universal space time coding a universal framework is developed for constructing full rate and full diversity coherent space time codes for systems with arbitrary numbers of transmit and receive antennas the proposed framework combines space time layering concepts with algebraic component codes optimized for single input single output siso channels each component code is assigned to a thread in the space time matrix allowing it thus full access to the channel spatial diversity in the absence of the other threads diophantine approximation theory is then used in order to make the different threads transparent to each other within this framework a special class of signals which uses algebraic number theoretic constellations as component codes is thoroughly investigated the lattice structure of the proposed number theoretic codes along with their minimal delay allow for polynomial complexity maximum likelihood ml decoding using algorithms from lattice theory combining the design framework with the cayley transform allows to construct full diversity differential and noncoherent space time codes the proposed framework subsumes many of the existing codes in the literature extends naturally to time selective and frequency selective channels and allows for more flexibility in the tradeoff between power efficiency bandwidth efficiency and receiver complexity simulation results that demonstrate the significant gains offered by the proposed codes are presented in certain representative scenarios

on optimal multilayer cyclotomic space time code designs high rate and large diversity product or coding advantage or coding gain or determinant distance or minimum product distance are two of the most important criteria often used for good space time code designs in recent linear lattice based space time code designs more attention is paid to the high rate criterion but less to the large diversity product criterion in this paper we consider these two criteria together for multilayer cyclotomic space time code designs in a previous paper we recently proposed a systematic cyclotomic diagonal space time code design over a general cyclotomic number ring that has infinitely many designs for a fixed number of transmit antennas where diagonal codes correspond to single layer codes in this paper in this paper we first propose a general multilayer cyclotomic space time codes we present a general optimality theorem for these infinitely many cyclotomic diagonal or single layer space time codes over general cyclotomic number rings for a general number of transmit antennas we then present optimal multilayer full rate cyclotomic space time code designs for two and three transmit antennas we also present an optimal two layer cyclotomic space time code design for three and four transmit antennas the optimality here is in the sense that for a fixed mean transmission signal power its diversity product is maximized or equivalently for a fixed diversity product its mean transmission signal power is minimized it should be emphasized that all the optimal multilayer cyclotomic space time codes presented in this paper have the nonvanishing determinant property

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

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

blind channel identifiability for generic linear space time block codes linear space time block codes stbcs have proven their effectiveness in performance improvement of wireless multiple input multiple output communication systems their successful decoding however requires reliable channel knowledge at the receiver in this paper we present a semiblind channel estimation method for linear stbc without the usual code orthogonality condition we provide a set of identification conditions that are mostly verifiable a priori in terms of code parameters and antenna array configuration we also present a simple channel estimation algorithm finally we provide simulation results that illustrate the performance of the proposed scheme

linear dispersion codes for mimo systems based on frame theory multiple input multiple output mimo wireless communication systems provide high capacity due to the plurality of modes available in the channel existing signaling techniques for mimo systems have focused primarily on multiplexing for high data rate or diversity for high link reliability in this paper we present a new linear dispersion code design for mimo rayleigh fading channels the proposed design bridges the gap between multiplexing and diversity and yields codes that typically perform well both in terms of ergodic capacity as well as error probability this is important because as we show designs performing well from an ergodic capacity point of view do not necessarily perform well from an error probability point of view various techniques are presented for finding codes with good error probability performance monte carlo simulations illustrate performance of some example code designs in terms of ergodic capacity codeword error probability and bit error probability

mixed q linear space time codes a new modulation method for linear space time codes is proposed based on using constellations of different sizes for different symbols it is shown that the proposed method significantly reduces the complexity of the sphere decoding algorithm the complexity reduction is more pronounced in high rate codes where each code matrix carries a large number of symbols we also show that the choice of constellation size provides a tradeoff between performance and complexity using this some guidelines for choosing constellation size are presented as one introduces more constellation disparity in the code the complexity is further reduced while the performance loss grows typically a complexity reduction of one to two orders of magnitude can be achieved at the expense of about 3 db coding gain we suggest a simple modification in our design to reduce this loss to about 2 db

a construction of a space time code based on number theory we construct a full data rate space time st block code over m 2 transmit antennas and t 2 symbol periods and we prove that it achieves a transmit diversity of 2 over all constellations carved from z i sup 4 further we optimize the coding gain of the proposed code and then compare it to the alamouti code it is shown that the new code outperforms the alamouti see ieee j select areas commun vol 16 p 1451 58 1998 code at low and high signal to noise ratio snr when the number of receive antennas n 1 the performance improvement is further enhanced when n or the size of the constellation increases we relate the problem of st diversity gain to algebraic number theory and the coding gain optimization to the theory of simultaneous diophantine approximation in the geometry of numbers we find that the coding gain optimization is equivalent to finding irrational numbers the furthest from any simultaneous rational approximations

