ofdm based on low complexity transform to increase multipath resilience and reduce papr this paper introduces a new multicarrier system using a low computational complexity transform that combines the walsh hadamard transform wht and the discrete fourier transform dft into a single fast orthonormal unitary transform the proposed transform is used in a new orthogonal frequency division multiplexing t ofdm system leading to a significant improvement in bit error rate ber and reasonable reduction in the peak to average power ratio papr use of the proposed transform with ofdm has been found to attain high frequency diversity gain by combining all data samples resulting in the transmission over many subcarriers consequently the detrimental effect arising from channel fading on the subcarrier power is minimized theoretical analysis of the uncoded t ofdm performance over additive white gaussian noise awgn flat fading quasi static fixed within the entire period of ofdm symbol transmission frequency selective fading channel models with zero forcing zf and minimum mean square error mmse equalizers is presented in this work moreover the low superposition of the subcarriers passing through the t transforms leads to a reduction in the high peak of the transmitted signal whilst preserving the average transmitted power and data rate analytical results confirmed by simulations demonstrated that the proposed t ofdm system achieves lower papr and the same ber over awgn and flat fading channels compared to ofdm t ofdm is found to have better ber when mmse equalizer is used but slightly worse when zf equalizer is used

iterative soft compensation for ofdm systems with clipping and superposition coded modulation this paper deals with the clipping method used in orthogonal frequency division multiplexing ofdm systems to reduce the peak to average power ratio papr an iterative soft compensation method is proposed to mitigate the clipping distortion which can outperform conventional treatments the impact of signaling schemes on the residual clipping noise power is studied via the symbol variance analysis it is found that superposition coded modulation scm can minimize the residual clipping noise power among all possible signaling schemes this indicates that scm based ofdm systems are more robust to clipping effect than other alternatives when soft compensation is applied it is also shown that a multi code scm scheme can further reduce the clipping effect and its overall performance can be quickly evaluated using a semi analytical evolution method numerical examples are provided to verify the analysis

lipschitz continuity of solutions of linear inequalities programs and complementarity problems it is shown that solutions of linear inequalities linear programs and certain linear complementarity problems e g those with p matrices or z matrices but not semidefinite matrices are lipschitz continuous with respect to changes in the right hand side data of the problem solutions of linear programs are not lipschitz continuous with respect to the coefficients of the objective function the lipschitz constant given here is a generalization of the role played by the norm of the inverse of a nonsingular matrix in bounding the perturbation of the solution of a system of equations in terms of a right hand side perturbation

on the general ber expression of one and two dimensional amplitude modulations quadrature amplitude modulation qam is an attractive technique to achieve high rate transmission without increasing the bandwidth a great deal of attention has been devoted to the study of bit error rate ber performance of qam and approximate expressions for the bit error probability of qam have been developed in many places in the literature however the exact and general ber expression of qam with an arbitrary constellation size has not been derived yet we provide an exact and general closed form expression of the ber for one dimensional and two dimensional amplitude modulations i e pam and qam under an additive white gaussian noise awgn channel when gray code bit mapping is employed the provided ber expressions offer a convenient way to evaluate the performance of pam and qam systems for various cases of practical interest moreover simple approximations can be found from our expressions which are the same as the well known approximations if only the dominant terms are considered

relaxation methods for problems with strictly convex costs and linear constraints consider the problem of minimizing a strictly convex possibly nondifferentiable and nonseparable cost subject to linear constraints we propose a dual coordinate ascent method for this problem that uses inexact line search and either essentially cyclic or gauss southwell order of coordinate relaxation we show under very weak conditions that this method generates a sequence of primal vectors converging to the optimal primal solution under an additional regularity assumption and assuming that the effective domain of the cost function is polyhedral we show that a related sequence of dual vectors converges in cost to the optimal cost if the constraint set has an interior point in the effective domain of the cost function then this sequence of dual vectors is bounded and each of its limit points is an optimal dual solution when the cost function is strongly convex we show that the order of coordinate relaxation can become progressively more chaotic these results significantly improve upon those obtained previously

