This chapter describes the objective of research work which is covered in the first

4.1 INTRODUCTION: This chapter describes the objective of research work which is covered in the first chapter. The chapter is divided into two sections. The first section evaluates PAPR reduction for basic OFDM system. The second section is dedicated for the reduction of the PAPR by using SLM method. This section includes the various simulation results showing the performance of the proposed PAPR reduction technique. The methodology adopted in this research work is simulation for the OFDM system. Initially the PAPR performance is carried out for basic OFDM system using different modulation techniques and simulation parameter of standard IEEE 802.11a. The results are obtained through the simulation using MatlabR2010. The analysis of basic OFDM system is followed by comparative study of conventional SLM method for PAPR reduction. Finally the results of the proposed PAPR reduction technique using Modified SLM which uses LBC Extended Hamming code and DQPSK as a modulation scheme are enumerated. 4.2 BASIC OFDM SYSTEM: The basic OFDM sytem is an uncoded system. No coding technique is provided and the data is mapped with a suitable modulation technique. This modulated data is transformed to an OFDM symbol by an IFFT. The size of IFFT is 64. A cyclic prifix (CP) is to be added to the OFDM symbol. As per IEEE standards 25% of the IFFT samples are selected as CP.[66] Thus the total OFDM symbol size is expressed as : 68

Actual data transmission Padding Cyclic Prefix = 52 bits = 12 Zeros = 16 Samples OFDM SYMBOL = 52 + 12 + 16 = 80 Further calculations are done to evaluate data rate, subcarrier spacing, guard period and total symbol time. Data rate of transmitter for the OFDM system using QPSK or DQPSK modulation technique is given by As QPSK or DQPSK utilize two bits for transmission and BPSK used one bit for transmission. Obviously the data rate for DQPSK is higher in context to BPSK. Substituting the values in the expression µ The relation between the various time is stated as: T sym = T G + T IFFT = 0.8 µs + 3.2µs = 4µs where T sym = Total symbol time in µs T G = Total time period of CP in µs T IFFT = Total IFFT symbol time in µs The period of CP T G is calculated as: µ 69

The subcarrier spacing is specified by µ 4.2.1 PAPR in basic OFDM system: An analysis is carried out for the PAPR values of a basic OFDM system for different modulation techniques such as BPSK, QPSK and DQPSK. In these systems the following specifications are used to find PAPR value of OFDM signal.[66] Table 4.1 shows the simulation parameters for basic OFDM system. Table 4.1: Simulation Parameters for the IEEE802.11a PARAMETER Data rate 26Mbps VALUE/TYPE No of carriers used 52 IFFT size 64 Point Cyclic prefix Length 16 Channel spacing 20MHz Subcarrier spacing Δf Guard period T G 312.5KHz 0.8µs IFFT Period T IFFT 3.2 µs T sym = T G + T IFFT 4 µs Signal Constellation Guard Type BPSK, QPSK, DQPSK Cyclic Prefix 70

Shown in Fig 4.1 is the flow chart of the Basic OFDM system to plot the PAPR graph of OFDM signal for different modulation technique. Initially FFT size is defined and then a random signal is generated. Numbers of subcarriers considered are 52 in one symbol. Further the numbers of symbols for n number of bits are calculated. Next initialize mode of modulation. The output of the IFFT is in parallel so that it is necessary to convert data into serial stream for transmission. Add cyclic prefix value at the output of IFFT to reduce ISI. Compute the mean power and peak value of signal and plot the PAPR graph. START Define FFT size Generate Random Signal Calculate number of Symbol Generate Mode for Modulation Take IFFT and Add cyclic Prefix Convert into serial stream for transmission Compute Mean power and peak value Plot the PAPR END Fig 4.1: Flow chart of basic OFDM 71

Considering the Basic OFDM system the PAPR performance is analyzed for different modulation scheme that are BPSK, QPSK and DQPSK. The results obtained are graphically represented in Fig 4.2.a, b, c for different modulation techniques. Fig 4.2a for BPSK, Fig 4.2b for QPSK, Fig 4.2c for DQPSK. The value of PAPR found of the Basic OFDM system for BPSK modulation scheme is approximately 12.5 db, whereas it is 11dB for QPSK modulation technique. The maximum PAPR achieved is 10dB when DQPSK modulation is used. From the values of the PAPR from different modulation techniques it is concluded that the PAPR is least for DQPSK modulation technique. The performance of the basic OFDM system is enhanced when DQPSK modulation technique is used. The PAPR performance is carried out for basic OFDM system using different modulation technique and simulation parameter of standard IEEE 802.11a. These results are tabulated in Table 4.2. Table 4.2: PAPR comparison for different modulation technique SYSTEM Basic OFDM System Maximum PAPR in db BPSK QPSK DQPSK 12.5 11 10 72

