This letter realizes direction of arrival (DOA) estimation by exploiting the noise subspace based estimator. Since single subspace feature extraction fails to achieve satisfactory results under unknown noise fields, we propose a two-step subspace feature extraction technique that is effective even in these fields. When a new noise subspace is attained, the proposed estimator without prewhitening can form the maximizing orthogonality especially for unknown noise fields. Simulation results confirm the effectiveness of the proposed technique.

We address a problem of sampling and reconstructing periodic piecewise polynomials based on the theory for signals with a finite rate of innovation (FRI signals) from samples acquired by a sinc kernel. This problem was discussed in a previous paper. There was, however, an error in a condition about the sinc kernel. Further, even though the signal is represented by parameters, these explicit values are not obtained. Hence, in this paper, we provide a correct condition for the sinc kernel and show the procedure. The point is that, though a periodic piecewise polynomial of degree R is defined as a signal mapped to a periodic stream of differentiated Diracs by R + 1 time differentiation, the mapping is not one-to-one. Therefore, to recover the stream is not sufficient to reconstruct the original signal. To solve this problem, we use the average of the target signal, which is available because of the sinc sampling. Simulation results show the correctness of our reconstruction procedure. We also show a sampling theorem for FRI signals with derivatives of a generic known function.

Permutation polynomial based interleavers over integer rings have recently received attention for their excellent channel coding performance, elegant algebraic properties and simplicity of implementation. In this letter, it is shown that permutation polynomial based interleavers of practical interest is decomposed into linear permutation polynomials. Based on this observation, it is shown that permutation polynomial based interleavers as well as their inverses can be efficiently implemented.

It is well known that an nth-order real polynomial D(z)= is Schur stable if its coefficients satisfy the monotonic condition, i.e., dn > dn-1 > > d1 > d0 > 0. In this letter it is shown that even if the monotonic condition is violated by one coefficient (say dk), D(z) is still Schur stable if the deviation of dk from dk+1 or dk-1 is not too large. More precisely we derive upper bounds for the admissible deviations of dk from dk+1 or dk-1 to ensure the Schur stability of D(z). It is also shown that the results obtained in this letter always yield the larger stability range for dk than an existing result.

The Workflow Management Coalition, WfMC for short, has given a protocol for interorganizational workflows, interworkflows for short. In the protocol, an interworkflow is constructed by connecting two or more existing workflows; and there are three models to connect those workflows: chained, nested, and parallelsynchronized. Business continuity requires the interworkflow to preserve the behavior of the existing workflows. This requirement is called behavioral inheritance, which has three variations: protocol inheritance, projection inheritance, and life-cycle inheritance. Van der Aalst et al. have proposed workflow nets, WF-nets for short, and have shown that the behavioral inheritance problem is decidable but intractable. In this paper, we first show that all WF-nets of the chained model satisfy life-cycle inheritance, and all WF-nets of the nested model satisfy projection inheritance. Next we show that soundness is a necessary condition of projection inheritance for an acyclic extended free choice WF-net of the parallelsynchronized model. Then we prove that the necessary condition can be verified in polynomial time. Finally we show that the necessary condition is a sufficient condition if the WF-net is obtained by connecting state machine WF-nets.

Many scientific applications require efficient variable-precision floating-point arithmetic. This paper presents a special-purpose Very Large Instruction Word (VLIW) architecture for variable precision floating-point arithmetic (VV-Processor) on FPGA. The proposed processor uses a unified hardware structure, equipped with multiple custom variable-precision arithmetic units, to implement various variable-precision algebraic and transcendental functions. The performance is improved through the explicitly parallel technology of VLIW instruction and by dynamically varying the precision of intermediate computation. We take division and exponential function as examples to illustrate the design of variable-precision elementary algorithms in VV-Processor. Finally, we create a prototype of VV-Processor unit on a Xilinx XC6VLX760-2FF1760 FPGA chip. The experimental results show that one VV-Processor unit, running at 253 MHz, outperforms the approach of a software-based library running on an Intel Core i3 530 CPU at 2.93 GHz by a factor of 5X-37X for basic variable-precision arithmetic operations and elementary functions.

