Set Of Orthogonal Sequences Research Articles

FPGA implementation of orthogonal hyperchaotic sequences generator based on the CNN: application in multi-user chaotic communications

In this article, we propose an efficient orthogonal hyperchaotic sequences generator for application in multi-user chaotic communication systems. The proposed generator consists of two blocks. The first block generates binary hyperchaotic sequences of varying lengths using a 6-Dimensional Cellular Neural Network (CNN) system, offering a wide range of sequence length choices. The second block uses an optimized selection method to generate multiple sets of orthogonal sequences with interesting correlation properties. The method is based on the balance and correlation properties, where zero cross-correlation between any two sequences is considered. A FPGA-based implementation of the proposed generator is presented. The hardware architecture is designed in VHDL and deployed on a Xilinx Virtex-6 FPGA ML605 evaluation kit. The generator is then analyzed and compared with the existing generator in terms of logic area consumption, throughput, latency, and randomness quality. The comparative analysis results show the effectiveness of the proposed generator, which can achieve a high throughput, low latency, and successfully pass all NIST statistical tests. Moreover, the generated orthogonal hyperchaotic sequences exhibit promising performance in a multi-user Differential Chaos Shift Keying (MU-DCSK) system, outperforming the Walsh-Hadamard sequences in terms of bit-error rate under various channel conditions.

Suppressing high-dimensional crystallographic defects for ultra-scaled DNA arrays

While DNA-directed nano-fabrication enables the high-resolution patterning for conventional electronic materials and devices, the intrinsic self-assembly defects of DNA structures present challenges for further scaling into sub-1 nm technology nodes. The high-dimensional crystallographic defects, including line dislocations and grain boundaries, typically lead to the pattern defects of the DNA lattices. Using periodic line arrays as model systems, we discover that the sequence periodicity mainly determines the formation of line defects, and the defect rate reaches 74% at 8.2-nm line pitch. To suppress high-dimensional defects rate, we develop an effective approach by assigning the orthogonal sequence sets into neighboring unit cells, reducing line defect rate by two orders of magnitude at 7.5-nm line pitch. We further demonstrate densely aligned metal nano-line arrays by depositing metal layers onto the assembled DNA templates. The ultra-scaled critical pitches in the defect-free DNA arrays may further promote the dimension-dependent properties of DNA-templated materials.

Phase orthogonal sequence sets for (QS)CDMA communications

Phase orthogonal sequence sets for (QS)CDMA communications

Construction and Assignment of Orthogonal Sequences and Zero Correlation Zone Sequences Over GF(p)

Orthogonal sequences can be assigned to a regular tessellation of hexagonal cells, typical for synchronised code-division multiple-access (S-CDMA) systems. The sequences within any cell should both be orthogonal in the adjacent cells and require a sufficient number of users in each cell. However, for binary sequences, the capacity of communication system is limited. So, a new family of non-binary orthogonal sequences is constructed, which has more sequences per cell than binary sequences in the network. Next, an efficient assignment of these orthogonal sequence sets to a regular tessellation of hexagonal cells is given, and also the sequence sets have large re-use distance. Finally, based on above the construction, we construct a family of orthogonal sequences with zero correlation zone (ZCZ) property which can reduce the interference among users in a multi-path environment. The constructed ZCZ sequences can be applied to the quasi-synchronous CDMA (QS-CMDA) spread spectrum systems. And the assignment of sequences has the same re-use distance.

Sequential Pull-Down Purification of DNA Origami Superstructures.

Higher-order superstructures of individual DNA origami building blocks are frequently used in DNA nanotechnology in order to increase the structure dimensions and complexity. Here, a purification method is presented to specifically enrich a fully assembled superstructure out of an excess of substructures. The approach is based on pull-down reactions with magnetic beads, where superstructures are captured via an anchor strand on a specific terminus and then become separated from terminus-free structures. By carrying out several pull-down reactions sequentially on different termini, the full superstructures that possess all termini become finally enriched. The approach is demonstrated by purifying linear origami superstructures with up to nine monomers by two-sided pull-down reactions and a T-shaped superstructure in a three-sided pull-down reaction. In all cases, high recovery yields and purities are obtained. A crucial prerequisite for the sequential pull-down scheme is the establishment of highly specific, orthogonal sequence sets for capture, and anchor strands. It is expected that the introduced approach provides a useful and universal method to purify complex DNA origami superstructures with high specificity and yield and this way allows the massive parallel fabrication of nanostructures at high homogeneity.

