direction of arrival estimation using parametric signal models we consider the problem of estimating the directions of arrival doas of narrowband sources with known center frequency the paper evaluates the potential improvement in estimation accuracy by using spatial temporal processing for signals obeying a deterministic parametric model one would expect that prior information about the temporal structure of the signals will yield some gain in performance by deriving the cramer rao bound crb on the doa estimates we quantify this gain and identify the cases for which the gain is significant we show that for the single source case spatial temporal processing does not yield any gain in performance relative to conventional spatial processing for multiple noncoherent signals incorporating temporal processing can achieve the single source performance yielding a significant gain for the case of multiple sources with small spatial separation relative to the beamwidth of the array however spatial temporal processing cannot yield any gain in performance for multiple coherent signals

smallest singular value of random matrices and geometry of random polytopes abstract we study the behaviour of the smallest singular value of a rectangular random matrix i e matrix whose entries are independent random variables satisfying some additional conditions we prove a deviation inequality and show that such a matrix is a good isomorphism on its image then we obtain asymptotically sharp estimates for volumes and other geometric parameters of random polytopes absolutely convex hulls of rows of random matrices all our results hold with high probability that is with probability exponentially in dimension close to 1

minimizing total tardiness in permutation flowshops we consider the permutation flowshop scheduling problem with the objective of minimizing total tardiness presented are several properties that are used to calculate lower bounds on total tardiness of jobs for a given partial sequence and to identify sequences dominated by others we develop a branch and bound algorithm using these bounds and a dominance rule results of computational experiments on randomly generated problems are reported

the circular law for random matrices we consider the joint distribution of real and imaginary parts of eigenvalues of random matrices with independent real entries with mean zero and unit variance we prove the convergence of this distribution to the uniform distribution on the unit disc without assumptions on the existence of a density for the distribution of entries we assume that the entries have a finite moment of order larger than two and consider the case of sparse matrices the results are based on previous work of bai rudelson and the authors extending results to a larger class of sparse matrices

subspace based estimation of time delays and doppler shifts this paper considers the problem of estimating the time delays and doppler shifts of a known waveform received via several distinct paths by an array of antennas the general maximum likelihood estimator is presented and is shown to require a 2d dimensional nonlinear minimization where d is the number of received signal reflections two alternative solutions based on signal and noise subspace fitting are proposed requiring only a d dimensional minimization in particular we show how to decouple the required search into a two step procedure where the delays are estimated and the dopplers solved for explicitly initial conditions for the time delay search can be obtained by applying generalizations of the music and esprit algorithms which are also outlined in the paper simulation examples are included to illustrate the algorithms performance relative to the cramer rao bound

limit of the smallest eigenvalue of a large dimensional sample covariance matrix in this paper the authors show that the smallest if p leq n or the p n 1 th smallest if p n eigenvalue of a sample covariance matrix of the form 1 n xx tends almost surely to the limit 1 sqrt y 2 as n rightarrow infty and p n rightarrow y in 0 infty where x is a p times n matrix with iid entries with mean zero variance 1 and fourth moment finite also as a by product it is shown that the almost sure limit of the largest eigenvalue is 1 sqrt y 2 a known result obtained by yin bai and krishnaiah the present approach gives a unified treatment for both the extreme eigenvalues of large sample covariance matrices

minimizing total completion time for re entrant flow shop scheduling problems in this paper we study re entrant flow shop scheduling problems with the objective of minimizing total completion time in a re entrant scheduling problem jobs may visit some machines more than once for processing the problem is np hard even for machine number m 2 a heuristic algorithm is presented to solve the problem in which an effective k insertion technique is introduced as the improvement strategy in iterations computational experiments and analyses are performed to give guidelines of choosing parameters in the algorithm we also provide a lower bound for the total completion time of the optimal solution when there are only two machines objective function values of the heuristic solutions are compared with the lower bounds to evaluate the efficiency of the algorithm for randomly generated instances the results show that the given heuristic algorithm generates solutions with total completion times within 1 2 times of the lower bounds in most of the cases

