Code-division Multiple-access Communication Systems Research Articles

Perfect Sequences Based on Golay Codes for Communication Systems

In data transmission systems, ensuring reliable communication while maximizing spectrum efficiency is a challenge. Code Division Multiple Access (CDMA) systems, widely used in wireless networks, depend on spreading codes to manage interference and support users. Achieving a balance between low cross-correlation and optimal auto-correlation properties is complex and involves trade-offs that affect system performance, especially as modern systems demand higher data rates and efficiency. In systems that use spectral spreading, achieving optimal autocorrelation characteristics often compromises cross-correlation characteristics, and vice versa. Codes with low cross-correlation values typically exhibit high out-of-phase autocorrelation values. Therefore, a balance between autocorrelation and cross-correlation properties is necessary for an efficient CDMA communication system. These desirable correlation properties are crucial in both periodic and aperiodic contexts. Recent innovations have led to a patented code generator derived from Golay codes/sequences, which exhibits low periodic cross-correlation values and a periodic autocorrelation function characterized by a prominent correlation peak and null values surrounding it. This development not only enhances signal quality but also mitigates interference in multi-user communication scenarios, making it particularly relevant for modern wireless networks. Furthermore, a novel solution is proposed to minimize the Peak-to-Average Power Ratio (PAPR) and reduce the cost of a new Orthogonal Perfect Discrete Fourier Transform Golay (OPDG) power transmission circuit. This approach leverages advanced signal processing techniques to achieve energy efficiency, addressing a critical challenge in high-performance communication systems. Experimental results demonstrate the practicality of these innovations in real-world implementations, paving the way for future advancements in CDMA technology.

Design of Polyphase Sequences With Low Integrated Sidelobe Level for Radars With Spectral Distortion via Majorization-Minimization Framework

Polyphase sequences with low aperiodic autocorrelation levels, assessed in terms of the integrated sidelobe level (ISL), can be applied in many engineering fields, such as radars, sonars, and code-division multiple access communication systems. In practice, a polyphase sequence that is optimal in some sense (for example, minimum ISL) could be significantly distorted, thus reducing the detection performance of the radar system. Hence in this article, we focus on designing ISL minimization-based polyphase sequences with spectral distortion taken into consideration, where we first derive an expression for the ISL under spectral distortion, i.e., distorted ISL (DISL), and then we propose an iterative algorithm based on majorization-minimization framework to solve the DISL minimization problem. The proposed algorithm is proved to be nonincreasing and is guaranteed to converge to a stationary point. A variety of design results utilizing the proposed algorithm in different scenarios are presented and compared with those by other methods or some known sequences. The proposed algorithm is proved to be effective to design polyphase sequences with low DISL.

Quantum CDMA Communication Systems

Barcoding photons can provide a host of functionalities that could benefit future quantum communication systems and networks beyond today's imagination. As a significant application of barcoding photons, we introduce code division multiple-access (CDMA) communication systems for various applications. In this context, we introduce and discuss the fundamental principles of a novel quantum CDMA (QCDMA) technique based on spectrally encoding and decoding of continuous-mode quantum light pulses. In particular, we present the mathematical models of various QCDMA modules that are fundamental in describing an ideal and typical QCDMA system, such as quantum signal sources, quantum spectral encoding phase operators, M$\times$M quantum broadcasting star-coupler, quantum spectral phase decoding operators, and the quantum receivers. In describing a QCDMA system, this paper considers a unified approach where the input continuous-mode quantum light pulses can take on any form of pure states such as Glauber states and quantum number states. For input number states, one can observe features like entanglement and quantum interference. More interestingly, due to Heisenberg's uncertainty principle, the quantum signals sent by photon number states obtain complete phase uncertainty at the time of measurement. Therefore, at the receiver output, the multiaccess inter-signal interference vanishes. Due to Heisenberg's uncertainty principle, the received signal intensity at the photodetector's output changes from a coherent detection scheme for input Glauber states to an incoherent detection scheme for input number states. Our mathematical model is valuable in the signal design and data modulations of point-to-point quantum communications, quantum pulse shaping, and quantum radar signals and systems where the inputs are continuous mode quantum signals.