relaxation methods for problems with strictly convex separable costs and linear constraints we consider the minimization problem with strictly convex possibly nondifferentiable separable cost and linear constraints the dual of this problem is an unconstrained minimization problem with differentiable cost which is well suited for solution by parallel methods based on gauss seidel relaxation we show that these methods yield the optimal primal solution and under additional assumptions an optimal dual solution to do this it is necessary to extend the classical gauss seidel convergence results because the dual cost may not be strictly convex and may have unbounded level sets

the direct extension of admm for multi block convex minimization problems is not necessarily convergent the alternating direction method of multipliers admm is now widely used in many fields and its convergence was proved when two blocks of variables are alternatively updated it is strongly desirable and practically valuable to extend the admm directly to the case of a multi block convex minimization problem where its objective function is the sum of more than two separable convex functions however the convergence of this extension has been missing for a long time neither an affirmative convergence proof nor an example showing its divergence is known in the literature in this paper we give a negative answer to this long standing open question the direct extension of admm is not necessarily convergent we present a sufficient condition to ensure the convergence of the direct extension of admm and give an example to show its divergence

optimal tone reservation for cdma systems in this paper we analytically analyze the tone reservation method for the reduction of the peak to average power ratio papr in code division multiple access systems that employ the walsh functions we find the best possible reduction of the papr and give one optimal information set that achieves this reduction interestingly when using more than one information carrier the smallest possible extension constant is independent of the size of the information set and has the value sqrt 2 we further show that the minimal extension constant can also be achieved with finite compensation sets and illustrate the findings with a numerical example for certain special cases we are also able to provide results for the system of complex exponentials which is employed in orthogonal frequency division multiplexing

a flexible peak to average power ratio reduction scheme for ofdm systems by the adaptive projected subgradient method one of the main issues of the orthogonal frequency division multiplexing ofdm modulation is the high peak to average power ratio papr of the transmitted signal which adversely affects the complexity of power amplifiers in this paper we consider transmitters that reduce the papr by slightly disturbing the symbols in carriers used to transmit information and by sending dummy symbols i e symbols not conveying information in unused carriers the optimal choice of the data and dummy symbols is determined by the solution of a convex optimization problem to reduce the papr with low complexity we apply a modified version of the adaptive projected subgradient method to a sequence of convex cost functions closely related to the original optimization problem the resulting algorithm achieves near optimal papr in practical scenarios generalizes existing algorithms based on polyak s method and can easily handle multiple constraints

optimized signal distortion for papr reduction of ofdm signals with ifft fft complexity via admm approaches in this paper we propose two low complexity optimization methods to reduce peak to average power ratio papr values of orthogonal frequency division multiplexing ofdm signals via alternating direction method of multipliers admm first we formulate a nonconvex signal distortion optimization model based on minimizing data carrier distortion such that the constraints are placed on papr and the power of free carriers second to obtain the model s approximate optimal solution efficiently we design two low complexity admm algorithms named admm direct and admm relax respectively third we show that in admm direct relax all the optimization subproblems can be solved semi analytically and the computational complexity in each iteration is roughly mathcal o ell n log 2 ell n where ell and n are over sampling factor and carrier number respectively moreover we show that the resulting solution of admm direct is guaranteed to be some karush kuhn tucker kkt point of the nonconvex model when the iteration algorithm is convergent for admm relax we prove that it has theoretically guaranteed convergence and can approach arbitrarily close to some kkt point of the model if proper parameters are chosen simulation results demonstrate the effectiveness of the proposed approaches

