PAPR REDUCTION IN OFFSET QPSK OFDM THROUGH LOSSY SOURCE CODING

International Journal of Electrical Engineering and Technology (IJEET) Volume 11, Issue 8, October 2020, pp. 1-10, Article ID: IJEET_11_08_001 Available online at http://www.iaeme.com/ijeet/issues.asp?JType=IJEET&VType=11&IType=8 ISSN Print: 0976-6545 and ISSN Online: 0976-6553 DOI: 10.34218/IJEET.11.8.2020.001 © IAEME Publication Scopus Indexed PAPR REDUCTION IN OFFSET QPSK OFDM THROUGH LOSSY SOURCE CODING Vasantha Lakshmi M, B. Kanmani Department of Electronics and Telecommunication, BMS College of Engineering, Bangalore, Affiliated to Visvesvaraya Technological University, Belagavi, Karnataka, India ABSTRACT Orthogonal Frequency Division Multiplexing along with the multiple accesses is the modulation technique used in the fourth generation wireless communication. With the fast growing technology and the huge demand for the increase in the bandwidth has made OFDM as the best modulation technique for high speed transmission. The spectrum of the bandwidth is effectively utilized in an OFDM. This provides higher efficiency and improves the overall performance of the system. Though OFDM has all these advantages there are certain drawbacks which need to be addressed. The major ones include Inter carrier Interference and the ratio of the peak to the average power. The research idea was to consider the drawback and try to overcome it. Hence ratio of the peak to the average power was considered. The methodology is to generate the OFDM symbols with Offset QPSK as the modulation technique and analyze the peak power and peak to average power ratio of the generated symbols and apply the proposed method to reduce it. The lossy coding method falls under the category of the signal distortion. The simulation is performed in MATLAB. The simulation results of the proposed method and the amount of the reduction achieved in ratio of the peak to average power along with the amount of the bit error rate have been discussed in the paper. Key words: OFDM, QPSK OFDM, OQPSK OFDM, PAPR, BER. Cite this Article: Vasantha Lakshmi M and B. Kanmani, PAPR Reduction in Offset QPSK OFDM Through Lossy Source Coding. International Journal of Electrical Engineering and Technology, 11(8), 2020, pp. 1-10. http://www.iaeme.com/IJEET/issues.asp?JType=IJEET&VType=11&IType=8 1. INTRODUCTION OFDM is a modulation technique with multiple carriers. The carriers are closely spaced with each other. When we apply the voice or the data to the carriers then the sidebands spreads out on either side. There may be overlapping of the sidebands. This can be overcome by making the carrier spacing equal to the reciprocal of the symbol interval. The receiver must be able to receive the symbols without any interference. This is based on the orthogonality nature of the http://www.iaeme.com/IJEET/index.asp 1 editor@iaeme.com PAPR Reduction in Offset QPSK OFDM Through Lossy Source Coding OFDM symbols. In an OFDM the high stream of data is divided into sub channels which are a multiple lower streams of data. Multiple sets of carriers are used to modulate these lower streams of data. Offset Quadrature Phase Shift Keying is considered as the modulation technique. The frequencies for the sub channels are selected in such a way that they are orthogonal to each other. The interference among the symbols is reduced based on the splitting of the larger bit streams into lower bit streams. The throughput remains the same after the splitting. This is the benefit of using OFDM [1]. Since the interference is eliminated based on the orthogonal nature of OFDM intercarrier guard bands are not required [2]. This reduces the design complexity of the modulator and the demodulator. OFDM requires the frequency synchronization to be very accurate. The deviation in the frequency will disturb the orthogonality nature of the OFDM symbols that results in the inter carrier interference [3]. The frequency deviation is caused based on the Doppler