In algebraic attack on stream ciphers based on LFSRs, the secret key is found by solving an overdefined system of multivariate equations. There are many known algorithms from different point of view to solve the problem, such as linearization, relinearization, XL and Grobner Basis. The simplest method, linearization, treats each monomial of different degrees as a new variable, and consists of variables (the degree of the system of equations is denoted by d). Thus it needs at least equations, i.e. keystream bits to recover the secret key by Gaussian reduction or other. In this paper we firstly propose a concept, called equivalence of LFSRs. On the basis of it, we present a constructive method that can solve an overdefined system of multivariate equations with less keystream bits by extending the primitive polynomial.

In this paper, a robust fractional order memory polynomial pre-distorter with two novel schemes to conduct digital base-band power amplifier pre-distortion is proposed. For the first scheme, fractional order terms are included in the conventional memory polynomial containing the odd and even order polynomial terms, which is called Scheme One. The second scheme, called Scheme Two, simply replaces even order polynomial terms with fractional order polynomial terms to improve the linear performance of power amplifiers. The mathematical expressions for these two schemes are derived. The computer simulations and numerical analysis show that, compared with the conventional pre-distortion methods, 11 dB and 8.5 dB more out-of-band suppression gain can be obtained by Scheme One and Scheme Two, respectively. Corresponding FPGA realization shows that the two schemes are cost-effective in terms of hardware resources.

In this letter, we determine the linear complexity and minimum polynomial of the frequency hopping sequences over GF(q) introduced by Chung and Yang, where q is an odd prime. The results of this letter show that these sequences are quite good from the linear complexity viewpoint. By modifying these sequences, another class of frequency hopping sequences are obtained. The modified sequences also have low Hamming autocorrelation and large linear complexity.

In this letter a simplified Jury's table for real polynomials is extended to complex polynomials. Then it is shown that the extended table contains information on the root distribution of complex polynomials with respect to the unit circle in the complex plane. The result given in this letter is distinct from the recent one in that root counting is performed in a different way.

In this paper, we present a specific type of irreducible polynomial which is an irreducible m-term polynomial of degree m. Designing the parallel multiplier over GF(2m) by the quadrinomial obtained from this irreducible polynomial, its critical delay path is smaller than that of conventional multipliers for some degree m.

Recently, pairing-based cryptographic application sch-emes have attracted much attentions. In order to make the schemes more efficient, not only pairing algorithm but also arithmetic operations in extension field need to be efficient. For this purpose, the authors have proposed a series of cyclic vector multiplication algorithms (CVMAs) corresponding to the adopted bases such as type-I optimal normal basis (ONB). Note here that every basis adapted for the conventional CVMAs are just special classes of Gauss period normal bases (GNBs). In general, GNB is characterized with a certain positive integer h in addition to characteristic p and extension degree m, namely type-⟨h.m⟩ GNB in extension field Fpm. The parameter h needs to satisfy some conditions and such a positive integer h infinitely exists. From the viewpoint of the calculation cost of CVMA, it is preferred to be small. Thus, the minimal one denoted by hmin will be adapted. This paper focuses on two remaining problems: 1) CVMA has not been expanded for general GNBs yet and 2) the minimal hmin sometimes becomes large and it causes an inefficient case. First, this paper expands CVMA for general GNBs. It will improve some critical cases with large hmin reported in the conventional works. After that, this paper shows a theorem that, for a fixed prime number r, other prime numbers modulo r uniformly distribute between 1 to r-1. Then, based on this theorem, the existence probability of type-⟨hmin,m⟩ GNB in Fpm and also the expected value of hmin are explicitly given.

Let q and f(x) be an odd characteristic and an irreducible polynomial of degree m over Fq, respectively. Then, suppose that F(x)=xmf(x+x-1) becomes irreducible over Fq. This paper shows that the conjugate zeros of F(x) with respect to Fq form a normal basis in Fq2m if and only if those of f(x) form a normal basis in Fqm and the compart of conjugates given as follows are linearly independent over Fq, {γ-γ-1,(γ-γ-1)q, …,(γ-γ-1)qm-1} where γ is a zero of F(x) and thus a proper element in Fq2m. In addition, from the viewpoint of q-polynomial, this paper proposes an efficient method for checking whether or not the conjugate zeros of F(x) satisfy the condition.

Binary maximal-length sequences (or m-sequences) are sequences of period 2m-1 generated by a linear recursion of degree m. Decimating an m-sequence {st} by an integer d relatively prime to 2m-1 leads to another m-sequence {sdt} of the same period. The crosscorrelation of m-sequences has many applications in communication systems and has been an important and well studied problem during more than 40 years. This paper presents an updated survey on the crosscorrelation between binary m-sequences with at most five-valued crosscorrelation and shows some of the many recent connections of this problem to several areas of mathematics such as exponential sums and Dickson polynomials.

