locally finite simple groups of 1 type abstract a locally finite simple group g is said to be of 1 type if every kegel cover for g has a factor which is an alternating group in this paper we study the finite subgroups of locally finite simple groups of 1 type we also introduce the concept of block diagonal embeddings for groups of alternating type we show that the groups of 1 type are exactly the groups which have an alternating kegel cover with block diagonal embeddings

nd convolutional codes i performance analysis a noncoherent coded system which incorporates convolutional codes in conjunction of multiple symbol noncoherent detection is presented in this two part paper where part i focuses on the performance analysis of the system and part ii deals with the structural properties of the underlying convolutional codes these convolutional codes are referred to as nd convolutional codes it is shown that nd convolutional codes provide a general framework for various noncoherent coding systems including differential systems two models of the carrier phase are examined and the relationships between them is established for the first one the carrier phase remains constant for l channels signals whereas for the second one it unvaries throughout the transmission period the regular structure of nd codes facilitates the evaluation of a simple upper bound on the pairwise and bit error probabilities as well as a simple expression for the generalized cutoff rate the exponential rate of the error probability which is the single parameter governing the error performance at large signal to noise ratios is identified via large deviations techniques this parameter leads to the interesting conclusion that increasing l does not necessarily monotonically improve the error performance of the noncoherent system the same conclusion is reached by examining upper bounds and computer simulation results of several interesting examples these examples also reveal that optimal codes for coherent detection are not necessarily optimal for noncoherent detection and a search for good codes some of which are tabulated in part ii of the paper is required

some applications of tree limits to groups part 1 sharper applications to group theory are given of an elegant construction the tree limit which s shelah circulated as a preprint in 1977 and used to obtain oo co enlargements to power 2 of certain countable homogeneous groups and skew fields in this paper we enlarge the class of groups to which this construction can be interestingly applied and we obtain permutation representations of countable degree of the tree limit groups we obtain uncountable subgroup incomparability for enlargements of countable existentially closed groups and even in nonhomogeneous cases we obtain the very strong archetypal direct limit property which implies oo x equivalence see 1 0 of the permutation representations we are able to control the permutation representations which get stretched by the tree limit by varying the point stabilizer subgroups see 5 5 in particular we can archetypally stretch in 2 subgroup incomparable ways any homogeneous permutation representation of a countable locally finite group in which every finite subgroup has infinitely many regular orbits theorem 4 we discuss cases where tree limits are subgroups of inverse limits 1 orientation and results here we give a number of new group theoretical applications of an elegant construction of s shelah 11 which we call the tree limit construction this construction was circulated in preprint form in 1977 by shelah in fact the present author had to decline an offer of coauthorship at that time the version 3 is formally quite different from shelah s original presentation which we have chosen to follow because of its naturalness the progress we have made comes mainly from the special types of amalgamations we use which provide an easy way to verify shelah s crucial lemma giving the tree limit group power 2 and which also provide a way of obtaining an embedding of the tree limit group in sym x we are also able to relax the requirement of homogeneity on the groups which get enlarged by the tree limit by making use of special properties of wreath products we also formulate and study the countable direct limit property which the tree limit group often satisfies this we feel is of such interest that it merits some new terminology 1 0 definition suppose g is a countable group and h is a group we say that h is an archetypal limit of g iff h u fs is e p i where p i is the set of finite subsets of i fs is finitely generated for all s e p i s c t e p i implies f5 c ft and there exists s c i with isi x such that for all s c t c i with

clt for linear spectral statistics of large dimensional sample covariance matrices let bn 1 n t1 2nxnx nt1 2n where xn xij is n n with i i d complex standardized entries having finite fourth moment and t1 2n is a hermitian square root of the nonnegative definite hermitian matrix tn the limiting behavior as n with n n approaching a positive constant of functionals of the eigenvalues of bn where each is given equal weight is studied due to the limiting behavior of the empirical spectral distribution of bn it is known that these linear spectral statistics converges a s to a nonrandom quantity this paper shows their rate of convergence to be 1 n by proving after proper scaling that they form a tight sequence moreover if exppx211 0 and expp x11 4 2 or if x11 and tn are real and exppx411 3 they are shown to have gaussian limits

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

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

asymptotic power of sphericity tests for high dimensional data this paper studies the asymptotic power of tests of sphericity against perturbations in a single unknown direction as both the dimensionality of the data and the number of observations go to infinity we establish the convergence under the null hypothesis and the alternative of the log ratio of the joint densities of the sample covariance eigenvalues to a gaussian process indexed by the norm of the perturbation when the perturbation norm is larger than the phase transition threshold studied in baik et al 2005 the limiting process is degenerate and discrimination between the null and the alternative is asymptotically certain when the norm is below the threshold the process is non degenerate so that the joint eigenvalue densities under the null and alternative hypotheses are mutually contiguous using the asymptotic theory of statistical experiments we obtain asymptotic power envelopes and derive the asymptotic power for various sphericity tests in the contiguity region in particular we show that the asymptotic power of the tracy widom type tests is trivial whereas that of the eigenvalue based likelihood ratio test is strictly larger than the size and close to the power envelope

