space time block codes from orthogonal designs we introduce space time block coding a new paradigm for communication over rayleigh fading channels using multiple transmit antennas data is encoded using a space time block code and the encoded data is split into n streams which are simultaneously transmitted using n transmit antennas the received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise maximum likelihood decoding is achieved in a simple way through decoupling of the signals transmitted from different antennas rather than joint detection this uses the orthogonal structure of the space time block code and gives a maximum likelihood decoding algorithm which is based only on linear processing at the receiver space time block codes are designed to achieve the maximum diversity order for a given number of transmit and receive antennas subject to the constraint of having a simple decoding algorithm the classical mathematical framework of orthogonal designs is applied to construct space time block codes it is shown that space time block codes constructed in this way only exist for few sporadic values of n subsequently a generalization of orthogonal designs is shown to provide space time block codes for both real and complex constellations for any number of transmit antennas these codes achieve the maximum possible transmission rate for any number of transmit antennas using any arbitrary real constellation such as pam for an arbitrary complex constellation such as psk and qam space time block codes are designed that achieve 1 2 of the maximum possible transmission rate for any number of transmit antennas for the specific cases of two three and four transmit antennas space time block codes are designed that achieve respectively all 3 4 and 3 4 of maximum possible transmission rate using arbitrary complex constellations the best tradeoff between the decoding delay and the number of transmit antennas is also computed and it is shown that many of the codes presented here are optimal in this sense as well

asymptotic equivalence for nonparametric regression with multivariate and random design we show that nonparametric regression is asymptotically equivalent in le cam s sense to a sequence of gaussian white noise experiments as the number of observations tends to infinity we propose a general constructive framework based on approximation spaces which allows asymptotic equivalence to be achieved even in the cases of multivariate and random design

high rate single symbol ml decodable precoded dstbcs for cooperative networks distributed orthogonal space time block codes dostbcs achieving full diversity order and single symbol maximum likelihood ml decodability have been introduced recently by yi and kim for cooperative networks and an upper bound on the maximal rate of such codes along with code constructions has been presented in this paper a new class of single symbol ml decodable precoded distributed space time block codes ssd pdstbcs called semiorthogonal ssd pdstbcs semi ssd pdstbcs is introduced wherein the source performs linear precoding of information symbols appropriately before transmitting it to all the relays it is shown that dostbcs are a special case of semi ssd pdstbcs a special class of semi ssd pdstbcs having diagonal covariance matrix at the destination is studied and an upper bound on the maximal rate of such codes is derived the bounds obtained are approximately twice larger than that of the dostbcs a systematic construction of semi ssd pdstbcs is presented when the number of relays k ges 4 the constructed codes are shown to achieve the upper bound on the rate when k is of the form 0 or 3 modulo 4 for the rest of the values of k the constructed codes are shown to have rates higher than that of dostbcs it is shown that semi ssd pdstbcs cannot be constructed with any form of linear processing at the relays when the source does not perform linear precoding of the information symbols

space time codes for high data rate wireless communication performance criteria in the presence of channel estimation errors mobility and multiple paths space time coding is a bandwidth and power efficient method of communication over fading channels that realizes the benefits of multiple transmit antennas specific codes have been constructed using design criteria derived for quasi static flat rayleigh or rician fading where channel state information is available at the receiver it is evident that the practicality of space time codes will be greatly enhanced if the derived design criteria remain valid in the absence of perfect channel state information it is even more desirable that the design criteria not be unduly sensitive to frequency selectivity and to the doppler spread this paper presents a theoretical study of these issues beginning with the effect of channel estimation error here it is assumed that a channel estimator extracts fade coefficients at the receiver and for constellations with constant energy it is proved that in the absence of ideal channel state information the design criteria for space time codes is still valid the analysis also demonstrates that standard channel estimation techniques can be used in conjunction with space time codes provided that the number of transmit antennas is small we also derive the maximum likelihood detection metric in the presence of channel estimation errors next the effect of multiple paths on the performance of space time codes is studied for a slowly changing rayleigh channel it is proved that the presence of multiple paths does not decrease the diversity order guaranteed by the design criteria used to construct the space time codes similar results hold for rapid fading channels with or without multiple paths the conclusion is that the diversity order promised by space time coding is achieved under a variety of mobility conditions and environmental effects

linear decoupled and quasi decoupled space time codes space time transmit diversity results in coupling of transmitted symbols across different antennas which increases the complexity of maximum likelihood decoding symbol coupling can be completely or partially avoided if the space time code stc satisfies specific decoupling conditions examples of such codes are orthogonal space time block codes and quasi orthogonal codes in this letter we study decoupling conditions for a linear full diversity stc quasi decoupled codes are proposed as a partially decoupled full diversity stc of any rate for any number of transmit antennas with minimum decoding delay by optimizing the coding gain of quasi decoupled codes it is shown that quasi orthogonal codes have competitive performance with respect to the alamouti code and the more recent threaded algebraic space time tast codes and abba codes a general full diversity decoupling condition is considered and the general solution to this case which also encompasses previously known orthogonal stcs is derived