Fig 4.2a: PAPR of basic BPSK OFDM system Fig 4.2b: PAPR of basic QPSK OFDM system 73

Fig 4.2c: PAPR of basic DQPSK OFDM system 4.3 RESULTS OF SELECTIVE MAPPING TECHNIQUE: Selective mapping technique is one of the PAPR reduction method. In this research work the conventional SLM technique is analyzed for PAPR values using QPSK and DQPSK modulation technique. A modified SLM technique is proposed for the reduction of PAPR using LBC with Extended Hamming code. The conventional SLM technique is an uncoded method. The signals are not coded in any form in this technique. Data is converted from serial to parallel which is then rotated appropriately. This rotated data is mapped and then transformed by IFFT. The symbol with lowest PAPR is selected for further transmission. 74

Cumulative Distribution Function (CDF): The graphical representation relating CDF of PAPR for Basic OFDM system and conventional SLM is shown in Fig 4.3. It is observed that PAPR seems to be distributed from around 4.5 db to a maximum value of 10 db then by central limit theorem. 1 0.9 SLM Basic 0.8 0.7 Probability, X <=x 0.6 0.5 0.4 0.3 0.2 0.1 0 0 5 10 15 PAPR, X db Fig 4.3: Cumulative distribution plot of PAPR from an OFDM signal 4.3.1 Theoretical PAPR of SLM OFDM system: PAPR is measured in complementary cumulative distribution function (CCDF). The probability that the PAPR of an OFDM frame exceeds a certain threshold z is given in eq. 4.1. Now it is assumed that D is statistically independent OFDM frames, 75

representing the same information. The probability of PAPR larger than a threshold z can be written as P(PAPR > z) = (1-(1-e -z ) N ) D (4.1) Fig 4.4 shows the theoretical CCDF curve as a function of PAPR distribution when SLM method is used for N=128, D=2 m, m=0, 1,. 7. It is seen that with an increase in value of D, the theoretical PAPR value gets smaller. Fig 4.4: Theoretical PAPR of SLM, N=128 For an OFDM system with number of subcarrier N=64. The CDF to describe the PAPR of a basic OFDM system is P(PAPR > z) = 1-(1-e -z ) N (4.2) 76

Fig 4.5: Theoretical PAPR of OFDM system and CONSLM system The graphical representation of theoretical PAPR for basic OFDM system and conventional SLM (CONSLM) for different values of D is shown in Fig 4.5. It is observed that the PAPR of the basic OFDM system is high in relation to the PAPR of conventional SLM.[67] SLM method improves the PAPR as compared to the basic OFDM system. The increase in the number of OFDM signal frames D will raise the computational complexity with benefit of small improvement of PAPR reduction performance. 4.3.2 Mean and Variance of PAPR: MATLAB provides a function to calculate the normal Cumulative Distribution Function (CDF). It determines the CDF of the normal distribution parameters mean and standard deviation of PAPR. A Conventional Selective Mapping (CONSLM) is considered for different values of D, such as CONSLM1 for D=8, CONSLM2 for 77

D=16 and CONSLM3 for D=32. The mean and variance values are calculated using MATLAB for basic OFDM system and CONSLM. The Table 4.3 shows the results for mean and variance of PAPR. It is seen that the mean and variance value of PAPR for CONSLM system is less than the basic OFDM system. As the value of D is increased the PAPR gets reduced for CONSLM system. A graphical representation of cumulative probability of basic OFDM and CONSLM system versus the generated data is shown in Fig 4.6. Table 4.3: Mean and Variance of PAPR PARAMETER OFDM CONSLM1, D=8 CONSLM2, D=16 CONSLM3, D=32 Mean (µ) 0.334963 0.261795 0.245716 0.231809 Variance(σ) 0.197184 0.175719 0.175719 0.169913 Fig 4.6: Comparative analysis of cumulative probability 78

