blind identification of mimo fir systems driven by quasistationary sources using second order statistics a frequency domain approach this paper discusses a frequency domain method for blind identification of multiple input multiple output mimo convolutive channels driven by white quasistationary sources the sources can assume arbitrary probability distributions and in some cases they can even be all gaussian distributed we also show that under slightly more restrictive assumptions the algorithm can be applied to the case when the sources are colored nonstationary signals we demonstrate that by using the second order statistics of the channel outputs under mild conditions on the nonstationarity of sources and under the condition that channel is column wise coprime the impulse response of the mimo channel can be identified up to an inherent scaling and permutation ambiguity we prove that by using the new algorithm under the stated assumptions a uniform permutation across all frequency bins is guaranteed and the inherent frequency dependent scaling ambiguities can be resolved hence no post processing is required as is the case with previous frequency domain algorithms we further present an efficient two step frequency domain algorithm for identifying the channel numerical simulations are presented to demonstrate the performance of the new algorithm

shifted fourier transform based tensor algorithms for the 2 d dct in this paper tensor algorithms for calculating the two dimensional 2 d discrete cosine transform dct are presented the tensor approach is based on the concept of the covering revealing the transforms which yields in particular the splitting of the shifted 2 sup r spl times 2 sup r point fourier and cosine transforms into 2 sup r 1 3 one dimensional 1 d incomplete 2 sup r point transforms the multiplicative complexity of the 2 d 2 sup r spl times 2 sup r point discrete cosine transforms in terms of the tensor representation is 4 sup r 3 2 sup r 2 r sup 2 7r 14 which is reduced to 4 sup r 8 3 2 sup r r sup 2 7r 10 20 3 when using the improved tensor algorithm the multiplicative complexity in the general l sup r spl times l sup r case with a prime l 2 as well as in the l sub 1 l sub 2 spl times l sub 1 l sub 2 case with arbitrary co prime l sub 1 l sub 2 1 is provided the examples of the tensor algorithms for calculating the 8 spl times 8 point dct through 104 88 and 84 multiplications are given in detail based on the proposed concept the fast algorithm for calculating the 1 d dct i is also developed the multiplicative complexity of the 2 sup r point dct i is 2 sup r 1 r 2 r 5 2 8 the comparative estimates with the known algorithms are given

a hyperplane based algorithm for the digital co channel communications problem the relationship between the blind digital co channel communications problem and the problem of finding a separating hyperplane in ir sup d is explored a simple model for the blind digital co channel communications problem is x as where x is a known ir sup d spl times n matrix a is an unknown full rank ir sup d spl times d matrix and s is an unknown full rank d spl times n matrix with elements drawn from a multiple amplitude shift keying m ask alphabet s an algorithm with proof is given that solves for a and s up to a simple matrix factor the algorithm is extended to the complex quadrature amplitude modulation qam alphabet the key step in this algorithm involves finding a separating hyperplane parallel to one of the hyperplanes defining the received signal vectors the geometric interpretation of this relationship is discussed examples with noisy data are presented and refinements to the algorithm are discussed

an analysis of real fourier domain based adaptive algorithms implemented with the hartley transform using cosine sine symmetries the least mean squared lms algorithm and its variants have been the most often used algorithms in adaptive signal processing however the lms algorithm suffers from a high computational complexity especially with large filter lengths the fourier transform based block normalized lms fbnlms reduces the computation count by using the discrete fourier transform dft and exploiting the fast algorithms for implementing the dft even though the savings achieved with the fbnlms over the direct lms implementation are significant the computational requirements of fbnlms are still very high rendering many real time applications like audio and video estimation infeasible the hartley transform based bnlms hbnlms is found to have a computational complexity much less than and a memory requirement almost of the same order as that of the fbnlms this paper is based on the cosine and sine symmetric implementation of the discrete hartley transform dht which is the key in reducing the computational complexity of the fbnlms by 33 asymptotically with respect to multiplications the parallel implementation of the discrete cosine transform dct in turn can lead to more efficient implementations of the hbnlms