trace orthonormal full diversity cyclotomic space time codes in this paper we consider the design of full diversity space time codes for a coherent multiple input multiple output mimo communication system starting from both the information theoretic and detection error viewpoints we first establish that a desirable property for general linear dispersion ld codes is to have an interunitary as well as an intraunitary structure a structure we call trace orthonormality by imposing the trace orthonormal structure on an ld code and applying cyclotomic number theory we establish for an arbitrary number of transmitter and receiver antennas a systematic and simple method to jointly design a unitary cyclotomic matrix the diophantine number and the corresponding constellation for an ld code as a result this enables us to construct full diversity rectangular cyclotomic ld codes with any symbol transmission rate less than or equal to the number of transmitter antennas in addition for the case when the number of transmitter antennas is greater than the number of receiver antennas by taking advantage of the delay we also arrive at the design of a special trace orthonormal full diversity cyclotomic space time block code which for the number of transmitter antenna being equal to 2m can be proved to minimize the worst case pairwise error probability of a maximum likelihood ml detector for a q ary quadrature amplitude modulation qam signal constellation and therefore achieves optimal coding gain computer simulations show that these codes have bit error performance advantages over currently available codes

fourth order statistics for blind classification of spatial multiplexing and alamouti space time block code signals blind signal classification a major task of intelligent receivers has important civilian and military applications this problem becomes more challenging in multi antenna scenarios due to the diverse transmission schemes that can be employed e g spatial multiplexing sm and space time block codes stbcs this paper presents a class of novel algorithms for blind classification of sm and alamouti stbc al stbc transmissions unlike the prior art we show that signal classification can be performed using a single receive antenna by taking advantage of the space time redundancy the first proposed algorithm relies on the fourth order moment as a discriminating feature and employs the likelihood ratio test for achieving maximum average probability of correct classification this requires knowledge of the channel coefficients modulation type and noise power to avoid this drawback three algorithms have been further developed their common idea is that the discrete fourier transform of the fourth order lag product exhibits peaks at certain frequencies for the al stbc signals but not for the sm signals and thus provides the basis of a useful discriminating feature for signal classification the effectiveness of these algorithms has been demonstrated in extensive simulation experiments where a nakagami m fading channel and the presence of timing and frequency offsets are assumed

weakly split spherical tits systems in quasi reductive groups we will prove that any weakly split spherical tits system b n in g bf g k bf g a quasi reductive k group such as a connected reductive k group satisfying some natural conditions is standard in particular if bf g is anisotropic over k then such a tits system is trivial i e b g n

on mimo beamforming systems using quantized feedback we propose the hadamard matrix as a codebook for multiple input multiple output mimo beamforming systems and show that a quantized equal gain transmission qegt scheme using the hadamard codebook has the same symbol error probability performance as a receiver selection diversity combining scheme operating in independent generalized rayleigh fading channels we show that a mimo beamforming system using quantized feedback over rician fading channels can be analyzed by considering a corresponding receiver selection combining scheme operating in single input multiple output simo systems over correlated generalized rician fading channels also we propose a greedy cophasing scheme for mimo beamforming systems using quantized feedback the greedy cophasing scheme provides 3 2 db power gain over an orthogonal space time block code when the number of transmit antennas is four the number of receive antennas is one and the number of feedback bits is three

differential space time modulation space time coding and modulation exploit the presence of multiple transmit antennas to improve the performance on multipath radio channels thus far most work on space time coding has assumed that perfect channel estimates are available at the receiver in certain situations however it may be difficult or costly to estimate the channel accurately in which case it is natural to consider the design of modulation techniques that do not require channel estimates at the transmitter or receiver we propose a general approach to differential modulation for multiple transmit antennas based on group codes this approach ran be applied to any number of transmit and receive antennas and any signal constellation we also derive low complexity differential receivers error bounds and modulator design criteria which we use to construct optimal differential modulation schemes for two transmit antennas these schemes can be demodulated with or without channel estimates this permits the receiver to exploit channel estimates when they are available the performance degrades by approximately 3 db when estimates are not available

distributed differential space time coding for wireless relay networks distributed space time coding is a cooperative transmission scheme for wireless relay networks with this scheme antennas of the distributive relays work as transmit antennas of the sender and generate a space time code at the receiver it achieves the maximum diversity although the scheme needs no channel information at relays it does require full channel information both the channels from the transmitter to relays and the channels from relays to the receiver at the receiver in this paper we propose a differential transmission scheme which requires channel information at neither relays nor the receiver for wireless relay networks as distributed space time coding can be seen as the counterpart of space time coding in the network setting this scheme is the counterpart of differential space time coding compared to coherent distributed space time coding the differential scheme is 3db worse in addition we show that alamouti square real orthogonal and sp 2 codes can be used differentially in networks with corresponding numbers of relays we also propose distributed differential space time codes that work for networks with any number of relays using circulant matrices