A hybrid OFDM–CDMA-based robust image watermarking technique

Digital watermarking is a process of embedding hidden information called watermark into different kinds of media objects. It uses basic modulation, multiplexing and transform techniques of communication for hiding information. Traditional techniques used are least significant bit (LSB) modification, discrete cosine transform (DCT), discrete wavelet transform (DWT), discrete Fourier transform (DFT), code division multiple access (CDMA) or a combination of these. Among these, CDMA is the most robust against different attacks except geometric attacks. This paper proposes a blind and highly robust watermarking technique by utilizing the basis of orthogonal frequency division multiplexing (OFDM) and CDMA communication system. In this scheme, the insertion process starts by taking DFT of host images, permuting the watermark bits in randomized manner and recording them in a seed as a key. Then PSK modulation follows inverse DFT (IDFT) that gives watermark information as OFDM symbols. These symbols are spread using spreading codes and then arithmetically added to the host image. Finally, scheme applies inverse DCT (IDCT) to get watermarked host images. The simulation results of the proposed scheme are compared with CDMA-based scheme in DCT domain. The results show that the robustness of the proposed scheme is higher than the existing scheme for non-geometric attacks.

Synchronization of Two Chaotic Stream Ciphers in Secure CDMA Communication Systems

In the basic processing of Code Division Multiple Access (CDMA) systems using chaotic code sequences, a pair of chaos generators in the transmitter and the receiver are used to generate the same sequence, in order to synchronize and retrieve the transmitted signals. In addition, a filter with a simple structure should be integrated into chaotic signals to achieve the maximum of the signal to noise ratio and mitigate the harmful effects of multipath. Another effective property of chaos signal is that a wireless multipath channel does not change the amount of contained information. Considering those issues, the present paper describes a practical system for synchronizing two chaotic generators used in a digital CDMA. Chaotic generators were used to spread the data and provide security against attack. Both receiver and transmitter were implemented using two separate Spartan 6 FPGA boards. Experimental results proved the robustness of the proposed method which could contribute towards the synchronization of chaotic signals in secure CDMA communication systems.

New Optical Codes Based on Construction of Parity Check Matrix of LDPC Codes

Abstract In this paper, new spectral optical codes based on the construction parity check matrix of LDPC codes were designed and implemented in an optical code-division multiple access communication system. Two types optical family codes can be obtained with respectively a cross correlation of λ c = 0 {\lambda _c} = 0 and λ c = 1 {\lambda _c} = 1 . In each case, the codes can either be decoded using the direct detection or the balanced detection. Performance was evaluated by referring to the Q factor, the bit error rate and the eye pattern diagrams using Optisystem 9.0.

Constructions of Quasi-Complementary Sequence Sets Associated With Characters

An $(\boldsymbol {M},\boldsymbol {K},\boldsymbol {N},\delta _{\max })$ -quasi-complementary sequence set (QCSS) is referred to as a set of $\boldsymbol {M}$ 2-D matrices of order $\boldsymbol {K}\times \boldsymbol {N}$ with periodic tolerance $\delta _{\max }$ . In a multicarrier code-division multiple-access (MC-CDMA) communication system, the set size $\boldsymbol {M}$ of a QCSS is equal to the maximum number of users it can support, and the periodic tolerance $\delta _{\max }$ determines the interference performance. For the application of a QCSS, it is desirable that the set size should be as large as possible, and the periodic tolerance should be as small as possible. In this paper, a framework of a periodic QCSS is proposed from additive and multiplicative characters associated with a specific integer set. It is then discovered that the parameters of the obtained QCSS are determined by the employed integer set. From this discovery, new classes of periodic QCSSs with large set sizes and low periodic tolerances are constructed and associated with some known integer sets.

Two Constructions of Asymptotically Optimal Quasi-Complementary Sequence Sets

An $(M,K,N,\delta _{\mathrm {max}})$ -quasi-complementary sequence set (QCSS) is referred to as a set of $M$ two-dimensional matrices of size $K\times N$ with maximum periodic correlation magnitude $\delta _{\mathrm {max}}$ . It can be applied to a multi-carrier code-division multiple-access communication system to achieve low-interference performance. Compared with perfect complementary sequence sets, QCSSs with maximum periodic correlation magnitudes achieving or asymptotically achieving the correlation lower bounds have the advantage of supporting more users. In this paper, two constructions of periodic QCSSs from additive characters and multiplicative characters of finite fields are developed. In the first construction, new QCSSs with constituent sequence length $N=p$ are proposed by using cyclic classes, where $p$ is a prime. In the second construction, QCSSs with constituent sequence length $N=q-1$ and $N=r^{2}-1$ are presented by employing almost difference sets and special sets proposed by Katz, respectively, where $q>5$ is an odd prime power and $r$ is a prime power. Notably, the parameters of QCSSs derived from the second construction are flexible and have not been covered in the literature. In addition, all the proposed periodic QCSSs are asymptotically optimal with respect to the correlation lower bounds.

