Performance Analysis of Chaotic Spread Spectrum Sequences

This paper presents the performance analysis of compound chaotic sequence (CCS)-based noise reduction differential chaos shift keying (NR-DCSK) system under multipath Rayleigh fading channel conditions. The special characteristics of chaotic sequences are their deterministic randomness behaviour that adds security and multipath immunity to the data when used as a carrier in communication systems. In this paper, the chaotic sequences are generated by combining the outputs of chaotic maps, such as logistic map, Chebyshev map, Bernoulli shift map, tent map, etc., leading to new complex sequences known as CCSs. This sequence possesses more randomness, overcomes severe interference levels encountered during transmission and provides higher multipath immunity compared with those of pseudo-noise (PN) codes. Since NR-DCSK is a spread spectrum technique, its performance in wireless multipath fading channels has important considerations. The CCS is used as a carrier in NR-DCSK systems, which leads to improved bit error rate (BER) performance. Comparisons of simulation results to theoretical BER expressions of additive white Gaussian noise (AWGN) and Rayleigh fading channels have been carried out to test the efficiency of the proposed CCS-based NR-DCSK system.

The paper presents combining k-error approximate entropy with some tests in NIST's STS randomness test suite to analyze cryptographical properties of several chaotic pseudo- random sequences generated by diverse maps and quantified methods, including Logistic map, Cubic map, Henon map, Sine map, Tent map, Chebyshev map, Piecewise-linear map, Piece- wise-square-root map. Simulation results show that the k-error approximate entropy can distinguish the stability of different sequences; that the cryptological properties are influenced by quantified methods; that the sequences generated by Logistic map, Chebyshev map, Piecewise-linear map and Piecewise- square-root map have the best pseudorandom properties, while the sequences generated by Henon map and Tent map have the worst stability.

In stream cipher systems, random key sequence generation is the primary task. The concept of chaotic systems can be considered in generating a random key sequence due to its inherent randomness property. Though the chaotic real sequences are random, the randomness will be lost after converting them to binary sequences. In this context, the authors propose a technique which uses a non‐linear feedback system to enhance the randomness of the binary sequences. In this work, three binary chaotic sequences using a logistic map are generated with three different initial conditions and each real value of the chaotic sequence is converted to ‘k’ bit binary value using a thresholding function. Some of the resulting sequences are not random. Hence, in this article a non‐linear structure is used to make the resulting sequence random. Here, a non‐linear function similar to the structure of the Simplified Data Encryption Standard is used to generate a sequence using two non‐random chaotic binary sequences. The resulting sequence is XORed with another non‐random chaotic binary sequence to get a random sequence. Sequences obtained from this nonlinear system are subjected to randomness tests and the results indicate that the sequences pass all the randomness tests. Hence, the sequences qualify as random key sequences, which can be used in a stream cipher based system to encrypt the data samples like audio, image, video, and so forth.

Chaotic sequences, have being widely used in mobile communications and cyberspace security. Using the sequences, various stochastic analysis schemes are developed. The Tent map is one of the widely used chaotic maps with good ergodic uniformity. In this paper, the variant maps are used to illustrate the Tent chaotic sequence under different lengths and control parameters to show the statistical characteristics of sequences. Results are shown that when the control parameter of Tent map is close to 0.5, the generated sequences have the symmetrical distribution, that is more stable if the sequence is longer.

As the widely investigation of chaotic sequence in the application of communication, binary and quaternary phaseshift keying modes have been extensively adopted in spread spectrum communication. Based on Chebyshev chaotic mapping, binary-phase and quadric-phase chaotic spreading sequences are generated, and the relationship among the performance of balance and fractal parameter, initial value and the period of sequence are analyzed. The non-balanced points which should be avoided in the chaotic sequence when applying in CDMA system are proposed. Aiming at the problem which the conventional degree of balance functions only investigates the balance of the 2- valued sequence, the maximum balanced difference method is proposed. The definition of maximum balanced difference is proposed. We analyze the balance performance of quadric-phase Chebyshev sequence. Experimental results show that the maximum balanced difference function can replace the traditional binary-phase degree of balance function to research the balance of digital 2-valued and multi-valued sequence, which has better universality.

Image encryption based on chaotic maps is an important method for ensuring the secure communication of digital multimedia on the Internet. To improve the encryption performance and security of image encryption systems, a new image encryption algorithm is proposed that employs a compound chaotic map and random cyclic shift. First, a new hybrid chaotic system is designed by coupling logistic, ICMIC, Tent, and Chebyshev (HLITC) maps. Comparison tests with previous chaotic maps in terms of chaotic trajectory, Lyapunov exponent, and approximate entropy illustrate that the new hybrid chaotic map has better chaotic performance. Then, the proposed HLITC chaotic system and spiral transformation are used to develop a new chaotic image encryption scheme using the double permutation strategy. The new HLITC chaotic system is used to generate key sequences used in the image scrambling and diffusion stages. The spiral transformation controlled by the chaotic sequence is used to scramble the pixels of the plaintext image, while the XOR operation based on a chaotic map is used for pixel diffusion. Extensive experiments on statistical analysis, key sensitivity, and key space analysis were conducted. Experimental results show that the proposed encryption scheme has good robustness against brute-force attacks, statistical attacks, and differential attacks and is more effective than many existing chaotic image encryption algorithms.

