service, high spectral efficiency and high data rates ... signal in terms of Bit Error Rate (BER) under different ... cellular radio, Digital Subscriber Line (DSL) and.
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 21 (2016) pp. 10475-10483 © Research India Publications. http://www.ripublication.com
Performance Assessment of Orthogonal Frequency Division Multiplexing (OFDM) in Wireless Communication System Nubailah binti Arshad and Nurul Asyikin Mohamed Radzi College of Graduate Studies, Universiti Tenaga Nasional, Jalan Ikram-Uniten, 43000 Kajang, Selangor, Malaysia.
Abstract Orthogonal Frequency Division Multiplexing (OFDM) is in demand for the next generation wireless communications system as it fulfills the requirements for quality and reliable service, high spectral efficiency and high data rates transmission. Study on OFDM is valuable for future researchers in simulating communication systems that are too theoretically complex to analyze. This paper focuses on the assessment of OFDM system performances, which incorporate two different multiplexing techniques; Phase Shift Keying (PSK) and Quadrature Amplitude Modulation (QAM) and two channel models; Additive White Gaussian Noise (AWGN) and multipath channel that are common in modeling wireless communication system. Additionally, this paper also observes the Peak Average Power Ratio (PAPR) distribution of OFDM signal to see how the PAPR distribution is affected by type and order of modulation and channel condition. The assessment is done by simulation of random data traveling in OFDM system. All OFDM model and channel model used in this project’s simulation is developed using MATLAB ver. R2013a. Project’s output shows the performance of OFDM signal in terms of Bit Error Rate (BER) under different channel model with added AWGN and multipath channel model and how modulation type and order affect the BER. Keywords: OFDM, Modeling, BER, SNR, PSK, QAM
INTRODUCTION The current growth in digital communication system is towards high speed and large capacity system with reliable transmission. In wireless transmission, signal travelled in multiple directions, due to the signal being reflected from large objects such as mountains or buildings. Hence, the receiver sees more than one copy of the signal. This is known as multipath communications. The indirect path signal will arrive at the receiver slightly delayed compared to straight path signal, which will cause the two signals to interfere with each other. This problem, known as Inter Symbol Interference (ISI) is a major problem that occurs in high-speed wireless communication system [1]. The overlapping of frequency bands, high speed data transfer and high quality of wireless link even under multipath conditions due to low symbol rate causes Orthogonal Frequency Division Multiplexing (OFDM) to be able to minimize ISI effects [2]. Hence, OFDM system is suited for today’s generation networks and next generation networks in terms of bandwidth efficiency.
OFDM is one of the multichannel access method that employs multiple sub carriers where channel is divided into number of narrowband channels to obtain spectral efficiency and minimize ISI. It is used in many applications including cellular radio, Digital Subscriber Line (DSL) and Asynchronous DSL modem, Digital Audio Broadcasting and wireless networking. OFDM can also be coupled with other techniques including Multi Input Multi Output (MIMO) and smart antennas to further enhance data rate and link reliability. In this paper, we develop a model of OFDM system to investigate its performances in wireless communication system. The model is not only beneficial for introduction to theory of OFDM technique, but can also be further expanded for continuous research on combination of OFDM and other access techniques in wireless communication system design. The investigation will be done by simulating conventional OFDM system using MATLAB. In order to demonstrate parallel transmission, digital modulation schemes will be used, which are Multilevel-Phase Shift Keying (M-PSK) and Multilevel-Quadrature Amplitude Shift Keying (M-QAM). The effect of transmission impairments will be investigated by using Additive White Gaussian Noise (AWGN) channel and Rayleigh channel. Besides, the Signal-to-Noise ratio (SNR), bit error rate (BER) and spectrum efficiency under different channel condition for each of the modulation scheme will also be investigated. The expected outcome is used to indicate the performance of OFDM system in the AWGN and Rayleigh channel model in terms of the value of SNR and BER. The rest of this paper is organized as follows. Section 2 presents related work and Section 3 presents the OFDM model. Section 4 proposes the simulation results followed by conclusion in Section 5.
RELATED WORKS Up to date, numerous researchers have done the study on OFDM [3-8]. One of the most studied OFDM performance parameter used in previous literature is BER. For an instance, the comparison of BER of Binary PSK (BPSK), 16–QAM and 64-QAM OFDM modulated data in AWGN channel model has been done by Katariya et al. using MATLAB simulation [3]. The output shows the relation between modulation order and BER values. Awon et al. assessed BER performance of 16/64-QAM OFDM modulated data in AWGN and Rayleigh channel. The BER is observed to see which channel resulted in less BER [4].
