Reliable Low-Rank Approximation of Matrices Detection Aided Multicarrier DCSK Receiver Design

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.

Recently, the differential detection scheme has attracted considerable attention as a demodulated scheme for digital mobile communications because of its robustness in the frequency nonselective fading channel. A problem of the differential detection scheme is that its bit error rate (BER) performance in the additive white Gaussian noise (AWGN) channel is inferior to that of the coherent detection scheme. To solve this problem, many methods to improve BER performance of the differential detection in the AWGN channel have been proposed. However, those methods require complex signal processings.This paper proposes a novel differential detection scheme as a simpler improvement method which estimates the differential phase of the transmitted signal by a sequence estimation scheme using the Viterbi algorithm. The proposed scheme is simplified in a manner such that its signal processing is composed of only additions and subtractions on the phase information of the received signal. Results of computer simulation show that BER performance of the proposed scheme is close to that of the ideal coherent detection in the AWGN channel. In addition, the trellis diagram of the Viterbi algorithm can be reduced without performance degradation introducing the signal processing similar to the Scarece State Transition (SST) type Viterbi decoding. The proposed scheme also is useful in the case of the fast Rician fading channel and the slow Rayleigh fading channel.

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 the general code-shifted differential chaos shift keying (GCS-DCSK) system, multiple bit-streams are simultaneously carried by CS-DCSK signal using Walsh codes. However, its data rate is limited by the available Walsh codes in the Walsh code matrix due to orthogonality constraint of GCS-DCSK signal. In this paper, we propose a new GCS-DCSK scheme with code index modulation (CIM-CS-DCSK), which can achieve higher spectrum efficiency using code index modulation to carry additional bits. In the proposed scheme, the reference chaotic signal is the same as that of GCS-DCSK, and the multiple information bearing signals are simultaneously modulated by the information symbols and the selected Walsh codes with specific indices, which are determined by an integer sequence mapped from information symbols via the natural numbers to $k$ -combinations mapping method. We derive bit error rate of the proposed scheme over the additive white Gaussian noise channel. The numerical results not only verify our analysis but also show the advantage of the proposed scheme over GCS-DCSK. Through analyzing and comparing the numbers of carried bits per transmitted symbol of CIM-CS-DCSK and GCS-DCSK, it is shown that the proposed scheme can obtain higher data rate than GCS-DCSK with the same resource constraints.

The Orthogonal Frequency Division Multiplexing (OFDM) is also known as multicarrier technology. Wideband digital communications in the recent past have increasingly utilized OFDM. It can withstand difficult channel circumstances, efficiently utilize spectrum resources, decrease ISI, and operate at a high data rate, among many other benefits. It has been used in several wireless and wired communication systems, including fourth generation Long-Term Evolution (4G LTE) mobile communications. The performance assessment and analysis of the OFDM system under Additive White Gaussian Noise (AWGN) channel has been carried out in this work. The factors in which system performance is assessed include the signal quality, Bit Error Rates (BERs), and Signal to Noise Ratios (SNRs) of the received signals. To improve performance while employing multicarrier modulation, the subcarriers must be kept orthogonal to one another, in the process known as OFDM. The sole focus of this study is the performance analysis of PAPR, BER, and SNR utilizing various modulation methods and schemes.

In this letter, we put forth a novel strategy to boost the reliability of orthogonal frequency division multiplexing differential chaos shift keying (OFDM-DCSK) systems over doubly selective fading channels. Provided the accessibility of channel state information, singular value decomposition is exploited to partition the channel into distinct sub-channels, which is realized by multiplying the right singular vectors by the symbol matrix at the transmitter. Subsequently, the sub-channel associated with the largest singular value is allocated to the reference chaotic sequence, leading to a higher signal-to-noise ratio (SNR) of demodulated symbols and lower bit error rate (BER) at the receiver. Inspired by the water-filling principle, the BER can be further reduced by permuting the symbols in a strategic manner. This approach of channel decomposition integrated with symbol reallocation, referred to as singular-vector pre-coded OFDM-DCSK (SVP-OFDM-DCSK), is able to escalate the SNR over doubly selective channels, ultimately enhancing the system reliability. The BER of the SVP-OFDM-DCSK system is also analyzed. Simulation results demonstrate that the proposed system with and without symbol permutation step achieves lower BERs than existing schemes over doubly selective fading channels.