grassmannian packings from operator reed muller codes this paper introduces multidimensional generalizations of binary reed muller codes where the codewords are projection operators and the corresponding subspaces are widely separated with respect to the chordal distance on grassmannian space parameters of these grassmannian packings are derived and a low complexity decoding algorithm is developed by modifying standard decoding algorithms for binary reed muller codes the subspaces are associated with projection operators determined by pauli matrices appearing in the theory of quantum error correction and this connection with quantum stabilizer codes may be of independent interest the grassmannian packings constructed here find application in noncoherent wireless communication with multiple antennas where separation with respect to the chordal distance on grassmannian space guarantees closeness to the channel capacity it is shown that the capacity of the noncoherent multiple input multiple output mimo channel at both low and moderate signal to noise ratio snr under the constraint that only isotropically distributed unitary matrices are used for information transmission is closely approximated by these packings

unitary space time modulation for multiple antenna communications in rayleigh flat fading motivated by information theoretic considerations we propose a signaling scheme unitary space time modulation for multiple antenna communication links this modulation is ideally suited for rayleigh fast fading environments since it does not require the receiver to know or learn the propagation coefficients unitary space time modulation uses constellations of t spl times m space time signals spl phi sub i l 1 l where t represents the coherence interval during which the fading is approximately constant and m t is the number of transmitter antennas the columns of each spl phi sub i are orthonormal when the receiver does not know the propagation coefficients which between pairs of transmitter and receiver antennas are modeled as statistically independent this modulation performs very well either when the signal to noise ratio snr is high or when t spl gt m we design some multiple antenna signal constellations and simulate their effectiveness as measured by bit error probability with maximum likelihood decoding we demonstrate that two antennas have a 6 db diversity gain over one antenna at 15 db snr

systematic design of unitary space time constellations we propose a systematic method for creating constellations of unitary space time signals for multiple antenna communication links unitary space time signals which are orthonormal in time across the antennas have been shown to be well tailored to a rayleigh fading channel where neither the transmitter nor the receiver knows the fading coefficients the signals can achieve low probability of error by exploiting multiple antenna diversity because the fading coefficients are not known the criterion for creating and evaluating the constellation is nonstandard and differs markedly from the familiar maximum euclidean distance norm our construction begins with the first signal in the constellation an oblong complex valued matrix whose columns are orthonormal and systematically produces the remaining signals by successively rotating this signal in a high dimensional complex space this construction easily produces large constellations of high dimensional signals we demonstrate its efficacy through examples involving one two and three transmitter antennas

invariant random subgroups of inductive limits of finite alternating groups abstract we classify the ergodic invariant random subgroups of inductive limits of finite alternating groups

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

a low complexity noncoherent iterative space time demodulator turbo coded unitary space time modulation ustm can provide large coding gain as compared to uncoded ustm because the noncoherent space time maximum a posteriori demodulator is very complicated in this letter we propose a new low complexity noncoherent iterative space time demodulator for the ustm constructed from pilot symbol assisted modulation the proposed demodulator utilizes both hard and soft decisions from the turbo decoder to simplify the computational task as well as produce reliable soft outputs several examples demonstrate that this demodulator has both low complexity and good error performance

fractional brownian motion with hurst index h 0 and the gaussian unitary ensemble the goal of this paper is to establish a relation between characteristic polynomials of n n gue random matrices h as n and gaussian processes with logarithmic correlations we introduce a regularized version of fractional brownian motion with zero hurst index which is a gaussian process with stationary increments and logarithmic increment structure then we prove that this process appears as a limit of d n z log det h zi on mesoscopic scales as n by employing a fourier integral representation we use this to prove a continuous analogue of a result by diaconis and shahshahani j appl probab 31a 1994 49 62 on the macroscopic scale d n x gives rise to yet another type of gaussian process with logarithmic correlations we give an explicit construction of the latter in terms of a chebyshev fourier random series

estimation of a multiplicative covariance structure in the large dimensional case abstract we propose a kronecker product model for correlation or covariance matrices in the large dimensional case the number of parameters of the model increases logarithmically with the dimension of the matrix we propose a minimum distance md estimator based on a log linear property of the model as well as a one step estimator which is a one step approximation to the quasi maximum likelihood estimator qmle we establish rates of convergence and central limit theorems clt for our estimators in the large dimensional case a specification test and tools for kronecker product model selection and inference are provided in a monte carlo study where a kronecker product model is correctly specified our estimators exhibit superior performance in an empirical application to portfolio choice for s p500 daily returns we demonstrate that certain kronecker product models are good approximations to the general covariance matrix

