A Differential Chaotic Bit-Interleaved Coded Modulation System Over Multipath Rayleigh Channels

In recent times, Chaos communication plays a significant role in addressing the security challenges that are more common in the regular communication systems. By exploiting the chaotic waveform properties, variety of chaos-based communication systems are proposed. Considering the aforementioned facets of communication, this research objective at merging the space-time block code (STBC) and orthogonal differential chaos shift keying (ODCSK) methods to improve the security aspects of multiple-input multiple-output (MIMO) based wireless system. Chaos signal is created by using the method called logistic mapping to achieve better secrecy. STBC method is used during the modulation stage for arranging the chaos signal. This system with different types of STBCs is aimed at analysing the differential chaos shift keying (DCSK) and orthogonal DCSK (ODCSK) modulation in AWGN channel. MATLAB software is used to simulate the Bit Error Rate [BER]. Initial simulation proves that the combination of orthogonal DCSK and Alamouti STBC with MIMO system gives better results for AWGN channel when compared to other combinations.KeywordsDifferential Chaos shift keyingSpace-time block codeMultiple-input multiple-output

The performance analysis of polarization M-ary differential chaos shift keying (P-MDCSK) has been expressed using a tight upper bound with the Q-function. However, evaluating the Q-function directly is not a closed expression and there has been less work on closed expression for the upper bound. In order to solve the problem, this paper presents approximate closed-form expressions on the error probability of P-MDCSK. This expression is derived by employing a polynomial approximation of the Q-function. These closed-form expressions are verified through simulations conducted under both additive white Gaussian noise (AWGN) and multipath Rayleigh fading channels. The simulation results reveal that there exists only a negligible gap between the simulations and the derived closed-form expressions. For example, it is observed that the theoretical approximate closed-form expressions exhibit a marginal deviation of approximately dB from the simulations when the bit error rate (BER) reaches . Although the proposed method can only give approximate closed-form expressions of the upper bound, it provides an effective method for other communication schemes where the exact BER closed-form formula cannot be obtained.

In this letter, a non-coherent discrete W transform based index-keying M-ary differential chaos shift keying (DWT-IK-MDCSK) system is proposed to tackle the high peak to average power ratio (PAPR) in the code-shifted DCSK systems and meet the demand of high-data-rate transmissions. In such system, multiple chaotic signals and their Hilbert transforms are cooperated closely to convey the M-ary information-bearing signals, and the resultant signals are extended by the index-keying discrete W vectors prior to being added up and transmitted over the channel. Since the index keying technique is used to select the specific discrete W vectors, extra information bits are conveyed by the indices of these vectors, thereby improving the data rate. Then, the analytical bit error rate (BER) expressions of DWT-IK-MDCSK are derived over additive white Gaussian noise (AWGN) and multipath Rayleigh fading channels. Finally, simulation results show the DWT-IK-MDCSK system has a lower PAPR and better BER performance compared to its competitors.

In this paper, we propose a multi-carrier initial-condition-index-aided differential chaos shift keying (MC-ICI-DCSK) scheme tailored for multipath fading channels. In the proposed scheme, the ICI bits are carried by the index of the initial condition of the chaotic sequences while the modulated bits are carried by positive/negative state of the chaotic signal. To adapt the ICI method for multipath fading channels, we design a cross-correlation-value-based detection scheme for ICI detection. In this detection scheme, multiple carriers can be combined for ICI detection. Meanwhile, ICI and modulated bit detections remain independent of each other. The theoretical bit-error-rate (BER) expression of MC-ICI-DCSK scheme is derived over multipath Rayleigh fading channels. Furthermore, the data rate, spectral efficiency, energy efficiency, and complexity of the proposed scheme are analyzed. Simulation results not only verify the accuracy of the theoretical analysis, but also demonstrate the superiority of the proposed MC-ICI-DCSK scheme. Consequently, the proposed MC-ICI-DCSK can be deemed to be a promising scheme for low-power and low-cost short-range wireless communications.

In this paper, a square-constellation-based M-ary differential chaos-shift-keying (M-DCSK) communication system framework is proposed. The symbol-error-rate expression of the proposed system is derived over additive white Gaussian noise as well as multipath Rayleigh fading channels. Moreover, the peak-to-average-power-ratio (PAPR) performance is carefully analyzed for the newly proposed system. Based on the square-constellation-based M-DCSK framework, a simple least-square estimator is designed to demodulate the information exploiting pilot-assistant symbols. Analytical and simulated results show that the proposed system benefits from a lower energy consumption, but suffers from a higher PAPR compared with the circle-constellation-based M-DCSK system.