In this paper, we discussed the possibility of introducing chaotic sequences into digital watermarking systems as potential substitutes to commonly used m-sequences. Chaotic sequences have several good properties including the availability of a great number of them, the ease of their generation, as well as their sensitive dependence on their initial conditions. And the quantization does not destroy the good properties. We focus our discussion on the discrete-time dynamical systems operating in chaotic state including Chebyshev maps and logistic maps. Both real valued and binary chaotic sequences are studied and experimented with a digital watermarking system similar to the well-known NEC system. Chaotic sequences are used to modulate information bits into white noise-like wideband watermark signals to be added into the cover objects. The robustness against common signal processing and lossy compression and robust test tools like Stirmark of these systems are tested and compared. Preliminary results are satisfactory. However, in this paper, we only test chaotic sequences scheme with digital images. Tests with other media including video and audio signals will be done at next step. And the good properties of chaos will be further explored, both theoretically and experimentally.

In wireless communication, the physical layer should facilitate multiuser, multirate transmission to support large number of users and applications with diverse needs. In this work chaotic sequences generated using logistic map were used to achieve multiple data rate in Orthogonal Frequency Division Multiple Access (OFDMA) system. Performance was compared with that of Orthogonal Variable Spreading Factor (OVSF) code. Increase in Peak to average power ratio (PAPR) due to variable spreading could be reduced by spreading using chaotic sequences. The spreading sequences could be chosen irrespective of the data rates used. It was also observed that chaotic sequences gave constant PAPR values for different combinations of data rates. Bit error rate was found to be comparable with that for OVSF codes.

The research on the balance of chaotic sequence has important significance to spread-spectrum communication. The relationship between the balance and the parameter of four typical chaotic maps (Chebyshev, improved Logistic, Logistic and Tent) was discussed. The new numeric ranges of initial value and fractal parameter were decided, which provided reference for the generation of chaotic spread-spectrum sequence. Through the graphs of the four chaotic sequences' balance and the error-bit rate performance of these systems with the four chaotic sequences' map parameters, the new numeric ranges were validated. Both simulation results and the analysis show that the balance of Chebyshev is the best.

This paper proposes an algorithm that improves the mean code acquisition time using an energy estimation mode (EEM) and dwell time values from direct-sequence spread spectrum (DS-SS) System. Until recently, DS-SS System has been used in many areas from Wireless LAN, cellular phone, and GPS to telecommunication. Meanwhile, the development of reducing of pseudonoise (PN) code acquisition time, the core technique of DS-SS system, is continuously explored. The algorithm in this paper added the EEM before a search mode (SM) from the conventional PN code acquisition system, which is composed of a SM and a verification mode (VM). In the EEM, dwell time and threshold values are determined for use in the SM and the VM depending on the correlation energy. This paper applies the proposed technique under Rayleigh-fading channel in performing a simulation of PN code acquisition time by a mathematical modeling to evaluate the proposed algorithm. Numerical results show that the proposed method improves the detection performance and the rejection performance of false code phases not only in the VM but also in the SM. Furthermore, the proposed algorithm reduces the mean code acquisition time by maximum 29% than the conventional algorithm.

Image encryption based on 3D Cubic-Sine Logistic Coupled Map and Improved Chirikov Map

Weighted fractional Fourier transform encrypted chaotic direct sequence spread spectrum (WFRFT-CD3S) signal is aperiodic and complex Gaussian distributed. The aperiodicity and complex Gaussian distribution are conducive to the covert transmission of information but also make it difficult to acquire the WFRFT-CD3S signal. An acquisition method implemented in two steps is proposed to acquire the Doppler-shifted WFRFT-CD3S signal. First, a bidirectional correlation search method is proposed to align the received signal with the local spreading sequence in the time domain. The correlation peak attenuation caused by the Doppler frequency shift is eliminated by differential. Second, the accumulated phase angle caused by the Doppler frequency shift is obtained by the differential correlation value between the aligned received signal and the local spreading sequence. Then, the Doppler frequency shift is estimated by the accumulated phase angle. The detection probability, the false alarm probability, and the root mean square error (RMSE) of the Doppler shift estimation are analyzed theoretically and simulated. The theoretical results are verified by simulation. Theoretical results and simulations show that the detection probability is higher than 0.999, the false alarm probability is less than 0.001, and the RMSE of Doppler shift estimation is lower than 63 Hz when the signal-to-noise ratio is higher than -7.3 dB.

This paper presents performance evaluation and comparison analysis of Direct Sequence Spread Spectrum (DSSS) and Frequency Hopping Spread Spectrum (FHSS) systems. The evaluation and analysis are done based on the systems performance against wideband interferences. The interferences are signals with similar spectrum characteristic to the transmitted signals of DSSS and FHSS systems. Bit Error Ratio (BER) is used as evaluation parameter to assess the performance of both systems. Simulation and mathematical analysis are performed to test and verify the performance of both systems. Mathematical analysis also verifies that increasing Spreading Frequency on certain conditions will reduce the BER. This research also points out that FHSS system has a better performance compared to DSSS system indicated by smaller BER.

In this paper, a fast convergent nonlinear adaptive algorithm for narrow-band interference rejection in direct sequence spread spectrum (DS-SS) systems is proposed. The new algorithm can significantly increase the convergence rate of the nonlinear adaptive filter by computer simulations.

Tone interference suppression in DS-SS systems with modified DFT