Efficient Image Communication in PAPR Distortion

Wireless Pers Commun DOI 10.1007/s11277-015-2568-y

Efficient Image Communication in PAPR Distortion Cases Naglaa F. Soliman1,2 • Emad S. Hassan3,4 • Abdel Hamid A. Shaalan1 • Mohammed M. Fouad1 Said E. El-Khamy5 • Yasser Albagory3,6 • Mohsen A. M. El-Bendary7 • Waleed Al-Hanafy3,8 • El-Sayed M. El-Rabaie3 • Moawad I. Dessouky3 • Sami A. El-Dolil3 • Saleh A. Alshebeili9 • Fathi E. Abd El-Samie3,10

•

Springer Science+Business Media New York 2015

Abstract In this paper, a proposed method for Peak-to-Average Power Ratio (PAPR) reduction of Orthogonal Frequency Division Multiplexing (OFDM) signals based on discrete transforms is presented for robust image communication. One of the discrete transforms such as discrete wavelet transform, discrete cosine transform, or discrete sine transform is applied to modify the OFDM signal at the output of the inverse fast Fourier transform stage. We first present the proposed OFDM system model with trigonometric transforms for PAPR reduction. Trigonometric transforms improve the performance of the OFDM system, and reduce the PAPR of the OFDM signal. Then, this scheme has been utilized for progressive image

& Fathi E. Abd El-Samie [email protected] Naglaa F. Soliman [email protected] Emad S. Hassan [email protected] Abdel Hamid A. Shaalan [email protected] Mohammed M. Fouad [email protected] Said E. El-Khamy [email protected] Yasser Albagory [email protected] Mohsen A. M. El-Bendary [email protected] Waleed Al-Hanafy [email protected] El-Sayed M. El-Rabaie [email protected]

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transmission using low-density parity-check coded OFDM over frequency-selective fading channels. The set partitioning in hierarchical trees algorithm is used for source coding of the images to be transmitted. The proposed scheme effectively resists the fading impact of frequency-selective fading channels using simple frequency-domain equalization. Simulation experiments are performed for a variety of multipath fading channels. We also propose a chaotic interleaving scheme based on the 2-D chaotic Baker map for PAPR reduction of OFDM signals. The distinctive feature of this scheme is that the transmitted signal has less correlation between samples, and hence the PAPR is minimized. Keywords

OFDM PAPR Discrete transforms LDPC-COFDM Chaotic Baker map

1 Introduction The design of a wireless communication system should always take into account the utilization efficiency of two primary resources; bandwidth and power. As an attractive airlink technology, Orthogonal Frequency Division Multiplexing (OFDM) offers a relatively high bandwidth and power efficiency [1, 2]. OFDM splits up a wide-band signal into many sub-carrier streams, and thus a wide-band frequency-selective fading channel can be converted into narrow-band flat-fading sub-channels. A high spectral efficiency can be expected by allowing overlapped orthogonal sub-carriers in the frequency domain [3]. Peak-to-Average Power Ratio (PAPR) is one of the major problems of transmitting OFDM signals. The OFDM receiver detection efficiency is very sensitive to the nonlinear devices used Moawad I. Dessouky [email protected] Sami A. El-Dolil [email protected] Saleh A. Alshebeili [email protected] 1

Department of Electronics and Communications, Faculty of Engineering, Zagazig University, Zagazig, Egypt

2

Faculty of Computer and Information Sciences, Princess Nourah Bint Abdulrahman University, Riyadh, Saudi Arabia

3

Department of Electronics and Electrical Communications, Faculty of Electronic Engineering, Menoufia University, Menouf 32952, Egypt

4

Department of Electrical Engineering, Jazan University, Jazan, Saudi Arabia

5

Department of Electrical Engineering, Faculty of Engineering, Alexandria University, Alexandria 21544, Egypt

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Departmrnt of Information Technology, College of Computers and Information Technology, Taif University, Taif, Saudi Arabia

7

Faculty of Industrial Education, Helwan University, Helwan, Egypt

8

Department of Electrical Engineering, Faculty of Engineering, Albaha University, Al Bahah, Saudi Arabia

9

Electrical Engineering Department, KACST-TIC in Radio Frequency and Photonics for the e-Society (RFTONICS), King Saud University, Riyadh, Saudi Arabia

10

KACST-TIC in Radio Frequency and Photonics for the e-Society (RFTONICS), King Saud University, Riyadh, Saudi Arabia

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Efficient Image Communication in PAPR Distortion Cases

in its signal processing loop such as High Power Amplifier (HPA), which may severely impair the system performance due to the induced spectral regrowth [4]. There are several techniques to reduce the PAPR in OFDM systems [5, 6], such as clipping [7–10], companding [11, 12], PTS [13], SLM [5, 14] and coding [15, 16]. An alternative technique to solve the PAPR problem is based on signal transformations [16–18]. This technique involves a signal transformation prior to amplification, then an inverse transformation at the receiver prior to demodulation. In [16], trigonometric transforms were suggested as alternatives for the FFT to reduce the PAPR. The Set Partitioning In Hierarchical Trees (SPIHT) is used for image transmission over the OFDM system in several research works [19–22], because it has a good rate-distortion performance for still images with comparatively low complexity, and it is scalable or completely embeddable. The success of this algorithm in compression efficiency and simplicity makes it well known as a benchmark for embedded wavelet image coding. To improve the Bit Error Rate (BER) performance of the OFDM system, several error correcting codes have been utilized. LDPC codes have attracted much attention, because they outperform turbo codes for long block lengths, but with a relatively low decoding complexity. The combination of the high spectral efficiency OFDM modulation technique and LDPC coding will be a good candidate for high-speed broadband wireless applications. The BER performance of the LDPC-COFDM system is influenced by the sub-channels, which have deep fade due to frequency selectivity. According to this combination, several algorithms were introduced into the LDPC-COFDM system to improve the BER by adaptive bit loading, and power allocation for each sub-carrier [23–28]. In [29], an iterative equalizer was proposed to reduce the Inter-Symbol Interference (ISI) in the channels. In [30], a peak power reduction method for LDPC-COFDM signals was introduced. In this method, sub-carriers are grouped into several clusters based on the construction of the parity-check matrix of the LDPC code, and the PAPR is reduced by multiplying weight factors in a similar way to the Partial Transmit Sequence (PTS) method. At the receiver, these factors are estimated by exploiting extrinsic information in the LDPC sum-product decoding. Strong mechanisms for error reduction such as powerful error correction codes [31] and efficient interleaving schemes [32] are required to reduce the channel effects on the data transmitted. Since the channel errors caused by the mobile wireless channels are bursty in nature. Several interleaver schemes have been proposed [32–37]. The simplest and most popular of such schemes is the block interleaver scheme [32, 33]. In spite of the success of this scheme to achieve a good performance in wireless communication systems, there is a need for a much powerful scheme for severe channel degradation cases. Various interleavers have been proposed to deal with the PAPR problem in OFDM systems [36–38]. Chaotic maps have been proposed for a wide range of applications in communications [39– 42], and cryptography [43–46]. Due to the inherent strong randomization ability of these maps, they can be efficiently used for data interleaving. In this paper, a proposed method for PAPR reduction of OFDM signals based on discrete transforms is presented. One of the discrete transforms such as DWT or DCT or DST is applied to modify the OFDM signal at the output of the IFFT stage. First, this paper presents the proposed OFDM system model with trigonometric transforms for PAPR reduction. Trigonometric transforms improve the performance of the OFDM system, and reduce the PAPR of the OFDM signal. Then, this scheme has been utilized for progressive image transmission using LDPC-COFDM over frequency-selective fading channels. The SPIHT algorithm is used for source coding of the images to be transmitted. The proposed scheme effectively resists the fading impact of frequency-selective fading channels using simple frequency-domain equalization. Simulation experiments are performed for a variety of multipath fading channels.

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Moreover, a chaotic interleaving scheme [34, 37, 42] based on the 2-D chaotic Baker map presented in [45] is proposed for PAPR reduction of OFDM signals. In the proposed OFDM system with chaotic interleaving prior to transmission, the OFDM signal after the IFFT is divided into in-phase and quadrature components, which are rearranged into a new matrix, then a chaotic randomization process is performed to this matrix such that the likelihood that both the real and imaginary components of the transmitted signal at a certain time are of large amplitude becomes lower. As a result, a reduction in the PAPR can be achieved. The distinctive feature of the proposed scheme is that the transmitted signal has less correlation between samples, and hence the PAPR is minimized. The rest of this paper is organized as follows. The proposed OFDM system model with discrete transform permutation is explained in Sect. 2. The DWT is first explained in Subsect. 2.1, and then Subsect. 2.2 provides the proposed OFDM system with trigonometric transforms (DCT/DST). Subsection 2.3 provides the numerical results and the discussion of the OFDM with trigonometric transforms over two different channel models; Additive White Gaussian Noise (AWGN) and Rayleigh frequency-selective fading channels. Section 3 introduces the performance with unequal power distribution. The proposed LDPC-COFDM system with trigonometric transforms is explained in Sect. 4. Section 5 presents the proposed OFDM system model with chaotic interleaving. Section 6, presents the proposed LDPC-COFDM system model. The numerical results and discussion for the proposed LDPC-COFDM system are also presented in this section. Finally, the concluding remarks are given in Sect. 7.

2 The Proposed OFDM System with Discrete Transform Permutation Figure 1 shows the block diagram of the proposed OFDM system with discrete transform permutation. The proposed transmitter system model consists mainly of 3 blocks; a data formatting block, an OFDM modulator block, and a discrete transform and replacement block. The main difference between the conventional OFDM and the proposed OFDM system with discrete transforms is the transform and replacement block. First, the data formatter converts the input data (image) to a binary bit stream, which can be further processed by the OFDM modulator. In the OFDM modulator, a high data rate sequence is split into a number of low data rate sequences that are transmitted, simultaneously, over a number of sub-carriers. Then, the transmitted data over each parallel sub-channel is modulated with QPSK. Finally, the modulated data are fed into an IFFT circuit, and an OFDM signal is generated.

Fig. 1 The block diagram of the proposed OFDM system with discrete transform permutation

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The output of the IFFT is modified by discrete transforms either DWT or DCT/DST. The sequence after this process can be named xd[n] with the subscript d referring to the discrete transformation process, which can be expressed as follows: " # N 1 j2pnk 1 X ð1Þ xd ½n ¼ T ½x½n ¼ T pffiffiffiffi Xk e N N k¼0 where T[] represents the transformation process. The PAPR of the modified OFDM signal in one symbol period can be defined as: maxjxd ½nj2 PAPRðxd ½nÞ ¼ h i E xd ½n2

ð2Þ

Finally, a Cyclic Prefix (CP) is added to the signal xd[n], in order to avoid ISI, which occurs in multi-path fading channels. Then, the transmitted signal is passed to the D/A converter followed by the HPA.

2.1 The DWT Transform Wavelets have become a popular tool in most image processing applications such as image fusion, denoising, compression, and restoration. The conventional DWT may be considered as equivalent to filtering the input signal with a bank of band pass filters, whose impulse responses are all approximately given by scaled versions of a mother wavelet. For the OFDM signal after the IFFT, most signal samples have small peaks, while a small number of signal samples have large peaks. The Haar transform is used to decompose a discrete signal into two sub-signals of half its length. One sub-signal is a running average or trend, and the other subsignal is a running difference or fluctuation. In this section, two techniques have been proposed to modify the OFDM signal. The first, or Type I technique, increases the PSNR but the reduction in the PAPR is small and the second, or Type II technique, reduces the PAPR, but it is very sensitive to noise and it is adopted to OFDM systems with good channel conditions.