Coded modulation (CM) is a bandwidth efficient framework to approach the capacity limit of the differential chaos shift keying (DCSK) systems. In this paper, we propose an M-ary DCSK system operated with CM based on nonbinary protograph low-density parity-check (LDPC) codes over Rayleigh fading channels. First, we investigate the performance of the proposed nonbinary channel coded DCSK (CM-DCSK) and bit-interleaved coded DCSK (BICM-DCSK). In particular, we show that CM-DCSK outperforms BICM-DCSK over Rayleigh fading channels in terms of capacity limit. Compared with BICM-DCSK, CM-DCSK can simplify the receiver structure, since it does not require turbo iteration between the noncoherent detector and channel decoder. Second, guided by the modified extrinsic information transfer (EXIT) analysis, we put forth two new types of nonbinary protograph LDPC codes to approach the capacity limit of CM-DCSK. Both EXIT analysis and simulation results demonstrate that the proposed protograph-coded CM-DCSK achieves a better error performance than BICM-DCSK even with iterative decoding. Furthermore, we show the performance superiority of nonbinary protograph-coded CM-DCSK over a practical ultra-wideband channel. Hence, we conclude that this proposed scheme offers a good alternative for wireless local area network applications.

The paper outlines an efficient approach to evaluating the performance of bit interleaved coded modulation (BICM) systems. Most existing approaches evaluate the probability of individual pairwise error events and obtain a union bound to the bit error probability. This gives very tight bounds on performance for SNRs above the BPSK modulation cutoff rate. However, for higher order modulation systems, the number of bit errors in a symbol slot depends on the two modulated symbols involved in an error event and the linearity of the code cannot be extended to include the modulator. The performance is usually approximated by a few dominant error events which are applicable to AWGN channels. Some approaches consider infinite depth interleaving to obtain a simplified linear model. We study the evaluation and convergence of union bounds for fading channels with finite code block sizes. We develop a general approach which assumes an ideal model for the modulator and enables us to extend the linearity of the considered codes to simplify the computation. This enables us to analyze the performance of concatenated codes with an interleaver of finite length. The approach also gives greater insight into the influence of modulator parameters and the block length of the code on the diversity achieved in BICM systems. The application of our analytical model is demonstrated with examples and simulations.

This paper proposes a chaos-based direct-sequence spread-spectrum (CDSSS) communication system using M-ary PSK modulation in combination with MIMO-OFDM technique. This combination aims at improving the performance as well as capacity of the conventional CDSSS systems over multipath fading channels. In the transmitter, the data is modulated by an M-PSK modulator whose output is fed to a MIMO encoder. Two resulting signals are spread by directly multiplying with chaos-NRZ sequences and then put into the corresponding OFDM modulators. The output signals are transmitted through a multipath fading channel using multiple transmitting and receiving antennas. In the receiver, beside the use of OFDM demodulation, chaotic despread-spectrum, and M-PSK demodulation, a V-BLAST algorithm with Minimum mean squared error (MMSE) equalization is applied to decode and recover the data. Schemes for the transmitter and receiver are described in detail and their BER performance over the multipath Rayleigh fading channel is evaluated by means of numerical simulations. The obtained results prove that the performance and capacity of the proposed system are significantly enhanced and can be adjusted by changing the values of M-ary level, spreading factor or the number of used antennas.

The principle of coding in the signal space follows directly from Shannon’s analysis of waveform Gaussian channels subject to an input constraint. The early design of communication systems focused separately on modulation, namely signal design and detection, and error correcting codes, which deal with errors introduced at the demodulator of the underlying waveform channel. The correct perspective of signal-space coding, although never out of sight of information theorists, was brought back into the focus of coding theorists and system designers by Imai’s and Ungerböck’s pioneering works on coded modulation. More recently, powerful families of binary codes with a good tradeoff between performance and decoding complexity have been (re-)discovered. Bit-Interleaved Coded Modulation (BICM) is a pragmatic approach combining the best out of both worlds: it takes advantage of the signal-space coding perspective, whilst allowing for the use of powerful families of binary codes with virtually any modulation format. BICM avoids the need for the complicated and somewhat less flexible design typical of coded modulation. As a matter of fact, most of today’s systems that achieve high spectral efficiency such as DSL, Wireless LANs, WiMax and evolutions thereof, as well as systems based on low spectral efficiency orthogonal modulation, feature BICM, making BICM the de-facto general coding technique for waveform channels. The theoretical characterization of BICM is at the basis of efficient coding design techniques and also of improved BICM decoders, e.g., those based on the belief propagation iterative algorithm and approximations thereof. In this text, we review the theoretical foundations of BICM under the unified framework of error exponents for mismatched decoding. This framework allows an accurate analysis without any particular assumptions on the length of the interleaver or independence between the multiple bits in a symbol. We further consider the sensitivity of the BICM capacity with respect to the signal-to-noise ratio (SNR), and obtain a wideband regime (or low-SNR regime) characterization. We review efficient tools for the error probability analysis of BICM that go beyond the standard approach of considering infinite interleaving and take into consideration the dependency of the coded bit observations introduced by the modulation. We also present bounds that improve upon the union bound in the region beyond the cutoff rate, and are essential to characterize the performance of modern randomlike codes used in concatenation with BICM. Finally, we turn our attention to BICM with iterative decoding, we review extrinsic information transfer charts, the area theorem and code design via curve fitting. We conclude with an overview of some applications of BICM beyond the classical coherent Gaussian channel.