lens rigidity for manifolds with hyperbolic trapped set for a riemannian manifold m g with strictly convex boundary m the lens data consists in the set of lengths of geodesics with endpoints on m together with their endpoints x x m m and tangent exit vectors v v t x m t x m we show deformation lens rigidity for manifolds with hyperbolic trapped set and no conjugate points a class which contains all manifolds with negative curvature and strictly convex boundary including those with non trivial topology and trapped geodesics for the same class of manifolds in dimension 2 we prove that the set of endpoints and exit vectors of geodesics ie the scattering data determines the riemann surface up to conformal diffeomorphism

blind stbc identification for multiple antenna ofdm systems this paper addresses the problem of space time block code stbc identification for multiple antenna ma orthogonal frequency division multiplexing ofdm systems operating over frequency selective channels for the first time in literature previous investigations published on the topic of stbc identification were restricted to single carrier systems operating over frequency flat channels ofdm systems make this topic more challenging to handle since the identifiers work in frequency selective channels with little or no knowledge of the beginning of the ofdm blocks ofdm parameters and frequency selective channel coefficients we show that by taking advantage of the space time redundancy stbc identification can be performed by exploiting the cross correlation of the signals received from different antennas as a discriminating feature using this feature we develop a binary hypothesis test for decision making the proposed method does not require information about the channel coefficients modulation format noise power or timing of the ofdm and stbc blocks moreover it does not need accurate knowledge of either clock timing information or ofdm parameters including the number of sub carriers and cyclic prefix length extensive simulation experiments have verified the effectiveness of the proposed method

multiuser detection of alamouti signals in a mimo multiple access channel where users employ space time block codes stbc interference cancellation can be used to suppress co channel interference and recover the desired signal of each user at the receiver leveraging the special properties of alamouti matrices we first show that spatial multiplexing of alamouti signals retains the space time diversity gain of alamouti signaling using our proposed low complexity alamouti blast mmse a blast algorithm next in contrast to traditional transmit diversity that focuses on stbc construction at the transmitter this paper looks at transmit diversity from the perspective of the receiver in other words the receiver gets to choose the stbciquests which are favourable to the channel assuming a fixed blast receive algorithm in a multiusermac setting we first present a systematic methodology to exploit different decomposition structure in alamouti matrices each with different tradeoff between performance and decoding complexity using possibly different mimo receive algorithms we then demonstrate that the notion of angles the inner product of two quaternionic vectors between multiuser channels determines the performance of mimo receive algorithms as an application of the general theory we transform the decoding problem for several types of quasi orthogonal stbc qostbc into multiuser detection of virtual alamouti users building upon our a blast algorithm we propose new algorithms for decoding single user and multiuser qostbc in particular we show that bit error probability is a function of the quaternionic angle between virtual users for a single user or multiple users this angle varies with the type of qostbc and leads to a new form of adaptive modulation called code diversity where feedback instructs the transmitter how to choose from a plurality of codes

analysis and optimization of diagonally layered lattice schemes for mimo fading channels embodiments of the diagonal bell laboratories layered space time d blast architecture for multiple input multiple output mimo communication are developed wherein information symbol vectors are encoded using codewords from a lattice code called a diagonally layered lattice dll code which are formatted onto the diagonals of a space time frame decoding is done using a sphere decoder for each diagonal based on soft statistics obtained after zero forcing zf or minimum mean square error mmse filtering and decision feedback these operations give rise to an effective parallel channel model with channel gains with nonidentical statistics and additive noise which is gaussian in the zf filtering case and non gaussian in the mmse filtering case the so called full modulation diversity fmd property is nevertheless shown to yield the maximum achievable diversity orders over the mimo channel for both the zf and the mmse filtering based decoders respectively for any arbitrary fading distribution in the case of the independent identically distributed i i d rayleigh fading mimo channel with k transmit and n receive antennas with ngesk these diversity orders are nk k k 1 2 and nk for zf and mmse filtering based decoding respectively the error probability analysis also yields a design criterion for optimizing transmit power allocations several lattice design methods are proposed for the effective parallel channel models two methods are proposed to achieve high coding gain in the rayleigh fading mimo channel a third method is proposed that minimizes the exact symbol error probability sep and can be tailored for any given fading distribution a novel soft decision feedback decoder is also proposed based on the list sphere decoder to mitigate error propagation due to hard decision feedback the salient feature of the proposed dll schemes is that they have nearly full rate and full or high diversity order and yet a much lower decoding complexity than other existing full rate full diversity space time block codes stbcs the frame error probability fep performance of the optimized dll schemes for moderate to high spectral efficiencies and a wide range of signal to noise ratios snrs can be quite close to the performance of the best performing but more complex to decode stbcs moreover the proposed dll schemes significantly outperform other existing mimo systems of comparable decoding complexity

rates of contraction of posterior distributions based on gaussian process priors we derive rates of contraction of posterior distributions on nonparametric or semiparametric models based on gaussian processes the rate of contraction is shown to depend on the position of the true parameter relative to the reproducing kernel hilbert space of the gaussian process and the small ball probabilities of the gaussian process we determine these quantities for a range of examples of gaussian priors and in several statistical settings for instance we consider the rate of contraction of the posterior distribution based on sampling from a smooth density model when the prior models the log density as a fractionally integrated brownian motion we also consider regression with gaussian errors and smooth classification under a logistic or probit link function combined with various priors

