Frequency Permutation Research Articles

MHTFPE2D: two-dimensional multi-scale hierarchical time–frequency permutation entropy for complexity measurement

MHTFPE2D: two-dimensional multi-scale hierarchical time–frequency permutation entropy for complexity measurement

Frequency Permutation Subsets for Joint Radar and Communication

Frequency Permutation Subsets for Joint Radar and Communication

Bit Modulated Frequency Permutation Waveforms for Joint Communications and Radar

Bit Modulated Frequency Permutation Waveforms for Joint Communications and Radar

Combined Radar and Communications With Phase-Modulated Frequency Permutations

This paper focuses on the combined radar and communications problem and conducts a thorough analytical investigation on the effect of phase and frequency change on the communication and sensing functionality. First, we consider the classical stepped frequency radar waveform and modulate data using M-ary phase shift keying (MPSK). Two important analytical tools in radar waveform design, namely the ambiguity function (AF) and the Fisher information matrix (FIM) are derived, based on which, we make the important conclusion that MPSK modulation has a negligible effect on radar local accuracy. Next, we extend the analysis to incorporate frequency permutations and propose a new signalling scheme in which the mapping between incoming data and waveforms is performed based on an efficient combinatorial transform called the Lehmer code. We also provide an efficient communications receiver based on a modified Hungarian algorithm. From the communications perspective, we consider the optimal maximum likelihood (ML) detector and derive the union bound and nearest neighbour approximation on the block error probability. From the radar sensing perspective, we discuss the broader structure of the waveform based on the AF derivation and quantify the radar local accuracy based on the FIM. Extensive numerical examples are provided to illustrate the accuracy of our results.

Frequency Permutations for Joint Radar and Communications

This paper presents a new joint radar and communication technique based on the classical stepped frequency radar waveform. The randomization in the waveform, which is achieved by using permutations of the sequence of frequency tones, is utilized for data transmission. A new signaling scheme is proposed in which the mapping between incoming data and waveforms is performed based on an efficient combinatorial transform called the Lehmer code. Considering the optimum maximum likelihood detection, the union bound and the nearest neighbour approximation on the communication block error probability is derived for communication in an additive white Gaussian noise channel. The results are further extended to incorporate the Rician fading channel model, of which the Rayleigh fading channel is presented as a special case. Furthermore, an efficient communication receiver implementation is discussed based on the Hungarian algorithm which achieves optimum performance with much less operational complexity when compared to an exhaustive search. From the radar perspective, two key analytical tools, namely, the ambiguity function and the Fisher information matrix are derived. Furthermore, accurate approximations to the Cramer-Rao lower bounds on the delay and Doppler estimation errors are derived based on which the range and velocity estimation accuracy of the waveform is analysed.

DOA-guided source separation with direction-based initialization and time annotations using complex angular central Gaussian mixture models

By means of spatial clustering and time-frequency masking, a mixture of multiple speakers and noise can be separated into the underlying signal components. The parameters of a model, such as a complex angular central Gaussian mixture model (cACGMM), can be determined based on the given signal mixture itself. Then, no misfit between training and testing conditions arises, as opposed to approaches that require labeled datasets to be trained. Whereas the separation can be performed in a completely unsupervised way, it may be beneficial to take advantage of a priori knowledge. The parameter estimation is sensitive to the initialization, and it is necessary to address the frequency permutation problem. In this paper, we therefore consider three techniques to overcome these limitations using direction of arrival (DOA) estimates. First, we propose an initialization with simple DOA-based masks. Secondly, we derive speaker specific time annotations from the same masks in order to constrain the cACGMM. Thirdly, we employ an approach where the mixture components are specific to each DOA instead of each speaker. We conduct experiments with sudden DOA changes, as well as a gradually moving speaker. The results demonstrate that particularly the DOA-based initialization is effective to overcome both of the described limitations. In this case, even methods based on normally unavailable oracle information are not observed to be more beneficial to the permutation resolution or the initialization. Lastly, we also show that the proposed DOA-guided source separation works quite robustly in the presence of adverse conditions and realistic DOA estimation errors.

