exact ber analysis of ostbcs in spatially correlated mimo channels the bit error rate ber performance of orthogonal space time block codes stbcs in correlated multiple input multiple output mimo channels is studied we first derive closed form exact ber equations for pulse amplitude modulation quadrature amplitude modulation and phase shift keying constellations in a correlated rayleigh mimo channel the ber expressions can be easily evaluated without any numerical methods then we consider correlated mimo channels where the line of sight components exist and they suffer from shadowing namely correlated shadowed rician mimo channels for three practical channel scenarios the ber is analyzed and closed form ber equations are presented

m psk and m qam ber computation using signal space concepts in this paper we introduce a simple geometric approach that is based on signal space concepts to efficiently evaluate the performance of m ary phase shift keying m psk and m ary quadrature amplitude modulation m qam schemes over an additive white gaussian noise channel in particular new bit error rate approximations are derived and shown to be in excellent agreement with monte carlo simulation results

on the index for array optimization and the discrete prolate spheroidal functions a class of array optimization problems is considered in which we seek to optimize the array response in a specified angular sector the optimization of array directivity is shown to be a special limiting case of these problems as the width of the specified angular sector approaches zero the optimum array patterns are also shown to be related to the well known prolate spheroidal functions

spatial spectral filtering with linearly constrained minimum variance beamformers in this paper orthogonal low dimension models for broad band sources as observed by an array delay line structure are developed the models are termed broad band source representation spaces and are subspaces of the observation space they are generated from eigenstructures of source sample covariance matrices and represent sources efficiently in the 2nd order statistical sense for a single broad band source propagating in a pure delay environment and observed with an isotropic array an accurate indication of the model dimension is derived which is independent on the array configuration being a function of the observed source time bandwidth product only using these representations procedures are described for controlling the spatial and spectral response of linearly constrained minimum variance broad band array beamformers the procedures employ linear constraints to control complex gain characteristics over selected bands of frequency for multiple points of 3 d regions of source locations and do not require the use of steering delays the constraints are derived from source representation spaces and are termed eigenvector constraints simulations are presented which illustrate the effectiveness of the new linear constraints

estimation of fmri response delays we present an efficient algorithm using the hilbert transform for estimating the delay of the bold response to neuronal stimulation with minimal additional computations the algorithm estimates parameters generated in the widely used cross correlation method and simplifies the interpolation required to estimate the response delay from the cross correlation function we examined errors in the hilbert based delay estimate associated with the use of dft on short duration discrete signals and proposed a method for minimizing these errors furthermore we compared the delay estimates obtained with the hilbert method to those obtained using the onset of the bold response the hilbert method resulted in less variance in the delay estimate despite the potential for higher variability in the latter part of the bold response this improved delay estimate was attributed to the reduced sensitivity of the hilbert method to noise contamination compared to the onset method

wide band nulling performance versus number of pattern constraints for an array antenna the problem of wide band pattern hulling for an array antenna is addressed in particular the relation between the number of constraints imposed and the sidelobe suppression achieved the two constraint methods considered are multiple nulling over a narrow angular sector and hulling of the pattern and its derivatives at a single point to first order the sidelobe cancellation is shown to be independent of the actual pattern type and is determined by only two parameters the number of null constraints m and the number of sidelobes v to be cancelled the latter parameter directly translates into a desired hulling bandwidth delta f a numerical solution to the problem is offered in the form of curves from which the number of nulls required to suppress a jammer over a given bandwidth can be conveniently estimated this number is indicative of how many degrees of freedom a conventional adaptive antenna system must allocate to attain a specific hulling performance

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

minimum ber linear transceivers for mimo channels via primal decomposition this paper considers the employment of linear transceivers for communication through multiple input multiple output mimo channels with channel state information csi at both sides of the link the design of linear mimo transceivers has been studied since the 1970s by optimizing simple measures of the quality of the system such as the trace of the mean square error matrix subject to a power constraint recent results showed how to solve the problem in an optimal way for the family of schur concave and schur convex cost functions in particular when the constellations used on the different transmit dimensions are equal the bit error rate ber averaged over these dimensions happens to be a schur convex function and therefore it can be optimally solved in a more general case however when different constellations are used the average ber is not a schur convex function and the optimal design in terms of minimum ber is an open problem this paper solves the minimum ber problem with arbitrary constellations by first reformulating the problem in convex form and then proposing two solutions one is a heuristic and suboptimal solution which performs remarkably well in practice the other one is the optimal solution obtained by decomposing the convex problem into several subproblems controlled by a master problem a technique borrowed from optimization theory for which extremely simple algorithms exist thus the minimum ber problem can be optimally solved in practice with very simple algorithms

spatial spectrum estimation in a location sector multiple narrowband source localization using arbitrarily configured arrays and spatial spectrum estimation is considered a new eigenspace based approach which uses projections onto a particular vector or vector set in the estimated noise only subspace is described several closest vector estimators are developed by using different measures of closeness first closest is a novel full dimensional element space approach to spatial spectrum estimation which has important performance advantages relative to pertinent established spatial spectrum estimators it incorporates a priori knowledge of the array manifold over a location sector of interest to provide snr spectral resolution thresholds which are lower than those of min norm for some arrays substantially lower second relationships between the closest approach and several established approaches to spatial spectrum estimation are established for a linear equispaced array min norm is shown to be a special case of the closest approach one which is based on projection onto a noise only subspace vector which is close to the array manifold over the entire field of view

a bayesian approach to robust adaptive beamforming an adaptive beamformer that is robust to uncertainty in source direction of arrival doa is derived using a bayesian approach the doa is assumed to be a discrete random variable with a known a priori probability density function pdf that reflects the level of uncertainty in the source doa the resulting beamformer is a weighted sum of minimum variance distortionless response mvdr beamformers pointed at a set of candidate doas where the relative contribution of each mvdr beamformer is determined from the a posteriori pdf of the doa conditioned on previously observed data a simple approximation to the a posteriori pdf results in a straightforward implementation performance of the approximate bayesian beamformer is compared with linearly constrained minimum variance lcmv beamformers and data driven approaches that attempt to estimate signal characteristics or the steering vector from the data