design of multilayer coded modulation for nonergodic block fading channels multilayer coded modulation mlyc in single antenna and multiple antenna wireless fading channels is investigated while the mlyc has been known to achieve ergodic fading channel capacity the problem of interest here is to design practical and efficient mlyc for nonergodic block fading channels we develop a design methodology which maximizes the information rate of mlyc subject to an upper bound on the decoding error probability moreover we show that the mlyc performs closer to channel capacity when the overall diversity order of the channel is higher and proper spatial interleaving is employed the relationship between the mlyc scheme and other transmission techniques such as multilevel coded modulation and bit interleaved coded modulation bicm is also discussed it is shown through simulation examples that in realistic block fading channels the mlyc with practical coded modulation outperforms the bicm without turbo receiver iteration we propose the mlyc as a promising alternative to bicm especially when turbo iterative processing is not desired e g for progressive layered media transmission

diversity multiplexing tradeoff and outage performance for rician mimo channels in this paper we analyze the diversity multiplexing tradeoff dmt originally introduced by zheng and tse and outage performance for rician multiple input multiple output mimo channels the dmt characteristics of rayleigh and rician channels are shown to be identical in a high signal to noise ratio snr regime the log log plot of outage probability versus snr curve for a rician channel is a shifted version of that for the corresponding rayleigh channel the snr gap between the outage curves of the rayleigh and rician channels is derived the dmt and outage performance are also analyzed for rician multiple input single output miso single input multiple output simo channels over a finite snr regime a closed form expression for the outage probability is derived and the finite snr dmt characteristic is analyzed it is observed that the maximum diversity gain can be achieved at some finite snr the maximum gain tends to increase linearly with the rician factor the finite snr diversity gain is shown to be a linear function of the finite snr multiplexing gain the consistency between the dmts for finite and infinite snrs is also shown

generally explicit space time codes with nonvanishing determinants for arbitrary numbers of transmit antennas nonvanishing determinants have emerged as an attractive criterion enabling a space time code achieve the optimal diversity multiplexing gains tradeoff it seems that cyclic division algebras play the most crucial role in designing a space time code with nonvanishing determinants in this paper we explicitly construct space time codes for arbitrary numbers of transmit antennas that achieve nonvanishing determinants and the optimal diversity multiplexing gains tradeoff over z i unlike previous methods usually arising a field compositum for two or more fields our scheme which only requires one simple extension constitutes a much more efficient and feasible advancement whether in theory or practice

efficient nonparametric bayesian inference for x ray transforms we consider the statistical inverse problem of recovering a function f m to mathbb r where m is a smooth compact riemannian manifold with boundary from measurements of general x ray transforms i a f of f corrupted by additive gaussian noise for m equal to the unit disk with flat geometry and a 0 this reduces to the standard radon transform but our general setting allows for anisotropic media m and can further model local attenuation effects both highly relevant in practical imaging problems such as spect tomography we study a nonparametric bayesian inference method based on standard gaussian process priors for f the posterior reconstruction of f corresponds to a tikhonov regulariser with a reproducing kernel hilbert space norm penalty that does not require the calculation of the singular value decomposition of the forward operator i a we prove bernstein von mises theorems for a large family of one dimensional linear functionals of f and they entail that posterior based inferences such as credible sets are valid and optimal from a frequentist point of view in particular we derive the asymptotic distribution of smooth linear functionals of the tikhonov regulariser which attains the semiparametric information lower bound the proofs rely on an invertibility result for the fisher information operator i a i a between suitable function spaces a result of independent interest that relies on techniques from microlocal analysis we illustrate the performance of the proposed method via simulations in various settings

rates of contraction for posterior distributions in lr metrics 1 r the frequentist behavior of nonparametric bayes estimates more specifically rates of contraction of the posterior distributions to shrinking lr norm neighborhoods 1 r of the unknown parameter are studied a theorem for nonparametric density estimation is proved under general approximation theoretic assumptions on the prior the result is applied to a variety of common examples including gaussian process wavelet series normal mixture and histogram priors the rates of contraction are minimax optimal for 1 r 2 but deteriorate as r increases beyond 2 in the case of gaussian nonparametric regression a gaussian prior is devised for which the posterior contracts at the optimal rate in all lr norms 1 r

mimo antenna subset selection with space time coding this paper treats multiple input multiple output mimo antenna subset selection employing space time coding we consider two cases differentiated based on the type of channel knowledge used in the selection process we address both the selection algorithms and the performance analysis we first consider the case when the antenna subsets are selected based on exact channel knowledge eck our results assume the transmission of orthogonal space time block codes with emphasis on the alamouti see ieee j select areas commun vol 16 p 1451 68 oct 1998 code next we treat the case of antenna subset selection when statistical channel knowledge sck is employed by the selection algorithm this analysis is applicable to general space time coding schemes when eck is available we show that the selection algorithm chooses the antenna set that maximizes the channel frobenius norm leading to both coding and diversity gain when sck is available the selection algorithm chooses the antenna set that maximizes the determinant of the covariance of the vectorized channel leading mostly to a coding gain in case of eck based selection we provide analytical expressions for average snr and outage probability improvement for the case when sck based selection is used we derive expressions for coding gain we also present extensive simulation studies validating our results