4.3.3 Conventional SLM: ALGORITHM FOR CONVENTIONAL SLM Initialize FFT size and number of carriers. Define signal set and rotation factor is +180, 180 for QPSK and +135, 135 for DQPSK. Select an array for PAPR. Start a loop for n=1 where n is the number of carrier signal Generate a signal randomly for FFT size keeping the signal in first row same as the signal set and other three signals are phase rotated according to step two. Now take the IFFT. Calculate Mean power, Peak power and PAPR. Select the lowest PAPR from set of signal and three other rotated signals. End the loop when carrier signal is over. Now a set of PAPR is received which have lowest values in their respective block. The PAPR values of QPSK and DQPSK are represented graphically. For the various values of subcarriers in a CONSLM with QPSK and DQPSK different values of PAPR are obtained. Fig 4.7a shows the PAPR of conventional selective OFDM using QPSK modulation scheme. The peak value of QPSK with CONSLM is 7.8 db and Fig 4.7b shows the PAPR of CONSLM DQPSK OFDM system with the peak value of 7.5 db.[53] It is stated that DQPSK gives a good performance in PAPR 79

reduction of CONSLM OFDM system. From the above discussion DQPSK modulation scheme seems to be simple and efficient. 8 PAPR of Con SLM-QPSK 7.5 7 6.5 PAPR in db 6 5.5 5 4.5 4 3.5 0 100 200 300 400 500 600 700 800 900 1000 Carriers Fig 4.7a: PAPR of CONSLM QPSK OFDM system 80

7.5 PAPR dqpsk Con SLM 7 6.5 PAPR con SLM 6 5.5 5 4.5 4 3.5 0 100 200 300 400 500 600 700 800 900 1000 Carriers Fig 4.7b: PAPR of CONSLM DQPSK OFDM system Simulation results in Table 4.4 show the PAPR values with and without using SLM technique QPSK/DQPSK modulation scheme. It is seen that DQPSK with SLM technique has better performance in PAPR reduction of OFDM system. Table 4.4: Comparison of the performance for PAPR reduction System Basic System (Without SLM) Conventional SLM Maximum PAPR in db QPSK DQPSK 11 10 7.8 7.5 81

4.4 REDUCTION IN PAPR USING PROPOSED METHOD: From the previous investigations it is inferred that the DQPSK modulation technique gives considerable results in PAPR reduction of the OFDM system. In the present investigation, an algorithm was developed for proposed Modified SLM. In this method decision criterion is used before IFFT block. The lowest value of coset is selected from standard array of LBC before IFFT block and the signal is transferred to constellation mapping and IFFT. The benefit of the decision criterion for selecting the lowest PAPR value is that the number of IFFT blocks are reduced to a single block. Thus this method contributes in reduction of the complexity in the circuit as well as the value of PAPR. ALGORITHM FOR MODIFIED SLM A binary information source is divided into blocks of 4 bits. Each information block is encoded into a codeword by a (7, 4) hamming encoder. A control bit added to codeword c to create an extended hamming code of 8 bits. Calculate the error table and coset leader, 16 in number Sixteen vectors are constructed as c+e 1, c+e 2,..., etc For each scrambled codeword calculate the value of Scrambled codeword with the minimum Z is selected and then transformed to OFDM signal by constellation mapping and IFFT. 82

The results gained for the proposed SLM system showed maximum PAPR value of 4.7 db and the average PAPR is 2.7924 db. Fig 4.8 exhibits the results of the proposed SLM technique with a reduction in PAPR value. 5 PAPR MOD SLM 4.5 4 3.5 PAPR MOD SLM 3 2.5 2 1.5 1 0.5 0 0 100 200 300 400 500 600 700 800 900 1000 Carriers Fig 4.8: PAPR of Modified DQPSK OFDM system An investigation is done for establishing the relation between IFFT length and the PAPR. Table 4.5 enumerates the maximum PAPR and Average PAPR values for different values of IFFT. The PAPR and average PAPR is calculated for CONSLM with QPSK, DQPSK and proposed SLM method. On observing the results it is concluded that average PAPR value reduces with the decrease in IFFT length. It is also inferred that average PAPR remains constant 2.79 db of the proposed method for any length of IFFT. 83