performance analysis of transmit beamforming for miso systems with imperfect feedback in this paper we analyze the performance of transmit beamforming on multiple antenna rayleigh fading channels with imperfect channel feedback we characterize the feedback imperfections in terms of noisy channel estimation feedback delay and finite rate channel quantization we develop a general framework that is valid for an arbitrary two dimensional linear modulation to capture the aforementioned imperfections and derive the symbol and bit error probability expressions for both m psk and m ary rectangular qam constellations with gray code mapping we show that the proposed analytical formulation is valid for a frequency domain duplexing system with without finite rate channel quantization and a time domain duplexing system we validate the accuracy of the analysis through simulations and assess the relative effects of channel estimation inaccuracy feedback delay and finite rate quantization on the symbol and bit error performances for various constellations

statistical precoding with decision feedback equalization over a correlated mimo channel the decision feedback df transceiver combining linear precoding and df equalization can establish point to point communication over a wireless multiple input multiple output channel matching the df transceiver design parameters to the channel characteristics can improve system performance but requires channel knowledge we consider the fast fading channel scenario with a receiver capable of tracking the channel state variations accurately while the transmitter only has long term channel distribution information the receiver design problem given channel state information is well studied in the literature we focus on transmitter optimization which amounts to designing a statistical precoder to assist the channel tailored df equalizer we develop a design framework that encompasses a wide range of performance metrics common cost functions for precoder optimization are analyzed thereby identifying a structure of typical cost functions transmitter design is approached for typical cost functions in general and we derive a precoder design formulation as a convex optimization problem two important subclasses of cost functions are considered in more detail first we explore a symmetry of df transceivers with a uniform subchannel rate allocation and derive a simplified convex optimization problem which can be efficiently solved even as system dimensions grow second we explore the tractability of a certain class of mean square error based cost functions and solve the transmitter design problem with a simple algorithm that identifies the convex hull of a set of points in r2 the behavior of df transceivers with optimal precoders is investigated by numerical means

an alternative expression for the symbol error probability of mpsk in the presence of i q unbalance this letter provides a new expression for the probability of the phase angle between two vectors perturbed by gaussian noise with in phase quadrature phase i q unbalance in order to simplify the analysis of the error probabilities of m ary phase shift keying mpsk the error probabilities symbol error rates or bit error rates for mpsk with i q balance or unbalance can be presented straightforwardly from the derived expression because the newly derived result is provided in terms of the conventional first order gaussian q function and the joint gaussian q function with a correlation coefficient dependent on m it readily allows rapid evaluation for various cases of practical interest

a simple algorithm to achieve desired patterns for arbitrary arrays a simple iterative algorithm which can be used to find array weights that produce array patterns with a given look direction and an arbitrary sidelobe specification is presented the method can be applied to nonuniform array geometries in which the individual elements have arbitrary and differing radiation patterns the method is iterative and uses sequential updating to ensure that peak sidelobe levels in the array meet the specification computation of each successive pattern is based on the solution of a linearly constrained least squares problem the constraints ensure that the magnitude of the sidelobes at the locations of the previous peaks takes on the prespecified values phase values for the sidelobes do not change during this process and problems associated with choosing a specific phase value are therefore avoided experimental evidence suggests that the procedure terminates in remarkably few iterations even for arrays with significant numbers of elements

multiple window based minimum variance spectrum estimation for multidimensional random fields spectrum analysis is viewed as the problem of estimating the power of a process contained within narrow bands this view leads naturally to consideration of filter based methods for estimating spectra multiple window based estimators where the power in a band is estimated as the average of the powers estimated at the outputs of multiple filters are considered the filters are designed using a linearly constrained minimum variance criterion commonly employed in adaptive beamforming this results in filters that automatically adjust their sidelobes to minimize leakage of energy from outside the band of interest expressions for the bias and variance of the power estimates are derived assuming the sample covariance matrix estimate is used to estimate the data covariance matrix and that the data are independent and identically gaussian distributed these expressions lead to the definition of a performance factor that indicates the degree of variance reduction obtained via multiple window processing a technique for obtaining increased suppression of energy leaking through the filter sidelobes at the expense of the response fidelity to energy in the band is presented simulations are presented to illustrate the effectiveness of the technique

the cramer rao lower bound for directions of arrival of gaussian cyclostationary signals the cramer rao lower bound on the variance of estimates of directions of arrival signal strengths and carrier frequencies and phases of cyclostationary signals arriving at an array is considered numerical evaluations of the bound for the estimates of directions of arrival show that it can be orders of magnitude lower than the corresponding bound for stationary signals despite the great number of unknown parameters in the former case comparisons with the mean squared error of direction estimates obtained by the cyclic least squares algorithm show that the bound is not overly optimistic

a new set of linear constraints for broad band time domain element space processors a new set of linear constraints for designing broad band time domain element space antenna array processors is presented the set of linear constraints is used to ensure that a desired look direction response of the processor over a frequency band of interest can be closely approximated the design technique is posed in such a way that three types of presteering can be handled no presteering coarse presteering and exact presteering the elimination of presteering time delays or the possibility to use coarse presteering is an attractive feature in a digital implementation of antenna array processors the relationship that the new processor has to other broad band processors is also established furthermore the approach enables various types of errors and mismatches between signal model and actual scenario to be incorporated in the problem formulation

log concavity property of the error probability with application to local bounds for wireless communications a clear understanding of the behavior of error probability ep as a function of signal to noise ratio snr and other system parameters is fundamental for assessing the design of digital wireless communication systems we propose an analytical framework based on the log concavity property of the ep which we prove for a wide family of multidimensional modulation formats in the presence of gaussian disturbances and fading based on this property we construct a class of local bounds for the ep that improve known generic bounds in a given region of the snr and are invertible as well as easily tractable for further analysis this concept is motivated by the fact that communication systems often operate with performance in a certain region of interest roi and thus it may be advantageous to have tighter bounds within this region instead of generic bounds valid for all snrs we present a possible application of these local bounds but their relevance is beyond the example made in this paper