a quadratic programming approach to blind equalization and signal separation blind equalization and signal separation are two well established signal processing problems in this paper we present a quadratic programming algorithm for fast blind equalization and signal separation by introducing a special non mean square error mse objective function we reformulate fractionally spaced blind equalization into an equivalent quadratic programming problem based on a clear geometric interpretation and a formal proof we show that a perfect equalization solution is obtained at every local optimum of the quadratic program because blind source separation is by nature and mathematically a closely related problem we also generalize the algorithm for blind signal separation we show that by enforcing source orthogonalization through successive processing the quadratic programming approach can be applied effectively moreover the quadratic program is easily extendible to incorporate additional practical conditions such as jamming suppression constraints we also provide evidence of good performance through computer simulations

the algebraic approach to the discrete cosine and sine transforms and their fast algorithms it is known that the discrete fourier transform dft used in digital signal processing can be characterized in the framework of the representation theory of algebras namely as the decomposition matrix for the regular module mathbb c z n mathbb c x x n 1 this characterization provides deep insight into the dft and can be used to derive and understand the structure of its fast algorithms in this paper we present an algebraic characterization of the important class of discrete cosine and sine transforms as decomposition matrices of certain regular modules associated with four series of chebyshev polynomials then we derive most of their known algorithms by pure algebraic means we identify the mathematical principle behind each algorithm and give insight into its structure our results show that the connection between algebra and digital signal processing is stronger than previously understood

blind detection of synchronous cdma in non gaussian channels most blind source separation algorithms assume the channel noise to be gaussian this paper considers the problem of noncooperative blind detection of synchronous direct sequence code division multiple access communications no knowledge of the spreading sequences or training data in non gaussian channels three iterative algorithms with different performance and complexity tradeoffs are proposed simulation results show that they significantly outperform gaussian optimal blind source separation algorithms in non gaussian channels the cramer rao lower bound for this problem is computed and the performance of the proposed algorithms is shown to approach this bound for moderate signal to noise ratios

blind high resolution localization and tracking of multiple frequency hopped signals this paper considers the problem of blind localization and tracking of multiple frequency hopped spread spectrum signals using a uniform linear antenna array without knowledge of hopping patterns or directions of arrival as a preprocessing step we propose to identify a hop free subset of data by discarding high entropy spectral slices from the spectrogram high resolution localization is then achieved via either quadrilinear regression of four way data generated by capitalizing on both spatial and temporal shift invariance or a new maximum likelihood ml based two dimensional 2 d harmonic retrieval algorithm the latter option achieves the best known model identifiability bound while remaining close to the cramer rao bound even at low signal to noise ratios snrs following beamforming using the recovered directions a dynamic programming approach is developed for joint ml estimation of signal frequencies and hop instants in single user tracking the efficacy of the proposed algorithms is illustrated in pertinent simulations

fractional cosine sine and hartley transforms in previous papers the fourier transform ft has been generalized into the fractional fourier transform frft the linear canonical transform lct and the simplified fractional fourier transform sfrft because the cosine sine and hartley transforms are very similar to the ft it is reasonable to think they can also be generalized by the similar way we introduce several new transforms they are all the generalization of the cosine sine or hartley transform we first derive the fractional cosine sine and hartley transforms frct frst frht they are analogous to the frft then we derive the canonical cosine and sine transforms cct cst they are analogous to the lct we also derive the simplified fractional cosine sine and hartley transforms sfrct sfrst sfrht they are analogous to the sfrft and have the advantage of real input real output we also discuss the properties digital implementation and applications e g the applications for filter design and space variant pattern recognition of these transforms the transforms introduced in this paper are very efficient for digital implementation we can just use one half or one fourth of the real multiplications required for the frft and lct to implement them when we want to process even odd or pure real imaginary functions we can use these transforms instead of the frft and lct besides we also show that the frct frst cct cst and sfrct sfrst are also useful for the one sided t spl isin 0 spl infin signal processing

a fast recursive algorithm for computing the discrete cosine transform the discrete cosine transform dct is widely applied in various fields including image data compression because it operates like the karhunen loeve transform for stationary random data this paper presents a recursive algorithm for dct with a structure that allows the generation of the next higher order dct from two identical lower order dct s as a result the method for implementing this recursive dct requires fewer multipliers and adders than other dct algorithms

