minimum probability of error for asynchronous gaussian multiple access channels consider a gaussian multiple access channel shared by k users who transmit asynchronously independent data streams by modulating a set of assigned signal waveforms the uncoded probability of error achievable by optimum multiuser detectors is investigated it is shown that the k user maximum likelihood sequence detector consists of a bank of single user matched filters followed by a viterbi algorithm whose complexity per binary decision is o 2 k the upper bound analysis of this detector follows an approach based on the decomposition of error sequences the issues of convergence and tightness of the bounds are examined and it is shown that the minimum multiuser error probability is equivalent in the iow noise region to that of a single user system with reduced power these results show that the proposed multiuser detectors afford important performance gains over conventional single user systems in which the signal constellation carries the entire burden of complexity required to achieve a given performance level

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

robust matched filters the problem of designing robust matched filters for situations in which there is uncertainty in the signal structure or noise statistics is considered two general aspects of this problem are treated first maximin robust designs are characterized for a general hilbert space formulation of the matched filtering problem and explicit solutions are given for two intuitively appealing models for uncertainty these results are seen to generalize earlier results for specific matched filtering problems the second general aspect treated is the application of the theoretical maximin results to the particular problem of designing filters to combat uncertain nonlinear channel distortion channel distortion is modeled by considering an unknown received signal which may differ in l 2 norm from the transmitted or nominal signal by no more than a fixed amount the effect of the channel distortion is seen to be equivalent to that of adding a white noise to the channel whose spectral height depends on the degree of distortion general expressions are developed for the determination of the robust filter and its performance and numerical results are presented for the case of baseband detection in gauss markov noise

optimum multiuser noncoherent dpsk detection in generalized diversity rayleigh fading channels the jointly optimum multiuser noncoherent detector for differential phase shift keying dpsk modulation over the generalized diversity rayleigh fading gdrf channel is derived and analyzed the gdrf channel includes time frequency receiver antenna diversity and allows fading correlations between the various diversity branches of each user noncoherent detection here refers to the case where the receiver has neither knowledge of the instantaneous phases nor of the envelopes of the users channels upper and lower bounds on the bit error probability of the optimum detector are derived for a given user for fast fading when the fading coefficients vary from one symbol interval to the next but are still essentially constant over one symbol interval the detector asymptotically for high signal to noise ratios snrs reaches an error floor which is bounded from below and above for different fast fading scenarios for slow fading when the channel is constant for at least two consecutive symbol intervals the upper bound is shown to converge asymptotically to the lower bound thus the asymptotic efficiency of optimum multiuser dpsk detection can be determined and is found to be positive in contrast to coherent detection however it is smaller than unity in general since the asymptotic efficiency is independent of the interfering users signal strengths the optimum detector is near far resistant while optimum multiuser detection is exponentially complex in the number of users its performance provides the benchmark for suboptimal detectors in particular it is seen that the previously suggested post decorrelative detectors can be far from satisfactory

some 2 spl times 2 unitary space time codes from sphere packing theory with optimal diversity product of code size 6 in this correspondence we propose some new designs of 2 spl times 2 unitary space time codes of sizes 6 32 48 64 with best known diversity products or product distances by partially using sphere packing theory in particular we present an optimal 2 spl times 2 unitary space time code of size 6 in the sense that it reaches the maximal possible diversity product for 2 spl times 2 unitary space time codes of size 6 the construction and the optimality of the code of size 6 provide the precise value of the maximal diversity product of a 2 spl times 2 unitary space time code of size 6

noncoherent ostbc ofdm for mimo and cooperative communications perfect channel identifiability and achievable diversity order this paper considers the context of orthogonal space time block coded ofdm ostbc ofdm without channel state information at the receiver assuming noncoherent maximum likelihood detection the interest herein lies in detection within one ostbc ofdm block motivated by its capability of accommodating relatively fast block fading channels our investigation focuses on analysis aspects where we seek to establish practical noncoherent bpsk qpsk ostbc ofdm schemes that have provably good channel identifiability and diversity properties we consider perfect channel identifiability pci a strong condition guaranteeing unique noncoherent channel identification for any nonzero channel through a judicious design involving special ostbcs and pilot placement we propose an ostbc ofdm scheme that is pci achieving and consumes fewer pilots compared to conventional pilot aided channel estimation methods we further our analysis by showing that a pci achieving scheme also achieves maximal noncoherent spatial diversity for the kronecker gaussian spatial temporal channel fading model which covers the popular i i d rayleigh fading channel and a variety of correlated and sparse multipath channels all these results are developed in parallel for the centralized point to point mimo scenario and a distributed relay communication scenario for the latter scenario our diversity analysis shows that the pci achieving scheme can also achieve maximal noncoherent cooperative diversity the performance merits of the proposed pci achieving scheme are demonstrated by simulations

tree search multiple symbol differential decoding for unitary space time modulation differential space time modulation dstm using unitary matrix signal constellations is an attractive solution for transmission over multiple input multiple output mimo fading channels without requiring channel state information csi at the receiver to avoid a high error floor for dstm in relatively fast mimo fading channels multiple symbol differential detection msdd has to be applied at the receiver msdd jointly processes blocks of several received matrix symbols and power efficiency improves as the blocksize increases but since the search space of msdd grows exponentially with the blocksize and also with the number of transmit antennas and the data rate the complexity of msdd quickly becomes prohibitive in this paper we investigate the application of tree search algorithms to overcome the complexity limitation of msdd we devise a nested msdd structure consisting of an outer and a number of inner tree search decoders which renders msdd feasible for wide ranges of system parameters decoder designs tailored for diagonal and orthogonal dstm codes are given and a more power efficient variant of msdd so called subset msdd is proposed furthermore we derive a tight symbol error rate approximation for msdd which lends itself to efficient numerical evaluation numerical and simulation results for different dstm constellations and fading channel scenarios show that the new tree search msdd achieves a significantly better performance complexity tradeoff than benchmark decoders

bounds for the spectrum of a two parameter matrix eigenvalue problem abstract we consider the two parameter eigenvalue problem t j v j 1 a j 1 v j 2 a j 2 v j 0 where j c t j a j k j k 1 2 are matrices bounds for the spectral radius of that problem are suggested our main tool is a norm estimate for the operator inverse to the operator a 11 a 22 a 12 a 21 where means the tensor product in addition by virtue of that norm estimate and the ostrowsky schneider theorem we establish a condition that provides the conservation of the number of the eigenvalues of the considered problem in a half plane

