMSE) algorithm to estimate the channel in terms of mean square error. In this work, common channel estimation used is least square, minimum mean square error and least square modified algorithms. 5.3.1
Least Square Algorithm Least square algorithm is a standard approach to find out the
approximate solution of over determined system which means that the overall
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solution minimizes the sum of the squares of the errors made in the results of every single equation. HLS = X-1 Y
(5.2)
where, X
- Input Matrix
Y
- Output Matrix
HLS - Channel matrix for LS algorithm 5.3.2
Minimum Mean Square Error Algorithm Minimum mean square error algorithm describes the approach that
minimizes the mean square error (MSE) and it is a common form of channel estimation algorithm. Mean square error is estimated using the equation given below. MSE =E{(H – HLS)^ (H-HLS)}
(5.3)
where, H
- Reference channel matrix
HLS - Channel matrix for least square algorithm MSE - Mean Square Error 5.3.3
Least Square Modified Algorithm Least square modified algorithm is used in data fitting area. The
best fit in the least-square minimizes the sum of squared residuals, a residual being the difference between values observed by a model and estimated values.
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HLS-Mod =
H est (i) H est (i 1) 2
(5.4)
where, Hest(i)
- Estimated channel matrix for ith value
Hest(i+1) - Estimated channel matrix for i+1th value
5.4
HLS-Mod
- Channel matrix for LS-Mod algorithm
STEPS
TO
CALCULATE
BIT
ERROR
RATE
FOR
CHANNEL Step 1:
Initialize the various parameters such as number of subcarrier inputs, pilots, Guard interval and signal to noise ratio.
Step 2:
Generate channel matrix by using formula.
Step 3:
Generate OFDM symbols for random input data and encode it by using trellis encoder.
Step 4:
Modulate the encoded data by BPSK modulation technique.
Step 5:
For AWGN channel, add the complex Gaussian noise to the data.
Step 6:
Take variance of noise and add data to the noise.
Step 7:
The channel is estimated by evaluating the bit error rate using LS, MMSE and LS-Modified algorithms.
Step8:
Finally the received data is demodulated and decoded by using viterbi decoder.
Step 9:
Plot the graph for signal to noise ratio versus bit error rate and end the process.
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5.5
SIMULATION RESULTS In this research, three channel models namely Additive White
Gaussian Noise, Rayleigh and Rician channels are considered and to estimate these channels Least Square (LS), Minimum Mean Square Error (MMSE) and Least Square Modified (LS-Mod) algorithms are used and its performance measured in terms of bit error rate and also pilot position represented.
Figure 5.4 Bit error rate for AWGN channel model Figure 5.4 shows the bit error rate value for Additive white Gaussian noise channel model. Three channel estimation algorithms such as least square, minimum mean square error and least square modified algorithms are applied in this channel model. Bit error rate values are plotted for corresponding values of signal to noise ratio. When least square algorithm is applied in AWGN channel, bit error rate is decreased as signal to noise ratio increases and mean square error algorithm is applied in the same channel bit error rate decreased more compared least square algorithm as signal to
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noise ratio increases. Similarly, when least square modified algorithm is applied in this channel bit error rate is reduced more compared to least square and minimum mean square error algorithm as signal to noise ratio increases. From this figure it is confirmed that least square modified algorithm provides the least bit error rate compared to least square and minimum mean square error algorithms. Table 5.2 Comparison of bit error rate for AWGN channel using LS, MMSE, LS-Modified algorithm Bit Error Rate SNR(dB) LS
MMSE
LS-MOD
1
0.3160
0.1
0.063
2
0.0251
0.01
2.51x10-3
3
2.51x10-3
6.39x10-4
2.51x10-4
4
2.51x10-4
5.011x10-5
2.58x10-5
5
3.16x10-5
3.98x10-6
1x10-6
Table 5.2 indicates the bit error rate value for Additive white Gaussian noise channel model. Three channel estimation algorithms such as least square, minimum mean square error and least square modified algorithms are applied in this channel model and bit error rate values are tabulated for corresponding values of signal to noise ratio. For 5dB SNR the value of bit error rate is observed as 3.16x10-5, 3.98x10-6 and 1x10-6 using least square, minimum mean square error and least square modified algorithm. From this table it is clear that least square modified algorithm provides the least bit error rate value compared to least square and minimum mean square error algorithms.
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2 1.8 1.6
Magnitude
1.4 1.2 1 0.8 0.6 0.4 0.2 0
10
20
30 40 Pilot Position
50
60
Figure 5.5 Pilot position representations for AWGN channel Figure 5.5 represents the pilot position for 64 subcarriers in transmitted signal in additive white Gaussian noise channel. Pilot is inserted between every 8 data subcarriers.