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

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

an optimal two transmit antenna space time code and its stacked extensions a space time code is proposed that exhibits the highest coding gain among competing full rate full transmit diversity space time codes for the two transmit and receive antenna coherent quasi static fading channel the proposed code is derived from a layered architecture with real rotation of quadrature amplitude modulation qam information symbols in two dimensions the existing codes of similar architecture concentrate on application of complex full modulation diversity rotations or asymmetric real rotations an analytic evaluation illustrates the significant improvement in coding gain achieved with the proposed code moreover the coding gain of the proposed code is independent of its rate this implies that the proposed code achieves the optimal diversity multiplexing tradeoff curve for the two transmit antenna system a stacked extension of the proposed code offers a reduced complexity capacity optimal alternative to the full diversity codes for larger number of transmit antennas performance enhancement in several scenarios is verified through simulations

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

full diversity high rate space time block codes from division algebras we present some general techniques for constructing full rank minimal delay rate at least one space time block codes stbcs over a variety of signal sets for arbitrary number of transmit antennas using commutative division algebras field extensions as well as using noncommutative division algebras of the rational field spl qopf embedded in matrix rings the first half of the paper deals with constructions using field extensions of spl qopf working with cyclotomic field extensions we construct several families of stbcs over a wide range of signal sets that are of full rank minimal delay and rate at least one appropriate for any number of transmit antennas we study the coding gain and capacity of these codes using transcendental extensions we construct arbitrary rate codes that are full rank for arbitrary number of antennas we also present a method of constructing stbcs using noncyclotomic field extensions in the later half of the paper we discuss two ways of embedding noncommutative division algebras into matrices left regular representation and representation over maximal cyclic subfields the 4 spl times 4 real orthogonal design is obtained by the left regular representation of quaternions alamouti s 1998 code is just a special case of the construction using representation over maximal cyclic subfields and we observe certain algebraic uniqueness characteristics of it also we discuss a general principle for constructing cyclic division algebras using the nth root of a transcendental element and study the capacity of the stbcs obtained from this construction another family of cyclic division algebras discovered by brauer 1933 is discussed and several examples of stbcs derived from each of these constructions are presented

finite fuzzy topological spaces abstract we compute for the first time the number of fuzzy topologies defined on a finite set and having a small number of open sets certain cases where the number of open sets is large are also considered several well known results are obtained as corollaries the paper is ended by some questions for future investigations

some designs and normalized diversity product upper bounds for lattice based diagonal and full rate space time block codes in this paper we first present two tight upper bounds for the normalized diversity products or product distances of 2ntn2 diagonal space time block codes from quadratic extensions on bbq i and bbq mmbzeta6 where i radic 1 and mmbzeta6 exp i 2pi 6 two such codes are shown to reach the tight upper bounds and therefore have the maximal normalized diversity products we present two new diagonal space time block codes from higher order algebraic extensions on bbq i and bbq mmbzeta6 for three and four transmit antennas we also present a nontight upper bound for normalized diversity products of 2ntn2 diagonal space time block codes with qam information symbols i e in bbz i from general 2ntn2 complex valued generating matrices we then present an nntnn diagonal space time code design method directly from 2n real integers based on extended complex lattices of generating matrix size nntn2n that are shown to have better normalized diversity products than the optimal diagonal cyclotomic codes do we finally use the optimal 2ntn2 diagonal space time codes from the optimal quadratic extensions to construct two 2ntn2 full rate space time block codes and find that both of them have better normalized diversity products than the golden code does