gallager bounds for noncoherent decoders in fading channels recently gallager s bounding techniques have been used to derive tight performance bounds for coded systems in fading channels most works in this field have thus far dealt with coherent decoding this paper develops gallager bounds for noncoherent systems in fading channels unlike coherent decoding the exact error probability of a noncoherent decoder detector conditioned on the fading coefficients does not admit a closed form expression this difficulty is overcome in this paper by employing the chernoff technique although it weakens the bounds to some extent the chernoff technique enables the derivations of the limit before average lba bound and gallager bounds in closed form for noncoherent fading channels numerical examples show that the proposed bounds are convergent and are tighter than the conventional union bound

full diversity blind space time block codes in this paper the systematic design of a space time block code is considered for a wireless communication system with multiple transmitter receiver antennas and flat fading in which channel state information is completely unknown from the viewpoint of blind signal processing a necessary and sufficient condition is given for the unique identification of the multi input multi output flat fading channel and transmitted signal then some novel unique factorizations for a pair of coprime p ary and q ary phase shift keying psk constellations are established with this and currently available coherent space time block code designs a method is developed to systematically construct full diversity blind nonunitary space time block codes as well as unitary codes by just performing the qr decomposition of the nonunitary codes it is proved that under a noise free environment the code design proposed in this paper can guarantee that the transmitted signals and the channel coefficients are uniquely identified and that under a complex gaussian noise environment in which pth order and q th order statistics p and q are co prime of the received signals are available the channel coefficients can be still uniquely identified in addition a closed form solution to determine the channel coefficients is obtained

remarks on space time codes including a new lower bound and an improved code this article presents a new asymptotically exact lower bound on pairwise error probability of a space time code as well as an example code that outperforms the comparable orthogonal design based space time odst code also contained in the article are an exact expression for pairwise error probability pep signal design guidelines and some observations relating to the reception of odst codes

asymptotic error probability analysis of quadratic receivers in rayleigh fading channels with applications to a unified analysis of coherent and noncoherent space time receivers a general asymptotic high signal to noise snr error analysis is introduced for quadratic receivers in frequency flat and multipath rayleigh fading channels with multiple transmit and receive antennas asymptotically tight expressions for the pairwise error probabilities are obtained for coherent noncoherent and differentially coherent space time receivers not only is our unified analysis applicable to more general modulation schemes and or channel models than previously considered but it also reveals a hitherto unrecognized eigenvalue structure that is common to all of these problems in addition to providing an easy recipe for computing the asymptotic pairwise error rates we make some conclusions regarding criteria for the design of signal constellations and codes such as a the same design criteria apply for both correlated and independent and identically distributed i i d fading processes and b for noncoherent communications unitary signals are optimal in the sense that they minimize the asymptotic union bound

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

exact symbol error probability analysis for orthogonal space time block codes two and higher dimensional constellations cases exact expressions are obtained for the symbol error probability of orthogonal space time block codes at the output of the coherent maximum likelihood decoder in the general case of arbitrary input signal constellation and code such expressions are derived for the cases of both deterministic fixed and random rayleigh ricean fading channels and both the two and higher dimensional constellations

analysis of the error performance of trellis coded modulations in rayleigh fading channels this work presents an exact expression for the pairwise error event probability of trellis coded modulation tcm transmitted over rayleigh fading channels it includes phase shift keying psk and multilevel quadrature amplitude modulation qam codes as well as coherent and partially coherent e g differential pilot tone etc detection due to the form of the exact pairwise error event probabilities this calculation technique cannot be used with the transfer function technique to obtain an upper union bound on the overall bit error probability for this reason the authors estimate the bit error probability by considering only a small number of short error events through simulations they found that the estimation is usually very accurate at high signal to noise ratios but not as accurate at lower signal to noise ratios they study several coded modulation schemes this way among the results are the fact that tcm provides significant improvement in the error floor when detected differentially and an asymmetry in the pairwise error event probability for 16 qam

asymptotic analysis of coherent and differential space time codes in non gaussian noise and interference in this paper we provide a unified framework for the asymptotic performance analysis of space time codes stcs in correlated ricean fading and non gaussian noise and interference in particular we derive simple and asymptotically tight expressions for the pairwise error probability pep of coherent and differential stcs which are valid for any type of noise and interference with finite moments and detection with general mahalonobis distance md metrics including euclidean distance ed and noise decorrelating nd metrics these pep expressions can be combined with truncated union bounds to obtain accurate asymptotic approximations for the bit symbol and frame error probabilities of stcs we show that while the diversity gain of an stc is independent of the type of noise and the type of md metric used the coding gain is not and depends on certain moments of the noise and interference we provide closed form expressions for these moments for several practically relevant types of noise and interference we show that for correlated noise significant performance gains can be achieved with the nd metric compared to the ed metric while noise correlations are beneficial at high signal to noise ratios if they can be exploited by the metric they are harmful if this is not the case and the simple ed metric is employed all our analytical findings are confirmed by simulations for various popular stcs and several different types of noise and interference

analysis and efficient evaluation of the ber of ostbcs with imperfect channel estimation in arbitrarily correlated fading channels an analysis of the exact bit error rate ber performance of orthogonal space time block codes ostbcs with maximum likelihood detection in the presence of channel estimation errors is presented the possibly correlated coefficients of the multiple input multiple output mimo propagation channel are assumed to be affected by flat block fading and the transmitted symbols belong to a pulse amplitude modulation or quadrature amplitude modulation signal constellation for both square and nonsquare ostbcs we derive approximate and exact ber expressions irrespective of the distribution of the fading it is also shown how the exact expressions can be efficiently and accurately evaluated using numerical integration techniques their application to the arbitrarily correlated nakagami m fading channel is presented and an efficient importance sampling technique is derived as the high diversity order resulting from the application of ostbcs gives rise to small ber values the numerical evaluation of the presented ber expressions is much faster than straightforward monte carlo simulations ber results have shown the impact of both imperfect channel estimation and antenna correlation on the performance of mimo ostbc systems it is also shown that under highly correlated conditions antenna correlation is the major source of ber degradation