Figure 5.6 Bit error rate for Rayleigh channel model Figure 5.6 shows the bit error rate value for Rayleigh channel model. Three channel estimation algorithms such as least square, minimum mean square error and least square modified algorithms are applied in this
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channel model and the bit error rate values are plotted for the corresponding values of signal to noise ratio. When least square algorithm is applied in Rayleigh channel, bit error rate is decreased as signal to noise ratio increases and mean square error algorithm is applied in the same channel bit error rate decreased more compared to least square algorithm as signal to noise ratio increases. Similarly, when least square modified algorithm is applied in this channel bit error rate is reduced more compared to least square and minimum mean square error algorithm as signal to noise ratio increases. From this figure it is confirmed that least square modified algorithm provides the least bit error rate value compared to least square and minimum mean square error algorithms. Table 5.3 Comparison of bit error rate for Rayleigh channel using LS, MMSE, LS-Modified algorithm
SNR(dB)
Bit Error Rate LS
MMSE
LS-MOD
1
0.199
0.1258
0.0630
2
3.162x10-2
0.01
2.51x10-3
3
1.99x10-3
6.3x10-4
1.58x10-4
4
1.99x10-4
6.3x10-5
1.25x10-5
5
2.51x10-5
3.9x10-5
1x10-6
Table 5.3 indicates the bit error rate value for Rayleigh noise channel model. Three channel estimation algorithms such as least square, minimum mean square error and least square modified algorithms are applied in this channel model and the bit error rate values are tabulated for corresponding values of signal to noise ratio. For 5dB SNR the value of bit error rate is observed as 2.51x10-5, 3.9x10-5 and 1x10-6 using least square, minimum mean square error and least square modified algorithm. From this table it is clear that least square modified algorithm provides the least bit error
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rate value compared to least square and minimum mean square error algorithms. 2 1.8 1.6
Magnitude
1.4 1.2 1 0.8 0.6 0.4 0.2 0
10
20
30 40 Pilot Position
50
60
Figure 5.7 Pilot position representations for Rayleigh channel model Figure 5.7 represents the pilot position for 64 subcarriers in transmitted signal in Rayleigh channel. Pilot is inserted between every 8 data subcarrier.
Figure 5.8 Bit error rate for Rician channel model
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Figure 5.8 shows the bit error rate value for Rician channel model. Three channel estimation algorithms such as least square, minimum mean square error and least square modified algorithms are applied in this channel model and the bit error rate values plotted for the corresponding values of signal to noise ratio. When least square algorithm is applied in Rician channel, bit error rate is decreased as signal to noise ratio increases. And mean square error algorithm is applied in the same channel bit error rate decreased more compared to least square algorithm as signal to noise ratio increases. Similarly, when least square modified algorithm is applied in this channel bit error rate is reduced more compared to least square and minimum mean square error algorithm as signal to noise ratio increases. From this figure it is confirmed that least square modified algorithm provides the least bit error rate value compared to least square and minimum mean square error algorithms. Table 5.4 Comparison of bit error rate for Rician channel using LS.MMSE, LS-Modified algorithm Bit Error Rate SNR(dB) LS
MMSE
LS-MOD
1
0.251
0.1258
6.3x10-2
2
3.16x10-2
1x10-2
2.51x10-3
3
3.162x10-3
6.3x10-4
1.58x10-4
4
2.81x10-4
5.01x10-5
1.25x10-5
5
1.99x10-5
3.9x10-6
1x10-6
Table 5.4 indicates the bit error rate value for Rician channel model. Three channel estimation algorithms such as least square, minimum mean square error and least square modified algorithms are applied in this channel model and the bit error rate values tabulated for corresponding values
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of signal to noise ratio. For 5dB SNR the value of bit error rate is observed as 1.99x10-5, 3.9x10-6 and 1x10-6 using least square, minimum mean square error and least square modified algorithm. From this table it is clear that least square modified algorithm provides the least bit error rate value compared to least square and minimum mean square error algorithms.
2 1.8 1.6
Magnitude
1.4 1.2 1 0.8 0.6 0.4 0.2 0
10
20
30 40 Pilot Position
50
60
Figure 5.9 Pilot position representations for Rician channel model Figure 5.9 represents the pilot position for 64 subcarriers in transmitted signal in Rician noise channel. Pilot is inserted between every 8 data subcarrier. For N=64 and SNR=1dB Table 5.5 Comparison of bit error rate for low value of signal to noise ratio
Channel Model
Bit Error Rate LS
MMSE
LS-MOD
AWGN Channel
0.316
0.1
0.063
Rayleigh Channel
0.199
0.1258
0.063
0.1258
0.063
Rician Channel
0.251
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Table 5.5 shows that at low SNR value MMSE is better than LS but, LS-Modified is the best among LS, MMSE algorithms For N=64 and SNR=30dB Table 5.6 Comparison of bit error rate for high value of signal to noise ratio Channel Model
LS
MMSE
LS-MOD
AWGN Channel
6.0157x10-13
3.567x10-13
3.632x10-14
Rayleigh Channel
6.142x10-13
3.962x10-13
3.852x10-14
Rician Channel
6.996x10-13
2.625x10-13
3.665x10-14
Table 5.6 shows that, at high SNR value LS is better than MMSE but, LS-Modified is the best algorithm among LS, MMSE.
BER Performance using LS,MMSE and LS-Mod algorithms 0.35 0.3 0.25 BER
LS
0.2 0.15
MMSE
0.1
LS-Mod
0.05 0 AWGN Channel
Rayleigh Channel
Rician Channel
Figure 5.10 Bit error rate performance of LS, MMSE and LS-Mod algorithms The channel models namely, Additive White Gaussian Noise (AWGN), Rayleigh and Rician are estimated using three algorithms namely
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Least Square (LS), Minimum Mean Square Error (MMSE) and Least Square Modified (LS–Mod) algorithms. The simulation results indicate that MMSE is better than that of LS and LS-Modified is better than that of MMSE and it is plotted for 1 dB SNR as shown in Figure 5.10. The results make it clear that the least square modified algorithm reduces the bit error rate and it gives the better result compared to the other algorithms in AWGN, Rayleigh and Rician Channels. 5.6
SUMMARY The MIMO-OFDM is an efficient wireless system with the efficient
use of available bandwidth, since the sub channels are overlapping. The performance of the MIMO-OFDM system is optimized with minimum bit error rate. OFDM with the multiple transmit and receive antennas form a MIMO system to increase the system capacity and thus the three channels are estimated using three algorithms. In the proposed system, AWGN, Rayleigh and Rician channel models are estimated using LS, MMSE and LS- Modified algorithms. From the graphs it is inferred that in low signal to noise ratio, MMSE is better than that of LS, and its main problem is its high computational complexity, but LS-Modified algorithm is more suitable in low and high signal to noise ratio.