2.1.1 Wavelet Decomposition For the wavelet transform of a signal S, it is passed through two complementary filters giving two signals. After the filtering, the signal is down-sampled by 2 to eliminate half of the S

LPF and downsampling by 2

HPF and downsampling by 2

cA (approximation) Low frequency

cD ( detail ) High frequency

Fig. 2 The one stage filtering scheme producing the approximation and detail components of the signal

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samples. The coefficient vectors are obtained by convolving S with the Low-Pass Filter LPF for approximation cA and with the High-Pass Filter HPF for details cD as shown Fig. 2. For many signals, the low-frequency content is the most important part. It is what gives the signal its identity. The high-frequency content, on the other hand, imparts flavor or nuance. In wavelet analysis, the approximations and details are considered. The approximations are the high-scale, low-frequency components of the signal. The details are the low-scale, high-frequency components. To gain a better appreciation of this process, let us perform a one-stage DWT of a signal. The signal will be a pure sinusoid with highfrequency noise added to it as shown in Fig. 3. Notice that the detail coefficients cD are small, containing low energy, and consisting mainly of high-frequency noise, while the approximation coefficients cA contains much less noise than does the original signal (containing low-frequency information).

2.1.2 In-Phase and Quadrature DWT Coefficients Concatenation and Mixing Technique (Type I) The output OFDM signal is applied to the transform and replacement stage using the DWT. The block diagram of the proposed permutation is shown in Fig. 4. After the IFFT

Fig. 3 A Sinusoidal signal with high-frequency noise

Fig. 4 The block diagram of the proposed in-phase and quadrature decomposition modified OFDM, Type I

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operation, the OFDM signal is split into two components; in-phase and quadrature. The DWT is applied to both components, separately. The output DWT coefficients for the inphase component are the approximate component (cAi) and the details component (cDi). Similarly, the output DWT coefficients for the quadrature component are the approximate component (cAq) and the details component (cDq). Then, the approximate samples of the in-phase component (cAi) are concatenated with that of the quadrature component (cAq) to form the new in-phase component. Similarly, the detail samples of the in-phase component after DWT (cDi) are concatenated with that of the quadrature component (cDq) to form the new quadrature component. Finally, the new components are added to produce a modified OFDM signal as shown in Fig. 4.

2.1.3 Simulation Results of the Proposed In-Phase and Quadrature Decomposition, Type I In this sub-section, computer simulations are implemented to evaluate the performance of this proposed technique for PAPR reduction. Lena image of size (128 9 128), Cameraman image of size 256 9 256, and the Mandrill image of size 480 9 500 are used. An AWGN channel is used as the transmission channel. The fidelity of the reconstructed image is measured with the Peak Signal-to-Noise Ratio (PSNR), which is usually expressed in terms of the logarithmic decibel scale. It can be defined as follows: ! ð255Þ2 ð3Þ PSNR ¼ 10 log10 MSE where MSE is the mean squared error between the original and the reconstructed images. The OFDM model considered uses 256 sub-carriers, each having 64 symbols and the CP length is 1/4 the symbol duration. The SNR is defined as the ratio between the average received signal power and the noise power. This PAPR is evaluated with the Complementary Cumulative Distribution Function (CCDF) curves [14]. Experiments have been performed for the three considered images. A comparison between the conventional OFDM and the OFDM with DWT (OFDM-DWT) in the CCDF of the PAPR distribution is shown in Fig. 5a, b, c. It is clear that the proposed technique has a PAPR reduction compared to OFDM by about 2, 3, and 1 dB for Lena, Cameraman, and Mandrill images, respectively at a CCDF of 10-2. Simulation experiments have been carried out to study the effect of the proposed Type I technique on the PSNR of the reconstructed images at different SNR values. Figures 6, 7, and 8 show the reconstructed Lena images at SNRs equal to 5, 7.5 and 10 dB, respectively. Figures 9, 10 and 11 show the reconstructed Cameraman images, and Figs. 12, 13 and 14 show the reconstructed Mandrill images at 5, 7.5, and 10 dB, respectively. It is clear that the proposed OFDM-DWT technique enhances the PSNR performance by about 1.5 and 2 dB at SNRs equal to 5 and 7.5 dB, respectively.

2.1.4 Amplitude-Phase DWT Coefficients Concatenation and Mixing Technique (Type II) The block diagram of the second proposed permutation technique is shown in Fig. 15. First, the output signal of the IFFT process is split into two components; amplitude and phase. Then, the DWT is applied to both components, separately. The output DWT coefficients of amplitude contain the approximation samples (cAa) and the detail samples

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Fig. 5 Comparison of the PAPR reductions for the three images. a Lena image, b Cameraman image, c Mandrill image

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Fig. 6 The reconstructed Lena image at SNR = 5 dB. a OFDM, PSNR = 23 dB, b OFDM-DWT, PSNR = 24.28 dB

Fig. 7 The reconstructed Lena image at SNR = 7.5 dB. a OFDM, PSNR = 31.73 dB, b OFDM-DWT, PSNR = 35.82 dB

(cDa), and the output DWT coefficients of the phase contain the approximation samples (cAp) and the detail samples (cDp). Notice that the detail coefficients (cDa and cDp) are small, containing low energy, and the approximation coefficients (cAa and cAp) are containing high energy. Therefore, the replacement is applied as follows; cAa is concatenated with cAp to form a new amplitude of the signal and cDa is concatenated with cDp to form a new phase of the signal. Finally the modified OFDM signal is built from the new amplitude and phase. At the receiver, the process is reversed.

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Fig. 8 The reconstructed Lena image at SNR = 10 dB. a OFDM, PSNR = 44.78 dB, b OFDM-DWT, PSNR = 90.28 dB

Fig. 9 The reconstructed Cameraman image at SNR = 5 dB. a OFDM, PSNR = 23.1 dB, b OFDMDWT, PSNR = 24.62 dB

2.1.5 Simulation Results of the Amplitude-Phase DWT Coefficients Concatenation and Mixing Modification Computer simulations have been performed to evaluate the performance of the second proposed technique on the Cameraman image of size 256 9 256. The transmission channel is an AWGN channel. A PAPR performance comparison between the proposed Type II OFDM-DWT technique and the traditional OFDM is shown in Fig. 16. It is clear that the type II proposed technique performance outperforms that of OFDM by about 13 dB.

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Fig. 10 The reconstructed Cameraman image at SNR = 7.5 dB. a OFDM, PSNR = 32.51 dB, b OFDMDWT, PSNR = 34.62 dB

Fig. 11 The reconstructed Cameraman image at SNR = 10 dB. a OFDM, PSNR = 49.07 dB, b OFDMDWT, PSNR = 51.86 dB

Figure 17 shows the PSNR performance of the proposed Type II OFDM-DWT technique at different SNRs. It is clear from this figure that, at SNRs of 30, 35 and 38 dB, the proposed Type II OFDM-DWT technique gives PSNRs of 19.86, 37.58 and 66.17 dB, respectively. This means that this technique is very sensitive to noise.

2.2 The Proposed OFDM System with Trigonometric Transforms The block diagram of the trigonometric transform and replacement stage is shown in Fig. 18 [47]. In the proposed scheme, the in-phase and quadrature components at the

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Fig. 12 The reconstructed Mandrill image at SNR = 5 dB. a OFDM, PSNR = 23.31 dB, b OFDM-DWT, PSNR = 24.39 dB

Fig. 13 The reconstructed Mandrill image at SNR = 7.5 dB. a OFDM, PSNR = 32.58 dB, b OFDMDWT, PSNR = 34.55 dB

output of the IFFT stage are subjected to either a DCT or a DST transform. The output sequence of the in-phase component is divided into a low-frequency component (Li) and a high-frequency component (Hi). Similarly, the output sequence of the quadrature component is divided into a low-frequency component (Lq) and a high-frequency component (Hq). The replacement process is performed as follows. The low-frequency components of both trigonometric transforms are concatenated into a new in-phase component, and similarly, the high-frequency components are concatenated into a new quadrature component. The elegant energy compaction property of the trigonometric transforms makes the new in-quadrature component contain only small-value samples, which leads to a reduction in the peak power of the overall transmitted signal.

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Fig. 14 The reconstructed Mandrill image at SNR = 10 dB. a OFDM, PSNR = 49.86 dB, b OFDMDWT, PSNR = 53.86 dB

Fig. 15 The bock diagram of the second proposed amplitude-phase DWT coefficients concatenation and mixing modification, Type II

A sequence of data, g(n) of the OFDM signal transformed with either the DCT or the DST will give a sequence G(k), according to the following formulas: rffiffiffiffiffi N 1 X bc pkð2n þ 1Þ gðnÞ; ð4 aÞ cos DCT : Gc ðkÞ ¼ 2N N n¼0 where bc is given by: bc ¼

1 k¼0 2 k ¼ 1; 2; . . .; N 1

rffiffiffiffiffi bs pðk þ 1Þð2n þ 1Þ gðnÞ; sin DST : Gs ðkÞ ¼ 2N N n¼0 N 1 X

ð4 bÞ

ð5 aÞ

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2pffiffiffi 2 2

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Fig. 17 Reconstructed Cameraman images using the Type-II OFDM-DWT technique at different SNRs. a SNR = 30 dB, PSNR = 19.86 dB, b SNR = 35 dB, PSNR = 37.58 dB, c SNR = 38 dB, PSNR = 66.17 dB

Fig. 18 Block diagram of the transform and replacement stage with trigonometric transforms

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The DCT concentrates the signal power in the first few samples. This means that the power of the signal is focused on some sub-carriers. For example, if N ¼ 10 and gðnÞ ¼ ½ 1 1 1 1 1 1 1 1 1 1 , then Gc ðkÞ ¼DCT ðgðnÞÞ ¼½ 0 2:8588

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It is clear that the power of the first half of samples after the DCT is larger than the power of the second half. In Eq. (6), the largest element of the sequence after being transformed is 2.8588, and the other elements are very small, which indicates that the energy of the OFDM sequence is focused by the DCT. In addition, the energy almost remains the same after the DCT, and thus the total energy remains unchanged as Eq. (7) indicates. The DST has a similar behavior. The OFDM systems with a trigonometric transform and replacement stage will be denoted as OFDM-DCT and OFDM-DST systems.

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On other hand for the DST Gs ðkÞ ¼ dstðgðnÞÞ ¼ ½ 0 6:9552 0

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ð8Þ ð9Þ

In Eq. (8), the largest elements of the sequence after being transformed are the 2nd, 6th and 10th having values of 6.9552, 2.1897, and 1.1541 respectively, and the other elements; the 4th and 8th are very small, which indicates that the energy of OFDM sequence is reallocated on some sub-carriers. Nevertheless, the energy after DST is very large in comparison to that before (so the exchange is important in this case).