signal design and convolutional coding for noncoherent space time communication on the block rayleigh fading channel we consider the problem of designing signal constellations for the multiple transmit multiple receive antenna rayleigh fading communication channel when neither the transmitter nor the receiver know the fading in particular by employing the asymptotic union bound aub on the probability of error we give a new formulation of the problem of signal design for the noncoherent fading channel since unitary signals are optimal for this channel in the limit of large signal to noise ratios snrs the problem can be posed in terms of packings on the grassmanian manifold a key difference in our approach from that of other authors is that we use a notion of distance on this manifold that is suggested by the union bound as a consequence of our use of this distance measure we obtain signal designs that are guaranteed to achieve the full diversity order of the channel a result that does not hold when the chordal distance is used we introduce a new method of recursively designing signals termed successive updates to approximately optimize this performance measure we then examine the use of our signals with several convolutional codes over the fading channel an upper bound on the bit error probability of the maximum likelihood decoder is presented together with an asymptotic analysis of that bound

representation theory for high rate multiple antenna code design multiple antennas can greatly increase the data rate and reliability of a wireless communication link in a fading environment but the practical success of using multiple antennas depends crucially on our ability to design high rate space time constellations with low encoding and decoding complexity it has been shown that full transmitter diversity where the constellation is a set of unitary matrices whose differences have nonzero determinant is a desirable property for good performance we use the powerful theory of fixed point free groups and their representations to design high rate constellations with full diversity furthermore we thereby classify all full diversity constellations that form a group for all rates and numbers of transmitter antennas the group structure makes the constellations especially suitable for differential modulation and low complexity decoding algorithms the classification also reveals that the number of different group structures with full diversity is very limited when the number of transmitter antennas is large and odd we therefore also consider extensions of the constellation designs to nongroups we conclude by showing that many of our designed constellations perform excellently on both simulated and real wireless channels

kronecker bases for linear matrix equations with application to two parameter eigenvalue problems abstract the general solutions of the homogeneous matrix equation axct bxdt 0 and the system of the matrix equations ax by 0 xct ydt 0 are described in terms of kronecker canonical forms i e in terms of kronecker invariants and kronecker bases for pairs of matrices a b and c d a canonical form for a pair of commuting matrices e f such that e2 f2 ef 0 is discussed these results are applied to construct a canonical basis for the second root subspace of a two parameter eigenvalue problem the corresponding relations for canonical invariants are given

effect of mmse channel estimation on ber performance of orthogonal space time block codes in rayleigh fading channels we present a simple closed form expression for the ber of orthogonal space time block codes ostbcs with mmse channel estimation assuming pam and qam constellations and flat rayleigh block fading the ber expression is exact for a certain class of ostbcs and provides a very accurate approximation for other ostbcs

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

root vectors for geometrically simple two parameter eigenvalues a class of multiparameter eigenvalue problems involving generally non self adjoint and unbounded operators is studied bases for lower order root subspaces at geometrically simple eigenvalues of fredholm type of arbitrary finite index are computed in terms of the underlying multiparameter system

a note on the approximation of two sided rayleigh quotient to eigenvalues abstract we consider the two sided rayleigh quotient introduced by ostrowski as convergence acceleration tool for eigenvalue solvers an interesting property of the two sided rayleigh quotient is established its approximation to eigenvalues depends on the eigenvalue condition number this fact is valid not only for matrix but also for matrix polynomial multiparameter system and periodic matrix pairs

analysis of differential orthogonal space time block codes over semi identical mimo fading channels we study the performance of differential orthogonal space time block codes ostbc over independent and semi identically distributed block rayleigh fading channels in this semiidentical fading model the channel gains from different transmit antennas to a common receive antenna are identically distributed but the gains associated with different receive antennas are nonidentically distributed arbitrary fluctuation rates of the fading processes from one transmission block to another are considered we first derive the optimal symbol by symbol differential detector and show that the conventional differential detector is suboptimal we then derive expressions of exact bit error probabilities beps for both the optimal and suboptimal detectors the results are applicable for any number of receive antennas and any number of transmit antennas for which ostbcs exist for two transmit antennas explicit and closed form bep expressions are obtained for an arbitrary number of transmit antennas a chernoff bound on the bep for the optimal detector is also derived our results show that the semi identical channel statistics degrade the error performance of differential ostbc compared with the identical case also the proposed optimal detector substantially outperforms the conventional detector when the channel fluctuates rapidly but in near static fading channels the two detectors have similar performances

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

on the relation of ostbc and code rate one qstbc average rate ber and coding gain recently the statistical properties of the equivalent channel representation of a multiple input multiple output mimo system employing code rate one quasi orthogonal space time block codes qstbc which are constructed by using orthogonal space time block codes ostbc as building elements was characterized based on these characterizations we analyze the average rate or mean mutual information the bit error rate performance and the coding gain achieved with qstbc for any number of receive and nt 2n n ges 2 transmit antennas first we study constellation rotation using a systematic approach in order to maximize the coding gain and to achieve full diversity qstbc moreover we present an upper bound on the coding gain we derive a lower and upper bound on the ber performance for qstbc furthermore we analyze the average rate achievable with qstbc in case of an uninformed transmitter and also the case in which the transmitter knows the mean channel matrix whereas the receiver has perfect csi along with the analysis we compare all the results of these performance measures with the results achieved with ostbc revealing important connections between ostbc and qstbc for example the coding gain of a qstbc is upper bounded by the coding gain of the underlying ostbc also the ber of a qstbc for nt transmit and nr receive antennas is tightly lower bounded by the ber of a full diversity providing intersymbol interference free system in addition to that we show that gains in terms of average rate by using a qstbc and thus with higher nt instead of the underlying ostbc are only attainable if the available channel state information at the transmitter csit is utilized finally we illustrate our theoretical results using numerical simulations

a numerical algorithm for computing a basis for the root subspace at a nonderogatory eigenvalue of a multiparameter system abstract a numerical algorithm for the calculation of a basis for the root subspace at a nonderogatory eigenvalue of a finite dimensional multiparameter system is given it is based on the algorithm proposed by kosir 1 the perturbation theory for the algorithm is studied and a new stopping criterion is proposed at the end two numerical examples are given

