Spread Code Division Multiple Access Research Articles

A class of nearly optimal codebooks and their applications in strongly regular Cayley graphs

<abstract><p>Codebooks with small inner-product correlations are desirable in many fields, including compressed sensing, direct spread code division multiple access (CDMA) systems, and space-time codes. The objective of this paper is to present a class of codebooks and explore their applications in strongly regular Cayley graphs. The obtained codebooks are nearly optimal in the sense that their maximum cross-correlation amplitude nearly meets the Welch bound. As far as we know, this construction of codebooks provides new parameters.</p></abstract>

Concatenative Complete Complementary Code Division Multiple Access and Its Fast Transform

Over multipath channels, complete complementary code division multiple access and convolutional spreading code division multiple access provide inter-channel interference free transmission with an enhanced spectral efficiency. However, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">convolutional spreading</i> (CS) operation of the systems is computationally complex and involves a high peak-to-average power ratio. To address such issues, we propose the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">concatenative complete complementary code</i> (CCCC) division multiple access, named (CCC-CDMA). Since the CCCCs can be generated from the rows of the Walsh-Hadamard or discrete Fourier transform matrices, the CS operation can be implemented using corresponding fast transforms to reduce computational complexity. Simulation results show that the enlargement of the spreading factor strengthens the robustness against clipping noise. The binary CCCC generated by Walsh-Hadamard matrix exhibited excellent robustness against Doppler frequency shifts.

New Constructions of Codebooks Nearly Meeting the Welch Bound

Optimal codebooks meeting the Welch bound with equality are desirable in many areas, such as direct spread code division multiple access communications, compressed sensing and so on. However, it is difficult to construct such optimal codebooks. There have been a number of attempts to construct codebooks nearly meeting the Welch bound. In this paper, we introduce a generic construction of codebooks using generalized bent functions from [Formula: see text] to [Formula: see text], where [Formula: see text] is a prime and [Formula: see text] is a positive integer with [Formula: see text]. With this construction, we obtain two new families of codebooks nearly meeting the Welch bound. These codebooks have new parameters and could have a small alphabet size. In particular, a class of regular generalized bent functions from [Formula: see text] to [Formula: see text] is presented.

Asymptotically Optimal Codebooks Derived From Generalised Bent Functions

Codebooks are required to have small inner-product correlation in many practical applications, such as direct spread code division multiple access communications, space-time codes and compressed sensing. In general, it is difficult to construct optimal codebooks. In this paper, two kinds of codebooks are presented and proved to be optimally optimal with respect to the Welch bound. Additionally, the constructed codebooks in this paper have new parameters.

Codebooks from generalized bent [formula omitted]-valued quadratic forms

Codebooks with small inner-product correlation have applications in unitary space–time modulations, multiple description coding over erasure channels, direct spread code division multiple access communications, compressed sensing, and coding theory. It is interesting to construct codebooks (asymptotically) achieving the Levenshtein bound. This paper presents a class of generalized bent Z4-valued quadratic forms, which contains functions proposed by Heng and Yue (2017). Using these generalized bent Z4-valued quadratic forms, we construct optimal codebooks achieving the Levenshtein bound. These codebooks have parameters (22m+2m,2m) and alphabet size 6.

A further construction of asymptotically optimal codebooks with multiplicative characters

Codebooks with small inner-product correlation are preferred in many practical applications such as direct spread code division multiple access communications, coding theory, compressed sensing and so on. Heng et al. (IEEE Trans Inf Theory 63(10):6179–6187, 2017), Heng (Discrete Appl Math 250:227–240, 2018) and Luo and Cao (IEEE Trans Inf Theory 64(10):6498–6505, 2018) proposed constructions of asymptotically optimal codebooks via character sums related to Jacobi sums. In this paper, we mainly present a further generalization of the work by Heng (2018). The construction in this paper is an extension and generalization of the above works, and deduces a class of asymptotically optimal codebooks. Furthermore, the parameters of the codebooks are flexible and new.

Constructions of Codebooks Asymptotically Achieving the Welch Bound With Additive Characters

Codebooks with small inner product correlation have wide applications in many fields, such as direct spread code-division multiple access communications, signal processing, and compressed sensing. It is extremely hard to produce optimal codebooks with respect to the Welch bound or the Levenstein bound. This letter focuses on constructing asymptotically optimal codebooks with additive characters of finite fields. Following the proposed constructions, two classes of asymptotically optimal codebooks with respect to the Welch bound are obtained. In addition, the resulting codebooks could have a small alphabet size.