a new representation of tast codes a simple and general form of threaded algebraic space time tast codes and constellations for arbitrary numbers of transmit and receive antennas and arbitrary input alphabets is given and analyzed this new form gives revealing insights on the tast framework elucidates the connection between space time constellation expansion and the peak to average power ratio par and establishes the equivalence between a certain class of tast constellations and constellations derived from division algebras

completely induced l fuzzy topological spaces abstract the first aim of this paper is to introduce and to study the concepts of complete scott continuity and completely induced l fuzzy topological space the second is to discuss the connections between some separation countability and covering properties of an ordinary topological space and its corresponding completely induced l fuzzy topological space

optimal normalized diversity product of 2 times 2 lattice based diagonal space time codes from qam signal constellations in this correspondence we prove that the optimal normalized diversity product of lattice based diagonal space time block codes with gaussian integer or qam signal constellations i e and any generating matrices of complex entries not necessarily algebraic extensions of as commonly used is this result implies that lattice based diagonal space time block codes with gaussian integer signal constellations and generating matrices of entries from quadratic algebraic extensions of have already reached the optimal normalized diversity product

stochastic gradient algorithms for design of minimum error rate linear dispersion codes in mimo wireless systems linear dispersion ld codes are a good candidate for high data rate multiple input multiple ouput mimo signaling traditionally ld codes were designed by maximizing the average mutual information which cannot guarantee good error performance this paper presents a new design scheme for ld codes that directly minimizes the block error rate bler in mimo channels with arbitrary fading statistics and various detection algorithms for mimo systems employing ld codes the error rate does not admit an explicit form therefore we cannot use deterministic optimization methods to design the minimum error rate ld codes in this paper we propose a simulation based optimization methodology for the design of ld codes through stochastic approximation and simulation based gradient estimation the gradient estimation is done using the score function method originally developed in the discrete event system community the proposed method can be applied to design the minimum error rate ld codes for a variety of detector structures including the maximum likelihood ml detector and several suboptimal detectors it can also design optimal codes under arbitrary fading channel statistics in particular it can take into account the knowledge of spatial fading correlation at the transmitter and receiver ends simulation results show that codes generated by the proposed new design paradigm generally outperform the codes designed based on algebraic number theory

on random rotations diversity and minimum mse decoding of lattices we establish a simple relation between high diversity multidimensional rotations obtained from totally complex cyclotomic fields and the discrete fourier transform the diversity distribution of an hadamard like random rotation is derived analytically it is shown that a random multidimensional rotation exhibits an excellent diversity distribution and can be combined to quadrature amplitude modulation qam constellations to combat channel fading we also describe a mean square error mse universal lattice decoder suitable for large dimensions up to 1024 the mse criterion treats the lattice structure as intersymbol interference the universal decoder is applied to both gaussian and rayleigh fading channels to decode dense lattice sphere packings and rotated cubic constellations respectively

the icosian code and the e_8 lattice a new 4 times 4 space time code with nonvanishing determinant this paper introduces a new rate 2 full diversity space time code for four transmit antennas and one receive antenna the 4times4 codeword matrix consists of four 2times2 alamouti blocks with entries from q i radic5 and these blocks can be viewed as quaternions which in turn represent rotations in r 3 the alamouti blocks that appear in a codeword are drawn from the icosian ring consisting of all linear combinations of 120 basic rotations corresponding to symmetries of the icosahedron this algebraic structure is different from the golden code but the complex entries are taken from a common underlying field the minimum determinant is bounded below by a constant that is independent of the signal constellation and the new code admits a simple decoding scheme that makes use of a geometric correspondence between the icosian ring and the e 8 lattice