on the structure of commutative matrices ii a finite set a of n n nilpotent commutative matrices that have one dimensional joint kernel is considered the theorem due to suprunenko and tyshkevich that the algebra a generated by a and the identity matrix has dimension equal to n is proved a canonical basis for a is given and related structure constants are discussed

noncoherent communication in multiple antenna systems receiver design and codebook construction in this paper we address the problem of space time codebook design for noncoherent communications in multiple antenna wireless systems in contrast with other approaches the channel matrix is modeled as an unknown deterministic parameter at both the receiver and the transmitter and the gaussian observation noise is allowed to have an arbitrary correlation structure known by the transmitter and the receiver in order to handle the unknown deterministic space time channel a generalized likelihood ratio test glrt receiver is considered a new methodology for space time codebook design under this noncoherent setup is proposed it optimizes the probability of error of the glrt receiver s detector in the high signal to noise ratio snr regime by solving a high dimensional nonlinear nonsmooth optimization problem in a two step approach first a convex semidefinite programming sdp relaxation of the codebook design problem yields a rough estimate of the optimal codebook this is then refined through a geodesic descent optimization algorithm that exploits the riemannian geometry imposed by the power constraints on the space time codewords the results obtained through computer simulations illustrate the advantages of our method for the specific case of spatio temporal white observation noise our codebook constructions replicate the performance of state of the art known solutions the main point here is that our methodology permits extending the codebook construction to any given correlated noise environment the simulation results show good performance of these new designed codes in colored noise setups

noncoherent hybrid ds sfh spread spectrum multiple access communications the performance of noncoherent reception in synchronous and asynchronous hybrid direct sequence slow frequency hopped spread spectrum multiple access communication systems operating through additive white gaussian noise channels is investigated systems with binary and m ary frequency shift keying modulation and noncoherent demodulation as well as systems with differential phase shift keying modulation and differentially coherent demodulation are examined and their probability of error is evaluated for random frequencyhopping patterns and signature sequences the multiple access capability of noncoherent hybrid spread spectrum is shown to be superior to that of noncoherent purely frequency hopped spread spectrum and inferior to that of noncoherent purely directsequence spread spectrum for systems with the same bandwidth expansion comparison of hybrid systems with coherent and noncoherent demodulation shows a considerable loss in the performance of the noncoherent systems

full diversity non coherent alamouti based toeplitz space time block codes recently the liu zhang wong s toeplitz space time block code and the shang xia s alamouti code based overlapped space time block code have been developed to enable coherent full diversity with the linear receivers for a wireless communication system having multiple transmitter antennas and a single receiver antenna in this paper such a noncoherent system is considered in which channel state information is unavailable at both the transmitter and receiver using the alamouti coding scheme and the toeplitz matrix structure a novel noncoherent nonunitary space time block code which is called an alamouti based toeplitz space time block code is proposed by the fundamentals of galois theory and algebraic number theory two important properties on the two alamouti codes generated from a pair of coprime phase shift keying psk constellations i e the uniqueness of factorization itself and the shift invariant uniqueness of factorization are first revealed and rigorously proved then it is further shown that it is these two kinds of unique factorizations that enable the unique blind identification of both the channel coefficients and the transmitted signals by only processing two block received signals as well as noncoherent full diversity with a generalized likelihood ratio test glrt receiver in addition a full diversity unitary code design is also proposed by simply applying the qr decomposition to the full diversity nonunitary alamouti based toeplitz space time block code computer simulations demonstrate that the nonunitary and unitary codes presented in this paper outperform the differential codes and the signal to noise ratio snr efficient training scheme based on the coherent orthogonal space time block codes in the current literature

performance of space time codes gallager bounds and weight enumeration since the standard union bound for space time codes may diverge in quasi static fading channels the limit before average lba technique has been exploited to derive tight performance bounds however it suffers from the computational burden arising from a multidimensional integral in this paper efficient bounding techniques for space time codes are developed in the framework of gallager bounds two closed form upper bounds the ellipsoidal bound and the spherical bound are proposed that come close to simulation results within a few tenths of a decibel in addition two novel methods of weight enumeration operating on a further reduced state diagram are presented which in conjunction with the bounding techniques give a thorough treatment of performance bounds for space time codes

on stability of invariant subspaces of commuting matrices we study the stability of joint invariant subspaces of a finite set of commuting matrices we generalize some of the results of gohberg lancaster and rodman for the single matrix case for sets of two or more commuting matrices we exhibit some phenomena different from the single matrix case we show that each root subspace is a stable invariant subspace that each invariant subspace of a root subspace of a nonderogatory eigenvalue is stable and that even in the derogatory case the eigenspace is stable if it is one dimensional we prove that a pair of commuting matrices has only finitely many stable invariant subspaces at the end we discuss the stability of invariant subspaces of an algebraic multiparameter eigenvalue problem

noncoherent multiuser detection for nonlinear modulation over the rayleigh fading channel the jointly optimum noncoherent multiuser detector is obtained for nonlinear nonorthogonal modulation over the frequency nonselective rayleigh fading multiple access channel upper and lower bounds on the average bit error probability are derived while these bounds are numerically computable they are too complicated to give insight into the relative influence of the system parameters on the essential behavior of the bit error rate hence this paper develops an asymptotic analysis of the average bit error probability in particular it is shown that the upper and lower bounds are asymptotically convergent an exact formula for the asymptotic efficiency of the optimum noncoherent detector is derived interestingly the asymptotic efficiency is found to be positive and independent of the signal strengths of the interfering users in contrast the noncoherent detector which would be optimal in a single user channel the conventional detector when used over the multiuser channel has an asymptotic efficiency that is identically equal to zero no matter what the powers of the interferers may be while the performance analysis of the optimum detector provides the fundamental limit on achievable error rate the implementational complexity of the optimum detector is exponential in the number of users as a low complexity alternative a decorrelative energy detector is also proposed and analyzed in terms of error probability and asymptotic efficiency