on the multiplicative complexity of discrete cosine transforms the multiplicative complexity of discrete cosine transforms dcts of arbitrary dimensions on input sizes which are powers of two are obtained new upper bounds on the multiplicative complexity of scaled dcts on input sizes which are powers of two are also obtained

restructured recursive dct and dst algorithms the discrete cosine transform dct and the discrete sine transform dst have found wide applications in speech and image processing as well as telecommunication signal processing for the purpose of data compression feature extraction image reconstruction and filtering in this paper we present new recursive algorithms for the dct and the dst the proposed method is based on certain recursive properties of the dct coefficient matrix and can be generalized to design recursive algorithms for the 2 d dct and the 2 d dst these new structured recursive algorithms are able to decompose the dct and the dst into two balanced lower order subproblems in comparison to previous research works therefore when converting our algorithms into hardware implementations we require fewer hardware components than other recursive algorithms finally we propose two parallel algorithms for accelerating the computation

scaled dct s on input sizes that are composite given efficient scaled discrete cosine transforms dct s of size p and q where p and q are relatively prime we present methods for constructing fast algorithms to compute scaled dct s and scaled inverse dct s of size pq extensions to multidimensional transforms are also given

an analytical constant modulus algorithm iterative constant modulus algorithms such as godard 1980 and cma have been used to blindly separate a superposition of cochannel constant modulus cm signals impinging on an antenna array these algorithms have certain deficiencies in the context of convergence to local minima and the retrieval of all individual cm signals that are present in the channel we show that the underlying constant modulus factorization problem is in fact a generalized eigenvalue problem and may be solved via a simultaneous diagonalization of a set of matrices with this new analytical approach it is possible to detect the number of cm signals present in the channel and to retrieve all of them exactly rejecting other non cm signals only a modest amount of samples is required the algorithm is robust in the presence of noise and is tested on measured data collected from an experimental set up

on the interrelationships among a class of convolutions in this paper some interrelationships among a class of circular operations are investigated based on matrix formulation it is shown that a class of convolutions representing forward backward and convolution correlation of two periodic sequences may be related to each other in terms of discrete transforms having the circular convolution property the results obtained are useful in efficient realization of adaptive digital filters using fast transforms

fast three dimensional discrete cosine transform a fast three dimensional discrete cosine transform algorithm 3d fct and a fast 3d inverse cosine transform 3d ifct algorithm are presented suitable for analysis of 3d data points many existing algorithms for three dimensional data points make use of either the 1d cosine transform or both the 2d and 1d cosine transforms existing algorithms based on the 1d discrete cosine transform dct apply the separable 1d transform to the data points in the x y and z directions respectively while those based on 2d and 1d transforms apply the 2d cosine transform for the x y planes and then the 1d cosine transform in the z direction the proposed 3d dct algorithms handle the 3d data points directly and have been shown to be computationally efficient they involve a 3d decomposition process where a data volume is recursively decomposed in each dimension until unit data cubes are obtained the algorithms are presented in the form of a signal flow graph which captures the various computations involved a complexity analysis along with empirical results is included demonstrating the performance of the proposed direct 3d dct algorithms as 3d fct and ifct are symmetric and relatively fast they can be used in any application requiring a real time symmetric codec such as video conferencing online multiparty video games and three dimensional graphics rendering

complex field coding for ofdm over fading wireless channels orthogonal frequency division multiplexing ofdm converts a time dispersive channel into parallel subchannels and thus facilitates equalization and de coding but when the channel has nulls close to or on the fast fourier transform fft grid uncoded ofdm faces serious symbol recovery problems as an alternative to various error control coding techniques that have been proposed to ameliorate the problem we perform complex field coding cfc before the symbols are multiplexed we quantify the maximum achievable diversity order for independent and identically distributed i i d or correlated rayleigh fading channels and also provide design rules for achieving the maximum diversity order the maximum coding gain is given and the encoder enabling the maximum coding gain is also found simulated performance comparisons of cfc ofdm with existing block and convolutionally coded ofdm alternatives favor cfc ofdm for the code rates used in a hiperlan2 experiment