computationally efficient angle estimation for signals with known waveforms this paper presents a large sample decoupled maximum likelihood deml angle estimator for uncorrelated narrowband plane waves with known waveforms and unknown amplitudes arriving at a sensor array in the presence of unknown and arbitrary spatially colored noise the deml estimator decouples the multidimensional problem of the exact ml estimator to a set of 1 d problems and hence is computationally efficient we shall derive the asymptotic statistical performance of the deml estimator and compare the performance with its cramer rao bound crb i e the best possible performance for the class of asymptotically unbiased estimators we will show that the deml estimator is asymptotically statistically efficient for uncorrelated signals with known waveforms we will also show that for moderately correlated signals with known waveforms the deml estimator is no longer a large sample maximum likelihood ml estimator but the deml estimator may still be used for angle estimation and the performance degradation relative to the crb is small we shall show that the deml estimator can also be used to estimate the arrival angles of desired signals with known waveforms in the presence of interfering or jamming signals by modeling the interfering or jamming signals as random processes with an unknown spatial covariance matrix finally several numerical examples showing the performance of the deml estimator are presented in this paper

subspace based adaptive generalized likelihood ratio detection subspace based adaptive detection performance is examined for the generalized likelihood ratio detector based on wilks spl lambda statistic the problem considered here is detecting the presence of one or more signals of known shape embedded in gaussian distributed noise with unknown covariance structure the data is mapped into a subspace prior to detection the probability of false alarm is independent of the subspace transformation and depends only on subspace dimension the probability of detection depends on the subspace transformation through a nonadaptive signal to noise ratio snr parameter subspace processing results in an snr loss that tends to decrease performance and a gain in statistical stability that tends to increase performance it is shown that the statistical stability effect dominates the snr loss for short data records and subspace detectors can require substantially less snr than full space detectors for equivalent performance a method for designing the subspace transformation to minimize the snr loss is proposed and illustrated through simulations

efficient maximum likelihood doa estimation for signals with known waveforms in the presence of multipath we present a large sample maximum likelihood ml algorithm for estimating the directions of arrival doa s and signal amplitudes of known possibly coherent signals impinging on an array of sensors the algorithm is an extension of the deml method of li et al that handles coherent multipath that may be present in the signals the algorithm is computationally efficient because the nonlinear minimization step decouples into a set of minimizations of smaller dimension

the littlewood offord problem and invertibility of random matrices abstract we prove two basic conjectures on the distribution of the smallest singular value of random n n matrices with independent entries under minimal moment assumptions we show that the smallest singular value is of order n 1 2 which is optimal for gaussian matrices moreover we give a optimal estimate on the tail probability this comes as a consequence of a new and essentially sharp estimate in the littlewood offord problem for i i d random variables x k and real numbers a k determine the probability p that the sum k a k x k lies near some number v for arbitrary coefficients a k of the same order of magnitude we show that they essentially lie in an arithmetic progression of length 1 p

complex amplitude estimation in the known steering matrix and generalized waveform case we consider a special growth curve sgc model with a known steering matrix and generalized waveform in the presence of unknown interference and noise several estimators of the complex amplitude based on this model are derived including the methods of approximate maximum likelihood aml minimum variance distortionless response mvdr and amplitude and phase estimation apes we analyze the statistical properties of these estimators and show that in the presence of temporally white but spatially correlated noise and interference aml is asymptotically statistically efficient for a large snapshot number while mvdr and apes are asymptotically equivalent but not statistically efficient via several numerical examples we also show that when the noise and interference are both spatially and temporally correlated the apes estimator can achieve better estimation accuracy and exhibit greater robustness than the other methods

array signal processing in the known waveform and steering vector case the amplitude estimation of a signal that is known only up to an unknown scaling factor with interference and noise present is of interest in several applications including using the emerging quadrupole resonance qr technology for explosive detection in such applications a sensor array is often deployed for interference suppression this paper considers the complex amplitude estimation of a known waveform signal whose array response is also known a priori two approaches viz the capon and the maximum likelihood ml methods are considered for the signal amplitude estimation in the presence of temporally white but spatially colored interference and noise we derive closed form expressions for the expected values and mean squared errors mses of the two estimators a comparative study shows that the ml estimate is unbiased whereas the capon estimate is biased downwards for finite data sample lengths we show that both methods are asymptotically statistically efficient when the number of data samples is large but not when the signal to noise ratio snr is high furthermore we consider a more general scenario where the interference and noise are both spatially and temporally correlated we model the interference and noise vector as a multichannel autoregressive ar random process an alternating least squares als method for parameter estimation is presented we show that in most cases the als method is superior to the model mismatched ml m sup 3 l method which ignores the temporal correlation of the interference and noise