Entropy Analysis of Neonatal Electrodermal Activity during the First Three Days after Birth

The entropy-based parameters determined from the electrodermal activity (EDA) biosignal evaluate the complexity within the activity of the sympathetic cholinergic system. We focused on the evaluation of the complex sympathetic cholinergic regulation by assessing EDA using conventional indices (skin conductance level (SCL), non-specific skin conductance responses, spectral EDA indices), and entropy-based parameters (approximate, sample, fuzzy, permutation, Shannon, and symbolic information entropies) in newborns during the first three days of postnatal life. The studied group consisted of 50 healthy newborns (21 boys, average gestational age: 39.0 ± 0.2 weeks). EDA was recorded continuously from the feet at rest for three periods (the first day—2 h after birth, the second day—24 h after birth, and the third day—72 h after birth). Our results revealed higher SCL, spectral EDA index in a very-low frequency band, approximate, sample, fuzzy, and permutation entropy during the first compared to second and third days, while Shannon and symbolic information entropies were lower during the first day compared to other periods. In conclusion, EDA parameters seem to be sensitive in the detection of the sympathetic regulation changes in early postnatal life and which can represent an important step towards a non-invasive early diagnosis of the pathological states linked to autonomic dysmaturation in newborns.

Quantizing the propagated field through a dielectric including general class of permutation symmetries for nonlinear susceptibility tensors

In this paper, we present a quantum theory for field propagation through a three-dimensional dielectric, when the frequency permutations of nonlinear susceptibility tensors should not be ignored. This treatment is important for the processes in which multiple frequencies are generated. The Hamiltonian of our system is obtained by introducing a unique Lagrangian and making use of the dual potential. This system is quantized by imposing the Dirac commutation relations. Finally, appropriate creation and annihilation operators are defined to derive the nonlinear Hamiltonian operator under frequency permutations of the nonlinear susceptibility tensors. As an example, our simulation results show the impact of frequency permutations on pulse propagation along a one-dimensional simple waveguide.

Increasing the Minimum Distance of Codes by Twisting

Twisted permutation codes, introduced recently by the second and third authors, belong to the family of frequency permutation arrays. Like some other codes in this family, such as the repetition permutation codes, they are obtained by a repetition construction applied to a smaller code (but with a "twist" allowed). The minimum distance of a twisted permutation code is known to be at least the minimum distance of a corresponding repetition permutation code, but in some instances can be larger. We construct two new infinite families of twisted permutation codes with minimum distances strictly greater than those for the corresponding repetition permutation codes. These constructions are based on two infinite families of finite groups and their representations. The first is a family of $p$-groups, for an odd prime $p$, while the second family consists of the $4$-dimensional symplectic groups over a finite field of even order. In the latter construction, properties of the graph automorphism of these symplectic groups play an important role.

Finite field constructions of combinatorial arrays

We survey a number of topics and constructions of combinatorial arrays based on finite fields. These combinatorial objects include orthogonal arrays, covering arrays, ordered orthogonal arrays, permutation arrays, frequency permutation arrays, hypercubes and Costas arrays.

Twisted permutation codes

Abstract We introduce twisted permutation codes, which are frequency permutation arrays analogous to repetition permutation codes, namely, codes obtained from the repetition construction applied to a permutation code. In particular, we show that a lower bound for the minimum distance of a twisted permutation code is the minimum distance of a repetition permutation code. We give examples where this bound is tight, but more importantly, we give examples of twisted permutation codes with minimum distance strictly greater than this lower bound.

Diagonally neighbour transitive codes and frequency permutation arrays

Constant composition codes have been proposed as suitable coding schemes to solve the narrow band and impulse noise problems associated with powerline communication. In particular, a certain class of constant composition codes called frequency permutation arrays have been suggested as ideal, in some sense, for these purposes. In this paper we characterise a family of neighbour transitive codes in Hamming graphs in which frequency permutation arrays play a central rode. We also classify all the permutation codes generated by groups in this family.

Estimates on the Size of Symbol Weight Codes

The study of codes for powerline communications has garnered much interest over the past decade. Various types of codes such as permutation codes, frequency permutation arrays, and constant composition codes have been proposed over the years. In this paper, we study a type of code called bounded symbol weight codes which was first introduced by Versfeld in 2005, and a related family of codes that we term constant symbol weight codes. We provide new upper and lower bounds on the size of bounded symbol weight and constant symbol weight codes. We also give direct and recursive constructions of codes for certain parameters.

Computing the ball size of frequency permutations under Chebyshev distance

Let Snλ be the set of all permutations over the multiset {1,…,1︷λts,m,…,m︷λ} where n=mλ. A frequency permutation array (FPA) of minimum distance d is a subset of Snλ in which every two elements have distance at least d. FPAs have many applications related to error correcting codes. In coding theory, the Gilbert-Varshamov bound and the sphere-packing bound are derived from the size of balls of certain radii.We propose two efficient algorithms that compute the ball size of frequency permutations under Chebyshev distance. Here it is equivalent to computing the permanent of a special type of matrix, which generalizes the Toepliz matrix in some sense. Both methods extend previous known results. The first one runs in O2dλdλ2.376logn time and O2dλdλ2 space. The second one runs in O2dλdλdλ+λλnλ time and O2dλdλ space. For small constants λ and d, both are efficient in time and use constant storage space.