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

distributed qam based space time block codes for efficient cooperative multiple access communication distributed space time block coding schemes based on quadrature amplitude modulation qam symbols are introduced that enable users in a wireless multiple access relay channel to cooperate with each other in order to improve the reliability of their information in a fair rate efficient manner the distributed coding schemes are designed for a system that consists of m users that need to send their information to a common destination each user is equipped with only one antenna and a half duplex transceiver so that it can transmit to the destination or any other user at one time and also receive signals from any other user at another time the destination is equipped with one or more receive antennas the goal is to design cooperative schemes which achieve the maximum diversity order which is equal to the diversity order of the outage probability while being fair to the users in terms of rate allocation two cooperative coding schemes are proposed that meet these requirements a two phase cooperative scheme and a single phase self information canceling linear scl scheme the two phase scheme is of lower decoding complexity and it requires the users to only transmit qam symbols the scl scheme is of higher complexity with the users transmitting linear combination of qam symbols but it also achieves better performance both schemes incorporate new classes of cooperation rules for deciding whether or not a user acts as a relay for another user the usual outage based cooperation rule whereby a user cooperates with another user provided the mutual information of the channel between them is greater than the rate is sufficient for deriving information theoretic limits but it cannot be used directly for analysis of a particular coding scheme even though the decoder used by the destination in the proposed coding schemes assumes that the inter user communication is always successful our performance analysis does not make this assumption in fact it rigorously accounts for the decoding errors arising from the information exchange between users consequently it sheds light on precisely what cooperation rules among the class of rules analyzed lead to maximal diversity

actions of finite groups on graphs and related automorphisms of free groups the proof will be completed in section 6 it is geometrical and the geometrical objects which will be used are graphs on which finite groups act g graphs the following lines are intended to describe the structure of the proof with the main intermediate results the translation into geometrical language is made possible by the realization theorem of culler s which states that every finite subgroup of out is realized by automorphisms of a graph see section 3 now if g is a finite subgroup of out cp and r a graph realizing g then the centralizer of g can be identified with the group out n t of equivariant conjugacy classes of automorphisms of rc f we shall turn to fundamental groupoids and prove with some effort sections 4 and 5 that if the g graph r is suitably chosen reduced then the natural homomorphism aut z7 r out z is surjective this way the problem reduces to the more tractable group aut n r of equivariant automorphisms of the free groupoid n r that this group is finitely generated will be proved in section 6 by an extension of the nielsen method in free groups a peculiarity which occurs in the study of aut iz ij is that we are forced to consider simultaneously a number of graphs related to r and all isomorphisms between fundamental groupoids of these graphs in the classical situation of automorphisms of a free group g trivial r a wedge of loops one proves that every automorphism of i e of n r can be expressed as a product of nielsen automorphisms what we have in the general situation is that under certain circumstances described in sec

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

the amplify and forward half duplex cooperative system pairwise error probability and precoder design in this paper an exact asymptotic pairwise error probability pep is derived for a half duplex cooperative system employing an amplify and forward af protocol when compared with the pep of a traditional multiple input multiple output mimo system the diversity gain for the cooperative system is no longer just a simple exponential function of the signal to noise ratio snr rather it involves the logarithm of the snr the term diversity gain function is used to designate this characteristic of the pep the coding gain on the other hand is found similar to that for the mimo system and is proportional to the determinant of the autocorrelation of the error matrix based on our analysis and observations we propose a design of unitary precoder for the cooperative system to achieve the full diversity gain function for the case of a 4 qam signal being transmitted we further optimize the coding gain and arrive at a closed form optimum precoder simulations indicate that our proposed precoder designs greatly improve the performance of the cooperative system

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

algebraic tools to build modulation schemes for fading channels a unified framework is presented in order to build lattice constellations matched to both the rayleigh fading channel and the gaussian channel the method encompasses the situations where the interleaving is done on the real components or on two dimensional signals in the latter case a simple construction of lattices congruent to the densest binary lattices with respect to the euclidean distance is proposed it generalizes in a sense to be clarified later the structural construction proposed by forney 1991 these constellations are next combined with coset codes the partitioning rules and the gain formula are similar to those used for the gaussian channel

space time coding ambiguities in joint adaptive channel estimation and detection this paper studies the error propagation effect that is caused by certain ambiguities in joint data detection channel tracking algorithms for transmission diversity schemes here we use a space time st receiver based on the maximum a posteriori map method that takes into account the channel estimation error assuming the unknown channel to have a given complex multivariate gaussian probability density function pdf i e a ricean channel the decision criterion that is expressed in quadratic form represents either a linear detector or a noncoherent nonlinear detector in extreme cases then the channel pdf for the next iteration is updated by estimates of the second order statistics of the channel coefficients and a very simple decision directed adaptive algorithm is derived for adaptive channel estimation the adaptive algorithm can efficiently track a fast rayleigh fading channel and as a result achieves robust performance however the occurrence of two types of ambiguities initiated in deep fades result in error propagation some remedies called space time ambiguity remedies stars are proposed to prevent error propagation a new time varying space time coding tvst scheme is suggested as a bandwidth efficient method to combat the permutation ambiguity impairment this coding scheme in conjunction with a differential detector can resolve the ambiguity problem