on the oblivious transfer capacity of generalized erasure channels against malicious adversaries the case of low erasure probability noisy channels are a powerful resource for cryptography as they can be used to obtain information theoretic secure key agreement commitment and oblivious transfer protocols among others oblivious transfer ot is a fundamental primitive since it is complete for secure multi party computation and the ot capacity characterizes how efficiently a channel can be used for obtaining string oblivious transfer ahlswede and csiszar isit 07 presented upper and lower bounds on the ot capacity of generalized erasure channels gecs against passive adversaries in the case of gec with erasure probability at least 1 2 the upper and lower bounds match and therefore the ot capacity was determined it was later proved by pinto et al ieee trans inf theory 57 8 that the ot capacity is identical for passive and malicious adversaries in the case of gec with erasure probability smaller than 1 2 the known lower bound against passive adversaries that was established by ahlswede and csiszar does not match their upper bound and it was unknown whether this ot rate could be achieved against malicious adversaries as well in this paper we show that there is a protocol against malicious adversaries achieving the same ot rate that was obtained against passive adversaries we obtain our results by a new combination of interactive hashing and typicality tests that are suitable for dealing with the case of low erasure probability p

a systematic approach to the design and analysis of optimum dpsk receivers for generalized diversity communications over rayleigh fading channels a generalized diversity channel is introduced that models a variety of wireless communication systems that use time frequency multipath and or antenna diversity with various interbranch correlations between signaling waveforms and the fading and additive noise processes in the context of this general model a systematic approach to the design and analysis of optimum noncoherent differential phase shift keying dpsk receivers is introduced in particular it is shown how the minimum error probability mep and the generalized likelihood ratio tests glrt can be applied to obtain optimal noncoherent combining rules a comparative error rate analysis of the glrt and mep detectors and an ad hoc equal gain combiner is provided for binary signaling and the suitability of the three schemes is determined as a function of fading characteristics the asymptotic bit error rate analysis is undertaken for the mep detector for slow and fast fading channels an estimator detector decomposition of the noncoherent mep rule is obtained which allows an insightful comparative study of the fundamental limits of binary phase shift keying and dpsk modulation detection methods for both slow and fast fading the results of this paper are also applicable to postdecorrelative receivers in multiuser channels

chernoff bounds on pairwise error probabilities of space time codes we derive chernoff bounds on pairwise error probabilities of coherent and noncoherent space time signaling schemes first general chernoff bound expressions are derived for a correlated ricean fading channel and correlated additive gaussian noise then we specialize the obtained results to the cases of space time separable noise white noise and uncorrelated fading we derive approximate chernoff bounds for high and low signal to noise ratios snrs and propose optimal signaling schemes we also compute the optimal number of transmitter antennas for noncoherent signaling with unitary mutually orthogonal space time codes

optimum receivers and low dimensional spreaded modulation for multiuser space time communications the jointly optimum receiver is obtained for multi user communications in a frequency nonselective rayleigh fading channel with n sub t transmit antennas per user and n sub r receive antennas based on a general analysis of quadratic receivers in zero mean complex gaussian vectors asymptotically tight expressions for high signal to noise ratio snr for the pairwise error probabilities are derived subsequently it is shown that n sub t dimensional single user signaling suffices to provide full diversity order n n sub t n sub r for all the users in other words the presence of other users does not increase the minimum dimension required beyond what is needed for the single user space time channel for the special case of low rank code division multiple access cdma signaling with n sub t 1 and provided the signatures of any two users are linearly independent it is shown that the error probability of a k user system asymptotically approaches single user like performance for every user remarkably therefore an increase in the number of users and hence an increase in the aggregate spectral efficiency does not require the users to transmit with more power to achieve single user like performance asymptotically a signal design algorithm is proposed to illustrate this point and examples are given these results are then generalized to the multiple transmit antenna case a new n sub t 1 dimensional signaling strategy is proposed for the multiuser channel that leverages existing single user space time signal designs while ensuring full diversity order and single user like performance asymptotically for every user

full diversity blind alamouti space time block codes for unique identification of flat fading channels in this paper we consider a systematic design of a full diversity blind alamouti space time block code for a wireless communication system having two transmitter antennas and a single receiver antenna in which the channel is completely unknown at both the transmitter and the receiver the key idea is to alternatively transmit alamouti codes with different phase shift keying psk constellations say with p psk and q psk to provide the theoretical analysis of its unique identification and full diversity conditions we first establish a general theorem for factorizing a pq psk constellation into a product of a p psk constellation and a q psk constellation then we prove that a necessary and sufficient condition for both the factorization and a set of solutions of the resulting alamouti diophantine equation from our code design to be unique is that p and q are coprime the same condition assures that the channel and the transmitted signal can be blindly and uniquely identified furthermore a closed form solution to determine the channel coefficients and the transmitted symbols are obtained also we prove that our code enables full diversity for the generalized likelihood ratio test glrt receiver if p and q are coprime when finite length of the received data is available the unitarity and linearity of our code design allow us to utilize the semi definite relaxation sdr decoder or the sphere decoder so that the joint estimation of the channel and symbols can be efficiently implemented

parallel group detection for synchronous cdma communication over frequency selective rayleigh fading channels a group detector jointly detects a group of users and a parallel group detection scheme is a bank of j independently operating group detectors one for each group of a j group partition of the k transmitting users of a code division multiple access cdma channel in this paper two group detectors are introduced for the frequency selective rayleigh fading fsrf cdma channel while the optimum multiuser detector has a time complexity per symbol tcs of o m sup k k for m ary signaling each of the two group detectors has a tcs of o m g g where g is the group size hence there are parallel group detection schemes based on each of the two group detectors that satisfy a wide range of complexity constraints that result from the choice of partition each of the two group detectors is minimax optimal in the corresponding conditional group near far resistance measure furthermore a succinct indicator of the average ber over high snr regions is defined via the asymptotic efficiency a lower bound and an exact formula for the asymptotic efficiency are derived for the first and second group detectors respectively the group detection approach for the fsrf cdma channel generalizes previous approaches to the complexity performance tradeoff problem it yields the optimum detector when the group size is k when the group size is equal to one the first group detector results in a new optimum linear detector and the second reduces to a recently proposed suboptimum linear detector all other nontrivial partitions yield new multiuser detectors whose performances are commensurate with their complexities