2.2.1 Results and Discussion Using Trigonometric Transforms Computer simulations have been implemented to evaluate the performance of the proposed technique for PAPR reduction. Two different wireless channels have been tested; an AWGN channel and a Rayleigh fading channel. Both Cameraman image and the Mandrill image have been used in the simulation experiments. The OFDM model considers 256 subcarriers, each having 64 symbols. The cyclic prefix length is 1/4 the symbol duration. A comparison is presented between the proposed OFDM system model with the trigonometric transforms and the conventional OFDM system. Figures 19 and 20 show the CCDF of the PAPR distribution of the Cameraman and Mandrill images, respectively. The figures reveal that the PAPR performance of the OFDM system with trigonometric transforms is noticeable. For the transmission of the Cameraman image with the proposed technique, a PAPR reduction of up to 13 and 15 dB can be achieved at a CCDF of 10-2 for OFDM-DCT and OFDM-DST systems, respectively. Figure 19b, c, d shows the PAPR variation with each data-symbol (sample). It is noticed that the peak value of the PAPR for the traditional OFDM occurs at 24 dB, and this peak is

Fig. 21 The reconstructed Cameraman images over an AWGN channel at SNR = 5 dB. For traditional OFDM, PSNR = 23.1 dB. a OFDM-DCT, PSNR = 24.88 dB, b OFDM-DST, PSNR = 24.33 dB

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decreased to 11 and 9 dB using the OFDM-DCT and OFDM-DST techniques, respectively. For the Mandrill image, Fig. 20 shows a significant PAPR reduction with the proposed techniques. 2.2.1.1 AWGN Channel Results Cameraman image has been transmitted over an AWGN. The reconstructed images at SNRs equal to 5, 7.5, and 10 dB are shown in Figs. 21, 22 and 23, respectively. It is clear from the obtained results that by increasing the SNR, the PSNR of the received images is increased, which reveals that the proposed

Fig. 22 The reconstructed Cameraman images over an AWGN channel at SNR = 7.5 dB. For traditional OFDM, PSNR = 32.51 dB. a OFDM-DCT, PSNR = 34.94 dB, b OFDM-DST, PSNR = 33.81 dB

Fig. 23 The reconstructed Cameraman images over an AWGN channel at SNR = 10 dB. For traditional OFDM, PSNR = 49.07 dB. a OFDM-DCT, PSNR = 53.16 dB, b OFDM-DST, PSNR = 50.88 dB

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technique improves the PSNR. It can also be noted that the improvement in the OFDMDCT technique is higher than that of OFDM-DST technique. The variation of the PSNR of the received image with the SNR of the channel for the Cameraman image is shown in Fig. 24. This figure demonstrates that the proposed technique maintains the transmitted image quality, to a great extent. A similar simulation experiment has been repeated for the Mandrill image, and its results are shown in Figs. 25, 26, and 27. These results confirm the previous results for the transmission of the Cameraman image. 55 50 45 40

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Fig. 24 Variation of the PSNR of the received image with the channel SNR for the Cameraman image over an AWGN channel

Fig. 25 The reconstructed Mandrill images over an AWGN channel at SNR = 5 dB. For traditional OFDM, PSNR = 23.31 dB. a OFDM-DCT, PSNR = 24.13 dB, b OFDM-DST, PSNR = 23.97 dB

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Fig. 26 The reconstructed Mandrill images over an AWGN channel at SNR = 7.5 dB. For traditional OFDM, PSNR = 32.58 dB. a OFDM-DCT, PSNR = 34.12 dB, b OFDM-DST, PSNR = 33.62 dB

Fig. 27 The reconstructed Mandrill images over an AWGN channel at SNR = 10 dB. For traditional OFDM, PSNR = 49.86 dB. a OFDM-DCT, PSNR = 51.84 dB, b OFDM-DST, PSNR = 49.12 dB

Tables 1 and 2 summarize the PAPR and PSNR values for the different types of discrete transformers. The results confirmed that the proposed techniques can improve the PSNR values of different types of images and achieve a significant PAPR reduction. 2.2.1.2 Rayleigh Fading Channel Results The channel for OFDM signals is characterized by various obstacles and reflections, which have a large influence on the received signal, when the radio wave is propagated from the base station to the mobile station. Since the path lengths of the direct, reflected, diffracted, and scattering waves are different, the time each takes to reach the mobile station will be different. In addition, the phase of the

123

Efficient Image Communication in PAPR Distortion Cases Table 1 PAPR reduction in dB for different discrete transformers at a CCDF of 10-2 Cameraman image DWT type I 3

DWT type II 13

Mandrill image Trigonometric transforms DCT

DST

13

15

DWT type I 1

DWT type II –

Trigonometric transforms DCT

DST

11

9

Table 2 PSNR values in dB over an AWGN channel SNR

Cameraman image Conv. OFDM

DWT Type I

Mandrill image Trigonometric transforms DCT

DST

Conv. OFDM

DWT Type I

Trigonometric transforms DCT

DST 23.97

5 dB

23.1

24.62

24.88

24.33

23.31

24.39

24.13

7.5 dB

32.51

34.62

34.94

33.81

32.58

34.55

34.12

33.62

10 dB

49.07

51.86

53.16

50.88

49.86

53.86

51.84

49.12

Fig. 28 The reconstructed Cameraman image over a frequency-selective Rayleigh fading channel at SNR = 10 dB. a OFDM, PSNR = 24.9 dB, b OFDM-DCT, PSNR = 26.55 dB, c OFDM-DST, PSNR = 26.41 dB

incoming wave varies because of reflections. As a result, the receiver receives a superposition consisting of several waves having different phases and delays. Then, the reception environment characterized by a superposition of delayed waves is called a multipath propagation environment. In a multi-path propagation environment, the received signal is sometimes intensified or weakened. This phenomenon is called multi-path fading and the signal level of the received wave changes from moment to moment. Multi-path fading raises the error rate of the received data [1]. Simulation programs have been carried out to study the effectiveness of the proposed OFDM system with trigonometric transforms over a multi-path frequency-selective channel. It has three Rayleigh fading taps at delays of 1, 1.5 and 2 ls, with relative powers of 0, -3, and -5 dB, respectively. The Doppler shift (fd) is 100 Hz and the SNR is set to 10 dB. Figures 28 and 29 show the PSNR performance for the Cameraman image transmission at SNR = 10 and 12.5 dB, respectively. It is clear that the proposed OFDM-DCT

123


Fig. 29 The reconstructed Cameraman image over a frequency-selective Rayleigh-fading channel at SNR = 12.5 dB. a OFDM, PSNR = 32.65 dB, b OFDM-DCT, PSNR = 34.36 dB, c OFDM-DST, PSNR = 34.83 dB

and OFDM-DST systems have higher improvement than conventional OFDM by about 1.65 and 1.5 dB, respectively at SNR = 10 dB. These results confirm the effectiveness of the proposed techniques for the transmission over a Rayleigh fading channel as well as an AWGN channel.

3 Performance with Unequal Power Distribution In this section, the effect of an unequal power distribution strategy on the proposed OFDM system with trigonometric transforms is studied. The PAPR distributions presented in [4] [18] are obtained under the assumption that all sub-carriers are active and given equal power. This assumption may not be valid due to the following facts [48]. Firstly, in all realistic OFDM systems, usually only a subset of sub-carriers is used to carry information (active sub-carriers) and the other sub-carriers (inactive sub-carriers) are set to zero. Secondly, due to the efficiency considerations, transmission power should be allocated to active sub-carriers. Thirdly, power allocation may vary depending on the different constellations used by the different active sub-carriers and their SNRs. The proposed approach is based on assigning powers to the different sub-carriers of OFDM using an unequal power distribution strategy (assigning powers to active sub-carriers, only) [48]. The OFDM symbol structure of the new approach consists of three types of sub-carriers as shown in Fig. 30; data sub-carriers for data transmission, pilot sub-carriers for channel estimation and synchronization, and null sub-carriers for guard bands. The data and pilot sub-carriers

Fig. 30 The OFDM symbol structure with an unequal power distribution strategy [48]

123


represent the active sub-carriers with Nactive denoting their number. The null sub-carriers are named as inactive sub-carriers with Ninactive denoting their number. If the sub-carrier at DC is nonzero, it is active; otherwise it is inactive. Table 3, shows the number of active sub-carriers in some popular standards. In this table, N0 represents the subcarrier at DC, Is represents an inactive sub-carrier at DC, and As represents an active sub-

Table 3 The number of active and inactive sub-carriers in some popular standards with N0 representing the sub-carrier at DC IEEE 802.11a

DAB I

DAB II

DVB I

DVB II

DVB III

N

64

256

512

2048

2048

4096

Nactive

52

192

384

1536

1705

3409

No

Is

Is

Is

Is

As

As

0

10

-1

CCDF

10

-2

10


-3

10

0

5

10

15

20

25

30

35

PAPR(dB)

35

35

30

30

30

25

25

25

20

15

PAPR (dB)

35

PAPR (dB)

PAPR (dB)

(a)

20

15

10

10

5

5

0

20

40

60

80

100

120

140

160

180

15

10

5

OFDM 0

20

OFDM - DCT 0

0

20

40

60

80

100

120

140

160

180

0

OFDM - DST 0

20

40

60

80

100

120

Symbol no.

Symbol no.

Symbol no.

(b)

(c)

(d)

140

160

180

Fig. 31 PAPR distribution for the Cameraman image, N = 2048, Nactive = 1536, and number of symbols = 64 at all schemes. a The CCDF curves for the three systems, b OFDM, c OFDM–DCT, d OFDM–DST

123


carrier [48]. For example, in the IEEE 802.11a standard, out of all 64 sub-carriers, only 52 sub-carriers are active (data and pilot sub-carriers) and the other 12 sub-carriers are inactive. In this case, the equivalent complex base-band OFDM signal can be rewritten as [48]: K 1 X Xk ej2pfk t ; xðtÞ ¼ pffiffiffiffi N k¼K

0 t T:

ð10Þ

where N = Nactive ? Ninactive. In Eq. (10), K = Nactive/2 if the sub-carrier at DC is inactive; otherwise K = (Nactive - 1)/2, if the DC sub-carrier is active. Let Pk be the power allocated to the kth sub-carrier and assume that equal powers are allocated to active sub-carriers, therefore Pk is constant. Figure 31 shows the PAPR distribution for the transmission of Cameraman image over DVB I standard according to Table 3. From Fig. 31a, it can be noticed that adding the trigonometric transforms for the proposed OFDM system with unequal power distribution improves the PAPR performance. The variation of the PAPR with the number of symbols is shown in Fig. 31b, c, d. Figures 32 and 33 show the reconstructed Cameraman image for the DVB I standard over an AWGN channel at SNR equal to 5 and 8 dB, respectively. Equal power has been allocated to each active sub-carrier. It is clear from the figures that adding the trigonometric transforms

Fig. 32 The reconstructed Cameraman image using the unequal power distribution for OFDM over an AWGN channel at SNR = 5 dB. a OFDM, PSNR = 27.28 dB, b OFDM-DCT, PSNR = 29.27 dB, c OFDM-DST, PSNR = 29.15 dB

Fig. 33 The reconstructed Cameraman image using the unequal power distribution for OFDM over an AWGN channel at SNR = 8 dB. a OFDM, PSNR = 41.67 dB, b OFDM-DCT, PSNR = 44.44 dB, c OFDM-DST, PSNR = 45.89 dB

123


Fig. 34 The reconstructed Cameraman image using the unequal power distribution for OFDM with DVB I over a frequency-selective channel at SNR = 8 dB. a OFDM, PSNR = 19.12 dB, b OFDM-DCT, PSNR = 20.27 dB, c OFDM-DST, PSNR = 20.1 dB

Fig. 35 The reconstructed Cameraman image using the unequal power distribution for OFDM with DVB I over a frequency-selective channel at SNR = 10 dB. a OFDM, PSNR = 23.92 dB, b OFDM-DCT, PSNR = 25.66 dB, c OFDM-DST, PSNR = 25.45 dB

for the proposed OFDM system with unequal power distribution improves the PSNR performance by nearly about 2 and 3 dB for SNR = 5 dB and SNR = 8 dB, respectively. Another simulation experiment has been carried out to study the effectiveness of the proposed OFDM system with trigonometric transforms and an unequal power distribution strategy over a multi-path frequency selective-fading channel. This channel has three Rayleigh fading taps with delays of 1, 1.5 and 2 ls, with relative powers of 0, -3, and -5 dB, respectively. The Doppler shift (fd) is 100 Hz. Figures 34 and 35 show the PSNR performance for the Cameraman image transmission at an SNR set to 8 and 10 dB, respectively. It is clear that the proposed OFDM-DCT and OFDM-DST systems have higher PSNRs than the normal OFDM by about 1 dB at SNR = 8 dB and 1.5 dB at SNR = 10 dB.

4 The Proposed LDPC-COFDM System with Trigonometric Transforms In this section, trigonometric transforms are applied with the LDPC-COFDM system. The input is a SPIHT compressed image. The frequency-domain Minimum Mean Square Error (MMSE) equalizer is used to resist the impact of fading on frequency-selective channels.

