the binary weight distribution of the extended 2m 2m 4 code of the reed solomon code over gf 2m with generator polynomial x α x α2 x α3 abstract consider an n k linear code with symbols from gf 2 m if each code symbol is represented by a binary m tuple using a certain basis for gf 2 m we obtain a binary nm km linear code called a binary image of the original code in this paper we present a lower bound on the minimum weight of a binary image of a cyclic code over gf 2 m and the weight enumerator for a binary image of the extended 2 m 2 m 4 code of the reed solomon code over gf 2 m with generator polynomial x x 2 x 3 and its dual code where is a primitive element in gf 2 m

testing by verifying walsh coefficients testing of logic networks by verifying the walsh coefricients of the outputs is explored measurement of one of these can detect arbitrarily many input leads stuck and just two measurements requiring little hardware can detect any single stuck at fault in appropriately designed networks

group theoretic signature analysis a new class of data compression techniques called group theoretic signature analysis gtsa for testing a logic network is proposed and the fault coverage of the method is analyzed this method is a generalization of accumulator compression testing built in self test for processor environments is feasible with gtsa

isospectral domains with mixed boundary conditions we construct a series of examples of planar isospectral domains with mixed dirichlet neumann boundary conditions this is a modification of a classical problem proposed by m kac

space time transmit code and receive filter design for colocated mimo radar this paper deals with the design of multiple input multiple output radar space time transmit code sttc and space time receive filter strf to enhance moving targets detection in the presence of signal dependent interferences an iterative procedure whose convergence is analytically proved is devised to maximize the signal to interference plus noise ratio sinr accounting for both a similarity constraint and a constant modulus requirement on the probing waveform each iteration of the algorithm involves the solution of hidden convex problems specifically both a convex problem whose solution is provided in closed form and a set of fractional programming problems that can be globally solved in polynomial time via the dinkelback s procedure are settled the computational complexity is linear with the number of iterations and polynomial with the sizes of the sttc and the strf in particular the proposed technique provides a monotonic sinr improvement without limitations on the size of the similarity constraint and ensures convergence to a stationary point filling these important gaps in the open literature besides the reported results highlight that the new devised procedure outperforms both in the optimized sinr value and the computational complexity than the available counterparts

accumulator compression testing a new test data reduction technique called accumulator compression testng act is proposed act is an extension of syndrome testing it is shown that the enumeration of errors missed by act for a unit under test is equivalent to the number of restricted partitions of a number asymptotic results are obtained for independent and dependent error modes comparison is made between signature analysis sa and act theoretical results indicate that with act a better control over fault coverage can be obtained than with sa experimental results are supportive of this indication built in self test for processor environments may be feasible with act however for general vlsi circuits the complexity of act may be a problem as an adder is necessary

muntz galerkin methods and applications to mixed dirichlet neumann boundary value problems solutions for many problems of interest exhibit singular behaviors at domain corners or points where the boundary condition changes type for these types of problems direct spectral methods with the usual polynomial basis functions do not lead to a satisfactory convergence rate we develop in this paper a muntz galerkin method which is based on specially tuned muntz polynomials to deal with the singular behaviors of the underlying problems by exploring the relations between jacobi polynomials and muntz polynomials we develop efficient implementation procedures for the muntz galerkin method and provide optimal error estimates as an example of applications we consider the poisson equation with mixed dirichlet neumann boundary conditions whose solution behaves like o r 1 2 near the singular point and demonstrate that the muntz galerkin method greatly improves the rates of convergence of the usual spectral method

zero aliasing for modeled faults when using built in self test bist for testing vlsi circuits the circuit response to an input test sequence which may consist of thousands to millions of bits is compacted into a signature which consists of only tens of bits usually a linear feedback shift register lfsr is used for response compaction via polynomial division the compacting function is a many to one function and as a result some erroneous responses may be mapped to the same signature as the good response this is known as aliasing in this paper we deal with the selection of a feedback polynomial for the compacting lfsr such that an erroneous response resulting from any modeled fault is mapped to a signature that is different from that for the good response such lfsrs are called zero aliasing lfsrs only zero aliasing lfsrs with primitive or irreducible feedback polynomials are considered due to their suitability for bist test pattern generation