engineering applications of correlation and spectral analysis 1994 engineering applications of correlation and spectral analysis technometrics vol 36 no 2 pp 220 221

closed form error analysis of variable gain multihop systems in nakagami m fading channels in this paper infinite integrals involving the product of bessel functions of different arguments are solved in closed form the obtained solutions form a framework for the error probability analysis of wireless amplify and forward af systems with an arbitrary number of variable gain relays operating over independent but not necessarily identical nakagami m fading channels here we show that the error probability can be described by generalized hypergeometric functions namely gauss s and lauricella s multivariate hypergeometric functions this work represents a significant improvement over previous contributions and extends previous formulas pertaining to dual hop transmissions over identical nakagami m fading channels numerical examples show an excellent match between simulation and theoretical results

dual hop relaying communications over fisher snedecor f fading channels in this paper we present a comprehensive framework for the performance analysis of dual hop relaying communications with variable gain amplify and forward af relays and operating in the presence of both multipath fading and shadowing modeled by the fisher snedecor mathcal f distribution novel closed form expressions for the probability density function pdf and the cumulative distribution function cdf of the end to end signal to noise ratio snr of the considered system subject to hardware impairments are first derived single integral expressions for the numerical evaluation of the n th moment of the end to end snr the outage probability op the ergodic capacity under different adaptive transmission schemes the effective capacity and the average bit error rate aber of m ary modulation schemes are further presented the proposed analytical expressions are valid for most of the well known fading distributions provided that the moment generating function mgf of the inverse snr of each hop is readily available for the special case of ideal hardware it is shown that the above performance metrics can be expressed in closed form it is worth pointing out that the proposed analysis is valid even when the destination node is equipped with multiple antennas and maximal ratio combining mrc is employed the correctness of the proposed mathematical analysis is validated through extensive numerically evaluated results accompanied with monte carlo simulations

performance of non adaptive and adaptive subcarrier intensity modulations in gamma gamma turbulence we investigate a variable rate constant power adaptive subcarrier intensity modulation employing m ary phase shift keying and rectangular quadrature amplitude modulation for optical wireless communication over the gamma gamma turbulence channels the adaptive schemes offer efficient utilization of optical wireless communication channel capacity by adapting the modulation order according to the received signal to noise ratio and a pre defined target bit error rate requirement novel closed form series solutions are presented for the achievable spectral efficiency average bit error rate and outage probability using a series expansion approach of the modified bessel function in addition asymptotic bit error rate and outage probability analyses are presented our asymptotic bit error rate analysis shows that the diversity order of both non adaptive and adaptive systems depends only on the smaller channel parameter of the gamma gamma turbulence numerical results demonstrate high accuracy of our series solutions with finite number of terms and improved spectral efficiency achieved by the adaptive systems without increasing the transmitter power or sacrificing bit error rate requirements

resolution bias errors in spectral density frequency response and coherence function measurements iv time delay bias errors the problem of time delay bias errors is treated in this part of the present series of papers as a special case of a general theory of resolution bias errors in spectral estimation presented in a previous part it is shown that the main effect of an additional time delay between the output and the input of a physical system is to multiply the frequency response and coherence estimators which would be obtained without delay with the normalized autocorrelation function of the window function and its square respectively experimental results for the rectangular and hanning windows are in accord with the theoretical predictions the theoretical results given in the literature previously are valid for the rectangular window only but not for an arbitrary window function

an exact performance analysis of mrc ostbc over generalized fading channels a unified analytical framework for evaluating the performance of maximal ratio combining mrc and orthogonal space time block coding ostbc over generalized fading channels is presented the basic motivation for developing such a framework pertains to analyzing the distribution of a sum of squared random variables rvs belonging to different families of fading distributions following a novel analytical approach stemming from the definition of a common moment generating function mgf model for these families of distributions the probability density function pdf and the cumulative distribution function cdf of a general sum of squared rvs are expressed by simple infinite gamma series expansions based on these expressions the capacity and error probability of mrc ostbc over generalized fading channels is thoroughly studied the developed theory is used to evaluate the performance of ostbc for a mixed nakagami m rice fading model and novel analytical results are presented the accuracy of the derived expressions is validated by extensive monte carlo simulations

on the design of minimum ber linear space time block codes for mimo systems equipped with mmse receivers in this paper we consider the design of a full rate linear space time block code for coherent multiple input multiple output mimo communication systems under a quasi static rayleigh flat fading environment our design targets specifically at the use of a linear minimum mean square error mmse receiver that minimizes the asymptotic average bit error rate ber when the transmitted signal is selected from a 4 qam constellation this optimization problem is solved in two main stages 1 a lower bound on the ber is first minimized and 2 how this minimized lower bound can be achieved is then shown by exploiting a rigorous convex optimization technique without any assumption on the code we prove that individual unitary and trace orthogonal structures are the necessary and sufficient conditions to assure the minimum asymptotic average ber with an mmse detector an algorithm is provided for an efficient generation of our codes and simulation results confirm that our optimally designed codes are indeed superior in performance compared to some other commonly used codes

minimum variance beamforming with soft response constraints soft constraints on the beamformer response to the signal are examined in the context of minimum variance beamforming a quadratic constraint on the beamformer weights is used to control the mean squared error between a desired response and the actual response in the signal direction the constraint is purposely chosen to permit distortion of the signal with the goal of achieving improved interference cancellation under the assumptions of known signal direction and spectral shape the signal to noise ratio is shown to be a nondecreasing function of the mean square distortion the distortion presented to the signal is easily computed from the beamformer weights and can be equalized after beamforming if desired properties of this beamforming method and its relationship to linear constrained beamforming are discussed simulations verify analytic results and illustrate the utility of the soft constrained approach