on gelfand pairs associated with solvable lie groups let g be a locally compact group and let k be a compact subgroup of aut g the group of automorphisms of g there is a natural action of k on the convolution algebra l g and we denote by lk g the subalgebra of those elements in l g that are invariant under this action the pair k g is called a gelfand pair if li g is commutative in this paper we consider the case where g is a connected simply connected solvable lie group and k c aut g is a compact connected group we characterize such gelfand pairs k g and determine a moduli space for the associated k spherical functions

a novel low complexity precoded ofdm system with reduced papr the computational complexity and peak to average power ratio papr of conventional precoded orthogonal frequency division multiplexing ofdm systems can be reduced using a t ofdm precoded system based on the walsh hadamard matrix the present paper proposes a novel precoding scheme for further reducing the computational complexity and papr of t ofdm in the proposed scheme the precoding matrix is combined with an inverse discrete fourier transform to construct a new transform matrix at the transmitter notably the transform matrix is both unitary and circulant with each column being a perfect gaussian integer sequence containing just four non zero elements of pm 1 pm j a low complexity receiver is additionally constructed for the proposed precoding scheme a closed form expression is derived for the bit error rate ber in t ofdm and the proposed precoding scheme under frequency selective fading channels the simulation results for the ber are shown to be in good agreement with the mathematical derivations in addition it is demonstrated that t ofdm and the proposed scheme have an equivalent ber performance when their precoding matrices are designed in such a way as to obtain full frequency diversity however the proposed scheme has a better papr performance and a lower computational complexity than t ofdm

a posteriori error bounds for the linearly constrained varitional inequality problem in this paper we derive a posteriori error bound of an approximate solution to a linearly constrained variational inequality problem three measures of error are used with each depending on a particular characterization of an exact solution and related to a certain class of iterative methods

on operator valued spherical functions abstract we consider the equation 1 k x k y dk x y x y g in which a compact group k with normalized haar measure dk acts on a locally compact abelian group g let h be a hilbert space b h the bounded operators on h let g b h any bounded solution of 0 1 with 0 i 1 assume g satisfies the second axiom of countability if is weakly continuous and takes its values in the normal operators then x k u k x dk x g where u is a strongly continuous unitary representation of g on h 2 assuming g discrete k finite and the map x x k x of g into g surjective for each k k i there exists an equivalent inner product on h such that x for each x g is a normal operator with respect to it conditions 1 and 2 are partial generalizations of results by chojnacki on the cosine equation

near shannon limit and low peak to average power ratio turbo block coded ofdm in this paper we present an advanced solution for the long standing problem of large peak to average power ratio papr in orthogonal frequency division multiplexing ofdm systems although the design of low papr codewords has been extensively studied and the existence of asymptotically good codes with low papr is also proven still no code has been constructed to satisfy all requirements the main goal of the paper is to develop a coding scheme that not only generates low papr codewords but it also performs relatively close to the shannon limit we achieve this goal by implementing a time frequency turbo block coded ofdm in this scheme we design the frequency domain component to have a tightly bounded papr the time domain component code is designed to obtain good performance while the decoding algorithm has reasonable complexity through comparative performance evaluation we show that utilizing the proposed method we achieve considerable improvement in terms of papr while we slightly loose the performance compared to capacity achieving codes with similar overall block length

polyphase codes for uplink ofdm cdma systems we propose a ofdm cdma system that employs polyphase codes to support variable spreading factors a systematic approach for constructing the polyphase code sequences of variable spreading factors is developed polyphase codes exhibit better auto and cross correlation properties than hadamard codes when employed in ofdm cdma systems polyphase codes result in certain structured multiple access interference mai caused by multipath analytical and numerical results show that ofdm cdma systems employing polyphase codes have better papr performance than those using hadamard codes the ber performance of the ofdm cdma system using polyphase codes is evaluated by numerical results and compared to that of the ofdm cdma system using hadamard codes with and without clipping