on the design of constant modulus probing signals for mimo radar probing signal waveforms play a central role in the signal processing performance of a multiple input multiple output mimo radar in practice for a given desired beam pattern we need to design a probing signal waveform whose beam pattern closely matches the desired one and whose autocorrelation and cross correlation sidelobes are kept low the latter properties are important to mitigate undesirable interference caused by multiple targets or scatterers in this correspondence we present an efficient optimization method to design a constant modulus probing signal which can synthesize a desired beam pattern while maximally suppressing both the autocorrelation and cross correlation sidelobes at between given spacial angles we formulate this problem as an unconstrained minimization of a fourth order trigonometric polynomial and propose an efficient quasi newton iterative algorithm to solve it besides we provide an analysis of the local minima of the fourth order trigonometric polynomial and prove that any local minima is a 1 2 approximation of its global optimal solution numerical examples show that the proposed approach compares favorably with the existing approach

on random pattern test length the testing of large logic networks with random patterns is examined work by previous workers for single faults is extended to a class of multiple fault situations not only is the problem of fault detection in the presence of nonmasking multiple faults treated but the question of distinguishing between them is also examined it is shown that a test that merely exposes each fault has a high probability of distinguishing between the faults the relationships between quality diagnostic resolution and random pattern test length are developed the results have application to self test schemes that use random patterns as stimuli

designing unimodular codes via quadratic optimization the np hard problem of optimizing a quadratic form over the unimodular vector set arises in radar code design scenarios as well as other active sensing and communication applications to tackle this problem which we call unimodular quadratic program uqp several computational approaches are devised and studied power method like iterations are introduced for local optimization of uqp furthermore a monotonically error bound improving technique merit is proposed to obtain the global optimum or a local optimum of uqp with good sub optimality guarantees the provided sub optimality guarantees are case dependent and may outperform the 4 approximation guarantee of semi definite relaxation several numerical examples are presented to illustrate the performance of the proposed method the examples show that for several cases including rank deficient matrices the proposed methods can solve uqps efficiently in the sense of sub optimality guarantee and computational time

on the probability of undetected error for linear block codes the problem of computing the probability of undetected error is considered for linear block codes used for error detection the recent literature is first reviewed and several results are extended it is pointed out that an exact calculation can be based on either the weight distribution of a code or its dual using the dual code formulation the probability of undetected error for the ensemble of all nonbinary linear block codes is derived as well as a theorem that shows why the probability of undetected error may not be a monotonic function of channel error rate for some poor codes several bounds on the undetected error probability are then presented we conclude with detailed examples of binary and nonbinary codes for which exact results can be obtained an efficient technique for measuring an unknown weight distribution is suggested and exact results are compared with experimental results

the isospectral fruits of representation theory quantum graphs and drums we present a method which enables one to construct isospectral objects such as quantum graphs and drums one aspect of the method is based on representation theory arguments which are shown and proved the complementary part concerns techniques of assembly which are both stated generally and demonstrated for this purpose quantum graphs are grist to the mill we develop the intuition that stands behind the construction as well as the practical skills of producing isospectral objects we discuss the theoretical implications which include sunada s theorem of isospectrality sunada 1985 ann math 121 169 arising as a particular case of this method a gallery of new isospectral examples is presented and some known examples are shown to result from our theory

a new class of zero correlation zone sequences in this correspondence two new methods for constructing sets of zero correlation zone zcz sequences are proposed these methods are based on perfect sequences and unitary matrices compared with previous methods the proposed methods can generate sets of nonbinary zcz sequences having a longer zero correlation zone the sequences obtained by these methods are suitable for approximately synchronized code division multiple access as cdma systems