fast imdct and mdct algorithms a matrix approach this paper presents a systematic investigation of the modified discrete cosine transform inverse modified discrete cosine transform mdct imdct algorithm using a matrix representation this approach results in new understanding of the mdct imdct enables the development of new algorithms and makes clear the connection between the algorithms we represent in a matrix form the imdct as the product of the type iv dct with simple scaling sign changing and permutation operations such that fast algorithms for the type iv dct can be simply modified for the imdct and vice versa then the simple symmetry and inversion properties of the type iv dct are used to develop new algorithms and establish the connection between existing fast imdct algorithms this approach also enables us to show that mdct and imdct share common core operation and present an efficient architecture for implementing both the mdct and the imdct in one hardware

prime factor dct algorithms in this correspondence new algorithms are presented for computing the l d and 2 d discrete cosine transform dct of even length by using the discrete fourier transform dft a comparison of the proposed algorithms to other fast ones points out their computational efficiency which is mainly based on the advantages of prime factor decomposition and a proper choice of index mappings

a fast 4 4 dct algorithm for the recursive 2 d dct the authors present an efficient algorithm for the computation of the 4 4 discrete cosine transform dct the algorithm is based on the decomposition of the 4 4 dct into four 4 point 1 d dcts thus only 1 d transformations and some additions are required it is shown that the proposed algorithm requires only 16 multiplications which is half the number needed for the conventional row column method since the 2 sup m 2 sup m dct can be computed using the 4 4 dct recursively for any m the proposed algorithm leads to a fast algorithm for the computation of the 2 d dct

low complexity multidimensional dct approximations for high order tensor data decorrelation in this paper we introduce low complexity multidimensional discrete cosine transform dct approximations 3d dct approximations are formalized in terms of high order tensor theory the formulation is extended to higher dimensions with arbitrary lengths several multiplierless 8 times 8 times 8 approximate methods are proposed and the computational complexity is discussed for the general multidimensional case the proposed methods complexity cost was assessed presenting considerably lower arithmetic operations when compared with the exact 3d dct the proposed approximations were embedded into 3d dct based video coding scheme and a modified quantization step was introduced the simulation results showed that the approximate 3d dct coding methods offer almost identical output visual quality when compared with exact 3d dct scheme the proposed 3d approximations were also employed as a tool for visual tracking the approximate 3d dct based proposed system performs similarly to the original exact 3d dct based method in general the suggested methods showed competitive performance at a considerably lower computational cost

a fast algorithm for computing multidimensional dct on certain small sizes this paper presents a new algorithm for the fast computation of multidimensional m d discrete cosine transform dct with size n sub 1 spl times n sub 2 spl times spl middot spl middot spl middot spl times n sub m where n sub i is a power of 2 and n sub i spl les 256 by using the tensor product decomposition of the transform matrix it is shown that the m d dct or inverse discrete cosine transform idct on these small sizes can be computed using only one dimensional 1 d dcts and additions and shifts if all the dimensional sizes are the same the total number of multiplications required for the algorithm is only 1 m times of that required for the conventional row column method we also introduce approaches for computing scaled dcts in which the number of multiplications is considerably reduced

an unconditionally convergent algorithm for the evaluation of the ultimate limit state of rc sections subject to axial force and biaxial bending we present a numerical procedure based upon a tangent approach for evaluating the ultimate limit state uls of reinforced concrete rc sections subject to axial force and biaxial bending the rc sections are assumed to be of arbitrary polygonal shape and degree of connection furthermore it is possible to keep fixed a given amount of the total load and to find the uls associated only with the remaining part which can be increased by means of a load multiplier the solution procedure adopts two nested iterative schemes which in turn update the current value of the tentative ultimate load and the associated strain parameters in this second scheme an effective integration procedure is used for evaluating in closed form as explicit functions of the position vectors of the vertices of the section the domain integrals appearing in the definition of the tangent matrix and of the stress resultants under mild hypotheses which are practically satisfied for all cases of engineering interest the existence and uniqueness of the uls load multiplier is ensured and the global convergence of the proposed solution algorithm to such value is proved an extensive set of numerical tests carried out for rectangular l shaped and multicell sections shows the effectiveness of the proposed solution procedure