integer forcing linear receivers linear receivers are often used to reduce the implementation complexity of multiple antenna systems in a traditional linear receiver architecture the receive antennas are used to separate out the codewords sent by each transmit antenna which can then be decoded individually although easy to implement this approach can be highly suboptimal when the channel matrix is near singular this paper develops a new linear receiver architecture that uses the receive antennas to create an effective channel matrix with integer valued entries rather than attempting to recover transmitted codewords directly the decoder recovers integer combinations of the codewords according to the entries of the effective channel matrix the codewords are all generated using the same linear code which guarantees that these integer combinations are themselves codewords provided that the effective channel is full rank these integer combinations can then be digitally solved for the original codewords this paper focuses on the special case where there is no coding across transmit antennas and no channel state information at the transmitter s which corresponds either to a multiuser uplink scenario or to single user v blast encoding in this setting the proposed integer forcing linear receiver significantly outperforms conventional linear architectures such as the zero forcing and linear minimum mean squared error receiver in the high signal to noise ratio regime the proposed receiver attains the optimal diversity multiplexing tradeoff for the standard multiple input multiple output mimo channel with no coding across transmit antennas it is further shown that in an extended mimo model with interference the integer forcing linear receiver achieves the optimal generalized degrees of freedom

lattice reduction based approximate map detection with bit wise combining and integer perturbed list generation for iterative detection and decoding idd in multiple input multiple output mimo systems the log likelihood ratio llr of each coded bit can be found by an optimal bit wise maximum a posteriori probability map detector however since this map detector requires a prohibitively high computational complexity low complexity suboptimal detectors are desirable in this paper lattice reduction lr based mimo detection is investigated to derive a low complexity detector that can achieve near map performance for idd in order to approximate llr values incorporating the extrinsic information provided by a soft input soft output siso decoder bit wise lr based minimum mean square error mmse filters are derived furthermore in order to minimize the performance degradation due to quantization or rounding errors in the lr based detection a low complexity integer perturbed list generation method is proposed where no tree search is used by taking advantage of a near orthogonal channel basis obtained by lr through a complexity analysis and simulations it is shown that the proposed approach achieves near optimal performance while the complexity is comparable with that of the mmse soft cancellation method which is known to be computationally efficient as a bit wise detector a parallel implementation of the proposed method would be straightforward which lowers the detection delay

euclidean and space time block codes relationship optimality performance analysis revisited an equivalent model for a multiple input multiple output communication system with space time block codes stbcs is proposed based on a revealed connection between stbcs and euclidean codes examples of distance spectra signal constellations and signal coordinate diagrams of euclidean codes equivalent to simplest orthogonal stbcs are given a new asymptotic upper bound for the symbol error rate ser of stbcs based on the distance spectra of the equivalent euclidean codes is derived and new general design criteria for signal constellations of the optimal code are proposed some bounds relating distance properties dimensionality and cardinality of stbcs with constituent signals of equal energy are given and new signal constellations with cardinalities of 8 and 16 for alamouti s code are designed a general methodology for performance analysis of stbcs is revisited as an example of the application of this methodology an exact evaluation of the ser of an orthogonal stbc is given namely a new expression for the ser of alamouti s code with binary phase shift keying signals is derived

two generalized complex orthogonal space time block codes of rates 7 11 and 3 5 for 5 and 6 transmit antennas space time block codes from orthogonal designs have two advantages namely fast maximum likelihood ml decoding and full diversity rate 1 real pulse amplitude modulation pam space time codes real orthogonal designs for multiple transmit antennas have been constructed from the real hurwitz radon families which also provides the rate 1 2 complex quadrature amplitude modulation qam space time codes complex orthogonal designs for any number of transmit antennas rate 3 4 complex orthogonal designs space time codes for three and four transmit antennas have existed in the literature but no high rate 1 2 complex orthogonal designs for other numbers of transmit antennas exist we present rate 7 11 and rate 3 5 generalized complex orthogonal designs for five and six transmit antennas respectively

the inverse problem for the local geodesic ray transform under a convexity assumption on the boundary we solve a local inverse problem namely we show that the geodesic x ray transform can be inverted locally in a stable manner one even has a reconstruction formula we also show that under an assumption on the existence of a global foliation by strictly convex hypersurfaces the geodesic x ray transform is globally injective in addition we prove stability estimates and propose a layer stripping type algorithm for reconstruction

deligne s topological central extension is universal abstract we give a purely local proof of the fact that the topological central extension of g k g an absolutely almost simple algebraic group defined and isotropic over a nonarchimedean local field k by the finite group k of roots of unity in k constructed by pierre deligne is a universal topological central extension of g k