an analysis of the use of rademacher walsh spectrum in compact testing earlier approaches to random compact testing use a random pattern generator which depends on the combinational function under test and a circuit signature which remains the same independent of the circuit in this correspondence we analyze the performance of a new scheme in which the pattern generator is simple and independent of the function being tested but the circuit signature is chosen to be a coefficient from the rademacher walsh rw spectrum of the function under test the analysis provides guidelines for choosing an rw coefficient a test length and an error tolerance so as to minimize the probabilities of rejecting a good unit or accepting a faulty one

aliasing probability for multiple input signature analyzer single and multiple multiple input signature register misr aliasing probability expressions are presented for arbitrary test lengths a framework based on algebraic codes is developed for the analysis and synthesis of misr based test response compressors for bist this framework is used to develop closed form expressions for the aliasing probability of misr for arbitrary test length an error model based on q ary symmetric channel is proposed using more realistic assumptions results are presented that provide the weight distributions for q ary codes q 2 sup m where the circuit under test has m outputs these results are used to compute the aliasing probability for the misr compression technique for arbitrary test lengths this result is extended to compression using two different misrs it is shown that significant improvements can be obtained by using two signature analyzers instead of one the weight distribution of a class of codes of arbitrary length is also given

design of phase codes for radar performance optimization with a similarity constraint this paper deals with the design of coded waveforms which optimize radar performances in the presence of colored gaussian disturbance we focus on the class of phase coded pulse trains and determine the radar code which approximately maximizes the detection performance under a similarity constraint with a prefixed radar code this is tantamount to forcing a similarity between the ambiguity functions of the devised waveform and of the pulse train encoded with the prefixed sequence we consider the cases of both continuous and finite phase alphabet and formulate the code design in terms of a nonconvex np hard quadratic optimization problem in order to approximate the optimal solutions we propose techniques with polynomial computational complexity based on the method of semidefinite program sdp relaxation and randomization moreover we also derive approximation bounds yielding a ldquomeasure of goodnessrdquo of the devised algorithms at the analysis stage we assess the performance of the new encoding techniques both in terms of detection performance and ambiguity function under different choices for the similarity parameter we also show that the new algorithms achieve an accurate approximation of the optimal solution with a modest number of randomizations

mimo radar waveform design with constant modulus and similarity constraints we consider the problem of waveform design for multiple input multiple output mimo radar in the presence of signal dependent interference embedded in white gaussian disturbance we present two sequential optimization procedures to maximize the signal to interference plus noise ratio sinr accounting for a constant modulus constraint as well as a similarity constraint involving a known radar waveform with some desired properties e g in terms of pulse compression and ambiguity the presented sequential optimization algorithms based on a relaxation method yield solutions with good accuracy their computational complexity is linear in the number of iterations and trials in the randomized procedure and polynomial in the receive filter length finally we evaluate the proposed techniques by considering their sinr performance beam pattern as well as pulse compression property via numerical simulations

weyl asymptotic formula for the laplacian on domains with rough boundaries we study asymptotic distribution of eigenvalues of the laplacian on a bounded domain in n our main results include an explicit remainder estimate in the weyl formula for the dirichlet laplacian on an arbitrary bounded domain sufficient conditions for the validity of the weyl formula for the neumann laplacian on a domain with continuous boundary in terms of smoothness of the boundary and a remainder estimate in this formula in particular we show that the weyl formula holds true for the neumann laplacian on a lip domain whenever d 1 d prove that the remainder in this formula is o d 1 and give an example where the remainder estimate o d 1 is order sharp we use a new version of the variational technique which does not require the extension theorem

a unified view of test compression methods a unified treatment of the various techniques to reduce the output data from a unit under test is given the characteristics of time compression schemes with respect to errors detected are developed the use of two or more of these methods together is considered methods to design efficient test compression structures for built in tests are proposed the feasibility of the proposed approach is demonstrated by simulation results

spectral problems with mixed dirichlet neumann boundary conditions isospectrality and beyond consider a bounded domain with the dirichlet condition on a part of the boundary and the neumann condition on its complement does the spectrum of the laplacian determine uniquely which condition is imposed on which part we present some results conjectures and problems related to this variation on the isospectral theme