analysis and design of short block ofdm spreading matrices for use on multipath fading channels we consider the use of block spreading in a multicarrier system to gain diversity advantage when employed over multipath fading channels the main idea is to split the full set of subcarriers into smaller blocks and spread the data symbols across these blocks via unitary spreading matrices in order to gain multipath diversity across each block at the receiver we pose the problem of designing the spreading matrix as a finite dimensional optimization problem in which the asymptotic error is minimized this formulation allows us to find explicit solutions for the optimal spreading matrices the performance is validated for the uncoded channel as well as for the coded channel employing turbo iterative decoding we further demonstrate that suboptimal linear complexity equalization strategies for spread orthogonal frequency division multiplexing ofdm do not gain any diversity advantage over traditional diagonal ofdm

fuzzy extractors how to generate strong keys from biometrics and other noisy data we provide formal definitions and efficient secure techniques for turning noisy information into keys usable for any cryptographic application and in particular reliably and securely authenticating biometric data our techniques apply not just to biometric information but to any keying material that unlike traditional cryptographic keys is 1 not reproducible precisely and 2 not distributed uniformly we propose two primitives a fuzzy extractor reliably extracts nearly uniform randomness r from its input the extraction is error tolerant in the sense that r will be the same even if the input changes as long as it remains reasonably close to the original thus r can be used as a key in a cryptographic application a secure sketch produces public information about its input w that does not reveal w and yet allows exact recovery of w given another value that is close to w thus it can be used to reliably reproduce error prone biometric inputs without incurring the security risk inherent in storing them we define the primitives to be both formally secure and versatile generalizing much prior work in addition we provide nearly optimal constructions of both primitives for various measures of closeness of input data such as hamming distance edit distance and set difference

a new view of performance analysis of transmit diversity schemes in correlated rayleigh fading this article provides a new formulation for the pairwise error probability for any coherently demodulated system in arbitrarily correlated rayleigh fading the novelty of the result is that the error probability expression can be described as a function of the eigenvalues of a signal only matrix we also provide the relationship between the pole location of the characteristic function and the resulting error probability this result allows us to approximate and bound the desired probability a new simple bound on the pairwise error probability is derived that is better than the standard chernoff bound and asymptotically tight with the signal to noise ratio snr to the true probability

a unified performance analysis framework for differential detection in mimo rayleigh fading channels in this paper a unified framework for the analysis of differential detection dd schemes in time variant multiple input multiple output rayleigh fading channels is provided the present results are very general in that they apply to transmission with differential phase shift keying unitary differential space time modulation dstm and block dstm and reception with conventional dd cdd multiple symbol dd msdd decision feedback dd dfdd and differentially coherent detection cd new result for general quadratic forms of gaussian random variables are derived which allows us to obtain elegant closed form expressions for the pairwise error probabilities peps of the dominant error events of the considered detectors furthermore it is shown that a unified treatment of all considered detectors is possible with a properly defined effective signal to noise ratio esnr and a useful connection between msdd and minimum mean squared error mmse interpolation is established interesting novel results obtained from this analysis include i dstm constellations designed for cdd and cd are also optimum for msdd and dfdd ii the error floor entailed by msdd and dfdd in time variant fading decreases exponentially with the observation window size n and iii in time variant fading with effective normalized fading bandwidth bh efft msdd with n rarr infin suffers only from an snr loss of 1 2bh efft compared to cd whereas dfdd suffers from a diversity loss of 1 2bh efft

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

design of channel estimate dependent space time block codes so far the assumption of no channel knowledge at the transmitter has generally been inherent in the design of space time codes this paper on the other hand assumes that quantized channel information obtained from a feedback link is available at the transmitter and investigates how such channel information can be incorporated into the design of unstructured space time block codes efficient codes are found by means of a gradient search over a continuous alphabet simulation results for an uncorrelated rayleigh fading scenario using two and four transmit antennas and one receive antenna show the benefits of the code designs

coded unitary space time modulation with iterative decoding error performance and mapping design this paper studies the bit error probability of coded unitary space time modulation with iterative decoding where neither the transmitter nor the receiver knows the channel fading coefficients the tight error bound with respect to the asymptotic performance is first analytically derived for any given unitary constellation and mapping rule design criteria regarding the choice of unitary constellation and mapping are then established furthermore using the unitary constellation obtained from orthogonal design with quadrature phase shift keying qpsk or 4 psk and 8 psk two different mapping rules are proposed the first mapping rule gives the most suitable mapping for systems that do not implement iterative processing which is similar to a gray mapping in coherent channels the second mapping rule yields the best mapping for systems with iterative decoding in particular analytical and simulation results show that with the proposed mappings of the unitary constellations obtained from orthogonal designs the asymptotic error performance of the iterative systems can closely approach a lower bound which is applicable to any unitary constellation and mapping

energy efficient full diversity collaborative unitary space time block code designs via unique factorization of signals in this paper a novel concept called a uniquely factorable constellation pair ufcp is proposed for the systematic design of a noncoherent full diversity collaborative unitary space time block code by normalizing two alamouti codes for a wireless communication system having two transmitter antennas and a single receiver antenna it is proved that such a unitary ufcp code assures the unique identification of both channel coefficients and transmitted signals in a noise free case as well as full diversity for the noncoherent maximum likelihood receiver in a noise case to further improve error performance an optimal unitary ufcp code is designed by appropriately and uniquely factorizing a pair of energy efficient cross quadrature amplitude modulation qam constellations to maximize the coding gain subject to a transmission bit rate constraint after a deep investigation of the fractional coding gain function a technical approach developed in this paper to maximizing the coding gain is to carefully design an energy scale to compress the first three largest energy points in the corner of the qam constellations in the denominator of the objective as well as carefully design a constellation triple forming two ufcps with one collaborating with the other two so as to make the accumulated minimum euclidean distance along the two transmitter antennas in the numerator of the objective as large as possible and at the same time to avoid as many corner points of the qam constellations with the largest energy as possible to achieve the minimum of the numerator in other words the optimal coding gain is attained by intelligent constellations collaboration and efficient energy compression computer simulations demonstrate that error performance of the optimal unitary ufcp code presented in this paper outperforms those of the differential code and the signal to noise ratio efficient training code