automorphisms of automorphism groups of free groups abstract if n 3 and f n is free of rank n then out aut f n out out f n 1

diagonal lattice space time codes from number fields and asymptotic bounds in this paper we reformulate some constructions of real and complex diagonal lattice space time codes from number fields which have been given explicitly or implicitly by other researchers these constructions establish a connection between good diagonal lattice space time codes and number fields with small absolute values of discriminants we present two tables for diversity products of some lattice space time codes from these constructions the maximal rank of diagonal lattice space time codes with positive diversity product is determined we also discuss the asymptotic problem of lattice space time codes by using an infinite tower of hilbert class field and a tamely ramified class field tower we obtain asymptotically good sequences of lattice space time codes some asymptotic upper bounds are given in the paper as well

abelian covers of graphs and maps between outer automorphism groups of free groups we explore the existence of homomorphisms between outer automorphism groups of free groups out f n out f m we prove that if n 8 is even and n m 2n or n is odd and n m 2n 2 then all such homomorphisms have finite image in fact they factor through det rm out f n to mathbb z 2 in contrast if m r n n 1 1 with r coprime to n 1 then there exists an embedding rm out f n hookrightarrow rm out f m in order to prove this last statement we determine when the action of out f n by homotopy equivalences on a graph of genus n can be lifted to an action on a normal covering with abelian galois group

space time block code designs based on quadratic field extension for two transmitter antennas space time block code designs based on algebraic field extension for full rate large diversity product and nonvanishing minimum determinant of codewords have received great attention there are many different types of codes available for two transmitter antennas such as cyclotomic space time block codes the golden space time block code and rotation based space time block codes in this paper a more general space time block code design scheme which is called quadratic space time block coding is proposed for the two transmitter antennas using quadratic field extension the optimal design of the quadratic space time block codes in terms of a diversity product criterion is also presented it is shown that the optimal quadratic space time block codes designed in this paper do not belong to the existing space time block code family such as the cyclotomic golden and rotation based space time block codes the simulation results demonstrate that the average codeword error rate of the optimal quadratic space time block code attains about 0 5 db signal to noise ratio gain over those of the optimal cyclotomic and golden space time block codes

on two high rate algebraic space time codes we examine some algebraic properties of two high rate linear space time block codes over m 2 3 transmit antennas although these high rate codes have positive coding gain the gain decreases when increasing the constellation size we give tight upper and lower bounds on the achieved coding gains as functions of the size of the constellations used we show that when using the irrational numbers spl radic 3 and spl radic 2 the coding gains express the approximation of these numbers by continued fractions depending on the constellations used the poor approximation of these numbers by rational numbers is then shown to make the coding gains decrease slowly when increasing the constellation size

systematic construction of full diversity algebraic constellations a simple and systematic approach for constructing full diversity m dimensional constellations carved from lattices over a number ring r is proposed for an arbitrary dimension m when r z wn the nth cyclotomic number ring all the possible dimensions that allow for achieving the optimal minimum product distances using the proposed approach are determined it turns out that one can construct optimal unitary transformations using our construction if and only if m factors into a power of 2 and powers of the primes dividing n for m not satisfying these conditions a method based on diophantine approximation theory is proposed to optimize the minimum product distance a lower bound on the product distance is given in this case thus ensuring full diversity with good minimum product distances furthermore the proposed approach subsumes the optimal unitary transformations proposed by giraud et al over r z w4 and r z w3 while giving optimal unitary transformations for infinitely many new values of n and m