123


4.1 Transmitter The proposed LDPC-COFDM system with trigonometric transforms is illustrated in Fig. 36. For robust wireless image transmission, the progressive SPIHT coder is chosen as the source coder due to its code rate flexibility and simplicity of design. The image coefficients stream is divided into several layers according to the importance of the progressive stream. Then, the image stream is converted to a binary format. Afterwards, the information bits are LDPC-encoded. The coded bit stream is fed into the OFDM modulator, where the modulation is implemented using an IFFT stage and the data is assigned to some OFDM symbols. The output of the IFFT processing is modified by trigonometric transforms as explained in Sect. 2. After pre-appending the CP to each data block and passing the signal through the D/A converter and the HPA, the OFDM signal xd(t) is transmitted. It passes through the multipath channel. The channel impulse response is modelled as a Wide-Sense Stationary Uncorrelated Scattering (WSSUS) process consisting of L discrete paths hðtÞ ¼

L1 X

hðlÞdðt sl Þ

ð11Þ

l¼0

where h(l) and sl are the channel gain and delay of the lth path, respectively. The continuous-time received signal rd(t) can be expressed as: rd ðtÞ ¼

L1 X

hðlÞxd ðt sl Þ þ no ðtÞ

ð12Þ

l¼0

where no(t) is a complex AWGN with single-sided power spectral density N.

4.2 Receiver At the receiver, the CP is discarded from the received signal, and then the frequencydomain equalization is performed by the FFT. As shown in Fig. 37, the received signal is

Fig. 36 OFDM system model with the proposed modifications

Fig. 37 The frequency-domain equalizer

123


equalized in the frequency domain. A major advantage of equalization in frequency domain is the low computational complexity [49]. The equalized signal is then transformed back into the time domain by an IFFT. The received signal on the kth (k = 0, 1,…, N - 1) sub-carrier after the FFT is given by: Rd ðkÞ ¼ HðkÞXd ðkÞ þ No ðkÞ

ð13Þ

where Rd(k), H(k), Xd(k), and No(k) are the NFFT-points FFT of rd(n), h(n), xd(n), and no(n), respectively. Let W(k), (k = 0, 1,…,NFFT - 1), denote the equalizer transfer function for the kth sub-carrier. The time-domain equalized signal xd ðnÞ; which is the soft estimate of xd(n), can be expressed as follows:

xd ðnÞ ¼

1

NX FFT 1

NFFT

k¼0

WðkÞRd ðkÞej2pkn=NFFT

ð14Þ

The equalizer transfer function W(k) is selected to minimize the Mean Squared Error (MSE) between the equalized signal xd ðnÞ and the original signal xd(n). According to W(k), there are several types of equalizers such as [49]: The Zero-Forcing (ZF) equalizer: 1 HðkÞ

WðkÞ ¼

ð15Þ

The MMSE equalizer: WðkÞ ¼

H ðkÞ

ð16Þ

jHðkÞj þðEb =N0 Þ1 2

In this subsection, the MMSE equalizer is performed so that the equalized signal can be defined by substituting Eqs. (13) and (16) into Eq. (14) as:

xd ðnÞ ¼

NX FFT 1

1

jHðkÞj2 Xd ðkÞ

ej2pkn=NFFT NFFT k¼0 jHðkÞj2 þðEb =N0 Þ1 |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} signal

þ

1

NX FFT 1

jHðkÞj NA ðkÞ

ð17Þ j2pkn =NFFT

e NFFT k¼0 jHðkÞj2 þðEb =N0 Þ1 |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} noise

The replacement and inverse transform are then applied to the equalized samples. Afterwards, the serial-to-parallel conversion and the OFDM sub-channel demodulation are implemented using an FFT stage. The received OFDM symbols generated by the FFT are demodulated. The demodulated bits are then decoded with each LDPC-encoded block, and the data bits are restored. These data bits are converted into an image format.

4.3 Results and Discussion Simulation experiments have been carried out to study the effectiveness of the proposed LDPC-COFDM system with trigonometric transforms for SPIHT compressed image

123


communication. Simulations have been performed for performance comparison over three different channel; AWGN, SUI-3 and Vehicular-A. The SUI-3 channel model is one of six channel models adopted by the IEEE 802.16a for evaluating broadband wireless systems in the 2–11 GHz bands [50]. It has three Rayleigh fading taps at delays of 0, 0.5, and 1 ls, with relative powers of 0, -5, and -10 dB, respectively. The fading is assumed to be quasi-static (constant during an FFT block). The IEEE 802.20 Vehicular-A delay profile

0

10

-1

CCDF

10

-2

10

System I System II System III

-3

10

4

6

8

10

12

14

16

18

14

16

18

PAPR (dB)

(a) 0

10

-1

CCDF

10

-2

10


-3

10

4

6

8

10

12

PAPR (dB)

(b) Fig. 38 CCDF of the PAPR for all systems. a r = 0.5, b r = 1

123


model assumes a six-path Rayleigh fading channel with almost exponential decay of the average received power. The paths with the delay times of 0, 310, 710, 1090, 1730, and 2510 ns have the average received powers of 0, 1, 9, 10, 15, and 20 dB, respectively. The delay profile model is used for a wireless link level simulation of the IEEE 802.20 standard physical layer adopted for a wideband channel [51]. The parameters used in the simulations are the number of sub-carriers of the LDPCCOFDM system N = 256, CP length = 64, and SPIHT rate r = 0 up to 1. An LDPC code rate of R = 1/2 is employed with sum-product decoding, and a (512, 1024) parity-check matrix is used. The maximum number of iterations in the iterative decoding is set to 10. The input Cameraman image, which has 8 bits per pixel has been used in the simulations. To better depict the performance of the proposed system, it is compared with the COFDM system. For simplicity, three systems are considered: System I: LDPC-COFDM system. System II: LDPC-COFDM system with the DCT. System III: LDPC-COFDM system with the DST. First, the simulation of the CCDF curves is presented. A comparison of the CCDF of the PAPR distribution is shown in Fig. 38a, b for the proposed systems II and III compared 0

0

10

10

-1

CCDF

CCDF

10

-1

10

-2

10


-3

10

2

4

6


-2

8

10

12

14

16

18

20

10

22

4

6

8

10

PAPR (dB)

12

(a) 0

18

20

22

24

100

CCDF

CCDF

16

(b)

10

-1

10


-2

10

14

PAPR (dB)

6

8

10

12

14

-1

10

-2

16

18

20

22

24

10

6


8

10

12

14

16

PAPR (dB)

PAPR (dB)

(c)

(d)

18

20

22

Fig. 39 CCDF of PAPR for all systems for different numbers of sub-carriers at r = 0.2 bpp. a N = 128, b N = 256, c N = 512, d N = 1024

123

N. F. Soliman et al. Fig. 40 The reconstructed Cameraman image over system I at r = 0.6 bpp. a AWGN, BPSK, c SNR = 10 dB, PSNR = 31.5 dB, b AWGN, QPSK, SNR = 10 dB, PSNR = 31.5 dB, c SUI-3, BPSK, SNR = 25 dB, PSNR = 31.5 dB, d SUI-3, QPSK, SNR = 25 dB, PSNR = 22.67 dB, e Vehicular-A, BPSK, SNR = 25 dB, PSNR = 31.5 dB, f Vehicular-A, QPSK, SNR = 25 dB, PSNR = 27.28 dB

with system I. The SPIHT rate is set to 0.5 and 1. Clearly, the PAPR performances of the proposed systems II and III outperform system I. The figure reveals that system III has a better reduction in the PAPR than system II; nearly up to 0.25 dB (Fig. 38b). It is also noted that the PAPR reduction can be achieved by increasing the SPIHT rate. The impact of the number of sub-carriers on the performance of the three systems has been studied. It is shown in Fig. 39 at a SPIHT rate of 0.2 bpp. It is clear that the system III provides a significant PAPR reduction, especially, for a large number of sub-carriers. A comparison between the reconstructed images at r = 0.6 bpp transmitted over the three systems is shown in Figs. 40, 41 and 42. This comparison reveals the channel effect and the modulation type effect. From these figures, it is clear that over an AWGN channel or a Vehicular-A channel, both BPSK and QPSK are suitable. However, for the SUI-3 channel, the BPSK is more effective than the QPSK for systems II and III. Table 4 clarifies the PSNR performance of the all systems over an AWGN channel. It can be noticed from this table that for BPSK at SNR = 5 dB, the PSNR performance is deteriorated for all systems, however at SNR = 10 dB or greater, all systems have the best performance, which is limited by the SPHIT compression effect. For the QPSK mapping at SNR = 10 dB, all systems have the best performance except system II at r C 0.8 bpp. A comparison of the PSNR performances of all systems has been considered over frequency-selective channels; SUI-3 channel and the Vehicular-A channel as shown in Tables 5 and 6, respectively. It is clear from Table 5 that by using the BPSK at SNR = 20 dB, all systems have the best response limited by the SPIHT compression rate. However, by using the QPSK at SNR = 25 dB, the PSNR performance is deteriorated except for system I at r = 0.6 bpp. Table 6, shows the PSNR performance for transmission over the Vehicular-A channel. It can be noticed that by using the BPSK at SNR = 20 dB, all systems have a reduction in the PSNR performance, however; by increasing the SNR to 25 dB, all systems have the best performance. Using QPSK at SNR 25 dB, all systems have a reasonable PSNR performance, but systems II and III are not suitable at r C 0.8 bpp. For system III with an AWGN channel, as the SPIHT rate is increased, the PSNR is also increased due to the fact of injecting more information about the image to the receiver, and thus it will have more ability to reproduce a good reconstructed image. However, this is not the case for the transmission over the SUI-3 channel or the Vehicular-A channel. As shown in the Tables 5 and 6, increasing the SPIHT rate does not necessarily increase the PSNR due to the fact that due to fading, bursts of error occur; and therefore, the receiver loses the ability to reconstruct a good image. By using BPSK at SNR = 20 dB, the transmission over the SUI-3 channel has a better PSNR performance than that of the Vehicular-A channel. However, by using the QPSK, the transmission over the Vehicular-A channel is more effective at r B 0.6 bpp for systems II and III.

5 The Proposed OFDM System Model with Chaotic Interleaving The block diagram of the proposed system model is shown in Fig. 43. The transmission system has mainly three blocks; data formatting, OFDM modulator and chaotic interleaving [34, 49].

123


123

N. F. Soliman et al. Fig. 41 The reconstructed Cameraman image over system II at r = 0.6 bpp. a AWGN, BPSK, c SNR = 10 dB, PSNR = 31.5 dB, b AWGN, QPSK, SNR = 10 dB, PSNR = 31.5 dB, c SUI-3, BPSK, SNR = 25 dB, PSNR = 31.5 dB, d SUI-3, QPSK, SNR = 25 dB, PSNR = 14.46 dB, e Vehicular-A, BPSK, SNR = 25 dB, PSNR = 31.5 dB, f Vehicular-A, QPSK, SNR = 25 dB, PSNR = 31.5 dB

At the transmitter, a sequence of multimedia base-band data is first converted into parallel data of N sub-channels. Then, the transmitted data of each parallel sub-channel is modulated by QPSK modulation. The modulated data; X(k) (k = 0,1,…N - 1) are fed into an IFFT circuit, such that the OFDM signal x(n) (n = 0,1,…N - 1) is generated. Both the real and imaginary fields of this OFDM signal are interleaved using the chaotic Baker map. The obtained sequence is xc(n) with the subscript c referring to the chaotic interleaving process. Finally, the OFDM signal is fed into a guard time insertion circuit to reduce the ISI. The guard interval is chosen as T/4 or T/8 to maximize the data throughput. After the insertion of the guard interval, the OFDM signal is transmitted to the receiver, however, the transmitted data is contaminated by multi-path fading and AWGN. At the receiver, the process is reversed. The receiver is assumed to have an ideal knowledge of the secret key of the chaotic map.

5.1 Interleaving Mechanisms Error correction codes are usually used to protect signals through transmission over wireless channels. Most of the error correction codes are designed to correct random channel errors. However, channel errors caused by mobile wireless channels are bursty in nature [49]. Interleaving is a process to rearrange the samples of the transmitted signal so as to spread bursts of errors over multiple codewords. The simplest and most popular of such interleavers is the block interleaver. Firstly, the basics of block interleaving [32], [34] are reviewed. Then, the proposed chaotic interleaving mechanism is presented in the next subsection.