New quaternary sequences of even length with optimal auto-correlation

Sequences with low auto-correlation property have been applied in code-division multiple access communication systems, radar and cryptography. Using the inverse Gray mapping, a quaternary sequence of even length $N$ can be obtained from two binary sequences of the same length, which are called component sequences. In this paper, using interleaving method, we present several classes of component sequences from twin-prime sequences pairs or GMW sequences pairs given by Tang and Ding in 2010; or two, three or four binary sequences defined by cyclotomic classes of order $4$. Hence we can obtain new classes of quaternary sequences, which are different from known ones, since known component sequences are constructed from a pair of binary sequences with optimal auto-correlation or Sidelnikov sequences.

Symbol synchronization in the OFDM–MFSK-based multiple access system

The dynamic range of the decentralized wideband code-division multiple access communications system based on OFDM–FSK modulation and noncoherent reception is studied depending on the clock oscillator accuracy and its jitter. The issues concerned with the symbol synchronization of the transmitter and receiver, as well as the dynamic range of the received signal, are investigated. The GOST 207 and GOST 231 unified standard radio wave propagation models, which are interpreted as communications channel models, are discussed.

Performance of a novel evolutionary genetic-based multi-user detector for multi-carrier CDMA communication systems

In this paper, we investigate the performance of a modified evolutionary multi-user detector (MUD) in multi-carrier direct-sequence code-division multiple-access (MC-CDMA) communication systems over frequency-selective fading channels. The genetic algorithm (GA), which tries to reduce the complexity in optimal detection due to greedy exhausted searching, performs using the adequate sub-optimal multi-user detector for MC-CDMA systems. In this paper, we propose a forcing mutation scheme for the genetic algorithm (GA) to perform a forcing mutation evolutionary multi-user detector (FME-MUD) and to largely reduce computational complexity. Simulation results show that with six generations, the proposed FME-MUD scheme outperforms the conventional GA-MUD, especially at heavy system loads.

A Survey on Complementary-Coded MIMO CDMA Wireless Communications

In this paper, we present a comprehensive survey on complementary code (CC)-based multiple-input multiple-output (MIMO) code-division multiple access (CDMA) for futuristic wireless communications. This paper starts with the construction of CCs and then proceeds to describe the design of CC-based CDMA and MIMO wireless communication systems. Complementary-coded chip-level space–time coding offers a unique paradigm to implement multiuser MIMO systems, opening up a new dimension to combine multiple-access and multiple-antenna techniques in a unified platform for a possible system design optimization of a wireless communication system in the future. In this paper, we will also discuss various potential research topics and technical challenges that need to be tackled before a complementary-coded MIMO CDMA system can be implemented in practical wireless applications.

Construction of a class of codebooks nearly meeting the Welch bound

Optimal and nearly optimal codebooks have important applications in code-division multiple-access (CDMA) communication systems to distinguish the signals of users. Most optimal codebooks are constructed by difference sets in a finite abelian group. By using almost difference sets, Ding and Feng constructed nearly optimal codebooks with more flexible parameters (codebook length and size) to fit their applications. Inspired by various construction methods for almost difference sets, we constructed series of nearly optimal codebooks with milder conditions than those employed by such almost difference sets. Recently, Ding et al. found a new series of almost difference sets in finite fields using cyclotomic classes with order eight. In this paper, we present a series of nearly optimal codebooks by performing a similar construction, but with milder requirements.

Two Conversion Formulas of Known Optimal Sequences

This paper investigates the construction methods of sequences with optimal autocorrelation functions. The approaches proposed by us are to convert the known optimal sequences into the required sequences. In order to arrive at our goal, we establish two conversion formulas, and summarize their performance. The proposed methods can provide lots of candidates of spread sequences for the applications of code-division multiple-access (CDMA) spread spectrum communication systems.