multiple antenna signaling over fading channels with estimated channel state information performance analysis multiple antenna concepts for wireless communication systems promise high spectral efficiency and low error rates by proper exploitation of the randomness in multipath propagation in this paper we investigate the impact of channel uncertainty caused by channel estimation errors on the error rate performance we consider a training based multiple antenna system that reserves a portion of time to sound the channel training symbols are used to estimate the channel by means of an arbitrary linear filter at the receiver no channel state information csi is assumed at the transmitter we present a new framework to analyze training based multiple antenna systems by introducing an equivalent system model that specifies the channel by the estimated and hence known channel coefficients and an uncorrelated data dependent multiplicative noise we derive the maximum likelihood ml detector and highlight its behavior in the limiting cases of perfect csi and no csi and its relation to several mismatched detectors we deduce new exact expressions and chernoff bounds of the pairwise error probability pep used to assess word error and bit error rate bounds for ml and mismatched detection finally we review the code design guidelines in terms of the deleterious effect of channel uncertainty for coherent and noncoherent signaling schemes and present numerical results

quaternion orthogonal designs from complex companion designs abstract the success of applying generalized complex orthogonal designs as space time block codes recently motivated the definition of quaternion orthogonal designs as potential building blocks for space time polarization block codes this paper offers techniques for constructing quaternion orthogonal designs via combinations of specially chosen complex orthogonal designs one technique is used to build quaternion orthogonal designs on complex variables for any even number of columns a second related technique is applied to maximum rate complex orthogonal designs to generate an infinite family of quaternion orthogonal designs on complex variables such that the resulting designs have no zero entries this second technique is also used to generate an infinite family of quaternion orthogonal designs defined over quaternion variables that display a regular redundancy the proposed constructions are theoretically important because they provide the first known direct techniques for building infinite families of orthogonal designs over quaternion variables for any number of columns

the boundary rigidity problem in the presence of a magnetic field abstract for a compact riemannian manifold with boundary endowed with a magnetic potential we consider the problem of restoring the metric g and the magnetic potential from the values of the mane action potential between boundary points and the associated linearized problem we study simple magnetic systems in this case knowledge of the mane action potential is equivalent to knowledge of the scattering relation on the boundary which maps a starting point and a direction of a magnetic geodesic into its end point and direction this problem can only be solved up to an isometry and a gauge transformation of for the linearized problem we show injectivity up to the natural obstruction under explicit bounds on the curvature and on we also show injectivity and stability for g and in a generic class g including real analytic ones for the nonlinear problem we show rigidity for real analytic simple g rigidity for metrics in a given conformal class and locally near any g g we also show that simple magnetic systems on two dimensional manifolds are always rigid

iterative receivers with bit level cancellation and detection for mimo bicm systems the multiple input multiple output mimo detection in the iterative receiver is investigated for a modulation of square constellation for computationally efficient mimo detection we employ the hard decision bit level cancellation blc to reduce the dimension of the mimo detection as it has advantages over the symbol level cancellation 1 it can provide better performance and 2 the extrinsic bit information can be directly used for the blc a set of reliably decoded bits from the channel decoder in iterations is used for hard decision blc to approximate the maximum a posteriori probability map detection under the partial map detection principle for the bits that are not canceled the nulling using projection is employed to approximate the map detection this approach is applicable for a lower order modulation for a higher order modulation the minimum mean square error mmse filtering with soft decision cancellation sc is applied to further mitigate the bits that are not canceled

approximation metric entropy and small ball estimates for gaussian measures a precise link proved by kuelbs and li relates the small ball behavior of a gaussian measure on a banach space e with the metric entropy behavior of k the unit ball of the reproducing kernel hilbert space of in e we remove the main regularity assumption imposed on the unknown function in the link this enables the application of tools and results from functional analysis to small ball problems and leads to small ball estimates of general algebraic type as well as to new estimates for concrete gaussian processes moreover we show that the small ball behavior of a gaussian process is also tightly connected with the speed of approximation by finite rank processes

an efficient detector for combined space time coding and layered processing group layered space time architecture glst combines space time block coding and layered space time processing where the transmit stream is partitioned into different groups and in each group space time block coding is applied in the traditional receiver of glst group detection is applied first to suppress the interference from other groups and then decoding is performed for the desired group in this letter a novel detector is proposed in which the entire groups are decoded first and then group detection is performed next theoretical analysis will demonstrate that the new detector can achieve a significant capacity gain compared with the traditional one simulation results will further show that the proposed detector can obtain at least 4 db gain at a frame error rate of 10 sup 2 for instance

iterative decoding of binary block and convolutional codes iterative decoding of two dimensional systematic convolutional codes has been termed turbo de coding using log likelihood algebra we show that any decoder can be used which accepts soft inputs including a priori values and delivers soft outputs that can be split into three terms the soft channel and a priori inputs and the extrinsic value the extrinsic value is used as an a priori value for the next iteration decoding algorithms in the log likelihood domain are given not only for convolutional codes but also for any linear binary systematic block code the iteration is controlled by a stop criterion derived from cross entropy which results in a minimal number of iterations optimal and suboptimal decoders with reduced complexity are presented simulation results show that very simple component codes are sufficient block codes are appropriate for high rates and convolutional codes for lower rates less than 2 3 any combination of block and convolutional component codes is possible several interleaving techniques are described at a bit error rate ber of 10 sup 4 the performance is slightly above or around the bounds given by the cutoff rate for reasonably simple block convolutional component codes interleaver sizes less than 1000 and for three to six iterations