Enhanced Channel Estimation in Massive MIMO via Coordinated Pilot Design

Pilot contamination is a limiting factor in multicell massive multiple-input multiple-output (MIMO) systems because it can severely impair channel estimation. Prior works have suggested coordinating pilot design across cells in order to reduce the channel estimation error caused by pilot contamination. In this paper, we propose a method for coordinated pilot design using fractional programming to minimize the weighted mean squared-error (MSE) in channel estimation. In particular, we apply the recently proposed quadratic transform to the MSE expression which allows the effect of pilot contamination to be decoupled. The resulting problem reformulation enables the pilots to be optimized in closed form if they can be designed arbitrarily. When the pilots are restricted to a given set of orthogonal sequences, pilot optimization reduces to an assignment problem which can be solved by weighted bipartite matching. Furthermore, we consider the max-min fairness of data rates with orthogonal pilots and obtain an extension of the proposed method to correlated Rayleigh fading. Finally, simulations demonstrate the advantage of the proposed (orthogonal and nonorthogonal) pilot designs as compared with state-of-the-art methods in combating pilot contamination.

Generation of Orthogonal Sequence Sets for M-ary Spread Spectrum Communications with OFDM Modulation

The number of orthogonal sequences is a key point of M-ary spread spectrum (MSS) communication system since more sequences mean higher data rate. When orthogonal frequency division multiplexing (OFDM) modulation is used into MSS system, the additional low peak-to-average power ratio (PAPR) property is required due to high power efficiency. Based on the segmentation-shift operation, multiple orthogonal sequence sets with the same size and sequence length are generated in this paper. By combining these orthogonal sequence sets, the number of the generated orthogonal sequences is very large. For any two orthogonal sequence sets, there exists good cross-correlation performance between them at zero shift. In addition to large set size and good correlation property, the generated multiple orthogonal sequence sets possess low PAPR, which is very suitable for OFDM modulation. The generation algorithm of multiple orthogonal sequence sets is provided in this paper, and the corresponding simulation results show the effectiveness of the provide method.

New Orthogonal Binary Sequences Using Quotient Rings Z/<i>n</i>Z Where <i>n</i> Is a Multiple of Some Prime Numbers

Orthogonal Sequences (as M-Sequences, Walsh Sequences,…) are used widely at the forward links of communication channels to mix the information on connecting to and at the backward links of these channels to sift through this information is transmitted to reach the receivers this information in a correct form, especially in the pilot channels, the Sync channels, and the Traffic channel. This research is useful to generate new sets of orthogonal sequences (with the bigger lengths and the bigger minimum distance that assists to increase secrecy of these information and increase the possibility of correcting mistakes resulting in the channels of communication) from quotient rings Z/nZ, where Z is the integers and n is not of the form pm, where p is prime, replacing each event number by zero and each odd number by one, also, the increase in the natural number does not necessarily lead to an increase in the size of the biggest orthogonal set in the corresponding quotient ring. The length of any sequence in a biggest orthogonal set in the quotient ring Z/nZ is n and the minimum distance is between (n-3)/2 and (n-1)/2 and the sequences can be used as keywords or passwords for secret messages.

Uplink Interference Suppression by Semi-Blind Adaptive Array With Decision Feedback Channel Estimation on Multicell Massive MIMO Systems

