MATERIALS AND METHODS

Block description of OFDM system
Modulation: In an OFDM system as shown in Fig. 1, the serial input data as in Fig. 2 is converted to a parallel form and the bits are grouped based on the modulation scheme adopted. The mapping employed can be Quadrature Amplitude Modulation (QAM), Binary Phase Shift Keying (BPSK) or Quadrature Phase Shift Keying (QPSK). The number of bits per symbol for BPSK is 1 bit, for QPSK is 2 bits and for QAM it is 3 bits.

The modulated and demodulated outputs are shown in Fig. 3 which indicates that the data has been demodulated correctly.

Inverse fast Fourier transform (IFFT): The modulated data is sent to IFFT which maps the frequency domain signal into the corresponding time domain signal. The output signal from IFFT will introduce Peak to Average Power Ratio (PAPR). Hence an Optimization technique to reduce PAPR has to be carried out. The IFFT output is shown in Fig. 4. It is mainly used in OFDM to provide orthogonal subcarriers to ensure high spectral efficiency.

Fig. 1:	Schematic diagram of the proposed OFDM system

Fig. 2:	Input bit stream to the OFDM system

Fig. 3:	Modulation and Demodulation of the input bit stream using BPSK

Fig. 4(a-b):	(a) IFFT and (b) FFT outputs

Fig. 5(a-b):	Cyclic (a) Prefix and (b) De-prefix outputs

Fig. 6(a-b):	(a) AWGN channel and (b) A/D conversion outputs

Cyclic prefix (CP): The CP is appended to the OFDM system by adding a part of the end symbol of the OFDM signal to the original signal. This reduces the Inter Symbol Interference (ISI) and improves the BER of the OFDM system. The CP and the cyclic de-prefix outputs are shown in Fig. 5.

Digital to analog conversion (D/A): The output digital data from the cyclic prefix should be converted into analog form before passing onto the channel.

Additive white Gaussian channel (AWGN): AWGN channel introduces additive white noise into the signal that passes through it. The signal output after passing on to the AWGN channel is shown in Fig. 6.

Analog to digital conversion (A/D): For data recovery at the receiver, the analog data output from the AWGN channel should be converted back to digital form. It includes sampling and quantization. The result is shown in Fig. 6.

Cyclic de-prefix: The reverse process of the cyclic prefix is implemented in the receiver. The data bits added to the OFDM symbol are removed to get back the original data. The implementation is shown in Fig. 5.

Fast Fourier transform (FFT): The time domain data is converted into frequency domain by the FFT process. For the demodulation to take place the data should be in frequency domain. The result of FFT is shown in Fig. 4.

Demodulation: The data in the frequency domain is demodulated at the receiver to recover the original input. The original bits sent at the transmitter end were recovered at the receiver end and is shown in Fig. 3.

Data embedding after modulator: The secret data has been embedded after modulator using the phase value as the key. Generally modulator output is given by:

φ represents the phase angle, E_s represents signal energy, T represents symbol duration and φ value varies based on the modulation techniques adopted. The in phase and Quadrature component values before and after embedding 0 and 1 when bit 0 and 1 was transmitted using BPSK modulation respectively is tabulated in Table 1.

The in phase and Quadrature component values before and after embedding 0 and 1 when bit 0 and 1 was transmitted using QPSK modulation respectively is tabulated in Table 2.

PAPR-SLM and PTS algorithms: In OFDM, the large number of independent subcarriers when added result in high PAPR. It is the ratio of Peak power/average power:

(1)

where, Maximum represents the OFDM signal’s peak power and E represents the expected value. a_k represents the data symbol with k=0 to k-1.

Table 1:	BPSK constellation table

Table 2:	QPSK constellation table

Fig. 7:	Block diagram for PTS algorithm

The modulated output in frequency domain is represented in complex form and is given as:

(2)

where, 0 = t = lT where l denotes the subcarrier and Δ_f represents subcarrier spacing.

CCDF is the performance measure to analyse PAPR. CCDF indicates that the probability (PAPR_data) should exceed threshold. CCDF =P(PAPR > Z) = 1- P(PAPR = Z).

Steps in PTS algorithm:

•	Divide the OFDM symbol into set of independent sub blocks as in Fig. 7
•	PAPR reduction can be achieved by rotating the subcarriers in each by some set of phase sequences
•	The frequency domain output of the signal mapper is denoted as A and is partitioned in to ‘i*’ set of sub blocks and is denoted as ai* where i*=1, 2…….I
•	A is the frequency domain output
•
•	Ai are independently phase rotated by
•	ci = cejφi
•	So
•	Then after passing onto the IFFT, it is given by y' = IFFT (AI)

If i-1 are the sub blocks and c is the phase vector, then c^i-1 values have to be verified to provide minimum PAPR.

Fig. 8:	Block diagram of SLM algorithm

Steps in SLM algorithm:

They are then passed through IFFT and the PAPR value is computed. The set with minimum value of PAPR is chosen and transmitted to D/A converter.

RESULTS AND DISCUSSION

Figure 9 shows the performance comparison of SLM and PTS using BPSK modulation for subcarrier values of 2, 4 and 8 in terms of Complementary Cumulative Distribution Function (CCDF) (Nguyen and Lampe, 2008; Gao and Xie, 2009) and Bit Error Rate (BER).

The performance comparison of SLM and PTS using QPSK modulation for subcarrier values of 2, 4 and 8 in terms of Complementary Cumulative Distribution Function (CCDF) and Bit error rate (BER) is given in Fig. 10.