θ qam a parametric quadrature amplitude modulation family and its performance in awgn and fading channels we study a parametric quadrature amplitude modulation qam family called qam which includes other known constellations such as square qam sqam and triangular qam tqam as special cases the versatile structure of the qam signal constellation which occurs from the varying angle between the signal points results in achieving the minimum symbol error rate ser or bit error rate ber under an average power constraint the theoretical study aims at providing insight into the trade off between error performance and complexity of this parametric modulation scheme exact analytical expressions are obtained for the ser in additive white gaussian noise awgn and nakagami m fading channels while highly accurate ber approximations are presented finally we find the optimum angles in a minimal ser or ber sense for a specific signal to noise ratio snr and modulation order m this serves as an indicator for the appropriate constellation with respect to channel conditions and ser or ber requirements the presented theoretical analysis is validated via extensive computer simulations

a recursive algorithm for the exact ber computation of generalized hierarchical qam constellations hierarchical constellations offer a different degree of protection to the transmitted messages according to their relative importance as such they find interesting application in digital video broadcasting systems as well as wireless multimedia services although a great deal of attention has been devoted in the literature to the study of the bit error rate ber performance of uniform quadrature amplitude modulation qam constellations very few results were published on the ber performance of hierarchical qam constellations we obtain exact and generic expressions in m for the ber of the generalized hierarchical m pam pulse amplitude modulation constellations over additive white gaussian noise awgn and fading channels we also show how these expressions can be extended to generalized hierarchical m qam constellations square and rectangular for the awgn case these expressions are in the form of a weighted sum of complementary error functions and are solely dependent on the constellation size m the carrier to noise ratio and a constellation parameter which controls the relative message importance because of their generic nature these new expressions readily allow numerical evaluation for various cases of practical interest

efficient numerically stabilized rank one eigenstructure updating signal processing rank one eigenvalue decomposition evd updating is well suited to the problem of tracking time varying subspaces previously published rank one evd updating algorithms suffer from a linear buildup of roundoff error which makes them impractical for a large number of recursive updates in the present work the authors develop a numerical stabilization technique which eliminates the error buildup problem in a computationally efficient manner and makes the rank one evd update a practical numerical tool for online computation a simplified eigenvalue iteration is also given it reduces the complexity of the algorithm somewhat as well as the computation time simulations are presented to illustrate numerical performance

artificial shifting of fmri activation localized by volume and surface based analyses spatial smoothing is an important post processing procedure that is used to increase the signal to noise ratio snr of blood oxygenation level dependent signals bold in common functional magnetic resonance imaging fmri applications however recent studies have shown that smoothing artificially shifts probabilistic local maxima of fmri activations in this study we show shifting of the localization of functional centers in hand motor areas of the cerebral cortex by three dimensional isotropic gaussian kernel smoothing or two dimensional heat kernel smoothing in volume and surface based fmri analyses activation maps derived from smoothed echo planar imaging epi data by volume and surface based analyses were assigned to the nodes of individual cortical surface models and local maxima in the primary motor area m1 and the primary somatosensory cortex s1 were compared with those derived from non smoothed risk map analysis which is commonly used in presurgical applications for each analysis the euclidean and geodesic distances between the correlation coefficients of local maxima derived from smoothed and non smoothed epi data were measured the results show that the correlation coefficients derived from the volume and surface based analyses were about 29 4 and 42 9 higher for smoothed than for non smoothed risk map analyses and show minimum shifting of localizations by 12 1 mm and 6 9 mm on average in euclidean distance respectively and about 9 5 mm and 5 7 mm on average in geodesic distance respectively

error probability for orthogonal space time block code diversity system using rectangular qam transmission over rayleigh fading channels in this paper theoretical symbol error probability sep expressions are derived for orthogonal space time block code ostbc diversity systems employing arbitrary rectangular m qam transmission over flat rayleigh fading channels independent fading between diversity channels is assumed channel average powers may be distinctive identical or mixed with both the rectangular m qam results are extended to square m qam m pam and binary antipodal signaling all derived expressions are in elementary forms without complicated high order transcendental functions and unevaluated integrals and hence are strictly exact and can be readily simulated by the computer moreover it is shown that mixed rayleigh fading results can be readily extended to various nakagami m fading results a four transmit antenna system with a half rate ostbc for 16 qam signaling is used to demonstrate that the theoretical result is in excellent agreement with the monte carlo simulated result from simulation curves it is shown that under the independent channel fading condition channels with identical powers have better error rate performance than channels with distinctive powers

diversity analysis and design of space time multiblock codes for mimo systems equipped with linear mmse receivers this paper addresses the problem of designing optimum full symbol rate linear space time block codes stbc for a multi input multi output mimo communication system with m transmitter and n m receiver antennas and a linear minimum mean square error mmse receiver by analyzing the detection error probability expression for the optimized stbc it is shown that for qam signaling the maximum diversity gain for such a system is n m 1 the minimum probability of error stbc design is then extended to systems in which the transmission spans l independent realizations from a block fading channel model and a multiblock linear mmse receiver is employed necessary and sufficient conditions for the optimality of the code are obtained and a systematic design method for generating codes that satisfy these conditions is presented the detection error probability and diversity gain of this optimized linear multiblock transceiver are analyzed it is proved that the error probability decreases with l and it is shown numerically that the diversity gain increases with l thus if the corresponding latency can be accommodated for sufficiently large l an optimally designed multiblock system with a linear receiver can exploit the temporal diversity provided by the block fading channel and achieve higher diversity gain than that of any single block system of the same symbol rate with a maximum likelihood ml receiver the optimized multiblock linear system achieves this diversity at a substantially lower computational cost in fact the structure of the optimal codes can be exploited to significantly reduce the cost of the multiblock linear receiver