Non-orthogonal multiple access (NOMA) is one of the potential future mobile network methods that can give better spectral efficiency, huge connectivity, and low latency. As a result, academic and industry researchers have studied the error performances and capacity of NOMA systems. The main drawback of NOMA methods is user interference, which is generally addressed by interference cancellation techniques such as Successive Interference Cancellation (SIC) at receivers. Therefore, it is better to obtain the bit error rate (BER) performance of NOMA. Each user's power level is determined by the power level assigned to them. As a result, this work presents BER analysis for two NOMA users using BPSK modulation in additive white Gaussian noise (AWGN), Rayleigh, and Rician fading channels. Initially, we assessed BER performance for various Signal to Noise Ratio (SNR) values by assuming two users who are equally spaced from the base station (BS). Later, the BER performance for various transmit powers is assessed by assuming two users are situated at varying distances from the BS. The performances are discussed using MATLAB simulations. The comparative BER analysis is also studied for various fading environments.KeywordsBERNOMABPSKSICFading

The use of open-loop coding can be easily extended to a closed-loop concatenated code if the transmitter has access to feedback. This can be done by introducing a feedback transmission scheme as an inner code. In this paper, this process is investigated for the case when a linear feedback scheme is implemented as an inner code and, in particular, over an additive white Gaussian noise (AWGN) channel with noisy feedback. To begin, we look to derive an optimal linear feedback scheme by optimizing over the received signal-to-noise ratio (SNR). From this optimization, a linear feedback scheme is produced that is asymptotically optimal in the sense of blocklength-normalized SNR; it is then compared to other well-known schemes. Then, the linear feedback scheme is implemented as an inner code to a concatenated code over the AWGN channel with noisy feedback. This code shows improvements not only in error exponent bounds, but also in bit error rate (BER) and frame error rate (FER). It is also shown that if the concatenated code has total blocklength L and the inner code has blocklength, N, the inner code blocklength should scale as N = O(C/R), where C is the capacity of the channel and R is the rate of the concatenated code. Simulations with low-density parity-check (LDPC) and turbo codes are provided to display practical applications and their error rate benefits.

In this paper, an improved Quadrature Multi-carrier Differential Chaos Shift Keying (QMC-DCSK) based on Chaotic Shape-forming Filter (CSF) and Cross Correction (CC) is proposed. The chaotic signal generated by CSF is used as reference spreading sequence in QMC-DCSK. Quadrature multi-carriers are used to carry the reference and multiple information bearing signals simultaneously in order to improve the Bit Transmission Rate (BTR). By this way, the proposed system is able to transmit <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$2M-1$</tex-math></inline-formula> bits Traditional Data Stream (TDS) during one traditional DCSK bit duration, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$M$</tex-math></inline-formula> is the number of carrier frequencies. Meanwhile, the reference signal transmits Additional Data Stream (ADS) encoded by CSF together with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$2M-1$</tex-math></inline-formula> identical or inverse data stream carried by the rest <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$2M-1$</tex-math></inline-formula> channels (information bearing signals). By this system configuration, the channel redundance can be used to improved bit error rate (BER) performance of ADS, after decoding TDS. In turn, the TDS reliability can also be improved by checking most ADS polarity of the corresponding carrier. This process is referred to as CC. The contribution of this work lies in the CC operation, by which the reliability of both TDS and ADS is improved significantly. It is the CSF and multi-carrier that make CC possible. The analytical BER is derived for the proposed method. The merits of the proposed system include, first, it improves the BTR as compared to that of QMC-DCSK, because ADS conveys more information bits; second, the ADS reliability is improved dramatically because the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\text{2}\,M$</tex-math></inline-formula> duplication can be used to improve the signal to noise ratio; third, the TDS reliability is improved as well because the information bits conveyed by each carrier frequency is enhanced and corrected by the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\text{2}\,M$</tex-math></inline-formula> repetitions. By this way, not only TDS and ADS are transmitted (i.e., the higher BTR is achieved), but also both reliability are improved (i.e. the lower BER is achieved). In order to testify the feasibility and superiority of the proposed method, simulation and wireless open-access research platform (WARP) experiment are conducted. The simulation and experiment results show that the proposed method is superior to other comparison methods.

In this paper, a novel coupled code shifted M-ary differential chaos shift keying modulation scheme is proposed as a simple and low-cost solution to reference removal. In this scheme, only two information-bearing signals are transmitted. Both signals are modulated by selected Walsh code sequences with specific indices determined by the index bits, and one of them also carries an additional M-ary information symbol. Since these two information-bearing signals are coupled by the same chaotic message bearer, data bits can be easily recovered according to the correlation between these two signals so that the transmission of reference signals can be completely avoided. Theoretical Bit Error Rate (BER) expressions are derived over the additive white Gaussian noise and multipath Rayleigh fading channels. Furthermore, simulations and comparisons indicate that the proposed system can achieve better BER performance with lower complexity.

The optical ZCZ code, which is a set of pairs of binary and biphase sequences with zero correlation zone, can provide code division multiple access (CDMA) communication system without co-channel interference. The M-ary amplitude shift keying spread spectrum (M-ary/ASK-SS) system using this code can detect a desired sequence without interference of undesired sequences. We have proposed the compact construction of a matched filter bank for this code, which is called the compact-type matched filter bank. However, M-ary/ASK-SS system using this filter bank might go down the bit error rate (BER) performance because input-output characteristics of this filter bank for this code with zero correlation zone 4n - 2 are nonlinear characteristics. In this paper, we clarify that BER performance in the M-ary/ASK-SS system over the additive white Gaussian noise (AWGN) channels is not influenced by nonlinear characteristics of this filter bank by the theoretical formula of BER characteristics and the computer simulation. The BER performance in the ASK-SS system using compact-type matched filter under the AWGN environment go down compared to that using direct-type matched filter as expected. But the BER performance in the M-ary/ASK-SS system using this compact-type matched filter bank under the AWGN environment is almost equal compared to that using parallel-type matched filter bank. In fact, this compact-type matched filter bank is effective in the M-ary/ASK-SS system.