on the convergence of the extremal eigenvalues of empirical covariance matrices with dependence consider a sample of a centered random vector with unit covariance matrix we show that under certain regularity assumptions and up to a natural scaling the smallest and the largest eigenvalues of the empirical covariance matrix converge when the dimension and the sample size both tend to infinity to the left and right edges of the marchenko pastur distribution the assumptions are related to tails of norms of orthogonal projections they cover isotropic log concave random vectors as well as random vectors with i i d coordinates with almost optimal moment conditions the method is a refinement of the rank one update approach used by srivastava and vershynin to produce non asymptotic quantitative estimates in other words we provide a new proof of the bai and yin theorem using basic tools from probability theory and linear algebra together with a new extension of this theorem to random matrices with dependent entries

applications of cumulants to array processing i aperture extension and array calibration an interpretation for the use of cumulants in narrowband array processing problems is proposed it is shown how fourth order cumulants of multichannel observations increase the directional information compared with second order statistics based on the interpretation it is shown how cumulants can be used to increase the effective aperture of an arbitrary antenna array the amount of partial information necessary to jointly calibrate an arbitrary array and estimate the directions of far field sources is also investigated it is proven that the presence of a doublet and use of fourth order cumulants is sufficient to accomplish this task the proposed approach is computationally efficient and more general than covariance based algorithms that have addressed the calibration problem under constraints a class of beamforming techniques is proposed to recover the source waveforms proposed estimation procedures are based on cumulants which bring insensitivity to the spatial correlation structure of additive gaussian measurement noise simulations are provided to illustrate the use of the proposed algorithms

covariance estimation for distributions with 2 e moments we study the minimal sample size n n n that suffices to estimate the covariance matrix of an n dimensional distribution by the sample covariance matrix in the operator norm with an arbitrary fixed accuracy we establish the optimal bound n o n for every distribution whose k dimensional marginals have uniformly bounded 2 e moments outside the sphere of radius o k in the specific case of log concave distributions this result provides an alternative approach to the kannan lovasz simonovits problem which was recently solved by adamczak et al j amer math soc 23 2010 535 561 moreover a lower estimate on the covariance matrix holds under a weaker assumption uniformly bounded 2 e moments of one dimensional marginals our argument consists of randomizing the spectral sparsifier a deterministic tool developed recently by batson spielman and srivastava siam j comput 41 2012 1704 1721 the new randomized method allows one to control the spectral edges of the sample covariance matrix via the stieltjes transform evaluated at carefully chosen random points

minimizing makespan in a class of reentrant shops we study the problem of scheduling a chain reentrant shop in which each job goes for its processing first to a machine called the primary machine then to a number of other machines in a fixed sequence and finally back to the primary machine for its last operation the problem is to schedule the jobs so as to minimize the makespan this problem is unary np hard for a general number of machines we focus in particular on the two machine case that is also at least binary np hard we prove some properties that identify a specific class of optimal schedules and then use these properties in designing an approximation algorithm and a branch and bound type optimization algorithm the approximation algorithm of which we present three versions has a worst case performance guarantee of 3 2 along with an excellent empirical performance the optimization algorithm solves large instances quickly finally we identify a few well solvable special cases and present a pseudo polynomial algorithm for the case in which the first and the last operations of any job on the primary machine are identical

smallest singular value of a random rectangular matrix we prove an optimal estimate of the smallest singular value of a random sub gaussian matrix valid for all dimensions for an nn matrix a with inde pendent and identically distributed sub gaussian entries the smallest singular value of a is at least of the order p np n 1 with high probability a sharp

the limit of the smallest singular value of random matrices with i i d entries abstract let a i j 1 i j be i i d real valued random variables with zero mean and unit variance and let an integer sequence n m m 1 satisfy m n m z for some z 0 1 for each m n denote by a m the n m m random matrix a i j 1 i n m 1 j m and let s m a m be its smallest singular value we prove that the sequence n m 1 2 s m a m m 1 converges to 1 z almost surely our result does not require boundedness of any moments of a i j s higher than the 2 nd and resolves a long standing question regarding the weakest moment assumptions on the distribution of the entries sufficient for the convergence to hold

