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

construction of multiblock space time codes from division algebras with roots of unity as nonnorm elements the authors give a construction of multiblock space time block codes from cyclic division algebras with a given nth root of unity as the nonnorm element the construction uses local class field theory multiblock codes with m blocks can achieve an m fold increase in diversity

selection and rate adaptation schemes for mimo multiple access channels with low rate channel feedback in this paper two selection schemes are proposed for coded transmission over multiple input multiple output mimo multiple access channels mac to yield a much higher diversity multiplexing gain tradeoff dmt performance these schemes require a channel feedback but at an extremely low rate the first scheme is based on user selection and can be easily implemented in the existing mimo mac systems upper bounds on the minimal computational complexity required by sphere decoders to decode dmt optimal codes for this scheme as well as for mimo mac without feedback are given it is shown that this scheme can offer both a much larger dmt and an exponential reduction on decoding complexity compared with the latter the second scheme selects jointly the users and their transmit antennas it requires an additional design of rate assignments for performance optimization a very general framework on the design of optimal rate assignments is thus provided it is shown that this scheme can yield dmt performances far superior to the optimal mimo mac dmt without channel feedback the simulation results confirm that in some cases this scheme can provide an astonishing snr gain of 14 64 db at outage probability 10 6 compared with the optimal mimo mac coding schemes without feedback

perfect space time block codes in this paper we introduce the notion of perfect space time block codes stbcs these codes have full rate full diversity nonvanishing constant minimum determinant for increasing spectral efficiency uniform average transmitted energy per antenna and good shaping we present algebraic constructions of perfect stbcs for 2 3 4 and 6 antennas

dirichlet neumann bracketing for horn shaped regions we use dirichlet neumann bracketing to obtain sharp upper and lower bounds for the spectral counting function of the dirichlet laplacian for a horn shaped region in rm the first and second term and an estimate for the remainder in the asymptotic expansion of the spectral counting function are obtained for a region in r2 given by x1 x2 x1er x2e x1 x2 1 2 12 212

the golden code a 2 spl times 2 full rate space time code with nonvanishing determinants in this paper the golden code for a 2 spl times 2 multiple input multiple output mimo system is presented this is a full rate 2 spl times 2 linear dispersion algebraic space time code with unprecedented performance based on the golden number 1 spl radic 5 2

reduced order dynamic observer error linearisation a natural extension of observer error linearisation this paper introduces the concept of reduced order dynamic observer error linearisation rdoel for multi output systems which is the problem of transforming a nonlinear system into a nonlinear observer canonical form with the aid of auxiliary dynamics the proposed rdoel framework is not only a modified version of dynamic observer error linearisation doel but also a natural extension of observer error linearisation oel we provide three necessary conditions for the rdoel problem and then derive a necessary and sufficient condition described in terms of lie algebras of vector fields furthermore from the result we also give a geometric necessary and sufficient condition for the oel problem which has not yet been completely established in the case where a diffeomorphism on the output of general form is considered

constructions of multiblock space time coding schemes that achieve the diversity multiplexing tradeoff constructions of multiblock space time coding schemes that are optimal with respect to diversity multiplexing d m tradeoff when coding is applied over any number of fading blocks are presented in this correspondence the constructions are based on a left regular representation of elements in some cyclic division algebra in particular the main construction applies to the case when the quasi static fading interval equals the number of transmit antennas hence the resulting scheme is termed a minimal delay multiblock space time coding scheme constructions corresponding to the cases of nonminimal delay are also provided as the number of coded blocks approaches infinity coding schemes derived from the proposed constructions can be used to provide a reliable multiple input multiple output mimo communication with vanishing error probability

explicit space time codes achieving the diversity multiplexing gain tradeoff a recent result of zheng and tse states that over a quasi static channel there exists a fundamental tradeoff referred to as the diversity multiplexing gain d mg tradeoff between the spatial multiplexing gain and the diversity gain that can be simultaneously achieved by a space time st code this tradeoff is precisely known in the case of independent and identically distributed i i d rayleigh fading for tgesnt nr 1 where t is the number of time slots over which coding takes place and nt nr are the number of transmit and receive antennas respectively for t nt case we present two general techniques for building d mg optimal rectangular st codes from their square counterparts a byproduct of our results establishes that the d mg tradeoff for all tgesnt is the same as that previously known to hold for tgesnt n r 1

eigenvalue asymptotics of the neumann laplacian of regions and manifolds with cusps abstract we study the eigenvalue asymptotics of a neumann laplacian n in unbounded regions of r2 with cusps at infinity a typical example is x y r 2 x 1 y x 2 and prove that n e n n e h v e 2 vol where hv is the canonical one dimensional schrodinger operator associated to the problem we establish a similar formula for manifolds with cusps and derive the eigenvalue asymptotics of a dirichlet laplacian d for a class of cusp type regions of infinite volume