can nonlinear compactors be better than linear ones this paper presents a new analytical method for estimating compaction quality based on the entropy maximization of the entropy of the signature results in an increase of compaction quality the paper studies the influence of the architecture of a compactor on the entropy growth this approach is suitable for nonlinear compactors widely known linear feedback shift registers lfsrs and the counting compactors as well useful theorems to determine entropy growth during the test have been given and proven furthermore the class of nonlinear compactors based on shift registers named cyclic feedback shift registers cfsrs which guarantee the maximal entropy growth and the aliasing probability of 2 sup n is found it is shown that they are considerably better than the simplest linear compactor feedback shift register and in many cases are quite as good as linear compactors lfsrs having primitive polynomials on the opposite side compactors based on counters are far worse than cfsrs the family of cfsrs is much greater than the already explored family of lfsrs and some cfsrs require less overhead

on binary probing signals and instrumental variables receivers for radar the so called merit factor approach mfa to radar binary sequence design has led to several theoretical contributions in fairly diverse research areas including information theory computer science combinatorial optimization and analytical number theory however the mfa which basically aims at minimizing the clutter effect on radar performance implicitly assumes the use of a least squares ls receiver that is optimal only when there is no clutter this problem can be eliminated by using a more general optimal instrumental variables iv receiver in lieu of the ls receiver the iv receiver can reject clutter more efficiently than the ls receiver additionally the binary sequence design problem associated with the iv approach has an interesting form

accumulator based compaction of test responses an accumulator based compaction abc scheme for parallel compaction of test responses is introduced the asymptotic and transient coverage drop introduced by accumulators with binary and 1 s complement adders is studied using markov chain models it is proven that the asymptotic coverage drop in abc with binary adders is 2 sup k where k is the number of bits in the adder that the fault can reach in abc with 1 s complement adders the asymptotic coverage drop for a fairly general class of faults is 2n 1 sup 1 where n is the total number of bits the analysis of transient behavior relates the coverage drop with the probability of fault injection the size of the accumulator and the length of the test experiment the process is characterized by damping factors derived for various values of these parameters

design of optimized radar codes with a peak to average power ratio constraint this paper considers the problem of radar waveform design in the presence of colored gaussian disturbance under a peak to average power ratio par and an energy constraint first of all we focus on the selection of the radar signal optimizing the signal to noise ratio snr in correspondence of a given expected target doppler frequency algorithm 1 then through a max min approach we make robust the technique with respect to the received doppler algorithm 2 namely we optimize the worst case snr under the same constraints as in the previous problem since algorithms 1 and 2 do not impose any condition on the waveform phase we also devise their phase quantized versions algorithms 3 and 4 respectively which force the waveform phase to lie within a finite alphabet all the problems are formulated in terms of nonconvex quadratic optimization programs with either a finite or an infinite number of quadratic constraints we prove that these problems are np hard and hence introduce design techniques relying on semidefinite programming sdp relaxation and randomization as well as on the theory of trigonometric polynomials providing high quality suboptimal solutions with a polynomial time computational complexity finally we analyze the performance of the new waveform design algorithms in terms of detection performance and robustness with respect to doppler shifts

code design to optimize radar detection performance under accuracy and similarity constraints this paper deals with the design of coded waveforms which optimize radar performances in the presence of colored gaussian disturbance we focus on the class of linearly coded pulse trains and determine the optimum radar code according to the following criterion maximization of the detection performance under a control on the region of achievable doppler estimation accuracies and imposing a similarity constraint with a prefixed radar code this last constraint is tantamount to requiring a similarity between the ambiguity functions of the devised waveform and of the pulse train encoded with the prefixed sequence the resulting optimization problem is nonconvex and quadratic in order to solve it we propose a technique with polynomial computational complexity based on the relaxation of the original problem into a semidefinite program thus the best code is determined through a rank one decomposition of an optimal solution of the relaxed problem at the analysis stage we assess the performance of the new encoding technique in terms of detection performance region of achievable doppler estimation accuracies and ambiguity function

