Metro - IRD India

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ISSN (PRINT) :2320 – 8945, Volume -1, Issue -1, 2013

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Comparative Analysis of Bit Error Rate (BER) for A-law Companded OFDM with different Digital Modulation Techniques

Vishwajit N. Sonawane & Sanjay V. Khobragade Dept. of E&Tc, Dr. BATU Lonere, MH, India E-mail : [email protected], [email protected]

Abstract – Orthogonal Frequency Division Multiplexing (OFDM) is the multicarrier modulation scheme which is very popular one. In this scheme, high rate data streams gets divided into a number of lower rate data streams which are then transmitted over a number of subcarriers.

The different digital modulation techniques like Quadrature Phase Shift Keying (QPSK), M-ary Phase Shift Keying (MPSK) and M-ary Quadrature Amplitude Modulation (MQAM) can be combined with A-law companded OFDM System for better transmission of data taking the advantage of both OFDM System and different digital modulation techniques. This paper discusses the reduced PAPR OFDM system using A-law companding where the message bits are already modulated by using QPSK, MPSK and MQAM processes. A comparative study of Bit Error Rate (BER) vs. Signal to Noise Ratio (SNR) under normal AWGN channel has been simulated &

discussed between several digital modulation techniques using MATLAB version 7.14 Simulink model.

Keywords – OFDM, QPSK, MPSK, MQAM, BER, AWGN channel.

I. INTRODUCTION

The ever increasing demand for very high rate wireless data transmission calls for technologies which make use of the available electromagnetic resource in the most intelligent way. Key objectives are spectrum efficiency (bits per second per Hertz), robustness against multipath propagation, range, power consumption, and implementation complexity. These objectives are often conflicting, so techniques and implementations are sought which offer the best possible trade-off between them. The Internet revolution has created the need for wireless technologies that can deliver data at high speeds in a spectrally efficient manner [3].

However, supporting such high data rates with sufficient robustness to radio channel impairments requires careful selection of modulation techniques.

Currently, the most suitable choice appears to be OFDM (Orthogonal Frequency Division Multiplexing).The main reason that the OFDM technique has taken a long time to become a prominence has been practical. It has been difficult to generate such a signal, and even harder to receive and demodulate the signal. The hardware solution, which makes use of multiple modulators and demodulators, was somewhat impractical for use in the civil systems. OFDM transmits a large number of narrowband carriers, closely spaced in the frequency domain. In order to avoid a large number of modulators and filters at the transmitter and complementary filters and demodulators at the receiver, it is desirable to be able to use modern digital signal processing techniques, such as Fast Fourier transform (FFT) [2].

The ability to define the signal in the frequency domain, in software on VLSI (Very Large Scale Integration) processors, and to generate the signal using the inverse Fourier transform is the key to its current popularity. Although the original proposals were made a long time ago, it has taken some time for technology to catch up. OFDM is currently being used for digital audio and video broadcasting. OFDM for wireless LANs is being used everywhere now, is operating in the unlicensed bands and is also being considered as a serious candidate for fourth generation cellular systems.

II. BASICSOFOFDM

Figure 1. shows the basic block diagram of OFDM transmitter and receiver used for simulation. OFDM is generated by choosing the spectrum required, based on the input data, and modulation scheme used. Each carrier to be produced is assigned da ta to be transmitted. The required amplitude and phase of the carrier is then calculated based on the modulation scheme (typically BPSK, QPSK, or QAM).

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Fig. 1 : Block Diagram of OFDM System For example, if we have to transmit incoming 8 bit digital data, we have to choose 8 different carrier signals, which are orthogonal to each other. Each carrier is assigned to a different bit and its amplitude and phase are chosen according to modulation scheme used. The required spectrum is then converted back to its time domain signal using an Inverse Fourier Transform. In most applications, an Inverse Fast Fourier Transform (IFFT) is used [12].

They are already in time domain, but here we pretend that the input bits are not time domain representations but are frequency amplitudes which if you are thinking clearly, will see that that is what they are. In this way, we can take these bits and by using the IFFT, we can create an output signal which is actually a time-domain OFDM signal. The IFFT is a mathematical concept and does not really care what goes in and what goes out. As long as what goes in is amplitudes of some sinusoids, the IFFT will crunch these numbers to produce a correct time domain result. Both FFT and IFFT will produce identical results on the same input.

We insist that only spectrums go inside the IFFT.

IFFT quickly computes the time-domain signal instead of having to do it one carrier at time and then adding. Calling this functionality IFFT may be more satisfying because we are producing a time domain signal, but it is also very confusing. Because FFT and IFFT are linear processes and completely reversible, it should be called a FFT instead of a IFFT. The results are the same whether you do FFT or IFFT. In literature you will see it listed as IFFT everywhere.

