Binary Sequences Of Length Research Articles

Maximum length binary sequences and spectral power distribution of periodic signals

The maximum length binary sequence (MLBS) is widely used as a broadband pseudo-random noise excitation signal, for example, for system identification. Although its properties have been known for decades, misleading or inaccurate statements can be found in many references. For example, it is sometimes stated that the spectrum of the MLBS is white, whereas in other references a sinc behavior is stated. In this paper, we therefore analyze the MLBS properties based on precise definitions for the given context (time-discrete vs. time-continuous, periodic vs. non-periodic, etc.), especially with respect to Fourier analysis. Another difficulty arises from the fact that in the literature the mathematical definitions are often simplified by means of normalizations which makes the physical interpretation difficult. Therefore, special emphasis is put on scaling factors which allow such a physical interpretation.

Binary Sequences for Online Electrochemical Impedance Spectroscopy of Battery Cells

Online diagnostic of lithium-ion battery (LIB) cells may have significant impact on chemical energy storage systems. Electrochemical impedance spectroscopy (EIS) is widely used for the characterization of LIBs and could be the most appropriate technique for online diagnostic, but its response time should be shortened. This work investigates the usage of multisine excitation to shorten the measurement time and simplify the hardware implementation for EIS of battery cells. Two types of multisine binary sequences are considered: sigma–delta modulated multisine sequences (SDMSs) and maximum length binary sequences (MLBSs). Their applicability to online and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in situ</i> EIS monitoring is evaluated by designing a measurement architecture also suitable to be implemented in a system-on-chip. The calibrated measurement system is compared with a benchtop reference instrument, reporting an RMSE deviation smaller than 5% in the frequency range of interest 1–200 Hz. The realized system is then used for online monitoring of the discharge process of a commercial 18650 LIB cell. The two proposed sequences are compared in terms of accuracy using a digital battery emulator circuit. Both the sequences demonstrated to be suitable for fast measurement and simple hardware integration, enabling online <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in situ</i> EIS monitoring at cell level.

Distribution of the number of fitness maxima in Fisher’s geometric model

Fisher’s geometric model describes biological fitness landscapes by combining a linear map from the discrete space of genotypes to an n-dimensional Euclidean phenotype space with a nonlinear, single-peaked phenotype-fitness map. Genotypes are represented by binary sequences of length L, and the phenotypic effects of mutations at different sites are represented by L random vectors drawn from an isotropic Gaussian distribution. Recent work has shown that the interplay between the genotypic and phenotypic levels gives rise to a range of different landscape topographies that can be characterised by the number of local fitness maxima. Extending our previous study of the mean number of local maxima, here we focus on the distribution of the number of maxima when the limit L → ∞ is taken at finite n. We identify the typical scale of the number of maxima for general n, and determine the full scaled probability density and two point correlation function of maxima for the one-dimensional case. We also elaborate on the close relation of the model to the anti-ferromagnetic Hopfield model with n random continuous pattern vectors, and show that many of our results carry over to this setting. More generally, we expect that our analysis can help to elucidate the fluctuation structure of metastable states in various spin glass problems.

Cover times for Markov-generated binary sequences of length two

We derive explicit formulas for the expected cover time and cover time distribution for Markov-generated binary patterns of length two, including the special case of sequences of independent observations. We include links to output and coding for Mathematica and R simulations and calculations as appropriate.

On the Eigenvalues Distribution in Threshold Graphs

A threshold graph G of order n is defined by binary sequence of length n. In this paper, we consider the adjacent matrix of a connected threshold graph, and give the eigenvalues distribution in threshold graphs. Moreover, we pick out all the threshold graphs with distinct eigenvalues, and determine the HOMO–LUMO index of threshold graphs.

No threshold graphs are cospectral

A threshold graph G on n vertices is defined by binary sequence of length n. In this paper we present an explicit formula for computing the characteristic polynomial of a threshold graph from its binary sequence. Applications include obtaining a formula for the determinant of adjacency matrix of a threshold graph and showing that no two nonisomorphic threshold graphs are cospectral.

Finite length sequences with large nonlinear complexity

Finite length sequences with large nonlinear complexity over $\mathbb{Z}_{p}\, (p≥ 2)$ are investigated in this paper. We characterize all $p$-ary sequences of length $n$ having nonlinear complexity $n-j$ for $j=2, 3$, where $n$ is an integer satisfying $n≥ 2j$. For $n≥ 8$, all binary sequences of length $n$ with nonlinear complexity $n-4$ are obtained. Furthermore, the numbers and $k$-error nonlinear complexity of these sequences are completely determined, respectively.