performance analysis for ofdm signals with peak cancellation peak cancellation pc is known as one of the simplest peak to average power ratio papr reduction techniques that are applicable to various communications standards the salient advantage of pc is its ease of hardware implementation but it induces in band distortion and out of band radiation in order to restrict the amount of distortion within an acceptable level it is critical to carefully design the cancelling pulses as well as the envelope threshold over which pc is applied in most studies however they are determined empirically through computer simulations this paper thus focuses on a rigorous theoretical analysis of pc applied to band limited orthogonal frequency division multiplexing ofdm signals and discusses its validity and limitation for practical applications based on the level crossing rate approximation of the peak distribution we derive a closed form expression for the achievable signal to distortion power ratio sdr we also analyze the adjacent channel leakage ratio aclr as well as error vector magnitude evm with which the symbol error rate ser over an additive white gaussian noise awgn channel is obtained all the theoretical results developed in this work are compared with those based on the corresponding computer simulations to justify our analytical approach it thus serves as a useful and accurate tool for designing cancelling pulses as well as the threshold level for given specific system requirements such as sdr or evm and aclr

interpolation by the fft revisited an experimental investigation a numerical investigation into the accuracy of interpolation by fast fourier transform fft using a sinusoidal test signal is described the method is precisely defined including a previously unnoticed detail which makes a significant difference to the accuracy of the result the experiments show that with no input windowing the accuracy of interpolation is almost independent of sinusoidal wavelength very close to the nyquist limit the resulting rms error is inversely proportional to input sequence length and is very low for sequence lengths likely to be encountered in practice as wavelength passes through the nyquist limit there is a sudden increase in error as is expected from sampling theory if the sequence ends are windowed by short cosine half bells accuracy is further improved at longer wavelengths in comparison small kernal convolution methods such as linear interpolation and cubic convolution perform badly at wavelengths anywhere near the nyquist limit

ber minimized ofdm systems with channel independent precoders we consider the minimization of uncoded bit error rate ber for the orthogonal frequency division multiplexing ofdm system with an orthogonal precoder we analyze the ber performance of precoded ofdm systems with zero forcing and minimum mean squared error mmse receivers in the case of mmse receivers we show that for quadrature phase shift keying qpsk there exists a class of optimal precoders that are channel independent examples of this class include the discrete fourier transform dft matrix and the hadamard matrix when the precoder is the dft matrix the resulting optimal transceiver becomes the single carrier system with cyclic prefix sc cp system we also show that the worst solution corresponds to the conventional ofdm system the conventional ofdm system has the largest ber in the case of zero forcing receivers the design of optimal transceiver depends on the signal to noise ratio snr for higher snr solutions of optimal precoders are the same as those of mmse receivers

line search procedures for the logarithmic barrier function barrier methods for constrained optimization widely applied in the 1960s and 1970s have recently enjoyed a revival of popularity a line search with respect to a logarithmic barrier function or related potential function is often part of modern interior methods standard line search procedures tend to be inefficient in this context for two reasons an inappropriate choice of initial trial step if any constraints are nonlinear and poor approximation of the barrier function by loworder polynomial interpolants this paper discusses line search strategies specifically designed for the logarithmic barrier function

applications of second order cone programming in a second order cone program socp a linear function is minimized over the intersection of an affine set and the product of second order quadratic cones socps are nonlinear convex problems that include linear and convex quadratic programs as special cases but are less general than semidefinite programs sdps several efficient primaldual interior point methods for socp have been developed in the last few years after reviewing the basic theory of socps we describe general families of problems that tan be recast as socps these include robust linear programming and robust leastsquares problems problems involving sums or maxima of norms or with convex hyperbolic constraints we discuss a variety of engineering applications such as filter design antenna array weight design truss design and grasping forte optimization in robotics we describe an efficient primaldual interior point method for solving socps which shares many of the features of primaldual interior point methods for linear program