10475
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 21 (2016) pp. 10475-10483 © Research India Publications. http://www.ripublication.com
Bathia et al. assessed BER of different modulation order for each M-PSK and M-QAM OFDM modulated data in multipath fading channel. The study derives the relationship between modulation orders and type in OFDM system with BER [5]. Rathore et al. assessed how much SNR is needed in order to achieve certain pre-determined bit rate value for different modulation order for PSK OFDM modulated data in AWGN channel model. The study also compares the SNR with single carrier transmission [6].
OFDM MODEL Figure 1 shows the basic OFDM model used in this project. From this basic model, simulation model using MATLAB is developed and insertion of cyclic prefix (CP) is included to mitigate the problem of ISI. CP is added to OFDM symbol after the Inverse Fast Fourier Transform (IFFT) process and later removed at the receiver before the FFT process. At the receiver, to estimate the transmitted signal, a single tap equalizer is used. OFDM model parameter will be based as in Table 1.
Similarly, Haq et al. also look into the amount of energy required for transmission over AWGN channel for BPSK and Quadrature PSK (QPSK) OFDM modulated data [7]. Acharya in his study however does not look into BER to assess the performance of OFDM system. Instead, the corresponding study focusing on the average power, channel power and noise power of 4/16/64-QAM OFDM modulated data in LTE network [8]. Majority of previous related study in the literature uses MATLAB programming to perform relevant simulation, whilst some make use of Simulink to design the OFDM block model. Two major parameters in assessing OFDM system performances are the BER and SNR. These two parameters are important in designing OFDM system to be used in wireless communication model. Wireless application requires certain BER to ensure reliable transmission. Eb/No, which is the energy per bit to noise power spectral density ratio (normalized SNR) is use to compare BER performance of different digital modulation schemes without taking bandwidth into account.
Figure 1: Basic OFDM Model [9]
Table 1: OFDM system parameter use in simulation It can be summarized that, previous study in the literature did comparison of BER by varying either the type of modulation scheme in the same channel model; or modulation order in different channel model. Hence, in this paper we will simulate the BER vs. SNR curves, which compare: a. Different modulation scheme (PSK/QAM) in the same channel and different channel model (AWGN/Rayleigh) b. Different modulation order (M=8/16/64) for each modulation scheme c. OFDM modulated data and single carrier This project will also observe the Peak Average Power Ratio (PAPR) of OFDM modulated data and compare it to single carrier modulated data. The developed OFDM model can be further used in the future study related to PAPR reduction techniques and how it affects the BER. The model can also be further enhanced to model interference limited channel or Rician channel.
Parameter FFT/IFFT size FFT Sampling Frequency Sub carrier spacing Cyclic Prefix length (s/samples) OFDM symbol per slot Sub frame duration Maximum delay spread
Value 128 192 MHz 15 KHz 32
256 3.84 MHz 64
6 6 0.5 ms 15 s (urban), 1s (indoor)
In wireless communication, receiver usually suffers from thermal noise, which is a function of absolute temperature and receiver’s bandwidth. This noise is modeled as Gaussian Random Process that is additive and has a flat spectrum known as white noise. This noise is added to received signal and makes the detection of especially weak signal challenging. This project use AWGN noise to model manmade noise and signal traveling under this condition is characterized by [10]: 𝑦(𝑡) = 𝑠(𝑡) + 𝑤(𝑡) ………………………… …. (1) where y(t) is the received signal, s(t) is the transmitted signal and w(t) is the AWGN noise.