This block can also be a FFT as long as on the receive side, you do the reverse. The IFFT performs the

transformation very efficiently, and provides simple ways of ensuring the carrier signals are orthogonal. The reverse process guarantees that the carriers generated are orthogonal. Consider the model shown in Figure 1. The random data generator generates the data system. This input serial data stream is formatted into the word size required for transmission. For example, 1 bit/word for BPSK & 2 bits/word for QPSK and then shifted into a parallel format. The data is then transmitted in parallel by assigning each data word to one carrier in the transmission.

The data to be transmitted one ach carrier is then mapped into a Phase Shift Keying (PSK) format. The data on each symbol is mapped to a phase angle based on the modulation method. For example, in QPSK the phase angles used are 0°, 90°, 180°, and 270°. The use of phase shift keying produces a constant amplitude signal and was chosen for its simplicity and to reduce problems with amplitude fluctuations due to fading.

The advantages of OFDM system are its high spectral efficiency, ability to resist fading and interference and ease of implementation due to the use of DSP tools like FFT & IFFT. But it suffers from disadvantages like sensitivity to frequency offset and high peak-to-average power ratio (PAPR) [3].

III. A-LAWCOMPANDING

Fig. 2 : Characteristic of A-law Compressor In the companding technique, the compression of OFDM signals at the transmitter and expansion at the receiver [8].This technique can be used to reduce the PAPR which is the main disadvantage of OFDM. In the A-law companding, the compressor characteristic is piecewise, made up of a linear segment for low level inputs and a logarithmic segment for high level inputs.

Figure 2. Shows the A-law compressor characteristics for different values of A.

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9 (1) Where

x=input signal.

y=output signal.

Sgn(x) =sign of the input (+ or -).

|x|=absolute value (magnitude of x).

A=87.6 (defined by CCITT).

IV. DIGITALMODULATIONTECHNIQUES A. QPSK

The Constellation diagram is shown in Figure 3.In communication systems we know that there are two main resources, i.e. transmission power and the channel bandwidth. The channel bandwidth depends upon the bit rate or signaling rate f_b . In digital band pass transmission, a carrier is used for transmission. This carrier is transmitted over a channel. If two or more bits are combined in some symbols, then the signaling rate is reduced. Therefore the frequency of the carrier required is also reduced.

Fig. 3 : Constellation Diagram of (a) QPSK (b) 8-PSK This reduces the transmission channel bandwidth.

Thus because of grouping of bits in symbols, the transmission channel bandwidth is reduced. In quadrature phase shift keying, two successive bits in the data sequence are grouped together.

This reduces the bits rate of signaling rate (i.e. f_b) and hence reduces the bandwidth of the channel. In QPSK two successive bits are combined.

This combination of two bits forms four distinct symbols. When the symbol is changed to next symbol the phase of the carrier is changed by 45°.

B. M-ary PSK

Constellation mapping points for various values of M are shown in Figure 4.BPSK transmits one bit at a time and it has only two symbols. Hence whenever the symbol is changed, the phase shift is

(2) In QPSK two successive bits are combined to form 4 distinct symbols. Hence whenever symbol is changed, the phase shift is

(3) This can be extended further for 'N' bits, if we combine N successive bits, then there will be

possible symbols. Whenever the symbol is changed the phase shift is

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Fig. 4 : Constellation Diagram of (a) 16-PSK (b) 32- PSK(c) 64-PSK

The duration of each symbol will be N T_b thus

(5) Since there are M-symbols, this method is called M-ary PSK, The transmitted waveform is represented in M-ary PSK as,

(6) Where

m=0, 1, 2,……, M-1.

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10 C. QASK Or QAM

In BPSK, QPSK, and M-ary PSK we transmit, in any symbol interval, one signal or another which are distinguished from one another in phase but are all of the same amplitude. In each of these individual systems the end points of the signal vectors in signal space falls on the circumference of a circle.

Now we have note that our ability to distinguished one signal vector from another in the presence of noise will depend on the distance between the vector end points. It is hence rather apparent that we shall be able to improve the noise immunity of a system by allowing signal vectors to differ, not only in phase but also in amplitude.

Fig. 5 : Constellation Diagram of (a) 8-QAM (b) 16-QAM We call this as amplitude and phase shift keying or Quadrature amplitude modulation (QAM). ASK is also combined with PSK to create hybrid systems such as Quadrature Amplitude Modulation (QAM) where both the amplitude and the phase are changed at the same time. QAM is a modulation scheme which conveys data by changing (modulating) the amplitude of two carrier waves.

These two waves, usually sinusoids, are out of phase with each other by 90° and are thus called quadrature carriers—hence the name of the scheme. As for many digital modulation schemes, the constellation diagram is a useful representation. In QAM, the constellation points are usually arranged in a square grid with equal vertical and horizontal spacing, although other configurations are possible.