This paper proposes a novel semi-blind uplink interference suppression scheme for multicell multiuser massive multiple-input multiple-output (MIMO) systems. The inter-cell interference (ICI) becomes intenser when a number of users are spatially multiplexed via massive MIMO. Here arises a pilot contamination problem due to the limitation of orthogonal sequence set and thus inter-user interference (IUI) also remains unsuppressed. Our proposal employs a constant modulus algorithm (CMA) known as a blind interference suppression scheme and exploits channel state information (CSI)-aided minimum mean square error (MMSE) postcoding weight as an initial weight of CMA. Although MMSE weight cannot suppress ICI and IUI due to the pilot contamination, it can help subsequent CMA to capture the desired signals which is required for CMA to effectively work. Since CMA can fully exploit degree of freedom of massive arrays by using uncorrelated data signal part, derived weight successfully suppresses ICI/IUI while resolving the pilot contamination problem. A decision feedback channel estimation (DFCE) is then introduced to further improve CSI estimation accuracy and subsequent interference suppression performance. A series of signal processing, MMSE–CMA–DFCE, can be iteratively performed. The computer simulation reveals that our proposal can improve outage probability and it satisfies below the fifth percentile of cumulative distribution with saved symbol amount.

Generating New Orthogonal Binary Sequences Using Quotient Rings Z/pm Z

Orthogonal Sequences (as M-Sequences, Walsh Sequences, …) are used widely at the forward links of communication channels to mix the information on connecting to and at the backward links of these channels to sift through this information is transmitted to reach the receivers this information in a correct form, especially in the pilot channels, the Sync channels, and the Traffic channel. This research is useful to generate new sets of orthogonal sequences (with the bigger lengths and the bigger minimum distance that assists to increase secrecy of these information and increase the possibility of correcting mistakes resulting in the channels of communication) from quotient rings Z/pmZ, where Z is the integers and p is prime, replacing each event number by zero and replacing each odd number by one.

Hamming Distance as a Concept in DNA Molecular Recognition

DNA microarrays constitute an in vitro example system of a highly crowded molecular recognition environment. Although they are widely applied in many biological applications, some of the basic mechanisms of the hybridization processes of DNA remain poorly understood. On a microarray, cross-hybridization arises from similarities of sequences that may introduce errors during the transmission of information. Experimentally, we determine an appropriate distance, called minimum Hamming distance, in which the sequences of a set differ. By applying an algorithm based on a graph-theoretical method, we find large orthogonal sets of sequences that are sufficiently different not to exhibit any cross-hybridization. To create such a set, we first derive an analytical solution for the number of sequences that include at least four guanines in a row for a given sequence length and eliminate them from the list of candidate sequences. We experimentally confirm the orthogonality of the largest possible set with a size of 23 for the length of 7. We anticipate our work to be a starting point toward the study of signal propagation in highly competitive environments, besides its obvious application in DNA high throughput experiments.

Large Sets of Orthogonal Sequences Suitable for Applications in CDMA Systems

In this paper, we employ the so-called semi-bent functions to achieve significant improvements over currently known methods regarding the number of orthogonal sequences per cell that can be assigned to a regular tessellation of hexagonal cells, typical for certain code-division multiple-access (CDMA) systems. Our initial design method generates a large family of orthogonal sets of sequences derived from vectorial semi-bent functions. A modification of the original approach is proposed to avoid a hard combinatorial problem of allocating several such orthogonal sets to a single cell of a regular hexagonal network, while preserving the orthogonality to adjacent cells. This modification increases the number of users per cell by starting from shorter codewords and then extending the length of these codewords to the desired length. The specification and assignment of these orthogonal sets to a regular tessellation of hexagonal cells have been solved regardless of the parity and size of $m$ (where $2^m$ is the length of the codewords). In particular, when the re-use distance is $D=4$ the number of users per cell is $2^{m-2}$ for almost all $m$, which is twice as many as can be obtained by the best known methods.

A General Construction of OVSF Codes With Zero Correlation Zone

In this letter, a general construction of orthogonal variable spreading factor (OVSF) codes with zero correlation zone (ZCZ) property is presented based on orthogonal sequence sets and -complementary sets. It is shown that the proposed general construction includes the conventional binary and ternary OVSF codes as special cases and can accommodate more flexible rate assignment in direct sequence code division multiple access (DS-CDMA) systems.

On the Performance of Chaos-Based Multicode DS-CDMA Systems

Multicode DS-CDMA systems assign more than one spreading sequence to each of the users. In these systems multiple access interference (MAI) is made of a synchronous and an asynchronous component. It is well known that asynchronous MAI alone can be minimized by means of chaos-based spreading. Here we address the trade-off between synchronous and asynchronous MAI by tuning the autocorrelation profile of the chaosbased spreading codes. Improvements in the number of users allowed in the system is demonstrated in certain load conditions with respect to the classical approach of providing each user with a set of orthogonal sequences taken from an i.i.d. process.