Low rank approximation of matrices is an important tool in machine learning. Given a data matrix, low rank approximation helps to find factors, patterns, and provides concise representations for the data. Research on low rank approximation usually focuses on real matrices. However, in many applications data are binary (categorical) rather than continuous. This leads to the problem of low rank approximation of binary matrices. Here we are given a d x n binary matrix A and a small integer k &lt; d. The goal is to find two binary matrices U and V of sizes d x k and k x n respectively, so that the Frobenius norm of A - U V is minimized. There are two models of this problem, depending on the definition of the dot product of binary vectors: The GF(2) model and the Boolean semiring model. Unlike low rank approximation of a real matrix which can be efficiently solved by Singular Value Decomposition, we show that approximation of a binary matrix is NP-hard, even for k=1.\nIn this paper, our main concern is the problem of Column Subset Selection (CSS), in which the low rank matrix U must be formed by k columns of the data matrix, and we are interested in the approximation ratio achievable by CSS for binary matrices. For the GF(2) model, we show that CSS has approximation ratio bounded by k/2+1+k/(2(2^k-1)) and this is asymptotically tight. For the Boolean model, it turns out that CSS is no longer sufficient to obtain a bound. We then develop a Generalized CSS (GCSS) procedure in which the columns of U are generated from Boolean formulas operating bitwise on selected columns of the data matrix. We show that the approximation ratio achieved by GCSS is bounded by 2^(k-1)+1, and argue that an exponential dependency on k is seems inherent.

Hierarchical constellations offer a different degree of protection to the transmitted messages according to their relative importance. As such they found interesting application in digital video broadcasting systems as well as wireless multimedia services. Although a great deal of attention has been devoted in the literature to the study of the bit error rate (BER) performance of uniform phase shift keyed (PSK) constellations, very few results were published on the BER performance of hierarchical PSK constellations. We obtain exact and generic expressions in M for the BER of the generalized hierarchical M-PSK constellations over additive white Gaussian noise (AWGN) and fading channels. For the AWGN case, these expressions are in the form of a weighted sum of Pawula (1982) F-functions and are solely dependent on the constellation size M, the carrier-to-noise ratio, and a constellation parameter which controls the relative message importance. Because of their generic nature, these new expressions readily allow numerical evaluation for various cases of practical interest.

The WiMax (Worldwide Interoperability for Microwave Access) is a technology in&lt;strong&gt; &lt;/strong&gt;broadband wireless access, which employs OFDM (Orthogonal Frequency Division Multiplexing) as an alternative transmission to enable high speed data in communication system. This research aim is to analyze the performance system of the OFDM-Based WiMAX, which used the cyclic prefix. The model was designed in four schemes of simulation method, the BPSK (Binary Phase Shift Keying, QPSK (Quadrature Phase Shift Keying), 16 QAM (Quadrature Amplitude Modulation) and 64 QAM. Each scheme was investigated BER (Bit Error Rate) on AWGN (Additive White Gaussian Noise) channel and multipath Rayleigh fading channel, which had applied the cyclic prefix. By simulation of the cyclic prefix was produced the modulation measurement of the BPSK, QPSK, 16 and 64 QAM. The performance result of Eb/No 15 dB was obtained the BER of BPSK and QPSK of 1.11E-11, the BER of 16 QAM and 64 QAM of 8.69E-06 and 0.00333 respectively. Those results indicated much smaller BER value than EbNo 0 dB which BPSK and QPSK of 1 BER, 1.5 and 1.75 BER for 16 QAM and 64 QAM respectively. In conclusion, a higher value of EbNo, hence the BER value would be lower.

In this paper, we study the impact of timing synchronization errors on the performance of Multicarrier Differential Chaos Shift Keying systems over wireless channels. Considering the challenges posed by selective-frequency Rayleigh fading and multipath propagation, we analyze the system’s performance under random timing errors and fading effects. Using analytical modeling, including probability density functions for fading coefficients and truncated density functions for timing synchronization errors, the Bit Error Rate (BER) performance is derived. Numerical simulations validate the theoretical findings and highlight critical system parameters that influence robustness. Our results demonstrate that timing synchronization errors significantly degrade BER performance, particularly under harsh wireless channel conditions. To mitigate this degradation, we analyze and evaluate the effect of timing errors and related parameters on system performance, identifying technical solutions such as increasing the receiver sampling frequency within the chip duration and selecting an optimal spreading factor. These findings provide valuable insight into the design of more resilient noncoherent chaos-based communication systems.