dmt optimal codes constructions for multiple access mimo channel explicit code constructions for multiple input multiple output mimo multiple access channels mac with k users are presented in this paper the first construction is dedicated to the case of symmetric mimo mac where all the users have the same number of transmit antennas nt and transmit at the same level of per user multiplexing gain r furthermore we assume that the users transmit in an independent fashion and do not cooperate the construction is systematic for any values of k nt and r it is proved that this newly proposed construction achieves the optimal mimo mac diversity multiplexing gain tradeoff dmt provided by tse at high snr regime in the second part of the paper we take a further step to investigate the mac dmt of a general mimo mac where the users are allowed to have different numbers of transmit antennas and can transmit at different levels of multiplexing gain the exact optimal mac dmt of such channel is explicitly characterized in this paper interestingly in the general mac dmt some users might not be able to achieve their single user dmt performance as in the symmetric case even when the multiplexing gains of the other users are close to 0 detailed explanations of such unexpected result are provided in this paper finally by generalizing the code construction for the symmetric mimo mac explicit code constructions are provided for the general mimo mac and are proved to be optimal in terms of the general mac dmt

on the densest mimo lattices from cyclic division algebras it is shown why the discriminant of a maximal order within a cyclic division algebra must be minimized in order to get the densest possible matrix lattices with a prescribed nonvanishing minimum determinant using results from class field theory a lower bound to the minimum discriminant of a maximal order with a given center and index the number of tx rx antennas is derived also numerous examples of division algebras achieving the bound are given for example a matrix lattice with quadrature amplitude modulation qam coefficients that has 2 5 times as many codewords as the celebrated golden code of the same minimum determinant is constructed also a general algorithm due to ivanyos and ronyai for finding maximal orders within a cyclic division algebra is described and enhancements to this algorithm are discussed also some general methods for finding cyclic division algebras of a prescribed index achieving the lower bound are proposed

diversity and multiplexing tradeoff in general fading channels the optimal tradeoff between diversity gain and multiplexing gain for multiple inputmultiple output mimo channels has been studied recently under the independent and identically distributed i i d rayleigh fading assumption in this correspondence this result is extended and the optimal tradeoff performance is derived for generalized fading channel conditions including different fading types nonidentical fading distributions spatial correlation and nonzero channel means our results include many known models as special cases and shed light on the effects of different channel parameters on the optimal tradeoff performance

approximately universal codes over slow fading channels performance of reliable communication over a coherent slow fading multiple input multiple output mimo channel at high signal to noise ratio snr is succinctly captured as a fundamental tradeoff between diversity and multiplexing gains this paper studies the problem of designing codes that optimally tradeoff the diversity and multiplexing gains the main contribution is a precise characterization of codes that are universally tradeoff optimal i e they optimally tradeoff the diversity and multiplexing gains for every statistical characterization of the fading channel this characterization is referred to as approximate universality the approximation is in the connection between error probability and outage capacity with diversity and multiplexing gains respectively the characterization of approximate universality is then used to construct new coding schemes as well as to show optimality of several schemes proposed in the space time coding literature

perfect space time codes for any number of antennas in a recent paper perfect n times n space time codes were introduced as the class of linear dispersion space time st codes having full rate nonvanishing determinant a signal constellation isomorphic to either the rectangular or hexagonal lattices in 2n 2 dimensions and uniform average transmitted energy per antenna consequence of these conditions include optimality of perfect codes with respect to the zheng tse diversity multiplexing gain tradeoff dmt as well as excellent low signal to noise ratio snr performance yet perfect space time codes have been constructed only for two three four and six transmit antennas in this paper we construct perfect codes for all channel dimensions present some additional attributes of this class of st codes and extend the notion of a perfect code to the rectangular case

on the spectrum of the dirichlet laplacian for horn shaped regions in rn with infinite volume abstract an inequality for trace et d is proven where d is the dirichlet laplacian for horn shaped regions d in rn the results of rozenbljum and simon for the leading asymptotics for the growth of the number of eigenvalues of the two dimensional dirichlet laplacian in the regions x y x y 1 0 are easily recovered an example of a horn shaped region in r2 where that asymptotics is exponential is given

stbc schemes with nonvanishing determinant for certain number of transmit antennas a space time block code scheme stbc scheme is a family of stbcs c snr indexed by the signal to noise ratio snr such that the rate of each stbc scales with snr an stbc scheme is said to have a nonvanishing determinant if the coding gain of every stbc in the scheme is lower bounded by a fixed nonzero value the nonvanishing determinant property is important from the perspective of the diversity multiplexing gain dm g tradeoff a concept that characterizes the maximum diversity gain achievable by any stbc scheme transmitting at a particular rate this correspondence presents a systematic technique for constructing stbc schemes with nonvanishing determinant based on cyclic division algebras prior constructions of stbc schemes from cyclic division algebra have either used transcendental elements in which case the scheme may have vanishing determinant or is available with nonvanishing determinant only for two three four and six transmit antennas in this correspondence we construct stbc schemes with nonvanishing determinant for the number of transmit antennas of the form 2 sup k 3 spl middot 2 sup k 2 spl middot 3 sup k and q sup k q 1 2 where q is any prime of the form 4s 3 for cyclic division algebra based stbc schemes in a recent work by elia et al the nonvanishing determinant property has been shown to be sufficient for achieving dm g tradeoff in particular it has been shown that the class of stbc schemes constructed in this correspondence achieve the optimal dm g tradeoff moreover the results presented in this correspondence have been used for constructing optimal stbc schemes for arbitrary number of transmit antennas by elia et al