10476
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 21 (2016) pp. 10475-10483 © Research India Publications. http://www.ripublication.com To simulate multipath channel, Rayleigh flat fading is considered. Signal traveling in multipath is modeled as n impulse transmitted from a transmitter and will reach the receiver as sequence of impulses. If s(t) is the transmitted bandpass signal, 𝑠(𝑡) = ℜ{𝑠𝑏 (𝑡)𝑒 𝑗2𝜋𝑓𝑐 𝑡} …………………………. (2) [11] where sb (t) = baseband signal and fc = carrier frequency. This signal will reach the receiver via multipath where nth path has an attenuation, 𝛼𝑛 (𝑡) and delay 𝜏𝑛 (𝑡) . Hence, the received signal y(t), will be: 𝑦(𝑡) = ∑𝑛 𝛼𝑛 (𝑡)𝑠[𝑡 − 𝜏𝑛 (𝑡)]
……………. ……. (3) [11]
Equation (2) will be: 𝑠(𝑡) = ℜ{∑𝑛 𝛼𝑛 (𝑡)𝑠𝑏 [𝑡 − 𝜏𝑛 (𝑡)] 𝑒 𝑗2𝜋𝑓𝑐 (𝑡 − 𝜏𝑛 (𝑡))} ….. (4)
well as easy implementation in terms of less hardware complexity. This paper is to observe the performance of OFDM based communication system with the presence of AWGN noise and multipath channel model. Hence, the performance output measured is BER vs. SNR with simulation parameters consists of modulation scheme use (PSK or QAM) and level (M-ary). The BER curve for M-PSK and M-QAM OFDM are plotted together with BER curve for single carrier, for each value of M = 8, 16 and 64. The channel model used is AWGN channel. The output is shown in Figure 2 – Figure 4. Figure 2 shows the BER curve comparison for 8-PSK. BER improved for 8PSK OFDM as can be observed in Figure 2(b) where the curve is enlarged focusing at Eb/No=10 dB. The curve of 8PSK OFDM is slightly below the curve of single carrier 8PSK indicating smaller BER values differences for each corresponding Eb/No.
The equivalent received basedband signal now become 𝑦𝑏 (𝑡) = ∑𝑛 𝛼𝑛 (𝑡)𝑒 −𝑗2𝜋𝑓𝑐 𝜏𝑛 (𝑡) 𝑠𝑏 [𝑡 − 𝜏𝑛 (𝑡)] = ∑𝑛 𝛼𝑛 (𝑡)𝑒 −𝑗𝜃𝑛(𝑡) 𝑠𝑏 [𝑡 − 𝜏𝑛 (𝑡)]
………… (5) ………… (6)
The phase of the nth path, 𝜃𝑛 (𝑡)= 2𝜋𝑓𝑐 𝜏𝑛 (𝑡). This correspond to impulse response of ℎ𝑏 (𝑡) = ∑𝑛 𝛼𝑛 (𝑡)𝑒 −𝑗𝜃𝑛 (𝑡) ………………………… (7) [10] The phase for each path changes by 2 radian when the delay changes by 1/fc. However, since the distances between the devices are much larger than the wavelength of the carrier frequency, it is assume that the phase is uniformly distributed between 0 and 2 radian and each path are independent. When there are many paths, Central Limit Theorem is applied and results in each path to be modeled as circularly symmetric complex Gaussian random variable with time as the variable. This model is use to reflect Rayleigh fading channel model [10-11]. In wireless communication, which operates in multipath fading environments, a constant amplitude modulation technique with non-linear amplifiers is favored. PSK is one of the basic digital modulation techniques that provide constant amplitude transmission, which is desirable in the presence of signal fading environment. QAM in other hand is use to increase the transmission bit rate over a bandwidth limited channel [12]. Hence, this project will use these two modulation techniques, M-PSK and M-QAM with modulation order, M specified as 8/16/64.
PERFORMANCE MEASUREMENT In wireless communication system, the communication channel largely affects performance of the entire system. Channel performance can be measured in terms of bandwidth, SNR, BER, Probability of Error or others. [12] To achieve a good system performance, digital communication system is usually preferred as it has lower BER and SNR compared to analog communication system as
Figure 2 (a): Comparison between bit error curve for random data with 8-PSK modulation in OFDM and single carrier system (AWGN channel) (b) zoom at Eb/No=10 dB Similarly, BER also improved for 16 and 64-PSK OFDM technique as shown in Figure 3 and Figure 4, where the curve line of 16/64-PSK OFDM is under the single carrier 16/64PSK. However, it can be observed that the gap between the curve of single carrier M-PSK and M-PSK OFDM BER are very small indicating the improvement of OFDM technique is very minimal for M-PSK modulation type or order 8,16 and 64. It is also observed that the trend of the BER curve for MPSK OFDM is still the same as single carrier M-PSK where there is a rapid decrease in BER value from 10 -2 to 10-6.