blind identification of fir systems excited by discrete alphabet inputs an algorithm for the identification of finite impulse response fir system parameters from output measurements for systems excited by discrete alphabet inputs is described the approach taken is algebraic it does not rely directly on the statistical properties of the measurements but rather it essentially solves the nonlinear equations appearing in the problem by converting them to equivalent linear equations using the discrete alphabet property of the input signal the proposed algorithm was tested by computer simulations and some of these simulations are illustrated

on the computation of the length 2 sup m discrete cosine and sine transforms via the permuted difference coefficient an intrinsic property wherein the set of numbers formed using the magnitudes of a basis vector s elements is the same for all basis vectors in a length 2 sup m type iii discrete sine transform dst and discrete cosine transform dct is proved we also show that the set of numbers formed using the magnitudes of any basis vector s elements in a length 2 sup m type iii dst is the same as that in a length 2 sup m type iii dct the same characteristics exist for the length 2 sup m type iv dst and dct a new combinational vlsi architecture that is only composed of adders for implementing the length 2 sup m type iii dst or dct dst iii dct iii using the intrinsic property and the permuted difference coefficient pdc algorithm is developed the advantages of this new architecture are high structural regularity very high speed and suitability for vlsi realization the other advanced sequential structure which is composed of registers multiplexers and an accumulator is also proposed to give a much lower complexity than the combinational structure this new sequential structure is very suitable for chip level microprocessor based or vlsi realization the quantization error that exhibits the effect of the internal finite word length representations of the input and the coefficient is also analyzed it is shown that if the length of data sequence is quadrupled then to maintain the same signal to noise ratio one additional bit must be added to represent both the input and the coefficient it is also shown that the roundoff error of the coefficients is less sensitive than that of the inputs

fast algorithms for the dft and other sinusoidal transforms a new matrix factorization is proposed for dct iv which is the basis of fast algorithms for many sinusoidal transforms the new fast algorithm for dft based on the new factorization requires the same number of multiplications and far fewer additions than the preuss algorithm

analytical integration of elasto plastic uniaxial constitutive laws over arbitrary sections summary we present the preliminary results of a novel approach to the state determination of polygonal sections of arbitrary shape endowed with elasto plastic uniaxial constitutive laws by means of a suitable application of gauss theorem we prove that the normal stress resultants can be computed analytically as sum of finite quantities evaluated solely at the vertices of the section for this reason the proposed approach has been termed fiber free to emphasize the fact that it does not require any subdivision of the section in fibers numerical results show that the fiber approach is grossly inaccurate and that the number of fibers required to achieve a degree of accuracy comparable with that entailed by the fiber free approach is at least one order of magnitude greater than the one commonly suggested in commercial software for nonlinear frame analysis copyright 2012 john wiley sons ltd

a generalized output pruning algorithm for matrix vector multiplication and its application to compute pruning discrete cosine transform in this correspondence a generalized output pruning algorithm for matrix vector multiplication is proposed it is shown that for a given decomposition of the matrix of the transform kernel and the pruning pattern the unnecessary operations for computing an output pruning discrete cosine transform dct can be eliminated thoroughly by using the proposed algorithm

analysis of a nonlinear least squares procedure used in global positioning systems iterated least squares ils is a widely used parameter estimation algorithm for nonlinear least squares problems the ils estimation error covariance is usually written gtr 1g 1 where g is the jacobian matrix at the solution and r is the noise covariance using a first order expansion of the gain matrix in ils we provide a rigorous justification for the covariance formula the analysis includes uncertainty in the initial estimate and is capable of modeling the transient performance of the algorithm given convergence the usual ils covariance is obtained asymptotically the analysis makes use of matrix differential calculus to obtain the first differential of the ils gain matrix and includes as a special case the r i case where the gain matrix is the pseudoinverse of the jacobian matrix the results are harnessed to obtain a sensitivity analysis of the ils algorithm to additional random parametric variations the analysis is then applied to a global positioning system problem to characterize the effect of ephemeris errors on the ils position estimates results from a comparative monte carlo simulation demonstrate the approach s effectiveness