alternating direction method with gaussian back substitution for separable convex programming we consider the linearly constrained separable convex minimization problem whose objective function is separable into m individual convex functions with nonoverlapping variables a douglas rachford alternating direction method of multipliers adm has been well studied in the literature for the special case of m 2 but the convergence of extending adm to the general case of m ge 3 is still open in this paper we show that the straightforward extension of adm is valid for the general case of m ge 3 if it is combined with a gaussian back substitution procedure the resulting adm with gaussian back substitution is a novel approach towards the extension of adm from m 2 to m ge 3 and its algorithmic framework is new in the literature for the adm with gaussian back substitution we prove its convergence via the analytic framework of contractive type methods and we show its numerical efficiency by some application problems

fast alternating linearization methods for minimizing the sum of two convex functions we present in this paper alternating linearization algorithms based on an alternating direction augmented lagrangian approach for minimizing the sum of two convex functions our basic methods require at most o 1 epsilon iterations to obtain an epsilon optimal solution while our accelerated i e fast versions of them require at most o 1 sqrt epsilon iterations with little change in the computational effort required at each iteration for both types of methods we present one algorithm that requires both functions to be smooth with lipschitz continuous gradients and one algorithm that needs only one of the functions to be so algorithms in this paper are gauss seidel type methods in contrast to the ones proposed by goldfarb and ma in fast multiple splitting algorithms for convex optimization columbia university 2009 where the algorithms are jacobi type methods numerical results are reported to support our theoretical conclusions and demonstrate the practical potential of our algorithms

a walsh hadamard coded spectral efficient full frequency diversity ofdm system a full frequency diversity cofdm fd cofdm scheme based on sub channel multiplexing is proposed to improve the performance of cofdm without sacrificing spectral efficiency since the channel suffers the frequency selective fading the received signal contains strong inter symbol interference isi to obtain the diversity and code gains an iterative receiving algorithm is presented by jointly using diversity combining interference cancellation and soft decoding the proposed iterative receiving algorithm properly decodes the information bits in the strong isi environment consequently all the subcarriers of fd cofdm participate in diversity so that the system can achieve full frequency diversity in most practical channels the new receiving algorithm is relatively simple compared to the maximum likelihood estimation algorithm and is therefore a better alternative to balance the algorithm complexity and system performance

on the o 1 n convergence rate of the douglas rachford alternating direction method alternating direction methods adms have been well studied in the literature and they have found many efficient applications in various fields in this note we focus on the douglas rachford adm scheme proposed by glowinski and marrocco and we aim at providing a simple approach to estimating its convergence rate in terms of the iteration number the linearized version of this adm scheme which is known as the split inexact uzawa method in the image processing literature is also discussed

local linear convergence of the alternating direction method of multipliers on quadratic or linear programs we introduce a novel matrix recurrence yielding a new spectral analysis of the local transient convergence behavior of the alternating direction method of multipliers admm for the particular case of a quadratic program or a linear program we identify a particular combination of vector iterates whose convergence can be analyzed via a spectral analysis the theory predicts that admm should go through up to four convergence regimes such as constant step convergence or linear convergence ending with the latter when close enough to the optimal solution if the optimal solution is unique and satisfies strict complementarity

simplified approach to optimized iterative clipping and filtering for papr reduction of ofdm signals iterative clipping and filtering icf is a well known technique to reduce the peak to average power ratio papr of orthogonal frequency division multiplexing ofdm signals recently wang and luo investigated the clipped signal and proposed a modified algorithm called optimized icf oicf this is an optimal algorithm since it can achieve the required papr reduction with minimum in band distortion and far fewer iterations however oicf needs to solve a convex optimization problem with o n3 complexity where n represents the number of subcarriers in this paper instead of analyzing the clipped signal we study the clipping noise and propose a simplified oicf algorithm in the new algorithm solving the convex optimization problem is approximated by some simple algebraic operations and the computational complexity reduces to o n simulation results show that after three iterations the original oicf algorithm can achieve the desired papr while the simplified one exhibits almost the same performance for a 128 subcarrier and quadrature phase shift keying qpsk modulated ofdm system the papr reduction performance difference between the two algorithms are 5 10 3db at a 10 4 clipping probability and the bit error rate performance difference is 6 10 3 db at a 10 7 error probability