Tutorial: GPS receiver architectures, front-end and baseband signal processing

This tutorial provides an overview of the hardware architectures and signal processing that form the core of satellite-based navigation receivers such as GPS. The concepts of spread spectrum and code division multiple access are introduced along with their roles in signal acquisition and tracking. The super-heterodyne front-end architecture will be described as well as the baseband architecture that utilizes in-phase and quadrature processing. Tracking loops are discussed along with measurement generation. The tutorial concludes with a brief look at so-called modernized satellite-based navigation signals.

Two constructions of asymptotically optimal codebooks

Codebooks with low-coherence have wide applications in many fields such as direct spread code division multiple access communications, compressed sensing, signal processing and so on. In this paper, we propose two constructions of complex codebooks from the operations of certain sets. The complex codebooks produced by these constructions are proved to be asymptotically optimal with respect to the Welch bound. In addition, the parameters of the complex codebooks presented in this paper are new and flexible in some cases.

Two Constructions of Asymptotically Optimal Codebooks via the Hyper Eisenstein Sum

Codebooks with low-coherence have wide utilization in many fields, such as direct spread code division multiple access communications, compressed sensing and so on. There are two major ingredients in this paper. The first is to present a new character sum, the hyper Eisenstein sum and study the properties of this character sum. As an application, the second ingredient is to propose two constructions of codebooks with the hyper Eisenstein sum. The codebooks generated by these constructions asymptotically meet the Welch bound. The parameters of these codebooks are new.

Nearly optimal codebooks based on generalized Jacobi sums

Codebooks with small inner-product correlation are applied in many practical applications including direct spread code division multiple access (CDMA) communications, space–time codes and compressed sensing. It is extremely difficult to construct codebooks achieving the Welch bound or the Levenshtein bound. Constructing nearly optimal codebooks such that the ratio of its maximum cross-correlation amplitude to the corresponding bound approaches 1 is also an interesting research topic. In this paper, we firstly study a family of interesting character sums called generalized Jacobi sums over finite fields. Then we apply the generalized Jacobi sums and their related character sums to obtain two infinite classes of nearly optimal codebooks with respect to the Welch or Levenshtein bound. The codebooks can be viewed as generalizations of some known ones and contain new ones with very flexible parameters.

New Constructions of Asymptotically Optimal Codebooks With Multiplicative Characters

In practical applications, such as direct spread code division multiple access communications, space-time codes and compressed sensing, and codebooks with small inner-product correlation are required. It is extremely difficult to construct codebooks achieving the Levenshtein bound. In this paper, two new constructions of infinitely many codebooks with multiplicative characters of finite fields are presented. These constructions produce complex codebooks asymptotically achieving the Levenshtein bound and codebooks asymptotically achieving the Welch bound. The codebooks presented in this paper have new parameters.

Signature Design of Sparsely Spread Code Division Multiple Access Based on Superposed Constellation Distance Analysis

Sparsely spread code division multiple access (SCDMA) is a non-orthogonal superposition coding scheme that allows concurrent communications between a base station and multiple users over a common channel. However, the detection performance of an SCDMA system is mainly determined by its signature matrix, which should be sparse to facilitate the belief propagation (BP) detection. On the other hand, to guarantee good maximum likelihood (ML) detection performance, the minimum Euclidean distance for the equivalent signal constellation after multi-user superposition should be maximized. In this paper, a code distance analysis is proposed for SCDMA systems with a finite number of users and spreading lengths. Based on this analysis, good signature matrices whose factor graphs have very few short cycles and possess large superposed signal constellation distances are designed. The proposed signature matrices have both good BP and ML detection performances. Moreover, their BP detection performances exactly converge to their ML detection performances with few iterations. It is worth pointing out that the proposed signature matrix design could be directly applied to the 5G non-orthogonal multiple access systems.

A Construction of Codebooks Nearly Achieving the Levenstein Bound

Codebooks with small inner-product correlation are preferred in many practical applications such as direct spread code division multiple access communications, coding theory, and compressed sensing. The well-known Welch bound and Levenstein bound are useful benchmarks for the correlation of codebooks. In general, it is very hard to obtain codebooks achieving the Welch bound or the Levenstein bound. The objective of this letter is to present a construction of codebooks based on additive and multiplicative characters of finite fields. It generates codebooks nearly achieving the Levenstein bound.