exact ber analysis of distributed alamouti s code for cooperative diversity networks we analyze the bit error rate ber performance of the distributed alamouti s code for cooperative diversity networks consisting of a source two relays and a destination node over rayleigh fading channels it is assumed that the relays adopt the amplify and forward protocol firstly assuming the existence of the direct path component from the source to the destination we derive the exact ber expression in a one integral form for m pulse amplitude modulation pam and m quadrature amplitude modulation qam constellations we also present a series expansion of a very accurate ber approximation which does not require any numerical calculation and we prove this series is convergent secondly considering the system where the direct path component does not exist we obtain the exact ber expression in a one integral form and a series expansion of the exact ber expression numerical results confirm that the two exact ber expressions in a one integral form perfectly match the simulation results and the two series expressions of ber are very accurate even with a small truncation window

error rates of the maximum likelihood detector for arbitrary constellations convex concave behavior and applications motivated by a recent surge of interest in convex optimization techniques convexity concavity properties of error rates of the maximum likelihood detector operating in the awgn channel are studied and extended to frequency flat slow fading channels generic conditions are identified under which the symbol error rate ser is convex concave for arbitrary multidimensional constellations in particular the ser is convex in snr for any one and two dimensional constellation and also in higher dimensions at high snr pairwise error probability and bit error rate are shown to be convex at high snr for arbitrary constellations and bit mapping universal bounds for the ser first and second derivatives are obtained which hold for arbitrary constellations and are tight for some of them applications of the results are discussed which include optimum power allocation in spatial multiplexing systems optimum power time sharing to decrease or increase jamming problem error rate an implication for fading channels fading is never good in low dimensions and optimization of a unitary precoded ofdm system for example the error rate bounds of a unitary precoded ofdm system with qpsk modulation which reveal the best and worst precoding are extended to arbitrary constellations which may also include coding the reported results also apply to the interference channel under gaussian approximation to the bit error rate when it can be expressed or approximated as a nonnegative linear combination of individual symbol error rates and to coded systems

tight probabilistic sinr constrained beamforming under channel uncertainties in downlink multi user beamforming a single basestation is serving a number of users simultaneously however energy intended for one user may leak to other unintended users causing interference with signal to interference plus noise ratio sinr being one of the most crucial quality metrics to users beamforming design with sinr guarantee has always been an important research topic however when the channel state information is not accurate the sinr requirements become probabilistic constraints which unfortunately are not tractable analytically for general uncertainty distribution therefore existing probabilistic beamforming methods focus on the relatively simple gaussian and uniform channel uncertainties and mainly rely on probability inequality based approximated solutions resulting in conservative sinr outage realizations in this paper based on the local structure of the feasible set in the probabilistic beamforming problem a systematic method is proposed to realize tight sinr outage control for a large class of channel uncertainty distributions with channel estimation and quantization errors as examples simulation results show that the sinr outage can be realized tightly which results in reduced transmit power compared to the existing inequality based probabilistic beamformers

performance analysis of zf and mmse equalizers for mimo systems an in depth study of the high snr regime this paper presents an in depth analysis of the zero forcing zf and minimum mean squared error mmse equalizers applied to wireless multiinput multioutput mimo systems with no fewer receive than transmit antennas in spite of much prior work on this subject we reveal several new and surprising analytical results in terms of output signal to noise ratio snr uncoded error and outage probabilities diversity multiplexing d m gain tradeoff and coding gain contrary to the common perception that zf and mmse are asymptotically equivalent at high snr we show that the output snr of the mmse equalizer conditioned on the channel realization is mmse zf ssrsnr where zf is the output snr of the zf equalizer and that the gap ssrsnr is statistically independent of zf and is a nondecreasing function of input snr furthermore as ssr snr ura ssrsnr converges with probability one to a scaled f random variable it is also shown that at the output of the mmse equalizer the interference to noise ratio inr is tightly upper bounded by ssrsnr zf using the decomposition of the output snr of mmse we can approximate its uncoded error as well as outage probabilities through a numerical integral which accurately reflects the respective snr gains of the mmse equalizer relative to its zf counterpart the e outage capacities of the two equalizers however coincide in the asymptotically high snr regime we also provide the solution to a long standing open problem applying optimal detection ordering does not improve the d m tradeoff of the vertical bell labs layered space time v blast architecture it is shown that optimal ordering yields a snr gain of 10log10n db in the zf v blast architecture where n is the number of transmit antennas whereas for the mmse v blast architecture the snr gain due to ordered detection is even better and significantly so

the spatial extent of the bold response functional magnetic resonance imaging is routinely used to localize brain function with multiple brain scans averaged together to reveal activation volumes in this study we examine the seldom studied effect of multiple scan averaging on the extent of activation volume using restricted visual field stimulation we obtained a large number of scan repetitions and analyzed changes in activation volume with progressively increased averaging and across single scans activation volume increased monotonically with averaging and failed to asymptote when as many as 22 scans were averaged together expansions in the spatial extent of activation were not random rather they were centered about activation loci that appear with little or no averaging using empirical and simulated data changes with averaging in activation volumes and cross correlation coefficient distributions revealed the presence of considerably more activated voxels than commonly surmised many voxels have low snr and remain undetected without extensive averaging the primary source of such voxels was not downstream venous drainage since there was no significant and consistent delay difference between voxels activated at different averaging levels voxels with low snr may reflect a diffuse subthreshold activity centered about spiking neurons dephasing gradients from distal veins or simply a blood flow response extending beyond the locus of neuronal firing across single scans as much as twofold changes in activation volume were observed these changes were not correlated with the order of scan acquisition subject task performance or signal and noise properties of activated voxels instead they may reflect subtle changes between overlapping noise and signal frequency components

on the eigenstructure of the signal only tempo spatial covariance matrix of broad band sources using a circular array the eigenstructure of the signal only part of the data covariance matrix for broadband sources is considered it is well known that unlike the narrowband case all eigenstructure parameters the matrix rank eigenvalues and eigenvectors depend on source spectral and spatial parameters as well as on the relationship between sources it is proved that when a two dimensional equally spaced circular array with flat spectrum broadband sources is used the eigenstructure of the signal only tempo spatial covariance matrix tscm has properties similar to those for the narrowband case most importantly the effective rank of the tscm depends only on the number of sources consequently the authors suggest an alternative approach for resolving frequency location ambiguity in the broadband case that may lead to an effective eigenstructure based parameter estimation algorithm of the music type