minimizing the peak to average power ratio of ofdm signals using convex optimization the main disadvantage of orthogonal frequency division multiplexing ofdm is the high time domain peak to average power ratio par that limits transmitter power efficiency assuming no changes in receiver structure the transmitter can only reduce par by distorting the data carriers or by adding power to the free carriers this paper shows that the ofdm signal with globally minimum par subject to constraints on the allowed constellation error and the free carrier power can be efficiently computed using convex optimization simulation results are presented for the 802 11a g wireless local area network standard the globally minimum par subject to the constellation error constraint ranges from 0 7 db for 6 mbps binary phase shift keying to 4 1 db for 54 mbps 64 qam tradeoff analysis shows that the free carrier power can be drastically reduced by backing off from this globally minimum par by less than 1 db a customized interior point method ipm is derived for solving the ofdm optimization problem the ipm reaches the desired tradeoff between par and free carrier power within two iterations where the main computational complexity per iteration is four fast fourier transforms plus the solution of a linear system of equations the customized ipm is about 100 times faster than a general purpose optimization algorithm

convergence analysis of alternating direction method of multipliers for a family of nonconvex problems the alternating direction method of multipliers admm is widely used to solve large scale linearly constrained optimization problems convex or nonconvex in many engineering fields however there is a general lack of theoretical understanding of the algorithm when the objective function is nonconvex in this paper we analyze the convergence of the admm for solving certain nonconvex consensus and sharing problems we show that the classical admm converges to the set of stationary solutions provided that the penalty parameter in the augmented lagrangian is chosen to be sufficiently large for the sharing problems we show that the admm is convergent regardless of the number of variable blocks our analysis does not impose any assumptions on the iterates generated by the algorithm and is broadly applicable to many admm variants involving proximal update rules and various flexible block selection rules

on the convergence properties of hildreth s quadratic programming algorithm we prove the linear convergence rate of hildreth s method for quadratic programming in both its sequential and simulateneous versions we give bounds on the asymptotic error constant and compare these bounds to those given by mandel for the cyclic relaxation method for solving linear inequalities

on dual convergence and the rate of primal convergence of bregman s convex programming method bregman s method is an iterative algorithm for solving optimization problems with convex objective and linear inequality constraints it generates two sequences one the primal one is known to converge to the solution of the problem under the assumption of smoothness of the objective function at the solution it is proved that the other sequence the dual one converges to a solution of the dual problem and that the rate of convergence of the primal sequence is at least linear

optimized iterative clipping and filtering for papr reduction of ofdm signals iterative clipping and filtering icf is a widely used technique to reduce the peak to average power ratio papr of orthogonal frequency division multiplexing ofdm signals however the icf technique when implemented with a fixed rectangular window in the frequency domain requires many iterations to approach specified papr threshold in the complementary cumulative distribution function ccdf in this paper we develop an optimized icf method which determines an optimal frequency response filter for each icf iteration using convex optimization techniques the design of optimal filter is to minimize signal distortion such that the ofdm symbol s papr is below a specified value simulation results show that our proposed method can achieve a sharp drop of ccdf curve and reduce papr to an acceptable level after only 1 or 2 iterations whereas the classical icf method would require 8 to 16 iterations to achieve a similar papr reduction moreover the clipped ofdm symbols obtained by our optimized icf method have less distortion and lower out of band radiation than the existing method

linear codes with covering radius r 2 3 and codimension tr let n n r sub q r denote a linear code over f sub q with length n codimension r and covering radius r we use a modification of constructions of 2q 1 2q 3 sub q 2 and 3q 1 3q 5 sub q 3 codes q spl ges 5 to produce infinite families of good codes with covering radius 2 and 3 and codimension tr