Algorithm for Calculating the Exact Amount of n-bit Sequences with at Least One Run of Length k (k &amp;#8804; n)

A run of length k in a sequence of n bits (0, 1) is an equal bits string preceded or succeeded by a different bit (or none). In this paper a computational algorithm for calculating the exact amount of binary sequences of length n, containing at least one run of length k (k &#8804; n) is presented. The immediate application of this algorithm is to calculate the exact probability distribution of the number of n-bit sequences with containing at least one run of length k, and no one greater than k, for use for example as part of a test for randomness

Evaluation of Dead-Time Effect of Grid-Connected Inverters Using Broadband Methods

Power electronic inverters are devices that are used to interface renewables, such as photovoltaic panels or wind turbines, with the electrical power system. The inverter should control its output current to follow a sinusoidal reference to avoid distorting the voltage waveform of the power system. However, in real inverters dead-time is used in the control signals which causes unwanted harmonics, leading to lower power quality. The amount of harmonics is difficult to predict due to nonlinear nature of the dead-time. Moreover, the harmonic distortion depends on many variables, such as inverter control parameters and power system impedance. This paper shows that frequency response from inverter control signal (duty ratio) to grid current is linked to the detrimental dead-time effect and poor power quality. The frequency response is identified by perturbing the inverter control signal with a maximum length binary sequence (MLBS). The magnitude of the identified frequency response is shown to follow the same trend as the amount of current distortion. Therefore, the effect of dead-time on power quality could potentially be modeled using a linearized model allowing optimal control design in the presence of dead time.

M-Sequence Sensor and Continuous Basis Estimator for Wall Parameter Estimation Utilizing Through the Wall Sensing

Non-destructive estimation of the physical parameters of a medium is an important topic in sensing systems to characterize materials. It is also used in through-the-wall sensing to localize objects behind a medium. Achieving high accuracy and resolution using simple and cost-effective sensors are eminent points in this aim, which needs to note system design and signal processing categories. From the system viewpoint, using wideband signals can bring higher resolution, however, at the cost of more complexity of hardware. Although signal processing can be used to improve the resolution, since the estimation algorithms work on discrete grids, there will be a limited resolution defined by the sampling frequency. This paper provides an efficient approach from the viewpoints of system design and signal processing for low cost, accurate, and super resolution through the wall sensing. We have used maximum length binary sequence (M-sequence) as stimulus. After designing the sensor, a complementary algorithm based on continuous basis compressive time delay estimation is established to mitigate the imposed limitation by the data capturing unit. Our simulation and measurement results show that the proposed algorithm with the presented hardware can bring the unknown parameters of a sample of wall with an accuracy of more than 95% and with 50% improvement in the resolution of system. Furthermore, the distance of a metallic sheet placed behind the sample is also measured with an excellent accuracy of 95%.

Bounding the Peak Sidelobe Level of Binary Sequences of All Lengths

Improving upon 2010 results of Alon et al. , it was shown in 2014 by Schmidt that asymptotically, almost all binary sequences of length $n$ have peak sidelobe level close to $({2n\log n})^{1/2}\vphantom {\sum ^{R^{R}}}$ . One specific result of Alon et al. is that if we fix $ \varepsilon >0$ , then almost all binary sequences of length $n$ have peak sidelobe level at most $({2n(\log n-(1.5- \varepsilon )\log \log n)})^{1/2}$ , in the sense that the probability of not satisfying that bound approaches 0 as $n$ approaches infinity. In this note, we prove that for all sequence lengths $n>1$ , there is a binary sequence of length $n$ with peak sidelobe level at most $({2n(\log n-\log \log n+0.862)})^{1/2}$ .

Two constructions of binary sequences with optimal autocorrelation magnitude

In this Letter, two constructions of new binary sequences with optimal autocorrelation magnitude of length 4N derived from binary sequences with optimal autocorrelation of length N = 2 (mod 4) and almost-perfect binary sequences of length 2N using N × 2 interleaved structure is presented. The first construction is to use binary Sidelnikov sequences of length N = pn −1 whereas the second one is to use binary Ding–Helleseth–Martinsen sequences of length N = 2p. The obtained sequences have large linear complexity and can be used in communication and cryptography.

On pseudorandom binary sequences constructed by using finite fields

By using finite fields of order \(p^r\) with \(r \ge 2\) and their quadratic characters, Sarkozy and Winterhof presented a construction for binary sequences of length \(p^r\) with strong pseudorandom properties. In the special case \(r=2\) Gyarmati improved on their estimates for the pseudorandom measures of these sequences. Here we extend Gyarmati’s result and sharpen the estimates of Sarkozy and Winterhof for any prime power \(p^r\).

An Algorithmic Approach towards Construction of Long Binary Sequences using Modified Jacobi Sequences

Construction of long low autocorrelation binary sequences (LABS) is a complex process which involves many limitations. LABS have many practical applications. In pulse coding schemes, sequences with low autocorrelation side lobe energies are required to reduce the noise and to increase the capability of radars to detect multiple targets. In literature, numerous techniques were employed to solve the LABS problem. For short length sequences, search algorithms can be applied as the search space is manageable. But in our case of long length binary sequences, construction methods are suitable. The major limitations of search algorithms are time and computational power. DH Green [1] in their research utilized modified Jacobi sequences to construct merit factors for long binary sequences. In our case, we used the same construction methods and applied them to various search algorithms. We obtained better results with this implementation. We achieved a merit factor of 6.4534 whereas Green [1] managed to 5.99.