an adaptive generalized sidelobe canceller with derivative constraints an adaptive broad band beamforming structure is presented which employs a gradient based weight adjustment algorithm to minimize output variance subject to a set of j linear constraints on broadband directional derivatives in the desired look direction a generalized sidelobe cancelling structure is employed in which a nonadaptive conventional beamformer operates in parallel with an adaptive beamformer the conventional portion has a broad band beampattern which adheres to the specified constraints while the adaptive path is a cascade of a fixed signal blocking matrix and a set of tapped delay line filters blocking is employed to ensure that all incident waveforms which meet the specified constraints do not reach the tapped delay lines as a result an unconstrained least mean square lms power minimization algorithm is employed to adapt the delay line weights it is shown that with the addition of the directional derivative constraints the beamformer quiescent bcampattern becomes a function of the location of the phase center used to specify the constraints a design criterion for choosing this location is suggested and simulation experiments which illustrate the performance of this new adaptive beamformer are presented

broadband doa estimation using spatial only modeling of array data most of the existing techniques for doa estimation of broadband sources use both spatial and temporal modeling this may lead to increased complexity besides a large algorithmic delay we propose a technique that employs only spatial information in the form of a single spatial array covariance matrix assuming the source to have an ideal bandpass power spectral density we formulate two subspace based search functions for the estimation of the doas of broadband sources one of these employs a multidimensional search in the parameter space whereas the other requires a music like one dimensional 1 d search the multidimensional cost function is shown to be consistent yields performance close to the cramer rao cr bound and is insensitive to correlation between sources both the proposed methods are shown to be robust to deviations from the assumption of ideal bandpass power spectral density used in their formulation

exact expression for the ber of rectangular qam with arbitrary constellation mapping the exact closed form expression for the bit error rate ber of rectangular quadrature amplitude modulation qam is given the presented formula is independent of the bit mapping and it is thus particularly useful in the design and analysis of modulation schemes employing non gray mapping compared with the so called expurgated bound and the union bound our expression is shown to accurately predict the ber in the low signal to noise ratio range where the bounding techniques fail

analysis of the power spectral deviation of the general transfer function gsc in recent work we considered a microphone array located in a reverberated room where general transfer functions tfs relate the source signal and the microphones for enhancing a speech signal contaminated by interference it was shown that it is sufficient to use the ratio between the different tfs rather than the tfs themselves in order to implement the suggested algorithm an unbiased estimate of the tfs ratios was obtained by exploiting the nonstationarity of the speech signal in this correspondence we present an analysis of a distortion indicator namely power spectral density psd deviation imposed on the desired signal by our newly suggested transfer function generalized sidelobe canceller tf gsc algorithm it is well known that for speech signals psd deviation between the reconstructed signal and the original one is the main contribution for speech quality degradation as we are mainly dealing with speech signals we analyze the psd deviation rather than the regular waveform distortion the resulting expression depends on the tfs involved the noise field and the quality of estimation of the tf s ratios for the latter dependency we provide an approximated analysis of estimation procedure that is based on the signal s nanstationarity and explore its dependency on the actual speech signal and on the signal to noise ratio snr level the theoretical expression is then used to establish empirical evaluation of the psd deviation for several tfs of interest various noise fields and a wide range of snr levels it is shown that only a minor amount of psd deviation is imposed on the beamformer output the analysis presented in this correspondence is in good agreement with the actual performance presented in the former tf gsc paper

performance limits of the broadband generalized sidelobe cancelling structure in an isotropic noise field in acoustic applications the signal source of interest is generally broadband and the background noise field is predominantly isotropic in this letter the performance of the broadband generalized sidelobe canceller optimized with respect to an isotropic noise field is analyzed and compared against the performance of the conventional summing beamformer the comparison is based on an ideal continuous time infinite length generalized sidelobe canceller with the aim of determining the performance limits of this beamforming structure

eigenvalue beamforming using a multirank mvdr beamformer and subspace selection we derive eigenvalue beamformers to resolve an unknown signal of interest whose spatial signature lies in a known subspace but whose orientation in that subspace is otherwise unknown the unknown orientation may be fixed in which case the signal covariance is rank 1 or it may be random in which case the signal covariance is multirank we present a systematic treatment of such signal models and explain their relevance for modeling signal uncertainties we then present a multirank generalization of the mvdr beamformer the idea is to minimize the power at the output of a matrix beamformer while enforcing a data dependent distortionless constraint in the signal subspace which we design based on the type of signal we wish to resolve we show that the eigenvalues of an error covariance matrix are fundamental for resolving signals of interest signals with rank 1 covariances are resolved by the largest eigenvalues of the error covariance while signals with multirank covariances are resolved by the smallest eigenvalues thus the beamformers we design are eigenvalue beamformers which extract signal information from eigen modes of an error covariance we address the tradeoff between angular resolution of eigenvalue beamformers and the fraction of the signal power they capture

a spatial filtering approach to robust adaptive beaming the problem of controlling the superresolution in adaptive beamformers is treated a straightforward method is presented that works for both narrowband and broadband arrays the method is based on forming the blocking matrix in a general sidelobe canceller structure using a spatial fir filter the suppression of this spatial filter and the implicit noise of the leaky least mean square algorithm together determine the beamformer

gray coding for multilevel constellations in gaussian noise the problem of finding the optimal labeling bit to symbol mapping of multilevel coherent phase shift keying psk pulse amplitude modulation pam and quadrature amplitude modulation qam constellations with respect to minimizing the bit error probability bep over a gaussian channel is addressed we show that using the binary reflected gray code brgc to label the signal constellation results in the lowest possible bep for high enough signal energy to noise ratios and analyze what is high enough in this sense it turns out that the brgc is optimal for psk and pam systems whenever the target bep is at most a few percent which covers most systems of practical interest new and simple closed form expressions are presented for the bep of psk pam and qam using the brgc