10477
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 21 (2016) pp. 10475-10483 © Research India Publications. http://www.ripublication.com
Figure 4 (a) Comparison between bit error curve for random data with 64-PSK modulation in OFDM and single carrier system (AWGN channel) (b) zoom at Eb/No= 10 dB
Figure 3(a) Comparison between bit error curve for random data with 16-PSK modulation in OFDM and single carrier system (AWGN channel) (b) zoom at Eb/No=10dB
The next six figures (Figure 5 to Figure 7) compare the BER curve for M-QAM OFDM with single carrier M-QAM. The channel is also added with AWGN noise. Figure 5.1, Figure 6.1 and Figure 7 shows an improvement of BER for M-QAM OFDM over single carrier M-QAM modulation for modulation order of 8, 16 and 64 respectively. It is also observed that the BER improvement is more significant as the modulation order increases. This can be seen from the gap between the two curves.
Similarly, BER curve for M-PSK and M-QAM OFDM are plotted and compare with single carrier modulation technique but this time with different channel condition. For each value of M-ary (both PSK and QAM), the plot of BER curve between the random bit traveling in OFDM system and those traveling in single carrier system are compared. The channel model used is multipath (Rayleigh flat fading) channel with the addition of AWGN noise. The simulation output is shown in Figure 8 to Figure 10. From Figure 8, the BER for 8-PSK OFDM is slightly higher for value of Eb/No < 5 dB compare to single carrier. However for higher Eb/No values, the BER improve and significantly improved after Eb/No > 10 dB. The BER curve for 8-PSK OFDM is no longer looks linear like with single carrier 8-PSK.
10478
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 21 (2016) pp. 10475-10483 © Research India Publications. http://www.ripublication.com
Figure 5(a): Comparison between bit error curve for random data with 8-QAM modulation in OFDM and single carrier system (AWGN channel) (b): zoom at Eb/No= 10 dB
Figure 7(a): Comparison between bit Error curve for random data with 64-QAM modulation in OFDM and single carrier system (AWGN channel (b): zoom
Figure 8: Comparison between bit Error curve for random data with 8-PSK modulation in OFDM and single carrier system (multipath channel)
Figure 6(a): Comparison between bit error curve for random data with 16-QAM modulation in OFDM and single carrier system (AWGN channel) (b): zoom at Eb/No= 10 dB
10479
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 21 (2016) pp. 10475-10483 © Research India Publications. http://www.ripublication.com
Figure 11: Comparison between bit Error curve for random data with 8-QAM modulation in OFDM and single carrier system (multipath channel)
Figure 9: Comparison between bit Error curve for random data with 16-PSK modulation in OFDM and single carrier system (multipath channel)
Figure 12: Comparison between bit Error curve for random data with 16-QAM modulation in OFDM and single carrier system (multipath channel Figure 10: Comparison between bit Error curve for random data with 64-PSK modulation in OFDM and single carrier system (multipath channel) The next three figures (Figure 11 – Figure 13 shows the BER curves comparison between M-QAM OFDM and single carrier M-QAM for each modulation order of 8,16 and 64 in multipath channel model. The BER improvement is significant for value of Eb/No > 10 dB. For all three modulation order of 8,16 and 64-QAM OFDM, the BER curve is also no longer looks linear as in single carrier BER curve. Hence the BER decreases from value 10 -2 to 10-5 within Eb/No value of 10 dB, compare with the same BER value decreases , which require higher energy per bit (range of Eb/No of 25 dB). For the purpose of numerical comparison, the value of BER at the point Eb/No = 10 dB, are recorded based on the output curve obtained by simulation as in Table 2 and 3.
10480
Figure 13: Comparison between bit Error curve for random data with 64-QAM modulation in OFDM and single carrier system (multipath channel)
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 21 (2016) pp. 10475-10483 © Research India Publications. http://www.ripublication.com From Table 3, the BER improvement is most significant for modulation order of M=64. This applies for both 64-PSK OFDM and 64-QAM OFDM with BER differences of 0.1245 and 0.6878 respectively. The improvement is least significant for modulation order M=8, where BER improve by only 6.47 x 10-3 for 8-PSK OFDM and 5.75 x 10-3 for 8-QAM OFDM
level. Figure 14 – Figure 19 shows the PAPR distribution for both M-PSK and M-QAM modulation.