Time dependence of the time interval in distance/ intensity threshold in human listeners

The paper presents the distance threshold for complex virtual sounds localization in dependence of the time interval. The method of measurement was a forced-choice, three-down one-up staircase. The sound is a complex record of a click sound of 47 ms at 44.1 kHz measured by using a maximum length binary sequence in an anechoic chamber. The azimuth of the experimental is 0°, at the center of the human head where the ITD = 0, varying just the intensity. The investigation reported that the lowest distance thresholds of 0.06 m occurred for high inter click intervals at 200 ms–300ms. At lower ICIs, the distance threshold increases considerably. The experimental was carried out with the objective to find the distance threshold and time interval for implementing the data for a navigation device for blind people.

Real-Time MIMO Channel Sounder for Emulation of Distributed Ultrawideband Systems

This paper introduces an ultrawideband (UWB) channel sounding system. Its novel architecture allows real-time measurements of multiple time-variant radio propagation channels in different ultrawide frequency bands. Its architecture allows emulation of multiuser systems, sensor networks, localization systems, and distributed MIMO radar systems. The sounder uses a maximum length binary sequence (MLBS) excitation signal and correlation processing in the receiver. Its synchronous multichannel operation is supported by excellent timing stability and low power consumption of miniature size modules based upon custom integrated SiGe circuits. The paper describes the architecture, design, calibration, basic parameters, and application examples of the sounding system.

Some Notes on the Generalized Cyclotomic Binary Sequences of Length 2&lt;i&gt;p&lt;sup&gt;m&lt;/sup&gt;&lt;/i&gt; and &lt;i&gt;p&lt;sup&gt;m&lt;/sup&gt;&lt;/i&gt;

Some Notes on the Generalized Cyclotomic Binary Sequences of Length 2&lt;i&gt;p&lt;sup&gt;m&lt;/sup&gt;&lt;/i&gt; and &lt;i&gt;p&lt;sup&gt;m&lt;/sup&gt;&lt;/i&gt;

Basics of broadband impedance spectroscopy measurements using periodic excitations

Measuring the impedance frequency response of systems by means of frequency sweep electrical impedance spectroscopy (EIS) takes time. An alternative based on broadband signals enables the user to acquire simultaneous impedance response data collection. This is directly reflected in a short measuring time compared to the frequency sweep approach. As a result of this increase in the measuring speed, the accuracy of the impedance spectrum is compromised. The aim of this paper is to study how the choice of the broadband signal can contribute to mitigate this accuracy loss. A review of the major advantages and pitfalls of four different periodic broadband excitations suitable to be used in EIS applications is presented. Their influence on the instrumentation and impedance spectrum accuracy is analyzed. Additionally, the signal processing tools to objectively evaluate the quality of the impedance spectrum are described. In view of the experimental results reported, the impedance spectrum signal-to-noise ratio (SNRZ) obtained with multisine or discrete interval binary sequence signals is about 20–30 dB more accurate than maximum length binary sequence or chirp signals.

Perfect Secrecy Over Binary Erasure Wiretap Channel of Type II

We introduce a binary erasure wiretap channel of type II in which the number of eavesdropped bits μ becomes available a posteriori. We aim at achieving perfect secrecy over such a channel model. The most appropriate application is a secret key agreement scheme. We present a secret key agreement scheme that adopts the formulation S = HX of Wyner-Ozarows's linear coset coding. The scheme is based on the following simple observation: even if some information on a secret message leaked out, I(S; Xμ) >; 0, where Xμ is a binary sequence of length μ, it is still possible to have perfect secrecy I(SJ; Xμ) = 0 for some subsequence SJ of S. Our secret key agreement scheme achieves perfect secrecy by taking only those subsequences SJ that are independent of the eavesdropped bits Xμ. Our secret key agreement scheme naturally leads to defining a security measure DH(μ) for parity-check matrices such that the eavesdropper gets zero information on SJ as long as the length of SJ is less than DH(μ). We study basic properties of DH(μ) and prove the perfect secrecy of our key agreement scheme. For parity-check matrices of small sizes, we perform an exhaustive search for matrices maximizing DH(μ).

A Construction of Codebooks Associated With Binary Sequences

An (N, K) codebook is a set of N unit-norm code vectors in a K-dimensional vector space. For its applications, it is desired that the maximum magnitude of inner products between a pair of distinct code vectors should be as small as possible, meeting the Welch bound equality strictly or asymptotically. In this paper, an (N, K) codebook is constructed from a K × N partial matrix with K <; N, where each code vector is equivalent to a column of the matrix. To obtain the K × N matrix, K rows are selected from a J × N matrix Φ, associated with a binary sequence of length J and Hamming weight K, where a set of the selected row indices is equivalent to the index set of nonzero entries of the binary sequence. It is then discovered that the maximum magnitude of inner products between a pair of distinct code vectors is determined by the maximum magnitude of Φ-transform of the binary sequence. Thus, constructing a codebook with small magnitude of inner products is equivalent to finding a binary sequence where the maximum magnitude of its Φ-transform is as small as possible. From the discovery, new classes of codebooks with nontrivial bounds on the maximum inner products are constructed from Fourier and Hadamard matrices associated with binary sequences.