shift [4]. There are several advantages of OFDM systems. Despite of several advantages of the OFDM symbols there are two major concerns which need to be reduced for better performance of the system [4]. The Peak to average power ratio and the inter carrier interference are the two major concerns [5]. In this work peak to average power ratio have been considered as the factor and a new lossy coding method is proposed to reduce it for better performance of the system. The Generation and demodulation of the OFDM symbols using QPSK and OQPSK as the modulation technique and their comparative study are discussed in the Section 2. The Peak to average power ratio and the simulation results of QPSK and OQPSK are specified in Section 3. The proposed method of reducing the Peak to average power ratio and the amount of the bit error rate introduced along with the simulation results is specified in Section 4. Finally the conclusion is discussed in the Section 5. 2. QPSK AND OQPSK OFDM The Quadrature Phase Shift Keying (QPSK), modulation technique is widely used in OFDM. The QPSK modulation scheme, given by equation (1), the carrier phase  i , takes one of the four phase values, with each symbol mapped to two binary bits, through the signal constellation diagram. 2E cos  2 f ct  i  for 0  t  T T i being one of the phase angles   /4 or  3 /4 sQPSK i  t   (1) Here, E is the energy of the symbol, T is the symbol duration and f c the carrier frequency. The four distinct QPSK symbols can be represented using the two orthonormal basis functions, q1  t  and q2  t  , represented by equations (2) and (3) [6]. q1  t   2 cos  2 f ct  T 0t T (2) 2 sin  2 f ct  0t T (3) T With the above basis functions, the QPSK constellation diagram is given by Figure 1, where it is ensured that the adjacent symbols differ in only one bit. q2  t   http://www.iaeme.com/IJEET/index.asp 2 editor@iaeme.com Vasantha Lakshmi M and B. Kanmani Figure 1 Constellation diagram of QPSK Symbols On the other hand, the Offset-QPSK modulation scheme is represented by 2E cos  2 f ct  i  for 0  t  T T i being one of the phase angles   or   /2 sOQPSK i  t   (4) The four distinct Offset-QPSK symbols can also be represented using the orthonormal basis functions, q1  t  and q2  t  , and the signal constellation diagram, together with the mapping of the binary bits to the symbols is shown in Figure 2. Figure 2 Constellation diagram of OQPSK Symbols The probability of bit error of the QPSK and the Offset-QPSK are identical when the symbol energy is identical and is given by equation (5) http://www.iaeme.com/IJEET/index.asp 3 editor@iaeme.com PAPR Reduction in Offset QPSK OFDM Through Lossy Source Coding  E Pe  erfc   2 N0    (5) Where Pe is the probability of Bit error and N 0 is the average noise power. Having seen the QPSK and the Offset-QPSK (OQPSK), we now consider the QPSK OFDM generation and demodulation. 2.1. QPSK OFDM Generation and Demodulation The QPSK modulation scheme uses one sinusoidal carrier with four allowable phase angle, the instantaneous angle being dependant on the binary data and the signal constellation diagram. In the QPSK-OFDM modulation scheme, we use N-orthogonal carriers, with each carrier performing the QPSK modulation for the input pair of binary data. The block diagram of the QPSK-OFDM modulation scheme is shown in Figure 3. The first block converts the input binary data stream into N-parallel streams. Two bits from each of the input streams are QPSK modulated using one of the N-orthogonal carriers. In the final stage, the N-QPSK modulated waveforms are added to produce the QPSK-OFDM symbol to represent the 2N bits. Hence, there are a total of 2N unique OFDM symbols in this form of modulation. The QPSK modulation scheme involves a change in the phase of the carrier, and hence is always a signal of constant amplitude. On the other hand, the QPSK-OFDM scheme is through the addition of N-QPSK signals, and hence there is a change in both the amplitude