fast algorithms for the discrete cosine transform several fast algorithms for computing discrete cosine transforms dcts and their inverses on multidimensional inputs of sizes which are powers of 2 are introduced because the 1 d 8 point dct and the 2 d 8 8 point dct are so widely used they are discussed in detail algorithms for computing scaled dcts and their inverses are also presented these have applications in compression of continuous tone image data where the dct is generally followed by scaling and quantization

fast algorithms for multidimensional dct to dct computation between a block and its associated subblocks in this paper we first propose an efficient algorithm for computing one dimensional 1 d discrete cosine transform dct for a signal block given its two adjacent subblocks in the dct domain and then introduce several algorithms for the fast computation of multidimensional m d dct with size n sub 1 spl times n sub 2 spl times spl times n sub m given 2 sup m subblocks of dct coefficients with size n sub 1 2 spl times n sub 2 2 spl times spl times n sub m 2 where n sub i i 1 2 m are powers of 2 obviously the row column method which employs the most efficient algorithms along each dimension reduces the computational complexity considerably compared with the traditional method which employs only the one dimensional 1 d fast dct and inverse dct idct algorithms however when m spl ges 2 the traditional method which employs the most efficient multidimensional dct idct algorithms has lower computational complexity than the row column method besides we propose a direct method by dividing the data into 2 sup m parts for independent fast computation in which only two steps of r dimensional r 1 2 m idct and additional multiplications and additions are required if all the dimensional sizes are the same the number of multiplications required for the direct method is only 2 sup m 1 m2 sup m 1 times of that required for the row column method and if n spl ges 2 sup 2m 1 the computational efficiency of the direct method is surely superior to that of the traditional method which employs the most efficient multidimensional dct idct algorithms

analytical method for blind binary signal separation the blind separation of multiple co channel binary digital signals using an antenna array involves finding a factorization of a data matrix x into x as where all entries of s are 1 or 1 it is shown that this problem can be solved exactly and noniteratively via a certain generalized eigenvalue decomposition as indicated by simulations the algorithm is robust in the presence of noise an interesting implication is that certain cluster segmentation problems can be solved using eigenvalue techniques

on algebras related to the discrete cosine transform abstract an algebraic theory for the discrete cosine transform dct is developed which is analogous to the well known theory of the discrete fourier transform dft whereas the latter diagonalizes a convolution algebra which is a polynomial algebra modulo a product of various cyclotomic polynomials the former diagonalizes a polynomial algebra modulo a product of various polynomials related to the chebyshev types when the dimension of the algebra is a power of 2 the dct diagonalizes a polynomial algebra modulo a product of chebyshev polynomials of the first type in both dft and dct cases the chinese remainder theorem plays a key role in the design of fast algorithms

analysis of pruning in fast cosine transform the discrete cosine transform dct is now the established technique for image and video coding in most image coding set schemes a large number of high frequency transform coefficients can be neglected and need not be calculated therefore significant savings in computation can be obtained by applying pruning in the fast algorithms we analyze pruning in chan and ho s 1990 fast dct algorithm and evaluate the saving of operations

a new algorithm to compute the discrete cosine transform a new algorithm is introduced for the 2m point discrete cosine transform this algorithm reduces the number of multiplications to about half of those required by the existing efficient algorithms and it makes the system simpler

fast algorithm for the 3 d dct ii recently many applications for three dimensional 3 d image and video compression have been proposed using 3 d discrete cosine transforms 3 d dcts among different types of dcts the type ii dct dct ii is the most used in order to use the 3 d dcts in practical applications fast 3 d algorithms are essential therefore in this paper the 3 d vector radix decimation in frequency 3 d vr dif algorithm that calculates the 3 d dct ii directly is introduced the mathematical analysis and the implementation of the developed algorithm are presented showing that this algorithm possesses a regular structure can be implemented in place for efficient use of memory and is faster than the conventional row column frame rcf approach furthermore an application of 3 d video compression based 3 d dct ii is implemented using the 3 d new algorithm this has led to a substantial speed improvement for 3 d dct ii based compression systems and proved the validity of the developed algorithm