aliasing probability calculations for arbitrary compaction under independently selected random test vectors this paper discusses a systematic methodology for calculating the exact aliasing probability associated with schemes that use an arbitrary finite state machine to compact the response of a combinational circuit to a sequence of independently selected random test input vectors the proposed approach identifies the strong influence of fault activation probabilities on the probability of aliasing and uses an asymmetric error model to simultaneously track the states of two fictitious compactors one driven by the response of the fault free combinational circuit and one driven by the response of the faulty combinational circuit by deriving the overall markov chain that describes the combined behavior of these two compactors we are able to calculate the exact aliasing probability for any test sequence length in particular for long enough sequences the probability of aliasing is shown to only depend on the stationary distribution of the markov chain the insights provided by our analysis are used to evaluate the testing performance of simple examples of nonlinear compactors and to demonstrate regimes where they exhibit lower aliasing probability than linear compactors with the same number of states finally by establishing connections with previous work that evaluated aliasing probability in linear compactors our analysis clarifies the role played by the entropy of the stationary distribution of the compactor states

nodal domains on isospectral quantum graphs the resolution of isospectrality we present and discuss isospectral quantum graphs which are not isometric these graphs are the analogues of the isospectral domains in which were introduced recently in gordon et al 1992 bull am math soc 27 134 8 chapman 1995 am math mon 102 124 buser et al 1994 int math res not 9 391 400 okada and shudo 2001 j phys a math gen 34 5911 22 jakobson et al 2006 j comput appl math 194 141 55 and levitin et al 2006 j phys a math gen 39 2073 82 all based on sunada s construction of isospectral domains sunada t 1985 ann math 121 196 86 after presenting some of the properties of these graphs we discuss a few examples which support the conjecture that by counting the nodal domains of the corresponding eigenfunctions one can resolve the isospectral ambiguity

isospectral shapes with neumann and alternating boundary conditions the isospectrality of a well known pair of shapes constructed from two arrangements of seven congruent right isosceles triangles with the neumann boundary condition is verified numerically to high precision equally strong numerical evidence for isospectrality is presented for the eigenvalues of this standard pair in new boundary configurations with alternating dirichlet and neumann boundary conditions along successive edges good agreement with theory is obtained for the corresponding spectral staircase functions strong numerical evidence is also presented for isospectrality in an example of a different pair of shapes whose basic building block triangle is not isosceles some possible confirmatory experiments involving fluids are suggested

spectral decomposition of square tiled surfaces we consider n copies of a square s0 and define selfadjoint extensions of the euclidean laplacian acting on left mathcal c 0 infty s 0 right n by choosing some boundary conditions that are parametrized by two unitary matrices h and v acting on mathbb c n denoting by sp n h v the spectrum of such an operator we derive conditions on h and v so that the following spectral decomposition holds rm sp delta n h v bigcup 1 leq i leq k rm sp delta n i h i v i quad rm with sum 1 k n i n if h and v are permutation matrices this gives a spectral decomposition of the spectrum of the square tiled surface defined by the corresponding permutations we apply this to derive examples related to isospectrality and to high multiplicity

the hybrid spectral problem and robin boundary conditions the hybrid spectral problem where the field satisfies dirichlet conditions d on part of the boundary of the relevant domain and neumann n on the remainder is discussed in simple terms a conjecture for the c1 coefficient is presented and the conformal determinant on a 2 disc where the d and n regions are semi circles is derived comments on higher coefficients are made a separable second order hemisphere hybrid problem is introduced that involves robin boundary conditions and leads to logarithmic terms in the heat kernel expansion which are evaluated explicitly