Since in digital telecommunications the data is usually binary, the number of points in the grid is usually a power of 2 (2, 4, 8...). Since QAM is usually square, some of these are rare—the most common forms are 16-QAM, 64-QAM, 128-QAM and 256-QAM. By moving to a higher-order constellation, it is possible to transmit more bits per symbol. However, if the mean energy of the constellation is to remain the same (by way of making a fair comparison), the points must be

closer together and are thus more susceptible to noise and other corruption; this results in a higher bit error rate and so higher-order QAM can deliver more data less reliably than lower-order QAM.

If data-rates beyond those offered by 8-PSK are required, it is more usual to move to QAM since it achieves a greater distance between adjacent points in the I-Q plane by distributing the points more evenly.

The complicating factor is that the points are no longer all the same amplitude and so the demodulator must now correctly detect phase and amplitude, rather than just phase. 64-QAM and 256-QAM are often used in digital cable television and cable modem applications.

In the US, 64-QAM and 256-QAM are the mandated modulation schemes for digital cable. In the UK, 16- QAM and 64-QAM are currently used for digital terrestrial television.

Fig. 6 : Constellation Diagram of (a) 32-QAM (b) 64-QAM The constellation diagrams for various values of M in QAM are shown in Figure 5. And figure 6.

V. SIMULINKMODELS

Fig. 7 : OFDM System using QPSK

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Fig. 8 : OFDM System using M-PSK

Fig. 9 : OFDM System using M-QAM VI. SIMULATIONRESULTS

Fig. 10 : Comparison of Non-Companded & A-law Companded OFDM System

Fig. 11 : Comparison of QPSK & M-PSK schemes in A-law companded OFDM System

Fig. 12 : Comparison of M-QAM schemes in A-law companded OFDM System

Fig.13 : Comparison of QPSK, M-PSK and M-QAM schemes in A-law companded OFDM System

VII. CONCLUSION

As the value of M i.e. number of bits in symbol increases, bandwidth requirement gets decreased. But this Bandwidth Conservation gets achieved at the cost of increase in transmitted Power & Increase in error probability.

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12 In this paper we studied the performance of Bit Error Rate for different digital modulation techniques in normal AWGN channel with the help of MATLAB/Simulink 7.14. From the above graphs; we can say that as M increases, the error probability also increases. So, due to low error probability, lower order modulation schemes are preferred over higher order modulation schemes as the range of communication increases between a transmitter & receiver.

So to get reliable communication between transmitter & receiver along with higher data rates, then there should be a trade-off between error rate & data rate.

VIII. REFERENCES

[1] SB Pokle & K D Kulat, OFDM Techniques: A Novel Approach for Design of Wireless Communication System, Proceeding of National Level Conference on Advanced Communication Techniques, Act-2005 at BIT Durg, April 5-6, 2005, pp. 140-150.

[2] Van Nee R, Prasad R. ―OFDM for wireless multimedia communications‖. Artech House, 2000.

[3] Hui Liu & Guoqing Li (2005) OFDM Based Broadband Wireless Networks: Design and Optimization, John Wiley & Sons, New Jersey.

[4] Charan Langton, Orthogonal frequency division multiplexing (OFDM) tutorial.

http://www.complextoreal.com/chapters/ofdm2.p df

[5] Vallavraj A, Stewart BG, Harrison DK, Mcintosh FG. Reduction of peak to average power ratio of OFDM signals using companding. In:

Proceedings of IEEE Ninth International Conference on Communication Systems, Singapore, 2004. P. 160-4.

[6] P Coulon, Principles of Modulation in Wireless Communications, Essay presented at Dept. of Electrical & Comm. Engg., Helsinki University, Oct 1999.

[7] Theodore S.Rappaport, Wireless Communications, principles and practice, 2^nd Edition, prentice- Hall publications.

[8] Wang X, Tjhung TT, Ng CS. Reduction of peak- to-average power ratio of OFDM system using a companding technique. IEEE Transactions on Broadcasting 1999:45(3):303-7.

[9] A. Amin, (2011) ―Computation of Bit-Error Rate of Coherent and Non-Coherent Detection M-Ary PSK With Gray Code in BFWA Systems‖ International Journal of Advancements in Computing Technology, Vol.

3, No. 1, pp. 118-126.

[10] H. Kaur, B. Jain and A. Verma, (2011)

―Comparative Performance Analysis of M-ary PSK Modulation Schemes using Simulink‖, International Journal of Electronics &

Communication Technology, Vol. 2, Issue 3, pp.

204-209.

[11] S. Mahajan and G. Singh, (2011) ‖ Reed- Solomon Code Performance for M-ary Modulation over AWGN Channel‖, International Journal of Engineering, Science and Technology, Vol. 3, No. 5, pp.

International Journal of Advances in Engineering

& Technology, July 2012. 473 Vol. 4, Issue 1, pp.

3739-3745.

[12] Andrea Goldsmith (2005) Wireless Communication, Artech House, London.

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