and the phase of the modulated symbol. Figure 3 Generation of QPSK OFDM Symbols The demodulation of the QPSK-OFDM involves the process of recovering the 2N message bits from the modulated waveform. The first stage is to extract the frequency components present in the input symbol, through the discrete Fourier Transform, corresponding to the N-carriers. This process is usually represented as FFT in block diagrams in demodulation and by IFFT in a modulation. Each of the spectral components is then mapped through the signal constellation diagram to the binary data. It is similar to performing the QOPSK demodulation for each of the N- orthogonal carriers. http://www.iaeme.com/IJEET/index.asp 4 editor@iaeme.com Vasantha Lakshmi M and B. Kanmani Figure 4 Demodulation of QPSK OFDM Symbol Based on the constellation diagram of QPSK as described in the Fig 1, the adjacent bits mapping is gray code where there will be one bit change whereas in the opposite bit mapping there is two bit change. We can observe that the energy of each symbol is 2 . The procedure of generating and demodulating the OFDM symbols using OQPSK remains the same as the generation and demodulation with the normal QPSK. The only modification is instead of QPSK generation with N orthogonal carriers, we generate OQPSK with N orthogonal carriers as described in the Fig 3. The OFDM symbols generated using OQPSK are mapped based on the constellation diagram as described in Fig 2. We have generated the OFDM symbols using QPSK and OQPSK as the modulation technique as described in the Section 2. In the next section Peak to Average power ratio and the comparison with respect to QPSK and OQPSK are considered. 3. PEAK TO AVERAGE POWER RATIO As mentioned earlier both QPSK and OQPSK have similar BER performance. We know attempt to compare the corresponding OFDM symbols. At the transmitting end OFDM symbols are generated. Each symbol will have different values of the phases. All of them occur at different time instants. OFDM symbols are generated for varying symbol lengths. We have measured the peak of the symbols generated. Similarly we have measured the average power of the generated symbol. Then we have calculated the Peak to average power ratio for all the symbol lengths as given by equation (5). This has been implemented using simulation tool and the results of the same have been discussed in the Section 3.1. PAPR  PeakPower AveragePower (5) 3.1. Comparative Study of QPSK and OQPSK For a given bit pattern the QPSK and OQPSK OFDM symbols is shown in Figure 5 with N=8. In one period of the lowest carrier frequency the difference between the two modulation schemes is not clearly evident. We fix symbol length N and for a given N we generate 2 N distinct OFDM symbols for the QPSK OFDM modulation scheme. We repeat for the OQPSK OFDM. http://www.iaeme.com/IJEET/index.asp 5 editor@iaeme.com PAPR Reduction in Offset QPSK OFDM Through Lossy Source Coding QPSK OFDM Symbol for 01010101 Bit pattern OQPSK OFDM Symbol for 01010101 Bit pattern 4 3 4 2 2 1 0 0 -1 -2 -2 -4 -3 -4 -6 -5 -8 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Figure 5 QPSK and OQPSK OFDM symbol for 01010101 bit pattern From the generated symbols PAPR has been calculated for the 256 symbols. The Maximum value of Peak power was 28.8 with the PAPR of 7.24. The procedure is repeated for the different symbol lengths. This has been described in Fig 6. Similarly for the same symbol length OQPSK is used for the OFDM symbols generation and the procedure of Peak power and PAPR calculations are repeated. From the PAPR calculations it was observed that out of the total possible combinations only 8 combinations had high peak value as 31.9903 with the PAPR of 8.065. There was almost 50% reduction in the number of combinations having the high value of PAPR in OQPSK compared with the QPSK. This has been described in Fig 7. It can be seen that there are 8 different combinations for which PAPR is high. PAPR for the symbol