UCHT-based complex sequences for asynchronous CDMA system

The use of orthogonal spreading codes has attracted much attention due to their ability to suppress interference from other users, compared with the nonorthogonal sequences in the synchronous case. In this paper, new sets of orthogonal sequences derived from the unified complex Hadamard transforms (UCHTs) are investigated. Various correlation properties of the sequences are mathematically derived and analyzed. It is shown that some UCHT sequences provide better autocorrelation properties than orthogonal Walsh-Hadamard sequences. Performance comparisons between UCHT sequences, Gold, small set of Kasami, and m-sequences show that some UCHT sequences outperform these well-known spreading sequences under simulation of systems in the presence of multiple access interference and additive white Gaussian noise.

Spectral efficiency of the feedback receiver for two sets of orthogonal sequences

We present the spectral efficiency analysis of the recently proposed feedback receiver for two sets of orthogonal sequences (TSOS) scheme which is capable of supporting higher number of users than the spreading gain of the DS/CDMA system. The added complexity is minimal compared to the conventional matched filter. We show that in the case of coded system, spectral efficiency of this scheme is close to that of a Gaussian multiple access channel if the incomplete group of orthogonal sequences is detected first. We also discuss the choice of orthogonal sequences that maximizes the spectral efficiency. This analysis is extended for the case of flat fading channels.

A technique for deriving sets of orthogonal sequences from binary parents which preserves auto-correlation properties

Binary-valued Barker sequences have close to ideal autocorrelation (AC) properties but are extremely rare. The 11-chip Barker sequence is fundamental to the performance of the IEEE 802.11 WLAN standard. This letter presents a method of deriving new sets of sequences from a binary parent using a generalization of the technique derived previously by the author (see IEEE Trans. Commun., vol.45, p.1379-80, Nov. 1997). The method maintains the AC properties of the original binary source and can be used to produce sequence sets orthogonal to the original. This technique is applied to produce orthogonal sets of sequences with Barker-like AC properties.

Residue number system-based multicarrier CDMA system for high-speed broadband wireless access

This correspondence is concerned with a new method to enhance the bandwidth efficiency of a multicarrier CDMA system by using a residue number based representation for information symbols. The residues are mapped into a set of orthogonal sequences and are transmitted in parallel. A new modulation scheme is proposed to increase the data rate further by combining residue number representation, PSK/QAM modulation, orthogonal spreading and multicarrier modulation. The performance of the proposed system is evaluated in a frequency selective Rayleigh fading channel via extensive simulations. The present correspondence discusses the design issues associated with the system together with the performance results.

Iterative construction of optimum signature sequence sets in synchronous CDMA systems

Optimum signature sequence sets that maximize the capacity of single-cell synchronous code division multiple access (CDMA) systems have been identified. Optimum signature sequences minimize the total squared correlation (TSC); they form a set of orthogonal sequences, if the number of users is less than or equal to the processing gain, and a set of Welch (1994) bound equality (WBE) sequences, otherwise. We present an algorithm where users update their transmitter signature sequences sequentially, in a distributed fashion, by using available receiver measurements. We show that each update decreases the TSC of the set, and produces better signature sequence sets progressively. We prove that the algorithm converges to a set of orthogonal signature sequences when the number of users is less than or equal to the processing gain. We observe and conjecture that the algorithm converges to a WBE set when the number of users is greater than the processing gain. At each step, the algorithm replaces one signature sequence from the set with the normalized minimum mean squared error (MMSE) receiver corresponding to that signature sequence. Since the MMSE filter can be obtained by a distributed algorithm for each user, the proposed algorithm is amenable to distributed implementation.

Method for generating sets of orthogonal sequences

A new, systematic method of generating orthogonal sets of sequences with good correlation properties is described. An orthogonal set is defined as a collection of n sequences, of length n chips, that are mutually orthogonal. Although there are many possible orthogonal sets of a specified length, few have been identified with a structured method of generation such as Walsh codes and orthogonal Gold codes.