a new framework for designing and analyzing bist techniques and zero aliasing compression a general framework for shift register based signature analysis is presented and a mathematical model for this framework based on coding theory is developed there are two key features of this formulation first it allows for uniform treatment of lfsr misr and multiple misr based signature analyzer in addition using this formulation a new compression scheme for multiple output cut is proposed this scheme referred to as multiinput lfsr has the potential to achieve better aliasing than other schemes such as the multiple misr scheme of comparable hardware complexity several results on aliasing are presented and certain known results are shown to be direct consequences of the formulation also developed are error models that take into account the circuit topology and the effect of faults at the outputs using these models exact closed form expressions for aliasing probability are developed a closed form aliasing expression for misr under an independent error model is provided

spectral fault signatures for single stuck at faults in combinational networks a method is described for the derivation of fault signatures for the detection of stuck at faults in single output combinational networks these signatures consist of a set of values derived from the network any single stuck at fault causes at least one value to change the fault signatures developed are a generalization of syndrome testing the technique is developed in the rademacher walsh spectral domain but is easily implemented using conters and basic gates

optimal zero aliasing space compaction of test responses many built in self testing bist schemes compress the test responses from a k output circuit to q signature streams where q spl lt k a process termed space compaction the effectiveness of such a compaction method can be measured by its compaction ratio c k q a high compaction ratio can introduce aliasing which occurs when a faulty test response maps to the fault free signature we investigate the problem of designing zero aliasing space compaction circuits with maximum compaction ratio c sub max we introduce a graph representation of test responses to study the space compaction process and relate space compactor design to a graph coloring problem given a circuit under test a fault model and a test set we determine q sub min which yields c sub max k q sub min this provides a fundamental bound on the cost of signature based bist we show that q sub min spl les 2 for all the iscas 85 benchmark circuits we develop a systematic design procedure for the synthesis of space compaction circuits and apply it to a number of iscas 85 circuits finally we describe multistep compaction which allows zero aliasing to be achieved with any q even when q sub min 1

syndrome and transition count are uncorrelated logic circuit testing in the testing of logic circuits two proposed data compression methods use the number of ones syndrome and the number of sequence changes transition count an enumeration n m k t of the number of length m binary sequences having syndrome value k and transition count t is developed examination of this result reveals that the parallel compression of these two methods has small overlap in error masking an asymptotic expression for n m k t is developed

constant modulus mimo radar waveform design with minimum peak sidelobe transmit beampattern this paper addresses the problem of minimum peak sidelobe transmit beampattern design for colocated multiple input multiple output radar systems two new methods are proposed to achieve it via designing constant modulus cm waveforms directly one is to maximize the ratio of the minimum mainlobe level to the peak sidelobe level psl without specifying pattern masks and another is to minimize psl under the mainlobe ripple and unspecified waveform modulus constraints the resultant optimization problems are difficult to solve due to the coupled numerator and denominator of the quadratic fractional programming problem formulation in the former and double sided quadratic constraints and unknown waveform modulus in the latter for the former we decouple the numerator and denominator by equivalent transformation and introduction of boundary type auxiliary variables in order that feasible methods are derived to tackle them independently and efficiently for the latter we simplify the coupled double sided quadratic constraints on the same waveform vector into those on different single auxiliary variables to tackle the corresponding nonconvex optimization problem numerical examples show that the proposed algorithms can attain sufficient low peak sidelobe beampattern levels under the cm constraints

quadratic optimization with similarity constraint for unimodular sequence synthesis this paper considers unimodular sequence synthesis under similarity constraint for both the continuous and discrete phase cases a computationally efficient iterative algorithm for the continuous phase case ia cpc is proposed to sequentially optimize the quadratic objective function the quadratic optimization problem is turned into multiple one dimensional optimization problems with closed form solutions for the discrete phase case we present an iterative block optimization algorithm specifically we partition the design variables into k blocks and then we sequentially optimize each block via exhaustive search while fixing the remaining k 1 blocks finally we evaluate the computational costs and performance gains of the proposed algorithms in comparison with power method like and semidefinite relaxation related techniques