On Optimum Asymptotic Multiuser Efficiency of Randomly Spread CDMA

We extend the result by Tse and Verdu on the optimum asymptotic multiuser efficiency of randomly spread code division multiple access (CDMA) with binary phase shift keying input. Random Gaussian and random binary antipodal spreading are considered. We obtain the optimum asymptotic multiuser efficiency of a $K$ -user system with spreading gain $N$ when $K$ and $N\rightarrow \infty $ and the loading factor, $({K}/{N})$ , grows logarithmically with $K$ under some conditions. It is shown that the optimum detector in a Gaussian randomly spread CDMA system has a performance close to the single user system at high signal-to-noise ratio when $K$ and $N\rightarrow \infty $ and the loading factor, $({K}/{N})$ , is kept less than $({\log _{3}K}/{2})$ . Random binary antipodal matrices are also studied and a lower bound for the optimum asymptotic multiuser efficiency is obtained. Furthermore, we investigate the connection between detecting matrices in the coin weighing problem and optimum asymptotic multiuser efficiency. We obtain a condition such that for any binary input, an $N \times K$ random matrix, whose entries are chosen randomly from a finite set, is a detecting matrix as $K$ and $N\rightarrow \infty $ .

A Digital Watermarking Algorithm Based on CDMA and HVS

Digital watermarking technology is an effective means to resolve problems on information security and copyright protection for digital media. The paper introduces CDMA (Code Division Multiple Access) to digital watermarking and proposes a digital watermarking algorithm for grayscale images based on CDMA and HVS (Human Visual System). The algorithm has adopted CDMA spread spectrum technology to orthogonalize the watermark to enhance security and considered human visual system when watermarks are embedded into the original images. Experiments have shown that the watermark can achieve invisibility and the algorithm is effective and robust.

Performance Improvement of Iterative Multiuser Detection for Large Sparsely Spread CDMA Systems by Spatial Coupling

Kudekar et al. proved that the belief-propagation (BP) performance for low-density parity check (LDPC) codes can be boosted up to the maximum-a-posteriori (MAP) performance by spatial coupling. In this paper, spatial coupling is applied to sparsely-spread code-division multiple-access (CDMA) systems to improve the performance of iterative multiuser detection based on BP. Two iterative receivers based on BP are considered: One receiver is based on exact BP and the other on an approximate BP with Gaussian approximation. The performance of the two BP receivers is evaluated via density evolution (DE) in the dense limit after taking the large-system limit, in which the number of users and the spreading factor tend to infinity while their ratio is kept constant. The two BP receivers are shown to achieve the same performance as each other in these limits. Furthermore, taking a continuum limit for the obtained DE equations implies that the performance of the two BP receivers can be improved up to the performance achieved by the symbol-wise MAP detection, called individually-optimal detection, via spatial coupling. Numerical simulations show that spatial coupling can provide a significant improvement in bit error rate for finite-sized systems especially in the region of high system loads.

ANALYSIS OF THE SEQUENCES WITH OPTIMAL CROSS-CORRELATION PROPERTY

The design of large family size with the optimal cross-correlation property is important in spread spectrum and code division multiple access communication systems. In this paper we present the sequences with the decimation $d

The Assignment of CDMA Spreading Codes Constructed from Hadamard Matrices and Almost Bent Functions

Almost bent functions and Hadamard matrices can be used to construct spreading codes for code-division multiple-access (CDMA) systems. Four specific Hadamard matrices can be constructed and each one can be divided into eight octants in such a way that spreading codewords from certain pairs of octants have zero correlation. It is possible to assign these octants to a regular tessellation of hexagonal cells in such a way that there is zero correlation between adjacent cells, small correlation between non-adjacent cells and a large codeword re-use distance. If synchronous CDMA is used in a satellite system, interference is reduced in comparison with the use of a single Hadamard matrix. In this case the regular hexagonal tessellation is usually a good model of the areas covered by satellite spot beams. The same approach can be advantageous when the Hadamard matrices are used to construct loosely synchronized codes for a terrestrial system. The tessellation of cells is unlikely to be a regular hexagonal tessellation and the question arises of whether an assignment to an irregular tessellation with these properties can be found. In this paper a positive answer is given to this question, confirming that the approach is applicable to a terrestrial system.

Combined code reuse scheme with two‐dimensional OVSF codes assignment algorithm for uplink multi‐user/multi‐rate block spread multi‐cellular CDMA

ABSTRACTThe two‐dimensional (2D) block spread code division multiple access (CDMA) can avoid the uplink multiple‐access interference with low‐complexity single‐user detection in a slow fading channel and, therefore, is very attractive. In the 2D spreading, orthogonal variable spreading factor (OVSF) is used for spreading; an important problem is how to efficiently assign the limited resource of OVSF codes to users with different data rates, while meeting the requirement of quality of service in a multi‐cell environment. In this paper, it is shown that the code reuse can improve the code reuse efficiency and the proposed code reuse scheme combined with code assignment algorithm can allow flexible multi‐rate uplink transmission. The computer simulation confirms that the proposed code assignment algorithm improves the code reuse efficiency while achieving lower blocking probability than traditional CDMA. Copyright © 2012 John Wiley &amp; Sons, Ltd.