Fig. 9(a-b):	CCDF plot for various subcarriers of 2, 4 and 8 using BPSK modulation for (a) SLM and (b) PTS

Fig. 10(a-b):	CCDF plot for various subcarriers of 2, 4 and 8 using QPSK modulation for (a) SLM and (b) PTS

Figure 11 shows the performance comparison of SLM and PTS using QAM modulation for subcarrier values of 2, 4 and 8 in terms of complementary cumulative distribution function (CCDF)) and Bit error rate (BER)

From Fig. 9-11 it is noted that the PAPR reduction is at its best for U = 8 and comparatively low for U = 2 (Singhal et al., 2009; Badran and El-Helw, 2011). When the number of phase vectors is increased, a better reduction of PAPR can be achieved as discussed in (Chen and Hu, 2010; Wang et al., 2009; Latif and Gohar, 2003). The phase vectors U = 2, 4 and 8 are used for SLM while V = 2, 4, 8 are considered for PTS. It is seen that the PAPR decreases as the number of U and V values are increased in SLM and PTS respectively as mentioned in (Wu, 2011; Liang et al., 2010; Kasari and Dehghani, 2009). From the results obtained, QAM provides better PAPR reduction compared to QPSK and BPSK. Similarly PTS with U = 8 provides better PAPR reduction.

Figure 12 shows the BER comparison between SLM and PTS techniques for the subcarrier value of 8.

Fig. 11(a-b):	CCDF plot for various subcarriers of 2, 4 and 8 using QAM modulation for (a) SLM and (b) PTS

Fig. 12(a-b):	Comparison between BPSK, QPSK and QAM for 8 subcarriers for (a) SLM and (b) PTS

The BER comparison between SLM and PTS techniques for the subcarrier value of 4 is given in Fig. 13.

Figure 14 shows the BER comparison between SLM and PTS techniques for the subcarrier value of 2.

The BER comparison between SLM and PTS techniques using QPSK for the subcarrier value of 8 and BPSK for the subcarrier value of 2 is given Fig. 15.

The comparison between SLM and PTS using QAM is plotted in Fig. 16.

From the results obtained through the plots 12 to 16, BPSK with U = 8 for PTS outperforms than the other two modulation schemes. As the phase vector values are increased, better reduction in PAPR is achieved for both SLM and PTS algorithms.

In PTS, all the elements present in the sub blocks are being multiplied by the equal phase values. In PTS, the phase rotation vectors are limited to specific values.

Fig. 13(a-b):	Comparison between BPSK, QPSK and QAM for 4 subcarriers for (a) SLM and (b) PTS

Fig. 14(a-b):	Comparison between BPSK, QPSK and QAM for 2 subcarriers for (a) SLM and (b) PTS

In the case of SLM, data sequences are required to be rotated with different phase sequences_. PTS provides comparatively superior reduction in Peak values. In PTS, it is clear that the PAPR decreases obviously as the number of sub-blocks get increased with respect to primary OFDM. When there are redundant bits in OFDM symbol, SLM can be considered. PTS is more suitable when design complexity is considered.

Fig. 15(a-b):	Comparison between SLM and PTS using (a) QPSK modulation for 8 subcarriers and (b) BPSK modulation for 2 subcarriers

Fig. 16:	Comparison between SLM and PTS using QAM

Both the techniques scramble the serial data input symbols and the one with the lowest peak average power ratio is transmitted to reduce the probability of high Peak Average Power (PAP).

In SLM, phase sequences used are in a pseudorandom fashion, so no knowledge about the phase values at the transmitter end which increases the receiver complexity, are known. In PTS, the phase vector set consists of only few values which are known at the transmitter end reducing the complexity of designing the receiver. SLM requires more number of phase vector set to select the optimized one with least PAPR while in PTS, an efficient phase vector set is sufficient for reducing the PAP.

Comparing all three modulation schemes, PTS outperforms SLM. Design complexity in the transmission and reception part decreases the rate of the data to provide distortion-less system in SLM.

Fig. 17:	Constellation diagram of BPSK before and after data embedding

Fig. 18:	Constellation diagram of QPSK before and after data embedding

Complexity is an important consideration as far as the OFDM system is considered. So PTS could be a better candidate in reducing PAPR. When both PAPR reduction and redundancy are taken into account, both the schemes provide almost the same results. SLM is more appropriate for the system that can withstand redundancy in the information. In both the techniques, phase vectors are added along with the information which helps in data recovery.

Constellation diagram before and after embedding 0 when input bit is 1 and 0 and before and after embedding when input bit is 1 and 0 using BPSK modulation is shown in Fig. 17.

In addition, Fig. 18 shows the constellation diagram before and after embedding 0 when input bit is 1 and 0 and before and after embedding when input bit is 1 and 0 using QPSK modulation.

From Fig. 17 and 18, it is clear that the secret data can be extracted before demodulator by knowing the in phase and quadrature phase components, the bit transmitted and the bit embedded during transmission otherwise secret will be maintained as secret itself.

CONCLUSION

OFDM is a multicarrier modulation scheme and is preferred for high-speed data transmission over fading channels. It has various merits but also has one major stumbling block of very high PAPR. In this paper, the different characteristics of OFDM System are analyzed. The graphs are plotted using CCDF against BER for different modulation schemes employing different subcarriers. We employed PAPR reduction techniques such as PTS and SLM which reduces the PAPR of the proposed system. Among the two techniques it is found that both the PTS and SLM techniques provide considerable reduction of PAPR without any loss of input data. From the comparison of the SLM and PTS techniques, it is inferred that PTS is more efficient in PAPR reduction. However, SLM is appropriate when there exists redundant data bits. In terms of complexity, PTS is the promising candidate. Also, the number of computational steps is less in the case of PTS. For providing wireless security and confidentiality secret data has been embedded after modulation using the in phase and quadrature phase values of the modulator as the key.