5.1.1 The Block Interleaving Mechanism The idea of block interleaving can be explained with the aid of Fig. 44. After the IFFT, block interleaving is applied to the signal samples. The samples are first arranged to a matrix in a row-by-row manner and then read from this matrix in a column-by-column manner. Now, take a look at how the block interleaving mechanism can correct error bursts. Assume a burst of errors affecting four consecutive samples (1-D error burst) as shown in Fig. 44b with shades. After de-interleaving, the error burst is effectively spread among four different rows, resulting in a small effect for the 1-D error burst as shown in Fig. 44c. With a single error correction capability, it is obvious that no decoding error will result from the presence of such 1-D error burst. This simple example demonstrates the effectiveness of the block interleaving mechanism in combating 1-D bursts of errors [34], [49]. Let us examine the performance of the block interleaving mechanism when a 2-D (2 9 2) error burst occurs [34], as shown in Fig. 44b with shades. Figure 44c indicates that this 2 9 2 error burst has not been spread, effectively, so that there are adjacent samples in error in the first and the second rows. As a result, this error burst cannot be corrected using a single error correction mechanism. That is, the block interleaving mechanism cannot combat the 2 9 2 bursts of errors [34].

123


123

N. F. Soliman et al. Fig. 42 The reconstructed Cameraman image over system III at r = 0.6 bpp. a AWGN, BPSK, c SNR = 10 dB, SNR = 31.5 dB, b AWGN, QPSK, SNR = 10 dB, PSNR = 31.5 dB, c SUI-3, BPSK, SNR = 25 dB, PSNR = 31.5 dB, d SUI-3, QPSK, SNR = 25 dB, PSNR = 18.75 dB, e Vehicular-A, BPSK, SNR = 25 dB, PSNR = 31.5 dB, f Vehicular-A, QPSK, SNR = 25 dB, PSNR = 31.5 dB

5.1.2 The Proposed Chaotic Interleaving Mechanism As mentioned in the previous subsection, block interleavers are not efficient with 2-D bursts of errors. As a result, there is a need for advanced interleavers for this task. The 2-D chaotic Baker map in its discretized version is a good candidate for this purpose. The chaotic randomization step generates permuted sequences with lower correlation between their samples such that a reduction in the PAPR can be achieved. Also, the chaotic Baker map distributes the errors in a better way to samples after de-interleaving, so the PSNR is increased [45, 46, 49]. Moreover, the chaotic Baker map adds a degree of encryption to the transmitted signal. The OFDM signals have large PAPR due to high correlation between their data frames. If this long correlation pattern of the in-phase and the quadrature components are broken down, a reduction in the PAPR can be achieved. Interleaving can be used to break these correlation patterns. The chaotic Baker map is used for the randomization of both components. The discretized Baker map is a good candidate to randomize the items in a square matrix. It can be described by B(n1,n2,……,nk), where the vector, [n1, …,nk], represents the secret key, Skey. Defining M as the number of data items in one row, the secret key is chosen such that each integer mi divides M, and m1 ? … ? mk = M. Let Mi = m1 ? … ? mi. The data item at the indices (r,s), is moved to the indices [49]: M M mi M ; þ Mi ð18Þ Bðm1 ;...;mk Þ ðr; sÞ ¼ ðr Mi Þ þ s mod s s mod mi mi M ni where Mi B r \ Mi ? mi, and 0 B s \ M. The chaotic permutation is performed as follows [34], [49]: (1) (2) (3) (4)

An M 9 M square matrix is divided into k rectangles of width mi and number of elements M. Each M 9 mi vertical rectangle is divided into mi boxes of dimension M/mi 9 mi, and every box contains M points. The elements in each box are rearranged to a row in the permuted one. Rectangles are taken from left to right beginning with upper rectangles and then lower ones. Inside each rectangle, the scan begins from the bottom left corner towards upper elements.

An example of the permutation of an (8 9 8) matrix is shown in Fig. 45 [49]. The secret key is, Skey = [m1, m2, m3] = [2, 4]. In this paper, the discretized Baker map is used to randomize the OFDM signal after the IFFT step and the process is as follows: 1. 2.

Both the in-phase and quadrature components of the OFDM signal are extracted. Both of them are randomized using the chaotic Baker map. This can be accomplished by the concatenation of their matrices to form a new matrix, which has a size of N rows and twice the number of symbols columns.

123


123

N. F. Soliman et al. Table 4 PSNR values in dB over an AWGN channel Rate

PSNR BPSK SNR = 5 dB

BPSK SNR = 10 dB

QPSK SNR = 10 dB

System

System

System

I

II

III

I

II

III

I

II

III

0.1

11.31

14.27

23.67

23.67

23.67

23.67

23.67

23.67

23.67

0.2

14.15

14.85

26.15

26.15

26.15

26.15

26.15

26.15

26.15

0.4

18.38

16.91

29.2

29.2

29.2

29.2

29.2

29.2

29.2

0.6

15.5

16.6

31.5

31.5

31.5

31.5

31.5

31.5

31.5

0.8

16.56

16.91

33.47

33.58

33.58

33.58

33.58

25.44

33.58

1

14.64

23.07

35.56

35.56

35.56

35.56

35.56

25.81

35.56

Table 5 PSNR values in dB over SUI-3 channel Rate


QPSK SNR = 20 dB

QPSK SNR = 25 dB

System

System

System

I

II

III

I

II

III

I

II

III

0.1

23.67

23.67

23.67

20.29

23.67

23.67

23.67

23.67

23.67

0.2

26.15

26.15

26.15

17.03

13.67

10.96

26.15

11.45

10.82

0.4

29.2

29.2

29.2

18.94

14.63

16.99

27.3

14.63

14.85

0.6

31.5

31.5

31.5

16.76

9.17

14.59

22.67

14.46

18.75

0.8

33.58

33.58

33.58

18.47

9.31

15.7

33.28

16.88

19.22

1

35.56

35.56

35.56

18.5

8.68

14.72

22.97

8.96

8.84

Table 6 PSNR values in dB over a Vehicular-A channel Rate


BPSK SNR = 25 dB

QPSK SNR = 25 dB

System

System

System

I

II

III

I

II

III

I

II

III

0.1

16.85

14.82

23.67

23.67

23.67

23.67

23.67

23.67

23.67

0.2

22.11

9.74

16.54

26.15

26.15

26.15

26.15

26.15

26.15

0.4

25.94

13.32

18.36

29.2

29.2

29.2

28.64

29.2

29.2

0.6

22.64

14.73

14.16

31.5

31.5

31.5

27.28

31.5

31.5

0.8

17.23

9.03

14.5

33.58

33.58

33.58

26.49

12.98

14.72

1

26.54

15.15

15.72

35.56

35.56

35.56

30.32

16.48

18.17

123


Fig. 43 Block diagram of the proposed OFDM system with chaotic interleaving

Fig. 44 Block interleaving of an 8 9 8 matrix [49]. a The 8 9 8 matrix, b block interleaving of the 8 9 8 matrix, c effect of error bursts after the de-interleaving

Fig. 45 Chaotic interleaving of an 8 9 8 matrix. a The 8 9 8 matrix divided into square rectangles, b chaotic interleaving of the 8 9 8 matrix, c effect of error bursts after the de-interleaving

3.

The resulting matrix is reshaped to form a 2-D square matrix. Chaotic interleaving is performed on the new square matrix. This guarantees that the effect of randomization on the in-phase and quadrature components is different.

123


4. 5.

The resulting square matrix is reshaped again to the same size as that before obtaining the square matrix. Finally, the in-phase and quadrature components are separated from the randomized matrix, and reshaped into 1-D sequences to build the signal to be transmitted.

At the receiver of the proposed system with chaotic interleaving, the received signal is then passed through an A/D converter, and then the CP is discarded.

5.2 Numerical Results and Discussion Simulation experiments have been carried out to demonstrate the performance of the OFDM system when chaotic interleaving is applied. The simulation parameters are the number of sub-carriers N equal to 256, with each sub-carrier having 32 symbols, and the guard interval length of 1/8 of the symbol duration. A chaotic map of size 128 9 128 is used. Both AWGN and frequency-selective channels are considered. The first simulation experiment has been performed on the Cameraman image shown in Fig. 46a. The received image with chaotic interleaving before the de-interleaving process at the receiver is shown in Fig. 46b. This illustrates that the proposed system adds a degree of encryption to the transmitted image. Firstly, the PSNR performance of the traditional OFDM system and the OFDM system with block interleaving (OFDM-Block int.) is shown in Figs. 47, 48, and 49 at SNR = 5, 7.5, and 10 dB, respectively. The block interleaving has a matrix of size 16 9 16. It is clear that it improves the PSNR, especially at SNR = 10 dB by about 6 dB, however; it does not have any reduction in the PAPR.

5.2.1 Effect of Secrete Key In this subsection, the effect of the secret key on the OFDM system with chaotic interleaving is demonstrated. For simplicity, refer to this system as the OFDM-Chaotic system. Some secret keys (Skey) are proposed as follows:

Fig. 46 Difference between the original Cameraman image and the encrypted one after chaotic interleaving. a Original Cameraman image, b encrypted image due to chaotic interleaving

123


Fig. 47 PSNR performance of the OFDM, and the OFDM-Block int. systems at SNR = 5 dB. a OFDM, PSNR = 23.45 dB, b OFDM-Block int., PSNR = 24.34 dB

Fig. 48 PSNR performance of the OFDM, and the OFDM-Block int. systems at SNR = 7.5 dB. a OFDM, PSNR = 32.64 dB, b OFDM-Block int., PSNR = 34.186 dB

Skey1 Skey2 Skey3 Skey4

= = = =

[8 4 4 16 2 8 32 8 2 16 16 4 8], [8 4 4 8 2 4 8 2 8 4 2 4 8 4 8 4 4 8 4 8 4 8 2 8], 2*ones (1, 64), 4*ones (1, 32).

A comparison in the PAPR performance between the OFDM and OFDM-Chaotic systems for the different proposed secret keys Skey is presented in Fig. 50. For Pr[PAPR [ PAPR0] = 10-2, in the case of Skey3, the PAPR reduction for the proposed

123


Fig. 49 PSNR performance of the OFDM and OFDM-Block int. systems at SNR = 10 dB. a OFDM, PSNR = 47.31 dB, b OFDM-Block int., PSNR = 53.1 dB 0

10

-1

CCDF

10

-2

10

-3

10

-4

10

0

OFDM OFDM-chaotic(Skey1) OFDM-chaotic(Skey2) OFDM-chaotic(Skey3) OFDM-chaotic(Skey4) 5

10

15

20

PAPR(dB) Fig. 50 PAPR performance of OFDM, and OFDM-Chaotic systems at different Skey

OFDM-Chaotic scheme is about 12 dB, when compared with the OFDM scheme. However, the reduction is smaller than that value in the case of Skey4 by about 0.3 dB. Figures 51 and 52 show a comparison in the PSNR performance between the OFDM and the proposed OFDM-Chaotic systems at SNRs = 7.5 and 10 dB. This comparison concentrates on the effect of the secret key; Skey. It is clear from Figs. 48 and 51 that at an SNR of 7.5 dB, the proposed OFDM-Chaotic system outperforms the OFDM system by about 3 dB at all SNRs. However at an SNR of

123


Fig. 51 PSNR performance of the OFDM-Chaotic system with different keys at SNR = 7.5 dB. a Skey1, PSNR = 35.93 dB, b Skey2, PSNR = 35.56 dB, c Skey3, PSNR = 35.83 dB, d Skey4, PSNR = 35.39 dB

10 dB, the proposed OFDM-Chaotic system outperforms the OFDM system significantly by about 6, 11.5, 15.5 dB and 3.4 dB for Skey1, Skey2, Skey3 and Skey4, respectively. This is a good performance improvement. According to Figs. 47, 51, and 52, the OFDM-Chaotic system has a better performance than that of the conventional OFDM and the OFDM-Block int. systems. The figures reveal that the proposed OFDM-Chaotic system solves the problems of the OFDM system. Furthermore, the best choice of Skey is Skey3 as it gives a good trade-off between SNR improvement and PAPR reduction. The Skey3 is selected for the rest of the paper.