ambiguity function shaping for cognitive radar via complex quartic optimization in this paper we propose a cognitive approach to design phase only modulated waveforms sharing a desired range doppler response the idea is to minimize the average value of the ambiguity function of the transmitted signal over some range doppler bins which are identified exploiting a plurality of knowledge sources from a technical point of view this is tantamount to optimizing a real and homogeneous complex quartic order polynomial with a constant modulus constraint on each optimization variable after proving some interesting properties of the considered problem we devise a polynomial time waveform optimization procedure based on the maximum block improvement mbi method and the theory of conjugate partial symmetric conjugate super symmetric fourth order tensors at the analysis stage we assess the performance of the proposed technique showing its capability to properly shape the range doppler response of the transmitted waveform

designing unimodular sequence sets with good correlations including an application to mimo radar a multiple input multiple output mimo radar system that transmits orthogonal waveforms via its antennas can achieve a greatly increased virtual aperture compared with its phased array counterpart this increased virtual aperture enables many of the mimo radar advantages including enhanced parameter identifiability and improved resolution practical radar requirements such as unit peak to average power ratio and range compression dictate that we use mimo radar waveforms that have constant modulus and good auto and cross correlation properties we present in this paper new computationally efficient cyclic algorithms for mimo radar waveform synthesis these algorithms can be used for the design of unimodular mimo sequences that have very low auto and cross correlation sidelobes in a specified lag interval and of very long sequences that could hardly be handled by other algorithms previously suggested in the literature a number of examples are provided to demonstrate the performances of the new waveform synthesis algorithms

unimodular sequence design based on alternating direction method of multipliers the topic of probing waveform design has received considerable attention due to its numerous applications in active sensing apart from having the desirable property of constant magnitude it is also anticipated that the designed sequence possesses low sidelobe autocorrelation and or specified spectral shape in this paper the alternating direction method of multipliers admm which is a powerful variant of the augmented lagrangian scheme for dealing with separable objective functions is applied for synthesizing the probing sequences to achieve impulse like autocorrelation we formulate the design problem as minimizing a nonlinear least squares cost function in the frequency domain subject to the constraint that all sequence elements are of unit modulus via introducing auxiliary variables we are able to separate the objective into linear and quadratic functions where the unimodular constraint is only imposed on the former which results in an admm style iterative procedure in particular fast implementation for the most computationally demanding step is investigated and local convergence of the admm method is proved to deal with the spectral shape requirement we borrow the concept in frequency selective filter design where passband and stopband magnitudes are bounded to formulate the corresponding optimization problem in this admm algorithm development unit step functions are utilized to transform the multivariable optimization into a quadratic polynomial problem with a single variable the effectiveness of the proposed approach is demonstrated via computer simulations

simple bounds on serial signature analysis aliasing for random testing it is shown that the aliasing probability is bounded above by 1 epsilon l approximately 1 l epsilon small for large l for test lengths l less than the period l sub c of the signature polynomial for test lengths l that are multiples of l sub c the aliasing probability is bounded above by 1 for test lengths l greater than l sub c and not a multiple of l sub c the aliasing probability is bounded above by 2 l sub c 1 these simple bounds avoid any exponential complexity associated with the exact computation of the aliasing probability simple bounds also apply to signature analysis based on any linear finite state machine including linear cellular automaton from these simple bounds it follows that the aliasing probability in a signature analysis design using beta intermediate signatures is bounded by 1 epsilon sup beta beta sup beta l sup beta for beta

a doppler robust max min approach to radar code design this correspondence considers the problem of robust waveform design in the presence of colored gaussian disturbance under a similarity and an energy constraint we resort to a max min approach where the worst case detection performance over the possible doppler shifts is optimized with respect to the radar waveform under the previously mentioned constraints the resulting optimization problem is a non convex quadratically constrained quadratic program qcqp with an infinite number of constraints which is np hard in general and typically difficult to solve hence we propose an algorithm with a polynomial computational complexity to generate a good sub optimal solution for the aforementioned qcqp the analysis conducted in comparison with some known radar waveforms shows that the sub optimal solutions by the algorithm lead to high quality radar signals