lower bound on the ber of a pre and postequalized vector communication system this paper is concerned with communication over a multiple input multiple output channel in the first reference a lower bound on the bit error rate of a pre and postequalized communication system was derived for uniform bit loading here we extend the lower bound to nonuniform bit loading the lower bound applies to communication systems for which 1 the cascade of the pre equalizer noise free channel and postequalizer is a diagonal matrix a generalized zero forcing condition satisfied by many designs in the literature and 2 the encoding modulation decoding demodulation is done independently over the dimensions of the pre equalizer input postequalizer output the lower bound is stated as a function of the bit loading channel and transmitter power only and applies to uncoded as well as coset coded systems toward deriving the lower bound we minimize a weighted average of the noise variances at the postequalizer output

generalized eigenspace based beamformers the generalized eigenspace based beamformer geib is presented here which utilizes the eigenstructure of the correlation matrix to enhance the performance of the linearly constrained minimum variance beamformer lcmvb the weight vector of the geib is found by projecting the lcmvb weight vector onto a vector subspace constructed from the eigenstructure of the correlation matrix the geib and the lcmvb have the same responses to the desired signal and the interferers however the weight vector of the geib has a smaller norm and generates a lower output noise power an additional advantage of the geib is that the linear constraints can be treated flexibly i e each linear constraint can be chosen to be preserved or not preserved the cost of preserving a linear constraint is to get more output noise power in addition to developing the geib we discuss the effects of imposing linear constraints on the output noise powers of the geib and the lcmvb computer simulations are also presented that demonstrate the merits of the geib

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

multichannel post filtering in nonstationary noise environments in this paper we present a multichannel post filtering approach for minimizing the log spectral amplitude distortion in nonstationary noise environments the beamformer is realistically assumed to have a steering error a blocking matrix that is unable to block all of the desired signal components and a noise canceller that is adapted to the pseudo stationary noise but not modified during transient interferences a mild assumption is made that a desired signal component is stronger at the beamformer output than at any reference noise signal and a noise component is strongest at one of the reference signals the ratio between the transient power at the beamformer output and the transient power at the reference noise signals is used to indicate whether such a transient is desired or interfering based on a gaussian statistical model and combined with an appropriate spectral enhancement technique we derive estimators for the signal presence probability the noise power spectral density and the clean signal the proposed method is tested in various nonstationary noise environments compared with single channel post filtering a significantly reduced level of nonstationary noise is achieved without further distorting the desired signal components

performance analysis of linear modulation schemes with generalized diversity combining on rayleigh fading channels with noisy channel estimates generalized diversity combining gdc also known as hybrid selection maximal ratio combining or generalized selection combining is a low complexity diversity combining technique by which a fixed subset of a large number of available diversity channels is chosen and then combined using the rules of maximal ratio combining in this paper we analyze the performance of gdc on time correlated rayleigh fading channels with noisy channel estimates we derive expressions for the probability of error for various linear modulation schemes with coherent detection and discuss the conditions under which the analysis can be extended to noncoherent and differentially coherent receiver structures throughout the paper using a fundamental approach to obtain the decision statistic at the combiner output a number of new expressions for the error probabilities are obtained in a rigorous way along with a presentation of their performance with channel estimation errors the final expressions have roughly the same complexity of evaluation as that for the channel with only additive gaussian noise our results correct various inaccuracies in the literature and show that coherent receivers based on imperfectly estimated channel knowledge incur a significant performance loss

the broad band wiener solution for griffiths jim beamformers the authors treat the problem of finding the wiener filters for a wideband adaptive beamformer explicit expressions are given for the filters and error power spectrum in the frequency domain the expressions are simple to program and give the possibility of investigating superresolution for wideband signals and of determining sufficient lengths of the finite impulse response filters in adaptive arrays the major results are an analytical expression for the broadband array wiener solution given for an arbitrary spectrum for target interference and noise and an approximate analytic expression for the angular 3 db beamwidth for broadband signals

eigenstructure based partially adaptive array design a procedure is presented for designing partially adaptive arrays having nearly fully adaptive performance under steady state conditions theory predicts that the required adaptive dimension is less than or equal to the rank of the spatially temporally correlated portion of the interference correlation matrix for arbitrary linearly constrained minimum variance beamformers knowledge of the eigenstructure of the interference correlation matrix is required to implement a beamformer with this adaptive dimension to avoid adaptive estimation of the eigenstructure the eigenstructure of an averaged correlation matrix which spans the interference scenarios of interest is utilized and the adaptive dimension is given by the rank of the averaged correlation matrix construction of a transformation for reducing adaptive dimension is addressed simulations illustrating the utility of the eigenstructure approach are provided

characterizing the hemodynamic response effects of presentation rate sampling procedure and the possibility of ordering brain activity based on relative timing rapid presentation event related functional mri er fmri allows neuroimaging methods based on hemodynamics to employ behavioral task paradigms typical of cognitive settings however the sluggishness of the hemodynamic response and its variance provide constraints on how er fmri can be applied in a series of two studies estimates of the hemodynamic response in or near the primary visual and motor cortices were compared across various paradigms and sampling procedures to determine the limits of er fmri procedures and more generally to describe the behavior of the hemodynamic response the temporal profile of the hemodynamic response was estimated across overlapping events by solving a set of linear equations within the general linear model no assumptions about the shape were made in solving the equations following estimation of the temporal profile the amplitude and timing were modeled using a gamma function results indicated that 1 within a region for a given subject estimation of the hemodynamic response is extremely stable for both amplitude r 2 0 98 and time to peak r 2 0 95 from one series of measurements to the next and slightly less stable for estimation of time to onset r 2 0 60 2 as the trial presentation rate changed from those spaced 20 s apart to temporally overlapping trials the hemodynamic response amplitude showed a small but significant decrease trial onsets spaced on average 5 s apart showed a 17 25 reduction in amplitude compared to those spaced 20 s apart power analysis indicated that the increased number of trials at fast rates outweighs this decrease in amplitude if statistically reliable response detection is the goal 3 knowledge of the amplitude and timing of the hemodynamic response in one region failed to predict those properties in another region even for within subject comparisons 4 across subjects the amplitude of the response showed no significant correlation with timing of the response for either time to onset or time to peak estimates 5 the within region stability of the response was sufficient to allow offsets in the timing of the response to be detected that were under a second placing event related fmri methods in a position to answer questions about the change in relative timing between regions