maximum likelihood angle estimation for signals with known waveforms maximum likelihood estimation mle of the arrival angles of narrowband plane waves when one or all signals have known waveforms is considered computationally efficient and rapidly converging algorithms that iteratively maximize the likelihood functions are presented cramer rao bounds for these estimators are obtained the conditions under which incorporating knowledge of one or all of the signal waveforms in the estimators improves the accuracy of the angle estimates are described

quantitative estimates of the convergence of the empirical covariance matrix in log concave ensembles let k be an isotropic convex body in rn given e 0 how many independent points xi uniformly distributed on k are neededfor the empirical covariance matrix to approximate the identity up to e with overwhelming probability our paper answers this question from 12 more precisely let x rn be a centered random vector with a log concave distribution and with the identity as covariance matrix an example of such a vector x is a random point in an isotropic convex body we show that for any e 0 there existsc e 0 su ch that if n c e n and xi i n are i i d copies of 1 n x then n i 1 xi xi id e with probability larger than 1 exp c n

performance analysis of multivariate complex amplitude estimators we consider multivariate complex amplitude estimation in the presence of unknown interference and noise two multivariate approaches maximum likelihood ml and capon are provided we derive the closed form expression of the crame spl acute r rao bound crb for the unknown complex amplitudes we also analyze the bias properties and mean squared errors mse of the two estimators a comparative study shows that the multivariate ml estimator is unbiased whereas the multivariate capon estimator is biased downward for finite snapshots both estimators are asymptotically statistically efficient when the number of snapshots is large

on the limit of the largest eigenvalue of the large dimensional sample covariance matrix in this paper the authors show that the largest eigenvalue of the sample covariance matrix tends to a limit under certain conditions when both the number of variables and the sample size tend to infinity the above result is proved under the mild restriction that the fourth moment of the elements of the sample sums of squares and cross products sp matrix exist

minimizing total tardiness on a two machine re entrant flowshop we present a branch and bound algorithm for a two machine re entrant flowshop scheduling problem with the objective of minimizing total tardiness in the re entrant flowshop considered here all jobs must be processed twice on each machine that is each job should be processed on machine 1 machine 2 and then machine 1 and machine 2 by regarding a job as a pair of sub jobs each of which represents a pass through the two machines we develop dominance properties a lower bound and heuristic algorithms for the problem and use these to develop a branch and bound algorithm for evaluation of the performance of the algorithms computational experiments are performed on randomly generated test problems and results are reported results of the experiments show that the suggested branch and bound algorithm can solve problems with up to 20 sub jobs in a reasonable amount of cpu time and the average percentage gap of the heuristic solutions is about 13

time delay and spatial signature estimation using known asynchronous signals this paper considers the problem of estimating the parameters of known signals received asynchronously by an array of antennas the parameters of primary interest are the time delays of the signals and their spatial signatures at the array estimates of the signal directions of arrival are also considered but are of secondary importance in this work maximum likelihood algorithms and more computationally efficient approximations are developed for both the case where all received signals are identical the channel estimation overlapping echo problem and where they are all distinct conditions are also derived under which the standard matched filter approach yields consistent and statistically efficient parameter estimates the issue of solution uniqueness is addressed and in particular an upper bound on the number of signals whose parameters may be uniquely identified is derived for a number of different cases typically the bound is far greater than the number of sensors and is limited only by the number of data samples collected some representative simulation examples are also included to illustrate the algorithms performance relative to the cramer rao bound

music maximum likelihood and cramer rao bound the performance of the music and ml methods is studied and their statistical efficiency is analyzed the cramer rao bound crb for the estimation problems is derived and some useful properties of the crb covariance matrix are established the relationship between the music and ml estimators is investigated as well a numerical study is reported of the statistical efficiency of the music estimator for the problem of finding the directions of two plane waves using a uniform linear array an exact description of the results is included

joint estimation of time delays and directions of arrival of multiple reflections of a known signal we present an efficient algorithm for estimating the time delays and the directions of arrival doas of multiple reflections of a known signal the algorithm is based on an iterative scheme that transforms the multidimensional maximum likelihood criterion into two sets of simple one dimensional 1 d maximization problems simulation results illustrating the performance of the algorithm in comparison with the cramer rao bound are included