Table 2: Comparison of Bit Error Rate for each M-PSK and M-QAM modulated random data in OFDM system vs. single carrier system with the presence of AWGN noise (at the point of Eb/No =10dB) Added AWGN noise (AWGN channel model) M-PSK M
M-QAM
8
OFDM system 0.0009531
Non OFDM system 0.0010470
OFDM system 0.0005937
Non OFDM system 0.0006400
16
0.0205000
0.0205100
0.0016840
0.0017670
64
0.1162000
0.1166000
0.0017370
0.0265100
Figure 14: PAPR Distribution for 8-PSK/8-PSK OFDM modulated random signal
Table 3: Comparison of Bit Error Rate for each M-PSK and M -QAM modulated random data in OFDM system vs. single carrier system with the multipath channel model (at the point of Eb/No =10dB) Rayleigh Flat Fading (Multipath channel model) M-PSK
M-QAM
M
OFDM system
Non OFDM system
OFDM system
Non OFDM system
8
0.03017
0.03664
0.03179
0.03754
16
0.06414
0.06552
0.03747
0.04237
64
0.03004
0.15460
0.07760
0.76540
It is shown that there is an improvement in terms of BER value for random data traveling in OFDM system compare to single carrier system. The BER improvement is more significant in QAM modulated random data in both AWGN and multipath channel model. It is also shown that QAM modulated random data in OFDM system shows a significant improvements for higher modulation level (M=64) especially for the value of Eb/No > 10 dB. Lower modulation level (M=8 and 16) shows smaller BER improvement, similar to behavior of PSK modulated random data.
Figure 15: PAPR Distribution for 16-PSK/16-PSK OFDM modulated random signal
Comparing the BER improvement in AWGN channel and multipath channel model, the simulation output shown that OFDM system resulted in better BER improvement in multipath channel model. Hence, OFDM is better suited to be applied for wireless communication where multipath is a common scenario. Using the same OFDM model used earlier in assessing BER performance, the PAPR distribution for both PSK and QAM modulated signal in OFDM system is plotted and compare to when it is in single carrier system. The distribution of PAPR is observed using CCDF. CCDF is used on the basis of power
10481
Figure 16: PAPR Distribution for 64-PSK/64-PSK OFDM modulated random signal
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 21 (2016) pp. 10475-10483 © Research India Publications. http://www.ripublication.com It is observed that PAPR for all level of M-PSK modulation random data signal is 1. It means that the Peak Power is equal to the average power. This happen due to the random data/bit signal generated is NRZ (Non return to zero) and unfiltered. The envelope of the signal is constant. T The numerical values of PAPR distribution are collected as in Table 4. The values are taken at the same point on the curve (Probability = 0.1) for comparison. Table 4: PAPR Values as observed from Simulation for both PSK and QAM modulated random signal in both OFDM and single carrier system
Figure 17: PAPR Distribution for 8-QAM/8-QAM OFDM modulated random signal
Figure 18: PAPR Distribution for 16-QAM/16-QAM OFDM modulated random signal
PSK signal
8-PSK 1
16-PSK 1
64-PSK 1
PSK-OFDM
9.75
10.2
10.4
8-QAM
16-QAM
64-QAM
QAM signal
2.235
2.567
3.695
QAM-OFDM
9.7
10.0
10.2
PAPR (dB)
PAPR (dB)
By observation, applying OFDM modulation to a M-PSK and M-QAM modulated signal cause the PAPR to increase. For example, PAPR increases by 6.505 dB and 10.4 dB by applying OFDM modulation to 64-QAM OFDM signal and 64-PSK OFDM signal respectively. If 30 dBm transmit power is needed to close a 64-QAM link, the power amplifier needs to have a maximum power of 33.7 dBm to ensure linear operation. If the same signal were then OFDM modulated, a 40.2 dBm power amplifier is required. Hence, despite OFDM improves BER of the communication system, it also causes a high PAPR, which causes non linearity at the receiving end as such require high power amplifier in implementation. For MPSK and M-QAM OFDM modulated random signal, the PAPR decreases as the modulation level (value of M-ary) increases.
SUMMARY AND CONCLUSION From the simulation output, it is observed that PSK and QAM modulated random data exhibit these characteristics: a. BER for PSK and QAM increases with the increase in modulation order (M-ary value) b. BER for PSK and QAM is also higher in multipath channel model compare to channel with the presence of AWGN noise only. c. BER curve for 8-PSK and 16-QAM modulated random data is very close to one another indicating that the value of BER for both modulation orders is similar in terms of performances.
Figure 19: PAPR Distribution for 64-QAM/64-QAM OFDM modulated random signal
Whilst, PSK and QAM OFDM modulated random data observations derive these characteristics: a. BER values for M-PSK and M-QAM OFDM improved and the improvement is more significant in QAM OFDM modulated random data
10482
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 21 (2016) pp. 10475-10483 © Research India Publications. http://www.ripublication.com b.
c.
d.