hadamard coded modulation for visible light communications visible light communication vlc systems using the indoor lighting system to also provide downlink communications require high average optical powers to satisfy the illumination needs this can cause high amplitude signals common in higher order modulation schemes to be clipped by the peak power constraint of the light emitting diode led and lead to high signal distortion in this paper we introduce hadamard coded modulation hcm to achieve low error probabilities in led based vlc systems needing high average optical powers this technique uses a fast walsh hadamard transform fwht to modulate the data as an alternative modulation technique to orthogonal frequency division multiplexing ofdm hcm achieves a better performance for high illumination levels because of its small peak to average power ratio papr the power efficiency of hcm can be improved by reducing the dc part of the transmitted signals the resulting so called dc reduced hcm dcr hcm is well suited to environments requiring dimmer lighting

the linearized alternating direction method of multipliers for dantzig selector the dantzig selector was recently proposed to perform variable selection and model fitting in the linear regression model it can be solved numerically by the alternating direction method of multipliers adm and in this paper we show that the application of adm to the dantzig selector can be speeded up significantly if one of its resulting subproblems at each iteration is linearized the resulting linearized adm for the dantzig selector is shown to be efficient for solving both synthetic and real world data sets

fast multiple splitting algorithms for convex optimization we present in this paper two different classes of general multiple splitting algorithms for solving finite dimensional convex optimization problems under the assumption that the function being minimized can be written as the sum of k convex functions each of which has a lipschitz continuous gradient we prove that the number of iterations needed by the first class of algorithms to obtain an epsilon optimal solution is o k 1 l epsilon where l is an upper bound on all of the lipschitz constants the algorithms in the second class are accelerated versions of those in the first class where the complexity result is improved to o sqrt k 1 l epsilon while the computational effort required at each iteration is almost unchanged to the best of our knowledge the complexity results presented in this paper are the first ones of this type that have been given for splitting and alternating direction type methods moreover all algorithms proposed in this paper are parallelizable which makes the

relaxation methods for network flow problems with convex arc costs we consider the standard single commodity network flow problem with both linear and strictly convex possibly nondifferentiable arc costs for the case where all arc costs are strictly convex we study the convergence of a dual gauss seide type relaxation method that is well suited for parallel computation we then extend this method to the case where some of the arc costs are linear as a special case we recover a relaxation method for the linear minimum cost network flow problem proposed in bertsekas 1 and bertsekas and tseng 2

on the peak to average power of ofdm signals based on oversampling orthogonal frequency division multiplexing ofdm introduces large amplitude variations in time which can result in significant signal distortion in the presence of nonlinear amplifiers we introduce a new bound for the peak of the continuous envelope of an ofdm signal based on the maximum of its corresponding oversampled sequence it is shown to be very tight as the oversampling rate increases the bound is then used to derive a closed form probability upper bound for the complementary cumulative distribution function of the peak to mean envelope power ratio of uncoded ofdm signals for sufficiently large numbers of subcarriers as another application of the bound for oversampled sequences we propose tight relative error bounds for computation of the peak power using two main methods the oversampled inverse fast fourier transform and the method introduced for coded systems based on minimum distance decoding of the code

constructions and families of covering codes and saturated sets of points in projective geometry in davydov 1990 constructions of linear binary covering codes were considered in the present paper constructions and techniques of the earlier paper are developed and modified for q ary linear nonbinary covering codes q spl ges 3 and new constructions are proposed the described constructions design an infinite family of codes with covering radius r based on a starting code of the same covering radius for arbitrary r spl ges 2 q spl ges 3 new infinite families of nonbinary covering codes with good parameters are obtained with the help of an iterative process when constructed codes are the starting codes for the following steps the table of upper bounds on the length function for codes with q 3 r 2 3 and codimension up to 24 is given the author proposes to use saturated sets of points in projective geometries over finite fields as parity check matrices of starting codes new saturated sets are obtained