Classical Turbo code suffers from high error floor due to its small minimum Hamming distance (MHD). Newly-proposed 3D-Turbo code can effectively increase the MHD and achieve a lower error floor by adding a rate-1 post encoder, through which part of the parity bits from the classical Turbo encoder are further encoded. In this paper, a novel bit-interleaved coded modulation (BICM) system is proposed by combining rotated mapping QAM and 3D-Turbo code to effectively improve the performance of 3D-Turbo code over Raleigh fading channels. A 2D iterative soft demodulating-decoding algorithm is developed for the proposed BICM system. Simulation results show that the proposed system can obtain about 0.8-1.0 dB gain at bit error rate (BER) of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-6</sup> , compared with the existing BICM system with Gray mapping QAM.

An approximate maximum likelihood (ML) method for joint estimation of time delays and directions-of-arrivals (DOAs) for the direct-sequence code-division multiple-access (DS-CDMA) systems over the multipath Rayleigh fading channels is developed. The proposed estimation scheme is developed by modeling the known training sequence of the desired user as the desired signal and the multiple access interference (MAI)-plus-AWGN as unknown colored Gaussian noise uncorrelated with the desired signal. An efficient iterative algorithm for estimating channel parameters (the time delays and DOAs of multipath signals) is proposed to reduce the computational complexity. The algorithm transforms the multi-dimensional maximization problem into two simple one-dimensional (1-D) maximization problems based on an iterative scheme. Analytical and simulation results are presented to illustrate the performance in comparison with the Cramer-Rao bounds (CRBs). It is shown that the proposed algorithm is near-far resistant for both time delay and DOA estimation and little performance loss is observed in comparison with the CRBs at reasonable SNRs.

The generalized mutual information (GMI) of bit-interleaved coded modulation (BICM) systems, sometimes called the BICM capacity, is investigated at low signal-to-noise ratio (SNR). The combinations of input alphabet, input distribution, and binary labeling that achieve the Shannon limit <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${- 1.59}\;{\rm dB}$</tex></formula> are completely characterized. The main conclusion is that a BICM system with probabilistic shaping achieves the Shannon limit at low SNR if and only if it can be represented as a zero-mean linear projection of a hypercube. Hence, probabilistic shaping offers no extra degrees of freedom to optimize the low-SNR BICM-GMI, in addition to what is provided by geometrical shaping. The analytical conclusions are confirmed by numerical results, which also show that for a fixed input alphabet, probabilistic shaping can improve the BICM-GMI in the low and medium SNR range.

By generalizing the waveform communications concept, this paper develops exact expressions, verified by computer simulations, for the noise performance of the coherent antipodal Chaos Shift Keying (CSK), coherent Differential Chaos Shift Keying (DCSK) and differentially coherent DCSK modulation schemes. We show that the properties of the basis functions have no effect on the noise performance of a modulation scheme, provided that the energy per bit is constant and the basis functions are orthogonal.

In this letter, a joint pulse position modulation (PPM) and permutation index differential chaos shift keying (PI-DCSK) modulation scheme (PPM-PI-DCSK) is proposed to increase the data rate and improve performance. In PPM-PI-DCSK, the bit stream is divided into blocks of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m_{p} + m_{c} +1 $ </tex-math></inline-formula> bits, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m_{p}$ </tex-math></inline-formula> bits are modulated by PPM, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m_{c}$ </tex-math></inline-formula> bits are modulated by PI modulation, and the last one bit is modulated by DCSK. The theoretical bit error rate (BER) performance of the proposed PPM-PI-DCSK is derived over multipath Rayleigh fading channels and validated via simulations. Simulation results show that the proposed PPM-PI-DCSK outperforms the benchmark DCSK-based schemes. Furthermore, the performance superiority is also demonstrated by the frequency-modulated PPM-PI-DCSK over a typical ultra-wideband (UWB) channel. This demonstrates the superiority and feasibility of the proposed scheme in practical applications.

In this paper, we propose an adaptive multistage parallel interference cancellation (PIC) structure for multipath fading channels. Similarly to the previous partial interference cancellation (IC) approach suggested in Divsalar et al. (1998), only part of the multiaccess interference (MAI) estimate is canceled at each stage. However, the weights employed in this proposed scheme are derived from an LMS algorithm which tries to minimize the mean-square error between the actual signal received and its replica. The complexity of the proposed adaptive multistage PIC scheme is much lower than that of linear multiuser detectors. Performance of the proposed structure in single-path Rician and multipath Rayleigh fading channels is evaluated by simulations. Our results show that the proposed technique outperforms the existing interference cancellation methods in multipath fading channels.