Higher order modulation (M=64) for QAM OFDM modulated random data has better BER improvement compare to when the order of modulation is 8 or 16. This also observed for higher SNR value (EB/No > 10dB) BER value PSK and QAM OFDM modulated random data is lower in multipath channel compare to the channel with the presence of AWGN noise only. BER curve for 8-PSK and 16-QAM OFDM modulated random data is also very close to one another indicating that the value of BER for both modulation order in OFDM system is similar in terms of performances.
To summarize, the paper shows that OFDM techniques do improve the BER of data transmitted and the technique is also resilient to multipath distortion. The paper also shows that the modulation technique and order does have an effect to system performance in terms of BER value. 64-QAM OFDM modulated random data has the best BER value in multipath channel model compare to PSK (M=8/16/64) or 8/16-QAM. BER for OFDM signal also has better improvement in multipath channel, which in line with the theoretical claim that OFDM is best suited for multipath environment. The project also verifies that despite the improvement in BER by applying OFDM technique, the PAPR also increases.
ACKNOWLEDGMENTS We would like to acknowledge and thank UNITEN for funding the Seed fund J510050611.
[6]
[7]
[8]
[9]
[10]
[11]
[12]
REFERENCES [1]
[2]
[3]
[4]
[5]
Proakis, J.G., and Sakhi, M., 2010, “Digital Transmission Through Bandlimited AWGN Channel,” in Communication Systems Engineering, 2nd ed., John Wiley & Sons (Asia), Singapore, pp. 556-560. Benarji, B., Sasibhusana Rao, G., and Pallam Setty. S., 2015, "BER Performance of OFDM System with various OFDM frames in AWGN, Rayleigh and Rician Fading Channel,” International Journal of Applied Engineering Research (IJAER), 3(4), pp. 6-11, 2015. Katariya, A., Yadav, A., and Jain, N., 2011, “Performance Evaluation Criteria for OFDM under AWGN Fading Channel using IEEE 802.11a,” International Journal of Soft Computing and Engineering (IJSCE), 1(3), pp. 10-13. Awon, N.T, Rahman, M. M., Islam, M. A., and Islam, A. T., 2012, “Effect of AWGN & Fading (Raleigh & Rician) channels on BER performance of a WiMAX communication System”, International Journal of Computer Science and Information Security (IJCSIS), 10(8), pp. 11-17. Bhatia, O., Gupta, M., and Gupta, Y.K., 2014, “Evaluation of Bit Error Rate Performance of Orthogonal Frequency Division Multiplexing System over multipath fading channel”, National Conference on Synergetic Trends in engineering and Technology International Journal of Engineering and Technical Research, Special issue, pp. 243-246.
10483
Rathore, R., and Sharma, B.K., 2014, “Performance Analysis of Different Modulation Techniques for OFDM System,” International Journals of Scientific Research and Engineering & Technology, pp. 95 – 100. Haq, A., Katiyar, R., and Padmaja, K.V., 2014, “BER Performance of BPSK and QPSK over Rayleigh Channel and AWGN Channel”, International Journal of Electrical & Electrical Engineering and Telecommunications, 32, pp. 12-16. Acharya, S., Kabiraj, P., and De, D., 2015, "Comparative analysis of different modulation techniques of LTE network," Third International Conference, Computer, Communication, Control and Information Technology, pp. 1-6. Viswanathan, M., 2013, “Channels Model and Fading; Orthogonal Frequency Division Multiplexing” in Simulation of Digital Communication Systems Using MATLAB, 2nd Edition for Kindle, Amazon, pp. 120 – 214. Schulzw, H., and Luders, C., 2005, “Basic of Digital Communications” in OFDM and CDMA Wideband Wireless Communications, John Wiley & Sons, ISBN13 978-0-470-85069-5, pp. 23-44. Tse, D., and Viswanath, P., 2004, “The Wireless Channel” in Fundamentals of Wireless Communication, Cambridge University Press, ISBN13: 978-0521845274, pp. 21-51. Proakis, J.G., Salehi, M., and Bauch, G., 2011, “Multicarrier Modulation and OFDM”, “Transmission Through Wireless Channel” in Contemporary Communication Systems using Matlab, 3rd Edition, Cengage Learning (electronic version), ISBN-13: 9780-495-08251-4, pp. 377-428.