Theoretical analysis and simulation of a code division multiple access system (CDMA) for secure signal transmission in wideband channels

Theoretical analysis and simulation of a code division multiple access system (CDMA) for secure signal transmission in wideband channels

PERFORMANCE COMPARISON OF BLIND ADAPTIVE MULTIUSER DETECTION ALGORITHMS

Blind multiuser detection algorithms are used to el iminate the Multiple Access Interference (MAI) and the Near-Far effect in mobile communication systems. Four kinds of blind multiuse r detection algorithms applied to code-division multiple-access (CDMA) communication system are studied in this paper. Tho se algorithms are the Least Mean Squares (LMS), Rec ursive Least Squares (RLS), Kalman filter and subspace-based Kalman filt er algorithms. The resultant signal to interference ratio (SIR) at the output of the receivers controlled by the four kinds of multi-use r detection algorithm has been discussed in this pa per. Simulation results show that the subspace based Kalman filter algorithm outperfo rms all other three algorithms. Subspace-based Kalm an filter algorithm has faster convergence speed, more practical and the ca pability of CDMA system can be increased.

A maximum-likelihood bound approaching minimum bit error rate linear multiuser detector for frequency-selective DS-CDMA systems

In this letter, a minimum bit error rate (MBER) linear multiuser detector (MUD) is considered for direct-sequence code-division multiple-access (DS-CDMA) communication systems, distorted by time-varying and frequency-selective multipath fading channels. Based on the approach for finding filter coefficients of the proposed MBER MUD, an efficient Newton method with a barrier parameter is developed. The BER performance of the MBER MUD is compared to other conventional detectors. The study finds that the proposed MBER MUD has more than 2dB gain over the linear minimum mean-squared error (LMMSE) detector. Furthermore, in the high SNR region, the BER performance of the proposed MBER MUD approaches the performance of the maximum-likelihood (ML) detector.

H∞Channel Estimation for DS-CDMA Systems: A Partial Difference Equation Approach

In the communications literature, a number of different algorithms have been proposed for channel estimation problems with the statistics of the channel noise and observation noise exactly known. In practical systems, however, the channel parameters are often estimated using training sequences which lead to the statistics of the channel noise difficult to obtain. Moreover, the received signals are corrupted not only by the ambient noises but also by multiple-access interferences, so the statistics of observation noises is also difficult to obtain. In this paper, we will investigate theH∞channel estimation problem for direct-sequence code-division multiple-access (DS-CDMA) communication systems with time-varying multipath fading channels. The channel estimator is designed by applying a partial difference equation approach together with the innovation analysis theory. This method can give a sufficient and necessary condition for the existence of anH∞channel estimator.

Optimal design of perfect DFT sequences

In this paper, we propose a novel scheme to construct a large set with N(N+1) perfect sequences of length N, derived from an Inverse Discrete Fourier Transform (IDFT) of Chu and maximum-length sequences. This optimum set of perfect periodic autocorrelation sequences has a maximum absolute value of periodic cross-correlation strictly lower than N and close to the well known lower bound SQRT(N). Moreover, we present a method to transform these perfect sequences into orthogonal sequences. A similar method is also proposed to obtain optimum bipolar codes derived from an alternative set of N2 perfect sequences.In the design of perfect sequences, the difficulty is to achieve both low cross-correlation and low peak-to-average power ratio (PAPR). Many of the proposed perfect DFT sequences should have low PAPR and thus can be applied in an OFDM–CDMA (Orthogonal Frequency-Division Multiplexing–Code Division Multiple Access) communication system or in a simple CDMA communication system. Alternatively, the proposed perfect DFT sequences may be useful for pre-coded mapping in OFDM communication systems or for the design of radar waveform diversity sets.

부분체를 이용한 비선형 수열의 상호상관관계의 효율적인 계산방법

Spreading sequence play an important role in wireless communications, such as in a CDMA(code division multiple access) communication system and multi-carrier spectrum communication system. Spreading sequences with low cross-correlation, in a direct-sequence spread spectrum communication system, help to minimize multiple access interference and to increase security degree of system. Analysis of cross-correlations between the sequences is a necessary process to design sequences. However it require lots of computing time for analysis of cross-correlations between sequences. In this paper we propose a method which is possible to compute effectively cross-correlation using subfield in the process of practical computation of cross-correlation between nonlinear binary sequences.