Table 4.5: FFT size with respective PAPR values FFT SIZE (N) 512 SLM Method Max PAPR in db Average PAPR in db CONSLM QPSK 9.1282 7.5725 CONSLM DQPSK 8.8067 7.4935 Proposed Modified 4.7712 2.7924 CONSLM QPSK 8.3572 7.0123 256 CONSLM DQPSK 8.6149 6.9747 Proposed Modified 4.7712 2.7924 CONSLM QPSK 8.5583 6.4043 128 CONSLM DQPSK 7.9435 6.3697 Proposed Modified 4.7712 2.7924 CONSLM QPSK 7.4212 5.7302 64 CONSLM DQPSK 7.7978 5.7042 Proposed Modified 4.7712 2.7924 In the proposed method the single lowest PAPR value is selected before IFFT and then it is transformed whereas in CONSLM the single lowest PAPR value is selected after the transformation. This selection criteria of the single lowest PAPR value before transformation of the proposed method gives a reward in the form of a constant average PAPR for any size of IFFT. PAPR is merely the function of IFFT length N of the OFDM transmitter i.e. PAPR reduces as number of subcarriers reduce. 84

Fig 4.9: Proposed Modified SLM Simulink model 85

4.4.1Simulink model for Modified SLM: The simulink software package provided by MATLAB is a good tool for designers. It is a tool which helps designers to create models, provide simulation and make their analysis. Simulink works successfully for linear as well as nonlinear systems which can be modeled in continuous time, sampled time or a combination of both. It comes very handy while dealing in real time problems. It has got facilities like data forwarding from one block to another branching, multiplexing and signal generation and many more. It only considers discrete time intervals for getting results and performance. The proposed Modified SLM simulink model is designed, some blocks are selected from simulink library and the key blocks are designed independently. The input data is encoded to which the decision criterion is applied. This information is modulated and transformed to get the PAPR values. Table 4.6: PAPR comparison for Modified SLM SYSTEM MAXIMUM PAPR in db Modified SLM by Yang Jie et al[18] 5.5 Proposed Modified SLM using MATLAB (Theoretical)[53] 4.7 Proposed Modified SLM by using simulink (simulation) 3.0103 86

The proposed method used SLM technique with extended Hamming Linear Block Code and DQPSK mapping technique to reduce PAPR value. In the proposed method the PAPR value 4.7dB is achieved as shown in Table 4.6. The MATLAB simulation results show improved performance of PAPR by 0.8 db in the proposed OFDM system as compared with (Yang Jie et al 2007) 6 PAPR in Modified SLM 5 4 PAPR in db 3 2 1 0 Modified SLM Yang Jie et.al. Proposed Modified SLM using MATLAB(Theoretical) Proposed Modified SLM by using Simulink(simulation) Series1 5.5 4.7 3.0103 Fig 4.10: Comparative analysis of Modified SLM 87

4.5 PAPR PERFORMANCE WITH INTERLEAVER: Data Encoder Matrix Interleaver Modulator IFFT PAPR Fig 4.11: OFDM system with interleaver A simulink model is also implemented along with interleaver block for PAPR reduction. Comparative analysis of the PAPR values of OFDM system with interleaver and without interleaver for different subcarriers that are 16, 32, 64 and128 as shown in graph. The Table 4.7 highlights the PAPR value for different input bits with and without interleaver which indicates interleaver improves the PAPR. Table 4.7: Effect of interleaver on PAPR value Input Bits PAPR value with interleaver in db PAPR value Without interleaver in db 16 3.8008 7.0969 32 4.8608 6.0879 64 6.1878 8.6415 128 6.1380 6.9138 88

Fig 4.12 : PAPR results of with and without interleaver 4.6 SUMMARY AND CONCLUSION: The PAPR values of a basic OFDM system are evaluated using different modulation techniques. The flow chart depicts the various steps involved for the evaluation of PAPR of the basic OFDM system. Simulation graphs for the modulation techniques BPSK, QPSK and DQPSK are plotted. The comparative study of the various PAPR values reveals that using DQPSK technique the value of PAPR is least. The PAPR analysis is done by the proposed SLM technique with LBC extended Hamming using DQPSK modulation scheme. The value of PAPR is obtained with the help of conventional SLM technique for QPSK and DQPSK. The distinguished results highlight that the CONSLM with DQPSK method shows the lower value of PAPR. 89

The results obtained for the proposed method modified SLM with LBC extended Hamming using DQPSK is 4.7dB. The proposed Modified SLM technique with DQPSK expressed in this investigation proves reliable and efficient for PAPR reduction. The DQPSK modulation is advantageous as no equalization is required at the receiver and the complexity of the circuit is thus reduced. 90