Recently a simple proof of Jury test for complex polynomials was given by the author. In this letter further extended results are presented. Another elementary proof of the Schur stability condition is provided. More importantly it is shown that the stability table can also be used to determine the root distribution of complex polynomials with respect to the unit circle in the complex plane.

This paper discusses an efficient discrete model for nonlinear RF power amplifier (PA) with long-term memory effects and analyzes its error. The procedure of converting RF signals and systems into a discrete domain is explained for a discrete baseband memory polynomial model. Unlike a previous simple memory polynomial model, the proposed discrete model has two different sampling frequencies: one for nonlinear system with long-term memory effects and one for input signal. A method to choose an optimal sampling frequency for the system and a discrete memory depth is proposed to minimize the sensitivity of the system for perturbation of the measured data. A two-dimensional sensitivity function which is a product of relative residual and matrix condition number is defined for least square problem of the proposed model. Examples with a wideband WiBro 3FA signal and a WCDMA 4FA signal for nonlinear transmitters are presented to describe the overall procedure and effectiveness of the proposed scheme.

Orthogonal frequency division multiplexing (OFDM) signals have high peak-to-average power ratio (PAPR) and cause large nonlinear distortions in power amplifiers (PAs). Memory effects in PAs also become no longer ignorable for the wide bandwidth of OFDM signals. Digital baseband predistorter is a highly efficient technique to compensate the nonlinear distortions. But it usually has many parameters and takes long time to converge. This paper presents a novel predistorter design using a set of orthogonal polynomials to increase the convergence speed and the compensation quality. Because OFDM signals are approximately complex Gaussian distributed, the complex Hermite polynomials which have a closed-form expression can be used as a set of orthogonal polynomials for OFDM signals. A differential envelope model is adopted in the predistorter design to compensate nonlinear PAs with memory effects. This model is superior to other predistorter models in parameter number to calculate. We inspect the proposed predistorter performance by using an OFDM signal referred to the IEEE 802.11a WLAN standard. Simulation results show that the proposed predistorter is efficient in compensating memory PAs. It is also demonstrated that the proposal acquires a faster convergence speed and a better compensation effect than conventional predistorters.

The linear Piece In Hand (PH, for short) matrix method with random variables was proposed in our former work. It is a general prescription which can be applicable to any type of multivariate public-key cryptosystems for the purpose of enhancing their security. Actually, we showed, in an experimental manner, that the linear PH matrix method with random variables can certainly enhance the security of HFE against the Grobner basis attack, where HFE is one of the major variants of multivariate public-key cryptosystems. In 1998 Patarin, Goubin, and Courtois introduced the plus method as a general prescription which aims to enhance the security of any given MPKC, just like the linear PH matrix method with random variables. In this paper we prove the equivalence between the plus method and the primitive linear PH matrix method, which is introduced by our previous work to explain the notion of the PH matrix method in general in an illustrative manner and not for a practical use to enhance the security of any given MPKC. Based on this equivalence, we show that the linear PH matrix method with random variables has the substantial advantage over the plus method with respect to the security enhancement. In the linear PH matrix method with random variables, the three matrices, including the PH matrix, play a central role in the secret-key and public-key. In this paper, we clarify how to generate these matrices and thus present two probabilistic polynomial-time algorithms to generate these matrices. In particular, the second one has a concise form, and is obtained as a byproduct of the proof of the equivalence between the plus method and the primitive linear PH matrix method.

The approximation expression about error accumulation of a long-term prediction is derived. By analyzing this formula, we find that the factors that can affect the long-term predictability include the model parameters, prediction errors and the derivates of the used basis functions. To enlarge the maximum attempting time, we present that more suitable basis functions should be those with smaller derivative functions and a fast attenuation where out of the time series range. We compare the long-term predictability of a non-polynomial based algorithm and a polynomial one to prove the success of our method.

In this Letter, we explore semi-definite relaxation (SDR) program for finding the real roots of a real polynomial. By utilizing the square of the polynomial, the problem is approximated using the convex optimization framework and a real root is estimated from the corresponding minimum point. When there is only one real root, the proposed SDR method will give the exact solution. In case of multiple real roots, the resultant solution can be employed as an accurate initial guess for the iterative approach to get one of the real roots. Through factorization using the obtained root, the reminding real roots can then be solved in a sequential manner.