soft heuristic detectors for large mimo systems we propose low complexity detectors for large mimo systems with bpsk or qam constellations these detectors work at the bit level and consist of three stages in the first stage maximum likelihood decisions on certain bits are made in an efficient way in the second stage soft values for the remaining bits are calculated in the third stage these remaining bits are detected by means of a heuristic programming method for high dimensional optimization that uses the soft values soft heuristic algorithm we propose two soft heuristic algorithms with different performance and complexity we also consider a feedback of the results of the third stage for computing improved soft values in the second stage simulation results demonstrate that for large mimo systems our detectors can outperform state of the art detectors based on nulling and canceling semidefinite relaxation and likelihood ascent search

semiorthogonal space time block codes in this paper a new class of full diversity rate one space time block codes stbcs called semiorthogonal algebraic space time block codes sast codes is proposed sast codes are delay optimal when the number of transmit antennas is even the sast codeword matrix has a generalized alamouti structure where the transmitted symbols are replaced by circulant matrices and the commutativity of circulant matrices simplifies the detection of transmit symbols sast codes with maximal coding gain are constructed by using rate one linear threaded algebraic space time ltast codes compared with ltsat codes sast codes not only reduce the complexity of maximum likelihood detection but also provide remarkable performance gain they also outperform other stbc with rate one or less sast codes also perform well with suboptimal detectors such as the vertical bell laboratories layered space time v blast nulling and cancellation receiver finally sast codes attain nearly 100 of the shannon capacity of open loop multiple input single output miso channels

interpolation based transmit beamforming for mimo ofdm with limited feedback transmit beamforming and receive combining are simple methods for exploiting spatial diversity in multiple input multiple output orthogonal frequency division multiplexing mimo ofdm system optimal beamforming requires channel state information in the form of the beamforming vectors for each ofdm subcarrier this paper proposes a limited feedback architecture that combines beamforming vector quantization and smart vector interpolation in the proposed system the receiver sends a fraction of information about the optimal beamforming vectors to the transmitter and the transmitter computes the beamforming vectors for all subcarriers through interpolation a new spherical interpolator is developed that exploits parameters for phase rotation to satisfy the phase invariance and unit norm properties of the transmitted beamforming vectors the beamforming vectors and phase parameters are quantized at the receiver and the quantized information is provided to the transmitter the proposed quantization system provides only a moderate increase in complexity versus over comparable approaches numerical simulations show that the proposed scheme performs better than existing diversity techniques with the same feedback data rate

a sharp stability estimate for tensor tomography in non positive curvature we consider the geodesic x ray transform acting on solenoidal tensor fields on a compact simply connected manifold with strictly convex boundary and non positive curvature we establish a stability estimate of the form l 2 mapsto h 1 2 t where the h 1 2 t space is defined using the natural parametrization of geodesics as initial boundary points and incoming directions fan beam geometry only tangential derivatives at the boundary are used the proof is based on the pestov identity with boundary term localized in frequency

reduced feedback mimo ofdm precoding and antenna selection transmitter precoding for multiple input multiple output orthogonal frequency division multiplexing mimo ofdm is an effective way of leveraging the diversity gains afforded by a multiple transmit multiple receive antenna system in a frequency selective environment in the limited feedback scenario optimal precoder representation for narrowband mimo systems using moderately sized codebooks designed on the grassmann manifold has been shown to perform remarkably well in mimo ofdm systems precoder matrices have to be designed for all subcarriers and the amount of feedback can get prohibitively large this is especially true for next generation wireless local area networks and wireless metropolitan area networks which have a large number of subcarriers in this paper we present techniques to reduce this feedback requirement and the performance of these algorithms is numerically shown to provide improvement over existing schemes

space time frequency shift keying frequency shift keying fsk is a popular modulation scheme in power limited communication links this paper introduces space time fsk st fsk which does not require any channel state information at the transmitter and the receiver as in conventional noncoherent fsk st fsk can be viewed as a special unitary st modulation design however st fsk has a number of advantages over existing unitary st modulation designs st fsk is easier to design and enjoys lower decoding complexity furthermore st fsk guarantees full diversity finally st fsk can be adopted in the digital as well as in the analog domain and merges very naturally with frequency hopping multiple access as expected all these advantages come at the cost of a decrease in spectral efficiency