a pseudorandom generator from any one way function pseudorandom generators are fundamental to many theoretical and applied aspects of computing we show how to construct a pseudorandom generator from any one way function since it is easy to construct a one way function from a pseudorandom generator this result shows that there is a pseudorandom generator if and only if there is a one way function

a differential space time modulation scheme for correlated rayleigh fading channels performance analysis and design differential space time modulation dstm is an encoding technique for multiantenna systems that allows the receiver to detect the transmitted signals without the knowledge of the fading channels it can be viewed as an extension of the differential phase shift keying scheme in single antenna systems in this paper we investigate the performance of multiantenna systems employing dstm under spatially correlated rayleigh fading channels we present three expressions for calculating the pairwise error probability pep of the dstm scheme the first expression allows us to numerically calculate the exact pep the remaining two are closed form expressions of the exact pep at asymptotically high signal to noise ratios and the pep upper bound it is found that when the distance matrix is proportional to the identity matrix the error probability is determined by the channel correlation matrix and the initial transmitted code matrix based on the new pep upper bound we derive a criterion for optimizing the initial code matrix for this special case simulation results show that the performance of the differential space time coded systems can be significantly improved by designing the initial transmitted code matrix according to the proposed design criterion

noncoherent mimo communication grassmannian constellations and efficient detection this paper considers the design of both a transmitter and a receiver for noncoherent communication over a frequency flat richly scattered multiple input multiple output mimo channel the design is guided by the fact that at high signal to noise ratios snrs the ergodic capacity of the channel can be achieved by input signals that are isotropically distributed on the compact grassmann manifold the first part of the paper considers the design of grassmannian constellations that mimic the isotropic distribution a subspace perturbation analysis is used to determine an appropriate metric for the distance between grassmannian constellation points and using this metric greedy direct and rotation based techniques for designing constellations are proposed these techniques offer different tradeoffs between the minimum distance of the constellation and the design complexity in addition the rotation based technique results in constellations that have lower storage requirements and admit a natural ldquoquasi set partitioningrdquo binary labeling

noncoherent multiuser detection for cdma systems with nonlinear modulation a non bayesian approach this paper considers the problem of multiuser detection for a system in which each user employs nonlinear modulation with an emphasis on noncoherent detection techniques which do not require knowledge of the users channel parameters at the receiver our goals are to gain fundamental insight into the capabilities of multiuser detection in such a setting and to provide practical algorithms that perform better than conventional matched filter reception we begin by providing fundamental performance benchmarks by considering coherent maximum likelihood ml detection which requires knowledge of the users channel parameters as well as noncoherent detection formulated in a non bayesian generalized likelihood ratio test glrt framework the asymptotic performance of each detector as the noise level vanishes is characterized yielding simple geometric criteria for near far resistance in general both the ml and glrt detectors have complexity which is exponential in the number of users we therefore propose the more practical sequential decision projection sdp detector which has complexity which is quadratic in the number of users it is shown that the sdp detector has nonzero asymptotic efficiency if the users powers are suitably disparate

effects of non identical rayleigh fading on differential unitary space time modulation non identical fading distribution in a multiple input multiple output mimo channel including unequal average channel gains and fade rates often occurs when antennas are not co located in this paper we present an analytical study of the effects of non identical rayleigh fading on the error performance of differential unitary space time modulation dustm the fading processes for different transmit receive antenna pairs are assumed to be independent and time variant we find that the maximum likelihood ml differential detector of dustm over such channels is involved except for differential cyclic group codes the conventional detector is proved to be asymptotically optimal in the limit of high signal to noise ratio snr over static fading channels applying the distribution of quadratic forms of gaussian vectors we then derive closed form expressions for the exact error probabilities of two specific unitary classes namely cyclic group codes and orthogonal codes simple and useful asymptotic bounds on error probabilities are also obtained our analysis leads to the following general findings 1 equal power allocation is asymptotically optimal and 2 non identical channel gain distribution degrades the error performance finally we also introduce a water filling based power allocation to exploit the transmit non identical fading statistics

performance analysis of differential space time modulation in this paper we analyze the performance of the differential space time modulation dstm in rayleigh fading channels by using the moment generating function mgf based approach we derive a number of closed form expressions for the pairwise error probability pep of the dstm in various fading environments for spatially independent channels we derive a closed form expression for the exact pep of the dstm for both slow and fast fading cases in the case of fast fading channels we show that an irreducible error floor exists in the pep and in the block error rate of the dstm and derive a closed form expression for the pep error floor in terms of the fading rate for spatially correlated channels we derive a new closed form expression for the pep at asymptotically high signal to noise ratios and show that an existing asymptotic pep expression derived by the residue method can also be obtained by using the mgf based approach finally we use computer simulations to verify the theoretical results

noncoherent space time coding an algebraic perspective the design of space time signals for noncoherent block fading channels where the channel state information is not known a priori at the transmitter and the receiver is considered in particular a new algebraic formulation for the diversity advantage design criterion is developed the new criterion encompasses as a special case the well known diversity advantage for unitary space time signals and more importantly applies to arbitrary signaling schemes and arbitrary channel distributions this criterion is used to establish the optimal diversity versus rate tradeoff for training based schemes in block fading channels our results are then specialized to the class of affine space time signals which allows for a low complexity decoder within this class space time constellations based on the threaded algebraic space time tast architecture are considered these constellations achieve the optimal diversity versus rate tradeoff over noncoherent block fading channels and outperform previously proposed codes in the considered scenarios as demonstrated by the numerical results using the analytical and numerical results developed in this paper nonunitary space time codes are argued to offer certain advantages in block fading channels where the appropriate use of coherent space time codes is shown to offer a very efficient solution to the noncoherent space time communication paradigm

orthogonal design of unitary constellations for uncoded and trellis coded noncoherent space time systems we construct unitary noncoherent space time constellations which can be considered as a concatenation of a training block with an orthogonal design with a simple construction our constellations are easy to design enjoy full antenna diversity allow for a simplified maximum likelihood ml detector and achieve error performance comparable to existing designs that rely on computer search to exploit the constellation structures and improve coding gains we further pursue a trellis coded modulation tcm approach based on the sequence pairwise error analysis we identify two simple parameters to quantify the asymptotic error performance which enables us to compare among different tcm schemes or uncoded alternatives