length 8 10 PAPR 8 6 4 2 0 0 50 100 150 Symbols(Bits) 200 250 Figure 6 PAPR for the symbol length 8 for QPSK OFDM Figure 7 PAPR for the symbol length 8 for OQPSK OFDM http://www.iaeme.com/IJEET/index.asp 6 editor@iaeme.com Vasantha Lakshmi M and B. Kanmani For the QPSK OFDM symbols generated, PAPR has been computed. The same computation has been repeated for the OFDM symbol generation by Offset QPSK. The comparitive study of the QPSK and the Offset QPSK with respect to the PAPR has been described in the Figure 8. Maximum Value Maximum value of PAPR for QPSK OFDM and OQPSK OFDM 14 12 10 8 6 4 2 0 6 8 10 12 Symbol Length QPSK OQPSK Figure 8 Comparision of PAPR with QPSK OFDM and OQPSK OFDM 3.2. Observation Based on the observations in the Fig 6 and 7, in the Offset QPSK method we have only 8 combinations where the PAPR is high irrespective of the length of the symbol. Hence it is convenient to use Offset QPSK for OFDM symbol generation than an normal QPSK.[5]. The 8 symbols for which the PAPR is high in an OQPSK are 00000000, 00110011, 01001011, 01111000 and the remaining combnations are the bit reversal of these four combinations. i.e. 10000111, 10110100, 11001100 ans 11111111 for the length of the symbol as 8. For the symbol length of 10, 0000000000, 0011001100, 0100101101, 0111100001, 1000011110, 1011010010, 1100110011 and 1111111111 are the 8 combinations. Similar pattern follows for the other symbol lengths. For the N OQPSK OFDM symbol the maximum and the minimum value of the OFDM symbol are given by the equations (6) and (7) and occur at different instants at T  0, 0.25, 0.5, 0.75 depending on the symbols in the duration 0 to T. SOQPSK  t max   N 2 SOQPSK  t  min   N 2 (6) (7) For the symbol length 8, the highest value is +4 and the lowest value is -4. Similarly for the symbol length 12, the highest value is +6 and the lowest value is -6. This observation remains same for the different symbol lengths. We can conclude that for the OQPSK OFDM symbols only 8 combinations as specified are having high PAPR. Hence the proposed coding method is based on lossy source coding method to reduce the PAPR of the 8 combinations for better performance of the system. This is described in the Section 4. 4. PROPOSED METHOD OF PAPR REDUCTION The method of PAPR reduction implementation of the proposed method is to encode the bit pattern after mapping to the constellation points of the OQPSK OFDM symbol generation. http://www.iaeme.com/IJEET/index.asp 7 editor@iaeme.com PAPR Reduction in Offset QPSK OFDM Through Lossy Source Coding The eight combinations of high PAPR are avoided in the proposed method of encoder. The 8 combinations with the high value of PAPR as specified are considered in the encoder. For N= 8 for the bit pattern of 00000000 the PAPR value was 7.477. The proposed method of the encoder is to toggle the LSB bit with the high PAPR. That is instead of transmitting the bit pattern as 00000000 we transmit the bit pattern as 00000001 by bit reversing the last bit position of the combination with the PAPR of 5.72. This will reduce the PAPR from 7.477 to 5.72. Similarly instead of transmitting the bit pattern as 00110011 we transmit the bit pattern as 00110010. This will reduce the PAPR from 8.02 to 5.948. The same procedure is repeated for all the eight combinations. The similar logic holds good for all the different symbol lengths. Table 1 specifies the simulation result of the proposed method. Table 1 Graph of proposed method of PAPR Symbol length 8 Proposed method of PAPR Proposed method-PAPR for the symbol length 8 10 8 6 4 2 0 0 50 100 150 200 250 Symbols(Bits) Proposed method-PAPR for the symbol length 10 10 15 PAPR 10 5 0 0 200 400 600 800 1000 Symbols(Bits) Proposed method-PAPR for the symbol length 12 12 15 PAPR 10 5 0 0 1000 2000 3000 4000 Symbols(Bits) http://www.iaeme.com/IJEET/index.asp 8 editor@iaeme.com Vasantha Lakshmi M and B. Kanmani From the table 1 we can conclude that the PAPR value is reduced as specified