a closed form expression for the exact ber of generalized pam and qam constellations we derive an explicit closed form expression for the exact bit error rate ber computation of generalized hierarchical m ary pulse amplitude modulations over additive white gaussian noise awgn and fading channels this expression can also be used to obtain the exact ber of generalized hierarchical quadrature amplitude modulations square and rectangular for the awgn case these expressions are in the form of a weighted sum of complementary error functions and are solely dependent on the constellation size m the carrier to noise ratio and a constellation parameter which controls the relative message importance

ber criterion and codebook construction for finite rate precoded spatial multiplexing with linear receivers precoded spatial multiplexing systems with rate limited feedback have been studied recently based on various precoder selection criteria instead of those based on indirect performance indicators we in this paper propose a new criterion directly based on the exact bit error rate ber that is applicable to systems with linear receivers and rectangular square quadrature amplitude modulation constellations the ber criterion outperforms any other alternative in terms of optimizing the ber performance for an uncoded system with linear receivers we then develop a precoder codebook construction method based on the generalized lloyd algorithm from the vector quantization literature this construction is not directly based on the ber criterion hence it is suboptimal in the ber sense however relative to those currently available our newfound codebooks improve considerably various minimum distances between any pair of codewords of the codebook finally we analyze the ber optimal precoder in the asymptotic case with infinite rate feedback that amounts to perfect channel knowledge at the transmitter the infinite rate optimal precoder based on the ber criterion is drastically different from the counterparts with other criteria and it leads to a benchmark performance for finite rate precoded spatial multiplexing systems we observe from numerical results that the ber performance of finite rate feedback with suboptimal codebooks approaches quickly the benchmark performance of infinite rate feedback this suggests that i the number of feedback bits in practical systems need not be large and ii the room for performance improvement via further codebook optimization shrinks quickly as the codebook size increases

convex primal decomposition for multicarrier linear mimo transceivers the design of linear transceivers for multiple input multiple output mimo communication systems with channel state information is particularly challenging for two main reasons first since several substreams are established through the mimo channel it is not even clear how the quality of the system should be measured second once a cost function has been chosen to measure the quality the optimization of the system according to such criterion is generally difficult due to the nonconvexity of the problem recent results have solved the problem for the wide family of schur concave convex functions resulting in simple closed form solutions when the system is modeled as a single mimo channel however with several mimo channels such as in multi antenna multicarrier systems the solution is generally more involved leading in some cases to the need to employ general purpose interior point methods this problem is specifically addressed in this paper by combining the closed form solutions for single mimo channels with a primal decomposition approach resulting in a simple and efficient method for multiple mimo channels the extension to functions that are not schur concave convex is also briefly considered relating the present work with a recently proposed method to minimize the average bit error rate ber of the system

adaptive convergence of linearly constrained beamformers based on the sample covariance matrix a statistical analysis of the adaptive convergence behavior of linearly constrained beamformers is given assuming the sample covariance estimator is used to estimate the covariance matrix the sensor data are assumed to be gaussian distributed and independent from data vector to data vector the output power and mean squared error in the absence of the desired signal are shown to be multiples of chi squared random variables the presence of the desired signal results in an excess mean squared error that is beta distributed and depends only on the signal power number of data vectors and number of adaptive degrees of freedom the expected value of the excess mean squared error resulting from the signal presence is directly proportional to the signal power and number of adaptive degrees of freedom but is inversely proportional to the number of data vectors

on the optimality of the binary reflected gray code this paper concerns the problem of selecting a binary labeling for the signal constellation in m psk m pam and m qam communication systems gray labelings are discussed and the original work by frank gray is analyzed as is noted the number of distinct gray labelings that result in different bit error probability grows rapidly with increasing constellation size by introducing a recursive gray labeling construction method called expansion the paper answers the natural question of what labeling among all possible constellation labelings will give the lowest possible average probability of bit errors for the considered constellations under certain assumptions on the channel the answer is that the labeling proposed by gray the binary reflected gray code is the optimal labeling for all three constellations which has surprisingly never been proved before

design of block transceivers with decision feedback detection this paper presents a method for jointly designing the transmitter receiver pair in a block by block communication system that employs intrablock decision feedback detection we provide closed form expressions for transmitter receiver pairs that simultaneously minimize the arithmetic mean squared error mse at the decision point assuming perfect feedback the geometric mse and the bit error rate of a uniformly bit loaded system at moderate to high signal to noise ratios separate expressions apply for the zero forcing and minimum mse mmse decision feedback structures in the mmse case the proposed design also maximizes the gaussian mutual information and suggests that one can approach the capacity of the block transmission system using independent instances of the same gaussian code for each element of the block our simulation studies indicate that the proposed transceivers perform significantly better than standard transceivers and that they retain their performance advantages in the presence of error propagation

ber evaluation of ofdm systems with joint effect of ti adc circuit s gain mismatch and channel estimation error the identification of maximum tolerable levels for potential mismatches is critical when designing communication systems in this paper we derive maximum tolerable levels for time interleaved analog to digital converter ti adc gain mismatch in orthogonal frequency division multiplexing ofdm systems to this end we first analytically evaluate the bit error rate ber for square quadrature amplitude modulated ofdm systems that are impaired by 1 the gain mismatch of a ti adc and 2 the channel estimation errors cees of a zero forcing equalizer our analysis includes the cases of a frequency selective rayleigh fading channel and a wired channel next built on the obtained ber expressions a threshold is established on the gain mismatch level at which an error floor caused by the gain mismatch is below a given ber value at high signal to noise ratios in the absence of cees finally numerical results further show that if and only if we set the gain mismatch level below 0 25 of this threshold there is essentially no ber performance degradation compared with the mismatch free case