5.2.2 Comparison Between Chaotic Interleaving and Other Techniques In this subsection, a comparison study between the proposed chaotic interleaving scheme as a PAPR reduction technique and other techniques, such as companding and clipping, is

123


Fig. 52 PSNR performance of the OFDM-Chaotic system with different keys at SNR = 10 dB. a Skey1, PSNR = 53.17 dB, b Skey2 at PSNR = 58.97 dB, c Skey3, PSNR = 62.88 dB, d Skey4, PSNR = 50.7 dB

presented. The chaotic interleaving has been implemented by secrete key; Skey3. The clipping technique has been performed with a low Clipping Ratio (CR) of 3 and 5 dB to avoid the degradation in the system performance. The l-law companding is performed with a l coefficient of 4, 8, and 30 dB. For simplicity, the OFDM with companding is referred to as OFDM-Comp and the OFDM with Clipping is referred to as OFDM-Clip. The simulation of the CCDF curves for the proposed OFDM-Chaotic, OFDM-Clip and OFDM-Comp systems are introduced in Fig. 53. Clearly, the PAPR performance of the proposed OFDM-Chaotic system is the best. For companding, the larger the values of l, the smaller are the values of the PAPR. As a result, a reduction in the PAPR can be achieved by increasing the value of the companding coefficient for the OFDM with companding system. This result is the same for clipping in the case of increasing the CR, however the degradation is higher in the case of clipping.

123

Efficient Image Communication in PAPR Distortion Cases 0

10

-1

CCDF

10

-2

10

OFDM OFDM-Chaotic OFDM-Clip. CR =3 OFDM-Clip. CR =5 OFDM-Comp.Mu=4 OFDM-Comp.Mu=8 OFDM-Comp.Mu=30

-3

10

-4

10

0

5

10

15

20

25

PAPR (dB) Fig. 53 A comparison in the CCDF of the PAPR between the OFDM-Chaotic, OFDM-Comp, and OFDMClip systems

Fig. 54 PSNR performance of the OFDM-Clip system at SNR = 10 dB. a OFDM-Clip, CR = 3 dB, PSNR = 30.84 dB, b OFDM-Clip, CR = 5 dB, PSNR = 27.36 dB

Figure 54 introduces the effect of clipping on the PSNR performance of the OFDM at SNR = 10 dB. The CR has been set to 3 and 5 dB, which results in a PSNR of 30.84 and 27.36 dB, respectively. From the figure, it is clear that the clipping adds additional noise to the OFDM system, and it degrades the system performance. The PSNR performance of the OFDM-Comp system is shown in Figs. 55 and 56 at SNR 7.5 and 10 dB, respectively. It is clear that the PSNR is increased more than that of OFDM

123


Fig. 55 PSNR performance of the OFDM-Comp system at SNR = 7.5 dB. a l = 4 dB, PSNR = 41.34 dB, b l = 8 dB, PSNR = 42.16 dB, c l = 30 dB, PSNR = 33.59 dB

Fig. 56 PSNR performance of the OFDM-Comp system at SNR = 10 dB. a l = 4 dB, PSNR = 71.35 dB, b l = 8 dB, PSNR = 68.35 dB, c l = 30 dB, PSNR = 47.84 dB

by 8.5, 9 and 1 dB at values of l equal to 4, 8, and 30, respectively. The PSNR performance improvement of the OFDM-Comp system at l = 4, l = 8 and l = 30, are about 23, 21, and 1 dB, respectively at SNR = 10 dB as shown in Fig. 56. It can be concluded that the application of the companding method in the OFDM system results in a significant improvement in the performance, while the complexity is maintained at a low level. As a result, increasing the amplitude compression will introduce both out-of-band and in-band interference, which leads to degradations in the PSNR performance. This implies that a companding coefficient should be chosen carefully in order to limit the PAPR without degrading the system performance. In the rest of experiments, l = 4 is chosen. New schemes for improving the performance of OFDM systems have also been investigated. They are the OFDM system with chaotic interleaving and clipping and the OFDM system with chaotic interleaving and companding. For simplicity, we refer to them as OFDMChaotic-Clip and OFDM-Chaotic-Comp. Both the OFDM-Chaotic-Clip and the OFDMChaotic-Comp systems are compared with the OFDM-Chaotic system. Figures 57 and 58 show comparisons in the PAPR performance between the different proposed schemes for two different images; Cameraman and Mandrill, respectively. For Pr[PAPR [ PAPR0] = 10-2, in the case of the Cameraman image, the PAPR performance enhancement of the proposed OFDM-Chaotic-Comp scheme with l = 4 is about 2 dB, when compared with

123


10

-1

CCDF

10

-2

10

-3

10

OFDM OFDM-Chaotic OFDM-Chaotic-Clip OFDM-Chaotic-Comp

-4

10

0

5

10

15

20

25

PAPR(dB) Fig. 57 CCDF of the PAPR for the transmitted Cameraman image over different systems

0

10

-1

CCDF

10

-2

10

-3

10

OFDM OFDM-Chaotic OFDM-Chaotic-Clip OFDM-Chaotic-Comp

-4

10

0

5

10

15

20

PAPR(dB) Fig. 58 CCDF of the PAPR for the transmitted Mandrill image over different systems

the OFDM-Chaotic scheme. However, the PAPR performance of the proposed OFDMChaotic-Clip scheme with CR = 3 is nearly equal to that of OFDM-Chaotic scheme. Table 7, provides a comparison of the PSNR performance between the proposed schemes for the two images. It is clear from the table that the OFDM-Chaotic-Comp scheme has the largest PSNR followed by the OFDM-Chaotic scheme in case of the Cameraman and Mandrill images. However, for the Lena image, the OFDM-Chaotic scheme has the best

123

N. F. Soliman et al. Table 7 PSNR values in dB for the different schemes Method

SNR = 7.5 dB

SNR = 10 dB

OFDM

OFDMchaotic

OFDMchaoticclip (CR = 3)

OFDMchaoticcomp (l = 4)

OFDM

OFDMchaotic

OFDMchaoticclip (CR = 3)

OFDMchaoticcomp (l = 4)

Cameraman (256 9 256)

32.64

35.83

33.1

46.5493

47.31

62.88

46.61

73.65

Medical image (512 9 512)

33.74

35.75

33.92

39.2773

50.11

52.88

48.59

55.83

performance. According to the obtained results, the performance of PAPR and PSNR in the proposed OFDM-Chaotic-Comp scheme is the best compared to the other proposed methods.

5.2.3 The Effect of Over-Sampling In this section, the PAPR performance of the proposed OFDM-Chaotic and OFDMChaotic-Comp schemes are considered in the case of over-sampling by a factor of Lsa = 4 under the assumption that all sub-carriers are active and allocated equal power. The oversampling has been performed to approximate the discrete PAPR performance to the analogue one. In this case, the chaotic interleaving matrix will become of size 256 9 256. After some simulations, it is found that the best Skey is 4* ones (1, 64). Figure 59 shows the PAPR performance of the proposed OFDM-Chaotic and OFDMChaotic-Comp scheme in the case of over-sampling at Lsa = 4. It is clear from this figure that the OFDM-Chaotic-Comp scheme provides a PAPR performance better than that of the OFDM-Chaotic scheme by about 2 dB. Table 6 shows the PSNR performance of the conventional OFDM scheme compared with OFDM-Chaotic and the OFDM-ChaoticComp schemes in the case of over-sampling. This comparison is applied for the two images explained above. The obtained results in Fig. 59 and Table 8 show that the new OFDMComp scheme improves the PAPR performance and PSNR performance.

5.2.4 Frequency-Selective Rayleigh Fading Channel Simulation experiments have been carried out to study the effectiveness of the proposed OFDM-Chaotic and OFDM-Chaotic-Comp systems over a Rayleigh fading multipath frequency-selective channels. The Doppler shift (fd) is 100 Hz and the SNR is equal to 10 dB. Figures 60 and 61 show the PSNR performance for different oversampling rates of 1 and 4, respectively for the Cameraman image. It is clear that the proposed OFDMChaotic-Comp scheme has a better performance than the OFDM-Chaotic scheme. For the case of oversampling, the system is more sensitive to the Rayleigh fading.

6 The Proposed LDPC-COFDM System Model with Chaotic Interleaving The block diagram of the proposed LDPC-COFDM system is illustrated in Fig. 62. As will be shown, the proposed modifications will be in the interleaver and the equalizer blocks. The SPIHT compressed image stream is converted into a binary format. Afterwards, the

123


10

-1

CCDF

10

-2

10

-3

10

OFDM OFDM-Chaotic OFDM-Chaotic-Comp

-4

10

10

12

14

16

18

20

22

24

26

28

30

PAPR (dB)

(a) 0

10

-1

CCDF

10

-2

10

-3

10

-4

10

10

OFDM OFDM-Chaotic OFDM-Chaotic-Comp 15

20

25

30

35

PAPR (dB)

(b) Fig. 59 CCDF of the PAPR for the OFDM-Chaotic and OFDM-Chaotic-Comp systems for the case of over-sampling. a Cameraman, b Medical image

information bits are LDPC encoded. Hence, the base-band data is first converted into parallel data of N sub-channels, so that each bit of a codeword is on a different sub-carrier. After the OFDM modulator, chaotic interleaving is applied to the COFDM signal. For the COFDM system with both chaotic interleaving and companding, the chaotic interleaver is followed by a l-law companding stage.

123

N. F. Soliman et al. Table 8 PSNR values in dB for the different schemes in the case of over-sampling Method

SNR = 7.5 dB OFDM

OFDMchaotic

SNR = 10 dB OFDM-chaotic companding

OFDM

OFDMchaotic

OFDM-chaotic companding

Cameraman (256 9 256)

34

39.04

55.83

47.57

72.21

83.99

Medical image (512 9 512)

35.38

38.97

42.99

51.38

58.55

64.92

Fig. 60 Cameraman image transmission over Rayleigh fading multi-path frequency selective channels at Lsa = 1 and SNR = 10 dB. a OFDM, PSNR = 24.19 dB, b OFDM-Chaotic, PSNR = 25.22 dB, c OFDMChaotic-Comp. PSNR = 27.28 dB

Fig. 61 Cameraman image transmission over Rayleigh fading multi-path frequency-selective channels at Lsa = 4 and SNR = 10 dB. a OFDM, PSNR = 20.25 dB, b OFDM-Chaotic, PSNR = 21.18 dB, c OFDMChaotic-Comp, PSNR = 22.74 dB

The obtained sequence is xc(n) with subscript c referring to chaotic interleaving. Each data block is padded with a CP of a length longer than the channel impulse response to mitigate the Inter-Block Interference (IBI). The continuous COFDM signal xc(t) is generated at the output of the D/A converter. The transmitted signal xc(t) passes through the multi-path channel. The channel impulse response is modelled as a Wide-Sense Stationary Uncorrelated Scattering (WSSUS) process consisting of L discrete paths, which can be expressed as:

123


Fig. 62 The LDPC-COFDM system model with chaotic interleaving

hðtÞ ¼

L1 X

hðlÞdðt sl Þ

ð19Þ

l¼0

where h(l) and sl are the channel gain and delay of the lth path, respectively. The continuous-time received signal rc(t) can be expressed as: rc ðtÞ ¼

L1 X

hðlÞxc ðt sl Þ þ no ðtÞ

ð20Þ

l¼0

where no(t) is a complex AWGN with a single-sided power spectral density N0. At the receiver, the CP is discarded from the received signal, and then frequencydomain equalization is performed. The chaotic de-interleaving is then applied to the equalized samples. Then, the OFDM sub-channel demodulation is implemented using an FFT. The received OFDM symbols generated by the FFT are demodulated followed by a serial-to-parallel conversion. Finally, the data bits are reconstructed by an LDPC decoder and converted into an image format.