Decoding Frequency Permutation Arrays Under Chebyshev Distance

A frequency permutation array (FPA) of length n = mλ and distance d is a set of permutations on a multiset over m symbols, where each symbol appears exactly λ times and the distance between any two elements in the array is at least d. FPA generalizes the notion of permutation array. In this paper, under the Chebyshev distance, we first prove lower and upper bounds on the size of FPA. Then we give several constructions of FPAs, and some of them come with efficient encoding and decoding capabilities. Moreover, we show one of our designs is locally decodable, i.e., we can decode a message bit by reading at most λ+1 symbols, which has an interesting application to private information retrieval.

Equidistant frequency permutation arrays and related constant composition codes

In this paper we study the special class of equidistant constant composition codes of type CCC(n, d, μ m ) (where n = m μ), which correspond to equidistant frequency permutation arrays; we also consider related codes with composition "close to" μ m . We establish various properties of these objects and give constructions for optimal families of codes.

Resampling in the frequency domain of time series to determine critical values for change-point tests

We study a model with an abrupt change in the mean and dependent errors that form a linear process. Dierent kinds of statistics are considered, such as maximum-type statistics (particularly dierent CUSUM procedures) or sum-type statistics. Approximations of the critical values for change-point tests are obtained through permutation methods in the frequency domain. The theoretical results show that the original test statistics and their corresponding frequency permutation counterparts follow the same distributional asymptotics. The main step in the proof is to obtain limit theorems for the corresponding rank statistics and then deduce the permutation asymptotics conditionally on the given data. Some simulation studies illustrate that the permutation tests usually behave better than the original tests if performance is measured by the - and -errors respectively.

Blind Source Separation Exploiting Higher-Order Frequency Dependencies

Blind source separation (BSS) is a challenging problem in real-world environments where sources are time delayed and convolved. The problem becomes more difficult in very reverberant conditions, with an increasing number of sources, and geometric configurations of the sources such that finding directionality is not sufficient for source separation. In this paper, we propose a new algorithm that exploits higher order frequency dependencies of source signals in order to separate them when they are mixed. In the frequency domain, this formulation assumes that dependencies exist between frequency bins instead of defining independence for each frequency bin. In this manner, we can avoid the well-known frequency permutation problem. To derive the learning algorithm, we define a cost function, which is an extension of mutual information between multivariate random variables. By introducing a source prior that models the inherent frequency dependencies, we obtain a simple form of a multivariate score function. In experiments, we generate simulated data with various kinds of sources in various environments. We evaluate the performances and compare it with other well-known algorithms. The results show the proposed algorithm outperforms the others in most cases. The algorithm is also able to accurately recover six sources with six microphones. In this case, we can obtain about 16-dB signal-to-interference ratio (SIR) improvement. Similar performance is observed in real conference room recordings with three human speakers reading sentences and one loudspeaker playing music

Permutation Correction in the Frequency Domain in Blind Separation of Speech Mixtures

This paper presents a method for blind separation of convolutive mixtures of speech signals, based on the joint diagonalization of the time varying spectral matrices of the observation records. The main and still largely open problem in a frequency domain approach is permutation ambiguity. In an earlier paper of the authors, the continuity of the frequency response of the unmixing filters is exploited, but it leaves some frequency permutation jumps. This paper therefore proposes a new method based on two assumptions. The frequency continuity of the unmixing filters is still used in the initialization of the diagonalization algorithm. Then, the paper introduces a new method based on the time-frequency representations of the sources. They are assumed to vary smoothly with frequency. This hypothesis of the continuity of the time variation of the source energy is exploited on a sliding frequency bandwidth. It allows us to detect the remaining frequency permutation jumps. The method is compared with other approaches and results on real world recordings demonstrate superior performances of the proposed algorithm.

Frequency permutation arrays

AbstractMotivated by recent interest in permutation arrays, we introduce and investigate the more general concept of frequency permutation arrays (FPAs). An FPA of length n = mλ and distance d is a set T of multipermutations on a multiset of m symbols, each repeated with frequency λ, such that the Hamming distance between any distinct x,y ∈ T is at least d. Such arrays have potential applications in powerline communication. In this article, we establish basic properties of FPAs, and provide direct constructions for FPAs using a range of combinatorial objects, including polynomials over finite fields, combinatorial designs, and codes. We also provide recursive constructions, and give bounds for the maximum size of such arrays. © 2006 Wiley Periodicals, Inc. J Combin Designs 14: 463–478, 2006