fast multiplierless approximations of the dct with the lifting scheme we present the design implementation and application of several families of fast multiplierless approximations of the discrete cosine transform dct with the lifting scheme called the bindct these bindct families are derived from chen s 1977 and loeffler s 1989 plane rotation based factorizations of the dct matrix respectively and the design approach can also be applied to a dct of arbitrary size two design approaches are presented in the first method an optimization program is defined and the multiplierless transform is obtained by approximating its solution with dyadic values in the second method a general lifting based scaled dct structure is obtained and the analytical values of all lifting parameters are derived enabling dyadic approximations with different accuracies therefore the bindct can be tuned to cover the gap between the walsh hadamard transform and the dct the corresponding two dimensional 2 d bindct allows a 16 bit implementation enables lossless compression and maintains satisfactory compatibility with the floating point dct the performance of the bindct in jpeg h 263 and lossless compression is also demonstrated

blind digital signal separation using successive interference cancellation iterative least squares blind separation of instantaneous linear mixtures of digital signals is a basic problem in communications when little or nothing can be assumed about the mixing matrix signal separation may be achieved by exploiting structural properties of the transmitted signals e g finite alphabet or coding constraints we propose a monotonically convergent and computationally efficient iterative least squares ils blind separation algorithm based on an optimal scaling lemma the signal estimation step of the proposed algorithm is reminiscent of successive interference cancellation sic ideas for well conditioned data and moderate snr the proposed sic ils algorithm provides a better performance complexity tradeoff than competing ils algorithms coupled with blind algebraic digital signal separation methods sic ils offers a computationally inexpensive true least squares refinement option we also point out that a widely used ils finite alphabet blind separation algorithm can exhibit limit cycle behavior

fast unified computation of the multi dimensional discrete sinusoidal transforms based on a one to one index mapping approach conversions of two types of m dimensional discrete w transforms into the multiple sums involving a number of one dimensional discrete w transforms 1 d dwts are first presented a unified fast m 1 dimensional polynomial transform m 1 d pt and 1 d dwts algorithm for computing these two types of m d dwts are then proposed by revealing the relationships among the m dimensional discrete w transforms m d dwts the m dimensional generalized discrete fourier transforms m d gdfts the m dimensional discrete cosine transforms m d dcts and the m dimensional discrete sine transforms m d dsts the generalized fast algorithms for 14 types of the m d discrete sinusoidal transforms including four types of m d dwts and the same number of types of m d gdfts and three types of m d dcts and the same number of types of m d dsts are presented the number of multiplications for all 14 types of the m d discrete sinusoidal transforms needed by the proposed algorithm is only 1 m times that of the widely used corresponding row column methods the number of additions required by the proposed algorithm is also reduced considerably finally with the help of the software platform visual c 6 0 for windows 98 the computation time comparisons between the proposed and the reported algorithms are given the numerical experiments show that the proposed algorithms are not only highly efficient but are also very simple in computational structure

blind separation of synchronous co channel digital signals using an antenna array i algorithms we propose a maximum likelihood ml approach for separating and estimating multiple synchronous digital signals arriving at an antenna array at a cell site the spatial response of the array is assumed to be known imprecisely or unknown we exploit the finite alphabet property of digital signals to simultaneously estimate the array response and the symbol sequence for each signal uniqueness of the estimates is established for bpsk signals we introduce a signal detection technique based on the finite alphabet property that is different from a standard linear combiner computationally efficient algorithms for both block and recursive estimation of the signals are presented this new approach is applicable to an unknown array geometry and propagation environment which is particularly useful in wireless communication systems simulation results demonstrate its promising performance

an algorithm for calculation of the discrete cosine transform by paired transform a new algorithm for splitting the one dimensional 1 d 2 sup r point discrete cosine transform dct into a set of short 2 sup k point type iv dcts k 1 r 1 is introduced the splitting is performed by means of paired transformation that is defined by the paired representation of signals with respect to the cosine transform a proposed method of calculating the 2 sup r point cosine transform requires 2 sup r 1 r multiplications and 2 sup r 1 3r 2 1 additions when r spl ges 2