6.1 Simulation Results Simulation experiments have been carried out to demonstrate the performance of the LDPC-COFDM system and the proposed systems; LDPC-COFDM system with chaotic interleaver, LDPC-COFDM system with companding, and LDPC-COFDM system with both chaotic interleaving and companding. Simulation results have been performed over an AWGN channel and two frequency-selective fading channel models; SUI-3 channel and Vehicular-A channel. The parameters used in the simulation are the number of sub-carriers of the LDPCCOFDM system, N, which is considered to be 128, number of symbols per each sub-carrier which is considered to be 4, CP = 16. The SPIHT rate r is considered to be 0 to 1. An LDPC code rate R of 1/2 is employed with sum-product decoding, and parity-check matrix of (512, 1024) is used. The maximum number of iterations, Nit, in sum-product decoding is set to 10. The QPSK is used as the modulation type. The Cameraman image is used as the input image in the simulations. The best choice for the companding coefficient is l = 4 determined through simulations to achieve a trade-off between PAPR reduction and enhancement in the PSNR. To better depict the performance, four transmission systems were considered:

123


10

-1

CCDF

10

-2

10

System I System II System III System IV

-3

10

0

2

4

6

8

10

12

14

16

PAPR(dB)

(a) 0

10

-1

CCDF

10

-2

10


-3

10

2

4

6

8

10

12

14

16

PAPR (dB)

(b) Fig. 63 CCDF of PAPR for the proposed systems. a r = 0.5 bpp, b r = 1 bpp

System I: The LDPC-COFDM system. System II: The LDPC-COFDM system with chaotic interleaving. System III: The LDPC-COFDM system with l-law companding. System IV: The LDPC-COFDM system with chaotic interleaver followed by l-law companding.

123


Fig. 64 The PSNR performance over the AWGN channel at SNR = 7 dB and r = 0.8 bpp. a System I, PSNR = 17.13 dB, b System II, PSNR = 33.58 dB, c System III, PSNR = 33.58 dB, d System IV, PSNR = 33.58 dB

First, the simulation of the CCDF curves is presented. A comparison in the CCDF of the PAPR distribution between the four systems is shown in Fig. 63a, b for r equal to 0.5 bpp and 1 bpp, respectively. According to this figure, it is clear that by increasing r, the PAPR will be reduced by about 1 dB, especially for system I. Clearly, at CCDF = 10-2, the PAPR reductions of systems are: The system II has a PAPR reduction of about 2 and 1.2 dB at r of 0.5 and 1, respectively. The system III has a PAPR reduction of about 4.5 and 4.2 dB at r of 0.5 and 1 respectively. The system IV has a PAPR reduction of about 5.2 and 5 dB at r of 0.5 and 1, respectively.

123


Fig. 65 The PSNR performance over the SUI-3 channel at SNR = 20 dB and r = 0.8 bpp. a System I, PSNR = 19.16 dB, b System II, PSNR = 16.54 dB, c System III, PSNR = 26.28 dB, d System IV, PSNR = 33.58 dB

From the above comparisons, the PAPR performance of system IV outperforms the other systems. On the other hand, the PSNR performance has been studied to obtain a trade-off between the PAPR reduction and the PSNR performance enhancement. A comparison between the four systems in PSNR performance at r = 0.8 bpp for transmission over AWGN, SUI-3, and Vehicular-A channels is introduced in Figs. 64, 65 and 66, respectively. For transmission over an AWGN channel at SNR = 7 dB, it can be noted that systems II, III, and IV are better than system I by nearly 16.45 dB. Both the three systems achieve 33.58 dB, which is the maximum obtainable PSNR due to SPHIT compression. For the transmissions over the frequency-selective channels shown in Figs. 65 and 66,

123


Fig. 66 The PSNR performance over the Vehicular-A channel at SNR = 20 dB and r = 0.8 bpp. a System I, PSNR = 14.37 dB, b System II, PSNR = 13.65 dB, c System III, PSNR = 22.07 dB, d System IV, PSNR = 33.58 dB

system II has the worst PSNR performance; however in system IV, the PSNR is increased to the optimum value. A Comparison in PSNR performance between the four systems for the effect of SPIHT rate, r, is shown in Figs. 67, 68, and 69 for transmission over the AWGN, SUI-3 and Vehicular-A channels. It is clear from Fig. 67 that by using the chaotic interleaving, the PSNR performance is improved at all SPHIT rates. This result is clear for systems II and IV for transmission over an AWGN channel at SNR = 7 dB. However, the situation is not the same for transmission over frequency-selective channels. As shown in Fig. 68, system II has the worst PSNR performance. From Fig. 69, system II outperforms system I at small SPIHT rates; however at r C 0.6 bpp, system I and system II have nearly the same response. From this comparison, it is clear that system IV has the best performance and it has a good trade-off between the PAPR reduction and PSNR performance.

123


35

30

PSNR

25

20

15

10

5

0 0.1

System I System II System III System IV 0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

r (bpp) Fig. 67 Variation of the PSNR with the SPHIT rate for an AWGN channel at SNR = 7 dB

40 35 30

PSNR

25 20 15 10 System I System II System III System IV

5

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

r (bpp) Fig. 68 Variation of the PSNR with the SPHIT rate for an SUI-3 channel at SNR = 20 dB

For the output of system II over an AWGN channel, as the SPIHT rate is increased, the PSNR is also increased due to the fact of injecting more information about the image to the receiver, and thus it will have more ability to reproduce a better reconstructed image. However, this is not the case for transmission over SUI-3 or Vehicular-A channels. As shown in Figs. 68 and 69, increasing the SPIHT rate does not necessarily increase the

123

Efficient Image Communication in PAPR Distortion Cases 40 35 30

PSNR

25 20 15 10


5 0 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

r (bpp) Fig. 69 Variation of the PSNR with the SPHIT rate for a Vehicular-A channel at SNR = 20 dB

PSNR due to the fact that in fading periods, bursts of error may be severe, which makes the randomization of the chaotic interleaving unable to reconstruct a good image. Designing the LDPC-COFDM system with chaotic interleaver followed by companding in system IV, the PSNR performance goes to the optimum limit set by the SPIHT compression. This system is immune to frequency-selective fading channels.

7 Conclusions In this paper, different PAPR reduction techniques have been presented for OFDM systems. This first one was implemented using different discrete transforms; DWT, DCT and DST. Simulation results on digital images revealed that this proposed technique achieves a significant reduction in the PAPR, and improves the transmitted image quality. The results show that the DWT can be used for PAPR reduction in two types of systems; Type I, which increases the PSNR with a little reduction in the PAPR of about 3 dB, and Type II, which gives a higher reduction in the PAPR, but it very sensitive to noise. This initial study confirms that wireless communication systems using the proposed OFDM-DST or OFDMDCT techniques are suitable for multimedia communications. These techniques reduce the PAPR greatly without the need to transmit side information. In addition, an efficient LDPC-COFDM system with trigonometric transforms supporting image transmission using the SPIHT compression technique has been presented. The effectiveness of the proposed system has been investigated through simulations over AWGN, SUI-3, and Vehicular-A channels. The main advantage of the proposed system is the great reduction in the PAPR and the improved performance for frequency-selective fading channels. For the transmission over an AWGN channel and a Vehicular-A channel, both BPSK and QPSK are effective. However, the transmission over the SUI-3 channel is immune to noise using the BPSK. The second technique depends on chaotic interleaving with the LDPC-COFDM

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system. It improves both the PSNR performance and the PAPR reduction performance. The proposed OFDM-Chaotic scheme has been compared with other schemes of PAPR reduction such as the clipping and companding schemes. The obtained results showed a noticeable performance improvement achieved by the proposed scheme. Chaotic interleaving has also been merged with companding or clipping to reduce the PAPR of OFDM signals. Simulation results have shown that the proposed OFDM-Chaotic-Comp system achieves a good trade-off between the PSNR performance and the PAPR performance. The effect of the over-sampling has been studied. Simulation results have demonstrated that the over-sampling increases the PSNR performance. The proposed schemes have been investigated with the LDPC-COFDM system and they achieved a great success in PAPR reduction, while maintaining a high PSNR.

References 1. Harada, H., & Prasad, R. (2002) Simulation and software radio for mobile communications. Published by Artech House, 31 Mar. 2002, Universal Personal Communications library. 2. Andrews, J. G., Ghosh, A., & Muhamed, R. (2007) Fundamentals of WiMAX: Understanding broadband wireless networking. Published by Prentice Hall. 3. Prasad, R. (2004) OFDM for wireless communications systems. Artech House. 4. Al-kamali, F. S., Dessouky, M. I., Sallam, B. M., Shawki, F., & Abd El-Samie, F. E. (2013). Impact of the power amplifier on the performance of the single carrier frequency division multiple access system. Telecommunication Systems, 52, 31–38. 5. Mohammady, S., Sidek, R. M., Varahram, P., Hamidon, M. N., & Sulaiman, N. (2011) Study of PAPR reduction methods in OFDM Systems. In: Proceedings of advanced communication technology (ICACT), 2011, 13th international conference on Feb. 13–16, pp. 127–130. 6. Jiang, T., & Wu, Y. (2008). An overview: peak-to-average power ratio reduction techniques for OFDM signals. IEEE Transactions on Broadcasting, 54(2), 257–268. 7. Guel, D., & Palicot, J. (2009). Analysis and comparison of clipping techniques for OFDM peak-toaverage power ratio reduction. In: Proceedings of ICDSP2009, on pp. 1. 8. Kimura, S., Nakamura, T., Saito, M., & Okada, M. (2008). PAR reduction for OFDM signals based on deep clipping. In: Proceedings of 3rd international symposium on communications, control and signal processing, pp. 911–916. 9. Boonsrimuang, P., Puttawong, E., Kobayashi, H., & Paungma, T. (2003) PAPR reduction using smooth clipping in OFDM system. In: The 3rd information and computer engineering postgraduate workshop 2003 (ICEP’2003), pp. 158–161. 10. Kim, J., & Shin, Y. (2008). An effective clipped companding scheme for PAPR reduction of OFDM signals. In: Proceedings of the IEEE ICC’08, pp. 668–672. 11. Jiang, T., Yao, W., Guo, P., Song, Y., & Qu, D. (2006). Two novel nonlinear companding schemes with iterative receiver to reduce PAPR in multi-carrier modulation systems. IEEE Transactions on Broadcasting, 51(2), 268–273. 12. Jiang, Y. (2010). New companding transform for PAPR reduction in OFDM. IEEE Communication Letters, 14(4), 282–284. 13. Wang, J., Guo, Y., & Zhou, X. (2009). PTS-clipping method to reduce the PAPR in ROF-OFDM system. IEEE Transactions on Consumer Electronics, 55(2), 356–359. 14. Hassan, E. S., El-Khamy, S. E., Dessouky, M. I., El-Dolil, S. A., & Abd El-Samie, F. E. (2009). Peakto-average power ratio reduction in space–time block coded multi-input multi-output orthogonal frequency division multiplexing systems using a small overhead selective mapping scheme. IET Communications, 3(10), 1667–1674. 15. Jiang, T., & Zhu, G. (2005). Complement block coding for reduction in peak-to-average power ratio of OFDM signals. IEEE Communications Magazine, 43(9), S17–S22. 16. Hsu, C. Y., & Do, H. G. (2006). The new peak-toaverage power reduction algorithm in the OFDM system. Wireless Personal Communications, 41(4), 517–525. 17. Hassan, E. S., Zhu, X., El-Khamy, S. E., Dessouky, M. I., El-Dolil, S. A., & Abd El-Samie, F. E. (2009) A continuous phase modulation single-carrier wireless system with frequency domain equalization. In:

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N. F. Soliman et al. 42. Hassan, E. S., El-Khamy, S. E., Dessouky, M. I., El-Dolil, S. A., Abd El-Samie, F. E. (2009) New interleaving scheme for continuous phase modulation based OFDM systems using chaotic maps. In: Proceedings of WOCN-09, Cairo, Egypt, pp. 28–30. 43. Matthews, R. (1989). On the derivation of a chaotic encryption algorithm. Cryptologia, XIII(1), 29–42. 44. Deffeyes, K. S. (1991). Encryption system and method. US Patent, no. 5001754, March 1991. 45. Fridrich, J. (1998). Symmetric ciphers bbased on two-dimensional chaotic maps. International Journal of Bifurcation and Chaos, 8, 1259–1284. 46. Han, F., Yu, X., & Han, S. (2006). Improved baker map for image encryption. In ISSCAA, pp. 1273–1276. 47. Soliman, N. F., Shaalan, A. A., El-Rabaie, S., & Abd El-samie, F. E. (2009) Peak power reduction of OFDM signals using trigonometric transforms. In: Proceedings of the international conference on computer engineering & systems (ICCES), Cairo, Egypt, pp. 333–337. 48. Hassan, E. S., El-Khamy, S. E., Dessouky, M. I., El-Dolil, S. A., Abd El-Samie, F. E. (2010). Peak to average power ratio distribution for OFDM signals with unequal power distribution strategy. In Proceedings of NRSC-10, Egypt, March 16–18. 49. Hassan, E. S., et al. (2013). Chaotic interleaving scheme for single-and multi-carrier modulation techniques implementing continuous phase modulation. Journal of the Franklin Institute, 350, 770–789. 50. Erceg, V., et al. (2001) Channel models for fixed wireless applications. IEEE 802.16a cont. IEEE 802.16.3c-01/29r1. 51. Kameda, S., Oguma, H., Izuka, N., Asano, Y., Yamazaki, Y., Takagi, T., & Tsubouchi, K. (2010). Issue of IEEE 802.20 vehicular-a delay profile model on estimating received signal level variation of wideband signal. In: Proceedings of EuCAP 2010, pp. 1–5. Naglaa F. Soliman received the B.Sc., M.Sc., and Ph.D. degrees from the faculty of Engineering, Zagazig University, Egypt in 1999, 2004, and 2011, respectively. She is currently a lecturer at the Department of Electronics and Communications Engineering, Faculty of Engineering, Zagazig University. Her areas of interest are digital communications, signal processing, image processing, and coding.

Emad S. Hassan received the B.Sc. (Honors), M.Sc., and Ph.D. from the Faculty of Electronic Engineering, Menoufia University, Egypt, in 2003, 2006, and 2010, respectively. He joined the teaching staff of the Department of Electronics and Electrical Communications, Faculty of Electronic Engineering, Menoufia University, Egypt, in 2010. In 2008, he joined the Communications Research Group at Liverpool University, Liverpool, UK, as a Visitor Researcher. He has published more than 45 scientific papers in national and international conference proceedings and journals. He is a reviewer for many international journals and conferences. He was a Technical Program Committee (TPC) member for many international conferences. His current research areas of interest include image processing, digital communications, cooperative communication, cognitive radio networks, OFDM, SC-FDE, MIMO and CPM based systems.

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Efficient Image Communication in PAPR Distortion Cases Abdel Hamid A. Shaalan received his M.Sc. in microwave engineering from Faculty of Engineering, Cairo University, Egypt in 1991. He received his Ph.D. in Microwave Engineering from Faculty of Engineering, Cairo University in 1996. He is an associate Professor in communication engineering at Faculty of engineering, Zagazig University, Egypt. His research interests include antenna engineering and its applications.

Mohammed M. Fouad received the B.Sc. (1978), M.Sc. (1984) in Communications Networks from the Faculty of Engineering, Monofia University, and Ph.D. (1991) in Communications Networks from the Faculty of Engineering, Alexandria University (Egypt). He was Head of Electronics and Communications Department (2009–2011) – Faculty of Engineering, Zagazig University, Egypt, since 2009. He has worked in the areas of image processing, communication networks and mobile communications.

Said E. El-Khamy received the B.Sc. (Honors) and M.Sc. degrees from Alexandria University, Alexandria, Egypt, in 1965 and 1967 respectively, and the Ph.D. degree from the University of Massachusetts, Amherst, USA, in 1971. He joined the teaching staff of the Department of Electrical Engineering, Faculty of Engineering, Alexandria University, Alexandria, Egypt, since 1972 and was appointed as a Full-time Professor in 1982 and as the Chairman of the Electrical Engineering Department from September 2000 to September 2003. He is currently an Emeritus Professor. Prof. El-Khamy has published more than three hundreds scientific papers in national and international conferences and journals and took part in the organization of many local and international conferences. His Current research areas of interest include Spread-Spectrum Techniques, Mobile and Personal Communications, Wave Propagation in different media, Smart Antenna Arrays, Space–Time Coding, Modern Signal Processing Techniques and their applications in Image Processing, Communication Systems, Antenna design and Wave Propagation problems. Prof. El-Khamy is a Fellow member of the IEEE since 1999. He received many prestigious national and international prizes and awards including the State Appreciation Award (Al-Takderia) of Engineering Sciences for 2004, the most cited paper award from Digital Signal Processing journal for 2008, the IEEE R.W.P. King best paper award of the Antennas and Propagation Society of IEEE, in 1980, the the A. Schuman’s-Jordan’s award for Engineering Research in 1982. He is also a Fellow of the Electromagnetics Academy and a member of Tau Beta Pi, Eta Kappa Nu and Sigma Xi.

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N. F. Soliman et al. Yasser Albagory B.Sc. in electronic engineering in 1998 and the M.Sc. in adaptive arrays for mobile radio communications in 2002 from the faculty of electronic eng. Egypt. He also has been awarded the Ph.D. degree in electronic engineering in high-altitude platform wireless communications system in 2008. Now, he is an assistant professor in the Information Technology Department, College of Computers and Information Technology, Taif University, Saudi Arabia. His research interests are in adaptive antenna arrays, mobile communications, and high altitude platforms. He joined and referees many papers in international conferences in wireless communications and has many journal papers in the area of smart antennas and highaltitude platforms.

Mohsen A. M. El-Bendary received his BS in 1998, MSc in 2008, all in communication engineering, from Menoufia University, Faculty of electronic Engineering. He is now a lecturer assistant and Ph.D. student. His research interests cover wireless networks, wireless technology, channel coding, QoS over Bluetooth systems, and security systems which use wireless technology, such as fire alarm and access control systems. Topics of current interest include the use of convolutional plus chaotic coding, in the development of coding performance with new techniques of interleavers for high speed WPAN, WBAN development with wireless personal medical through ZigBee and Bluetooth.

Waleed Al-Hanafy received the B.Sc. (Honors) and M.Sc. degrees from the Faculty of Electronic Engineering, Menoufia University, Menouf, Egypt, in 1996 and 2002, respectively, and the Ph.D. from Strathclyde University, Glasgow, UK, in 2010. He joined the teaching staff of the Department of Electronics and Electrical Communications, Faculty of Electronic Engineering, Menoufia University, Menouf, Egypt, in 2010. He has published more than 20 scientific papers in national and international conference proceedings and journals. His current research areas of interest include the signal processing for communications in particular precoding and equalization methods of MIMO systems, adaptive power/bit loading approaches, Multi-User MIMO, OFDM systems, and resource allocation of wireless communication systems.

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Efficient Image Communication in PAPR Distortion Cases El-Sayed M. El-Rabaie (SM’92) was born in Sires Elian, Egypt, in 1953. He received the B.Sc. degree (with honors) in radio communications from Tanta University, Tanta, Egypt, in 1976, the M.Sc. degree in communication systems from Menoufia University, Menouf, Egypt, in 1981, and the Ph.D. degree in microwave Device engineering from Queen’s University of Belfast, Belfast, U.K., in 1986. In his doctoral research, he constructed a Computer-Aided Design (CAD) package used in nonlinear circuit simulations based on the harmonic balance techniques. Up to February 1989, he was a Postdoctoral Fellow with the Department of Electronic Engineering, Queen’s University of Belfast. He was invited as a Re-search Fellow in the College of Engineering and Technology, Northern Arizona University, Flagstaff, in 1992 and as a Visiting Professor at Ecole Polytechnique de Montreal, Montreal, QC, Canada, in 1994. He Has Authored and Co-authored of More Than 200 Papers and Eighteen text Books. He was Awarded several Awards (Salah Amer Award of Electronics in 1993, The Best Researcher on (CAD) from Menoufia University in 1995). He acts as a reviewer and member of the editorial board for several scientific journals. He Has Shared in Translating the First Part of the Arabic Encyclopedia. Professor EL-Rabaie was the Head of the Electronic and Communication Engineering Dept., Faculty of Electronic Engineering, Menoufia University, then the Vice Dean of Postgraduate Studies and Research in the same Faculty. Prof. S. El-Rabaie is Involved now in Different Research Areas including CAD of Nonlinear Microwave Circuits, Nanotechnology, Digital Communication Systems, and Digital Image Processing. Now he is Member of the National Electronic and Communication Eng. Promotion Committee and Reviewer of Quality Assurance and Accreditation of Egyptian Higher Education. Moawad I. Dessouky received the B.Sc. (Honors) and M.Sc. degrees from the Faculty of Electronic Engineering, Menoufia University, Menouf, Egypt, in 1976 and 1981, respectively, and the Ph.D. from McMaster University, Canada, in 1986. He joined the teaching staff of the Department of Electronics and Electrical Communications, Faculty of Electronic Engineering, Menoufia University, Menouf, Egypt, in 1986. He has published more than 200 scientific papers in national and international conference proceedings and journals. He is currently the vice dean of Faculty of Electronic Engineering, Menoufia University. He has received the most cited paper award from Digital Signal Processing journal for 2008. His current research areas of interest include spectral estimation techniques, image enhancement, image restoration, super resolution reconstruction of images, satellite communications, and spread spectrum techniques.

Sami A. El-Dolil received his B.Sc. and M.Sc. degrees in Electronic Engineering from Menoufia University, Menouf, Egypt, in 1977 and 1981, respectively. In 1986 he joined the Communications Research Group at Southampton University, Southampton, England, as a Research Student doing research on teletraffic analysis for mobile radio communication. He received his Ph.D. degree from Menoufia University, Menouf, Egypt, in 1989. He was a Post Doctor Research Fellow at the Department of Electronics and Computer Science, University of Southampton, 1991–1993. He is working as a Professor at the Department of Electronics and Electrical Communications, Faculty of Electronic Engineering, Menoufia University, Menouf, Egypt. His current research interests are in high-capacity digital mobile systems and multimedia networks.

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N. F. Soliman et al. Saleh A. Alshebeili is professor and chairman (2001–2005) of Electrical Engineering Department, King Saud University. He has more than 20 years of teaching and research experience in the area of communications and signal processing. Dr Alshebeili is member of the board of directors of Prince Sultan Advanced Technologies Research Institute (PSATRI), the Vice President of PSATRI (2008–2011), the director of Saudi-Telecom Research Chair (2008–2012), and the director (2011-Present) of the Technology Innovation Center, RF and Photonics in the e-Society (RFTONICS), funded by King Abdulaziz City for Science and Technology (KACST). Dr Alshebeili has been in the editorial board of Journal of Engineering Sciences of King Saud University (2009–2012). He has also an active involvement in the review process of a number of research journals, KACST general directorate grants programs, and national and international symposiums and conferences.

Fathi E. Abd El-Samie received the B.Sc.(Hons.), M.Sc., and Ph.D. degrees from Menoufia University, Menouf, Egypt, in 1998, 2001, and 2005, respectively. Since 2005, he has been a Teaching Staff Member with the Department of Electronics and Electrical Communications, Faculty of Electronic Engineering, Menoufia University. He is currently a researcher at KACST-TIC in Radio Frequency and Photonics for the e-Society (RFTONICs). He is a coauthor of about 200 papers in international conference proceedings and journals, and five textbooks. His current research interests include image enhancement, image restoration, image interpolation, super-resolution reconstruction of images, data hiding, multimedia communications, medical image processing, optical signal processing, and digital communications. Dr. Abd El-Samie was a recipient of the Most Cited Paper Award from the Digital Signal Processing journal in 2008.

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Efficient Image Communication in PAPR Distortion

Efficient Image Communication in PAPR Distortion

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