on the linear convergence of the alternating direction method of multipliers we analyze the convergence rate of the alternating direction method of multipliers admm for minimizing the sum of two or more nonsmooth convex separable functions subject to linear constraints previous analysis of the admm typically assumes that the objective function is the sum of only two convex functions defined on two separable blocks of variables even though the algorithm works well in numerical experiments for three or more blocks moreover there has been no rate of convergence analysis for the admm without strong convexity in the objective function in this paper we establish the global r linear convergence of the admm for minimizing the sum of any number of convex separable functions assuming that a certain error bound condition holds true and the dual stepsize is sufficiently small such an error bound condition is satisfied for example when the feasible set is a compact polyhedron and the objective function consists of a smooth strictly convex function composed with a linear mapping and a nonsmooth ell 1 l1 regularizer this result implies the linear convergence of the admm for contemporary applications such as lasso without assuming strong convexity of the objective function

novel conversion matrices for simplifying the ifft computation of an slm based papr reduction scheme for ofdm systems there have been a set of conversion matrices proposed recently by wang and ouyang to simplify the inverse fast fourier transform ifft computation involved in the selected mapping slm scheme for reduction of the peak to average power ratio papr in orthogonal frequency division multiplexing ofdm systems as compared to the conventional slm scheme the modified approach achieves close papr reduction with much lower complexity but degraded bit error rate ber performance in this paper we propose a new set of conversion matrices for the slm scheme such that the complexity can be reduced without sacrificing the ber performance it is shown that the improved slm method has better ber performance and lower complexity than the previous work by wang and ouyang at the cost of a slight papr reduction loss

a variable penalty alternating directions method for convex optimization we study a generalized version of the method of alternating directions as applied to the minimization of the sum of two convex functions subject to linear constraints the method consists of solving consecutively in each iteration two optimization problems which contain in the objective function both lagrangian and proximal terms the minimizers determine the new proximal terms and a simple update of the lagrangian terms follows we prove a convergence theorem which extends existing results by relaxing the assumption of uniqueness of minimizers another novelty is that we allow penalty matrices and these may vary per iteration this can be beneficial in applications since it allows additional tuning of the method to the problem and can lead to faster convergence relative to fixed penalties as an application we derive a decomposition scheme for block angular optimization and present computational results on a class of dual block angular problems

dual ascent methods for problems with strictly convex costs and linear constraints a unified approach consider problems of the form text p qquad min f x ex geqq b where f is a strictly convex possibly nondifferentiable function and e and b are respectively a matrix and a vector a popular method for solving special cases of p e g network flow entropy maximization quadratic program is to dualize the constraints ex geqq b to obtain a differentiable maximization problem and then apply an iterative ascent method to solve it this method is simple and can exploit sparsity thus making it ideal for large scale optimization and in certain cases for parallel computation despite its simplicity however convergence of this method has been shown only under certain very restrictive conditions and only for certain special cases of p in this paper a block coordinate ascent method is presented for solving p that contains as special cases both dual coordinate ascent methods and dual gradient methods it is shown under certain mild assumptions on f and p that this method

some properties of the hessian of the logarithmic barrier function more than twenty years ago murray and lootsma showed that hessian matrices of the logarithmic barrier function become increasingly ill conditioned at points on the barrier trajectory as the solution is approached this paper explores some further characteristics of the barrier hessian we first show that except in two special cases the barrier hessian is ill conditioned in an entire region near the solution at points in a more restricted region including the barrier trajectory itself this ill conditioning displays a special structure connected with subspaces defined by the jacobian of the active constraints we then indicate how a cholesky factorization with diagonal pivoting can be used to detect numerical rank deficiency in the barrier hessian and to provide information about the underlying subspaces without making an explicit prediction of the active constraints using this subspace information a close approximation to the newton direction can be calculated by solving linear systems whose condition reflects that of the original problem