periodic simple groups of finitary linear transformations a group is locally finite if every finite subset generates a finite subgroup a group of linear transformations is finitary if each element minus the identity is an endomorphism of finite rank the classification and structure theory for locally finite simple groups splits naturally into two cases those groups that can be faithfully represented as groups of finitary linear transformations and those groups that are not finitary linear this paper completes the finitary case we classify up to isomorphism those infinite locally finite simple groups that are finitary linear but not linear

leveraging coherent space time codes for noncoherent communication via training training codes are introduced for the multiple antenna noncoherent multiple block rayleigh fading channel in which the fading coefficients which are constant over a fixed number of dimensions coherence interval for each block and then change independently to a new realization are known neither at the transmitter nor at the receiver each codeword of a training code consists of a part known to the receiver used to form a minimum mean squared error mmse estimate of the channel and a part that contains codeword s of a space time block or trellis code designed for the coherent channel in which the receiver has perfect knowledge of the channel the channel estimate is used as if it were error free for decoding the information bearing part of the training codeword training codes are hence easily designed to have high rate and low decoding complexity by choosing the underlying coherent code to have high rate and to be efficiently decodable conditions for which the estimator detector e d receiver is equivalent to the optimal noncoherent receiver are established a key performance analysis result of this paper is that the training codes when decoded with the e d receiver achieve a diversity order of the error probability that is equal to the diversity order of the underlying coherent code in some cases the performance of training codes can be measured relative to coherent reception via training efficiency which is then optimized over the energy allocation between the training and data phases in the limit of increasing block lengths training codes always achieve the performance of coherent reception the examples of training codes provided in this work have polynomial complexity in rate but an error rate comparable to the best performing unitary designs available even though the latter require exponential decoding complexity

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

testing in high dimensional spiked models we consider ve dierent classes of multivariate statistical problems iden ti ed by james 1964 each of these problems is related to the eigenvalues of e 1 h where h and e are proportional to high dimensional wishart ma trices under the null hypothesis both wisharts are central with identity covariance under the alternative the non centrality or the covariance pa rameter of h has a single eigenvalue a spike that stands alone when the spike is larger than a case speci c phase transition threshold one of the eigenvalues of e 1 h separates from the bulk this makes the alternative easily detectable so that reasonable statistical tests have asymptotic power one in contrast when the spike is sub critical that is lies below the thresh old none of the eigenvalues separates from the bulk which makes the testing problem more interesting from the statistical perspective in such cases we show that the log likelihood ratio processes parameterized by the value of the sub critical spike converge to gaussian processes with logarithmic corre lation we use this result to derive the asymptotic power envelopes for tests for the presence of a spike in the data representing each of the ve cases in james classi cation

infinite alternating groups as finitary linear transformation groups abstract degree of a classical group as its natural projective representation degree see 6 2 case 1 of 2 6 is dispensed with using mal cev s local characterization of finite dimensional linear groups and their classification theorem 2 7 mal cev see 13 l l 91 let g be a iocally finite group with adeg g 00 then g is a finite dimensional linear group theorem 2 8 l 2 8 21 let g be an infinite group then is a simple locally finite linear group of finite degree if and only if g is isomorphic to an adjoint group of lie type over an infinite subfield fp the algebraic closure of f for some prime p 3 local characterization of finitary linear groups a theorem of mal cev type mal cev s theorem 2 7 provides a local characterization of locally finite linear groups g of finite degree the property of having a faithful linear representation of degree n passes from the set of finite subgroups of g to g itself under this section we provide a similar result for locally finite simple groups which are linitary linear remember that the linear transformation g of the vector space i is finitary if g fixes pointwise a subspace of finite codimension in v that is the subspace c g v e v 1 vg v has finite codimension in v or equivalently the subspace v g v g 1 1 v e v has finite dimension in v the collection of all linitary members of gl v forms a normal sub group fgl v and a group which is isomorphic to a subgroup of fgl v for some v is sometimes called a finitary linear group

finitary representations and images of transitive finitary permutation groups abstract we characterize the point stabilizers and kernels of finitary permutation representations of infinite transitive groups of finitary permutations moreover the number of such representations is determined

communication on the grassmann manifold a geometric approach to the noncoherent multiple antenna channel we study the capacity of multiple antenna fading channels we focus on the scenario where the fading coefficients vary quickly thus an accurate estimation of the coefficients is generally not available to either the transmitter or the receiver we use a noncoherent block fading model proposed by marzetta and hochwald see ibid vol 45 p 139 57 1999 the model does not assume any channel side information at the receiver or at the transmitter but assumes that the coefficients remain constant for a coherence interval of length t symbol periods we compute the asymptotic capacity of this channel at high signal to noise ratio snr in terms of the coherence time t the number of transmit antennas m and the number of receive antennas n while the capacity gain of the coherent multiple antenna channel is min m n bits per second per hertz for every 3 db increase in snr the corresponding gain for the noncoherent channel turns out to be m 1 m t bits per second per hertz where m min m n t 2 the capacity expression has a geometric interpretation as sphere packing in the grassmann manifold