and the amount of reduction achieved is given in the Figure 9. By bit reversing the Last bit position of the combinations we are introducing the Bit Error Rate. The BER calculations are discussed in the Section 4.1. PROPOSED METHOD OF PAPR REDUCTION Maximum Value 14 12 10 8 6 4 2 0 6 8 10 12 Symbol Length OQPSK OFDM Proposed method Figure 9 Comparision of PAPR with OQPSK OFDM and proposed method 4.1. Bit Error Rate Calculations To reduce the PAPR value of the 8 combinations as specified we bit reverse the last bit position. By doing so Bit error rate is introduced. For the symbol length of 8, the total possible combinations are 28. Hence the total transmitted bits will be 2048 (256 X 8). Since we are bit reversing the last bit position of the 8 combinations with the high value of PAPR, 8 bits will be in error. Hence the BER will be 0.0039 (8/2048). The BER for different symbol lengths are 0.781 X 10-3 for symbol length 10, 0. 162 X 10-3 for the symbol length 12, 0.0348X10-3for length of the symbol as 14 and foe the symbol length 16, BER is 0.007269 X 10-3 Since BER is introduced the symbol bits transmitted cannot be recovered back. Hence we propose the method as lossy coding method of PAPR reduction. Bit error rate is inversely related to the length of the symbol. Similar study is done for the BPSK OFDM symbols. The observation was that only 4 combinations were having high value of PAPR and hence the lossy coding method was proposed [7] [1]. The same work has been extended for QPSK OFDM. 5. CONCLUSION OFDM symbols are generated using QPSK and OQPSK as the modulated technique. We found that out of the two techniques OQPSK modulation provides the better results as discussed and hence the proposed method has been implemented using OQPSK. From the OFDM symbols generated PAPR have been calculated. The observation was that only 8 combinations out of the total combinations have high value of PAPR as specified in the Section 3. The observation remains same for the different symbol lengths. To reduce the PAPR, new method was proposed and implemented in MATLAB and the amount of the reduction achieved is specified in the section 4. We were able to achieve a significant reduction in the PAPR with OQPSK as the modulation technique for the OFDM symbol generation. The simulation results are discussed in the section 4. Since the proposed method is http://www.iaeme.com/IJEET/index.asp 9 editor@iaeme.com PAPR Reduction in Offset QPSK OFDM Through Lossy Source Coding based on bit reversing the last bit position of the combinations with the high value of PAPR, BER will be introduced as discussed in section 4.1. As the symbol length increases BER will be reduced as discussed in the table 4. ACKNOWLEDGEMENT The research work is supported by the college management and the TEQIP-III. The authors acknowledge them. REFERENCES [1] Vasantha lakshmi M, B.Kanmani, “Digital circuit simulation study of Lossy source coding for PAPR reduction”, 5th IEEE International Conference on Advanced Computing & Communication Systems, March 16-17, 2019 [2] https://www.gaussianwaves.com/2011/05/introduction-to-ofdm-orthogonal-frequencydivision-multiplexing-2 [3] www.gaussianwaves.com/2010/10/qpsk-modulation-and-demodulation-2 [4] www.radio-electronics.com/info/rf-technology-design/ofdm/ofdm-basics-tutorial.php [5] Mamta Bishti and Alok Joshi, “Various techniques to reduce PAPR in OFDM systems: A Survey” International Journal of Signal Processing, Image Processing and Pattern Recognition, volume 8, No.11, pp 195-206, 2015 ISSN: 2005-4254. [6] M.Vasantha Lakshmi, B.Kanman,” PAPR of QPSK OFDM modulation schemes: A comparitive study”, The IUP Journal of Electrical and Electronics Engineering, April 2019. [7] M.Vasantha Lakshmi, B.Kanmani, “PAPR reduction through Lossy coding” IEEE paper on international conference on algorithms, methodology, models and applications in emerging technologies, february 2017. http://www.iaeme.com/IJEET/index.asp 10 editor@iaeme.com