asymptotic information lossless designs and the diversity multiplexing tradeoff it is known that neither the alamouti nor the v blast scheme achieves the zheng tse diversity multiplexing tradeoff dmt of the multiple input multiple output mimo channel with respect to the dmt curve the alamouti scheme achieves the point corresponding to maximum diversity gain only whereas v blast meets only the point corresponding to maximum multiplexing gain it is also known that d blast achieves the optimal dmt for n transmit and n receive antennas but only under the assumption that the leading and trailing zeros are ignored when these zeros are taken into account d blast achieves the point corresponding to zero multiplexing gain but not the point corresponding to zero diversity gain the first scheme to achieve the dmt is the coding scheme of yao and wornell for the case of two transmit and two receive antennas in this paper we introduce the notion of an asymptotic information lossless aill design and obtain a necessary and sufficient condition under which a design is aill analogous to the result that full rank designs achieve the point corresponding to the zero multiplexing gain of the optimal dmt curve we show aill to be a necessary and sufficient condition for a design to achieve the point on the dmt curve corresponding to zero diversity gain we also derive a lower bound on the tradeoff achieved by designs from field extensions and show that the tradeoff is very close to the optimal tradeoff in the case of a single receive antenna a lower bound to the tradeoff achieved by designs from division algebras is presented which indicates that these designs achieve both extreme points corresponding to zero diversity and zero multiplexing gain of the optimal dmt curve finally we present simulations results for n transmit and n receive antennas for n 2 3 4 which suggest that designs from division algebras are likely to have the property of being dmt achieving

tensor tomography on surfaces we show that on simple surfaces the geodesic ray transform acting on solenoidal symmetric tensor fields of arbitrary order is injective this solves a long standing inverse problem in the two dimensional case

groups with less than n subgroups of index n we characterise residually finite groups which possess less than n subgroups of index n for almost all n

on the partial map detection with applications to mimo channels we investigate a multidimensional detection problem with a partial information of the a posteriori probability which is referred to as the partial maximum a posteriori probability map detection problem we show that the maximum likelihood ml detection of a higher dimension can be reduced to the ml detection of a lower dimension with cancellation under a certain condition through the formulation of the partial map detection problem using this we can propose a computationally efficient algorithm to apply to the detection problem for multiple input multiple output mimo channels including multiple transmit and multiple receive antenna mtmr channels and intersymbol interference isi channels it is shown that the proposed method has less error propagation effect and its performance is close to that of the full ml detection with a lower computational complexity

nonparametric bayesian posterior contraction rates for discretely observed scalar diffusions we consider nonparametric bayesian inference in a reflected diffusion model dx t b x t dt sigma x t dw t with discretely sampled observations x 0 x delta ldots x n delta we analyse the nonlinear inverse problem corresponding to the low frequency sampling regime where delta 0 is fixed and n to infty a general theorem is proved that gives conditions for prior distributions pi on the diffusion coefficient sigma and the drift function b that ensure minimax optimal contraction rates of the posterior distribution over holder sobolev smoothness classes these conditions are verified for natural examples of nonparametric random wavelet series priors for the proofs we derive new concentration inequalities for empirical processes arising from discretely observed diffusions that are of independent interest

multistage iterative decoding with complexity reduction for concatenated space time codes space time encoders exploiting concatenated coding structures are efficient in attaining the high rates available to large dimensional multiple transmitter multiple receiver wireless systems under fading conditions while also providing maximal diversity benefits we present a multistage iterative decoding structure that takes full advantage of the concatenated nature of the transmission path treating the modulator and channel stages as an additional encoder in serial concatenation this iterative decoder architecture allows an encoder employing decoupled coding and modulation to reach the performance of coded modulation systems it also admits reduced complexity decoding with a computational load that is nonexponential in the number of antennas or the transmission bit rate and makes practical decoding for large transmitter arrays possible the performance curves for these methods follow the shape of the fano bound with only a modest power penalty

valuation like maps and the congruence subgroup property let d be a finite dimensional division algebra and n a subgroup of finite index in d a valuation like map on n is a homomorphism n from n to a not necessarily abelian linearly ordered group satisfying n 1 n for some nonnegative such that n where n x n x we show that this implies the existence of a nontrivial valuation v of d with respect to which n is v adically open we then show that if n is normal in d and the diameter of the commuting graph of d n is 4 then n admits a valuation like map this has various implication in particular it restricts the structure of finite quotients of d the notion of a valuation like map is inspired by 27 and in fact is closely related to part u3 of the u hypothesis in 27

invariant distributions beurling transforms and tensor tomography in higher dimensions in the recent articles paternain et al j differ geom 98 147 181 2014 invent math 193 229 247 2013 a number of tensor tomography results were proved on two dimensional manifolds the purpose of this paper is to extend some of these methods to manifolds of any dimension a central concept is the surjectivity of the adjoint of the geodesic ray transform or equivalently the existence of certain distributions that are invariant under the geodesic flow we prove that on any anosov manifold one can find invariant distributions with controlled first fourier coefficients the proof is based on subelliptic type estimates and a pestov identity we present an alternative construction valid on manifolds with nonpositive curvature based on the fact that a natural beurling transform on such manifolds turns out to be essentially a contraction finally we obtain uniqueness results in tensor tomography both on simple and anosov manifolds that improve earlier results by assuming a condition on the terminator value for a modified jacobi equation