differential space time modulation with eigen beamforming for correlated mimo fading channels in this paper joint differential space time modulation dstm and eigen beamforming for correlated multiple input multiple output mimo fading channels while dstm does not require knowledge of each channel realization the channel s spatial correlation can be easily estimated without training at the receiver and exploited by the transmitter to enhance the error probability performance a transmission scheme is developed here that combines beamforming with differential multiantenna modulation based on orthogonal space time block coding error probability is analyzed for both spatially correlated and independent rayleigh fading channels based on the error probability analysis power loading coefficients are derived to improve performance the analytical and simulation results presented here corroborate that the proposed scheme can achieve considerable performance gain in correlated channels relative to dstm without beamforming

optimally near far resistant multiuser detection in differentially coherent synchronous channels the noncoherent demodulation of differentially phase shift keyed signals transmitted simultaneously via a synchronous code division multiple access cdma channel is studied under the assumption of white gaussian background noise a class of noncoherent linear detectors is defined with the objective of obtaining the optimal one the performance criterion considered is near far resistance that denotes worst case multiuser asymptotic efficiency over near far environments it is shown that the optimal linear detector is a noncoherent decorrelating detector the commonality between the properties of the decorrelating detectors for coherent and noncoherent channels is established in particular it is shown that no other differential phase shift keying dpsk multiuser detector achieves a higher near far resistance than does the noncoherent decorrelator

an algebraic approach to multiparameter spectral theory root subspaces for multiprameter eigenvalue problems are described using coalgebraic techniques an algorithm is given to construct bases for the root subspaces

multisampling decision feedback linear prediction receivers for differential space time modulation over rayleigh fast fading channels novel decision feedback df linear prediction lp receivers which process multiple samples per symbol interval in conjunction with optimal sample combining are proposed for differential space time modulation dstm over rayleigh fast fading channels performance analysis demonstrates that multisampling df lp receivers outperform their symbol rate sampling counterpart in fast fading substantially in addition an asymptotically tight upper bound on the pairwise error probability is derived in view of this bound the design criterion of dstm for fast fading is the same as that for block wise static fading to avoid the estimation of the second order statistics of the channel a polynomial model based df lp receiver is proposed it can approach the performance of the optimum df lp receiver at high signal to noise ratios provided fading is moderate

mpsk modulated constellation design for differential space time modulation the constellation design for differential space time modulation usually requires to construct l constellation size unitary matrices making the design complexity increasing rapidly with l in this correspondence we propose a new construction technique which exploits the rotational invariance of unitary matrices and the property of mpsk modulation the proposed constellations are derivable from a smaller set of d l m unitary matrices via rotations defined by an m ary psk symbol which in turn are parameterized by two unitary matrices u1 and u2 they share some good property of group constellations thereby considerably simplifying the optimization of u1 and u2 they also possess other good properties which allow for simplified maximum likelihood ml decoding extensive numerical examples are presented to demonstrate that the proposed constellations in general have larger diversity products than other constellations and thus better error performance

differential unitary space time modulation we present a framework for differential modulation with multiple antennas across a continuously fading channel where neither the transmitter nor the receiver knows the fading coefficients the framework can be seen as a natural extension of standard differential phase shift keying commonly used in single antenna unknown channel systems we show how our differential framework links the unknown channel system with a known channel system and we develop performance design criteria as a special ease we introduce a class of diagonal signals where only one antenna is active at any time and demonstrate how these signals may be used to achieve full transmitter diversity and low probability of error

backward error condition numbers and pseudospectra for the multiparameter eigenvalue problem we define and evaluate the normwise backward error and condition numbers for the multiparameter eigenvalue problem mep the pseudospectrum for the mep is defined and characterized we show that the distance from a right definite mep to the closest non right definite mep is related to the smallest unbounded pseudospectrum some numerical results are given

finite dimensional multiparameter spectral theory the nonderogatory case abstract a completeness theorem for nonderogatory eigenvalues of multiparameter systems is proved in a finite dimensional setting also a basis for the second root subspace of a simple eigenvalue is given weakly elliptic multiparameter systems are introduced it is shown that simple real eigenvalues of such systems are nonderogatory

on the theory of space time codes for psk modulation the design of space time codes to achieve full spatial diversity over fading channels has largely been addressed by handcrafting example codes using computer search methods and only for small numbers of antennas the lack of more general designs is in part due to the fact that the diversity advantage of a code is the minimum rank among the complex baseband differences between modulated codewords which is difficult to relate to traditional code designs over finite fields and rings we present general binary design criteria for psk modulated space time codes for linear bpsk qpsk codes the rank of binary projections of the unmodulated codewords as binary matrices over the binary field is a sufficient design criterion full binary rank guarantees full spatial diversity this criterion accounts for much of what is currently known about psk modulated space time codes we develop new fundamental code constructions for both quasi static and time varying channels these are perhaps the first general constructions other than delay diversity schemes that guarantee full spatial diversity for an arbitrary number of transmit antennas

two parameter eigenvalue problems for matrices abstract the linked pair of two parameter eigenvalue problems t m 1 v m 1 2 v m 2 x m 0 x m 0 x m h m is considered for hermitian matrices t m v m1 v m2 acting on on the finite dimensional hilbert spaces h m m 1 2 we dispense with customary definiteness conditions although for m 1 2 we assume the existence of a linear combination of v m1 v m2 which is definite an embedding technique is used to study eigenvalues r 2 of specified variational index the transition between real and nonreal eigenvalues and algebraic multiplicity

estimating statistical properties of mimo fading channels we propose maximum likelihood ml and restricted maximum likelihood reml methods for estimating the mean and covariance parameters of multi input multi output mimo ricean and rayleigh block fading channels using measurements from multiple coherent intervals containing both amplitudes and phases of the received signal correlated and independent fading scenarios with structured and unstructured line of sight los array response models are considered computationally efficient ml and approximate ml aml estimators are proposed for unitary space time modulation schemes and orthogonal designs in correlated fading we also derive crame spl acute r rao bounds crbs for the unknown parameters discuss initialization of the proposed algorithms and evaluate their performance via numerical simulations under the block and continuous fading scenarios