the maximum order of finite groups of outer automorphisms of free groups let fr be free group of rank r l and o u t f r a u t fr innfr the outer au tomorph ism group automorphisms modulo inner automorphisms we shall prove the following theorem the maximum order of a f ini te subgroup g of out f is 12 for r 2 and 2 r r for r 2 furthermore the f inite subgroup of out f realizing the maximum order is unique up to conjugacy for r 3 the proof of the above theorem is based on the following geometric realization result which was observed first in z p 478 see also cu proposition 0 let g be a finite subgroup of out f then there exist a f inite connected graph f with 1 f f and an action of g on f realizing the given action on f remarks and definitions let f be a subgraph obtained by deleting all free edges of f i e edges with vertex of valence 1 note that the g action restricts on the new graph f and the fundamental g roup and the induced action on it do not change so we may assume in proposi t ion 0 that f contains no vertex of valence 1 we use sym f to denote the symmetry group of f in a combina tor ial sense i e mapping vertices to vertices and oriented edges to oriented edges or equivalently homeomorph i sms acting linearly on edges in general we allow inversions of edges i e reflections in the midpoints of edges which is not considered as the identity then in proposi t ion 0 we may also assume that f has no vertices of valence 2 by amalgamat ing the two adjacent edges containing the same vertex of valence 2 into one edge again g acts on the new graph with the same induced action on the fundamenta l group we say that a g roup g acts effectively on f if it can be embedded into sym f or equivalently no non trivial element of g is the identity on f for a connected graph f its rank denoted by rank f is the rank of its fundamental group lemma 1 let f be a connected graph of rank r 1 without vertices of valence 1 and g be a f ini te group acting on f then g acts effectively on f if and only if the induced action on f injects into out f

good lattice constellations for both rayleigh fading and gaussian channels recent work on lattices matched to the rayleigh fading channel has shown how to construct good signal constellations with high spectral efficiency we present a new family of lattice constellations based on complex algebraic number fields which have good performance on rayleigh fading channels some of these lattices also present a reasonable packing density and thus may be used at the same time over a gaussian channel conversely we show that particular versions of the best lattice packings d sub 4 e sub 6 e sub 8 k sub 12 spl lambda sub 16 spl lambda sub 24 constructed from totally complex algebraic cyclotomic fields present better performance over the rayleigh fading channel the practical interest in such signal constellations rises from the need to transmit information at high rates over both terrestrial and satellite links some further results in algebraic number theory related to ideals and their factorization are presented and the decoding algorithm used with these lattice constellations are illustrated together with practical results

algebraic number precoding for space time block codes we propose a space time block coding framework based on linear precoding the codes for p transmit antennas are formed by transmitting the information vector with p independent information symbols l times where each time it is rotated by a distinct precoding matrix the framework generalizes conventional spatial multiplexing techniques and facilitates tradeoff between rate and diversity we propose a simple construction for precoding matrices whose parameters are chosen to guarantee maximal diversity using algebraic number theory our codes exhibit circular structure which greatly simplifies the performance analysis and facilitates linear decoding theoretical analysis and numerical simulations demonstrated excellent performance of the proposed algebraic precoding framework

lattice reduction aided conditional detection for mimo systems we introduce a low complexity detector with near optimal performance for transmission over multi antenna systems by using lattice basis reduction for generating almost orthogonal channel submatrices we enhance the conditional optimization technique to implement a fast yet efficient detector the lattice reduction aided lra conditional method is presented as a general detection technique over fading channels to yield significant saving in computational complexity while achieving close to maximum likelihood ml error performance by employing the orthogonality defect factor as a universal measure to select a near orthogonal channel submatrix for conditional detection we implement efficient detectors for mimo systems in particular an almost optimal decoder with linear complexity for the golden code is presented over quasi static channels

simple iterative methods to exploit the signal space diversity signal space diversity is a power and bandwidth efficient diversity technique to exploit the signal space diversity joint maximum likelihood ml detection at the receiver is usually needed where the complexity grows exponentially with the dimension of the lattice in this letter we propose a serial concatenated scheme and two simple iterative methods to exploit the signal space diversity the simple iterative methods are based on the idea of soft interference cancellation the first iterative method is based on a vector gaussian approximation while the second one is based on a scalar gaussian approximation the complexity of the first iterative method grows cubically with the dimension of the lattice and the simulations show that its performance approaches that of the optimal maximum a posteriori detection method the complexity of the second iterative method grows linearly with the dimension of the lattice and the simulations show that when the dimension of the lattice n 32 at bit error rate 10 sup 5 the performance gap between the rayleigh fading channel and the gaussian channel is only 0 3 db

the symmetries of outer space for n 3 the natural map out fn aut kn from the outer automorphism group of the free group of rank n to the group of simplicial automorphisms of the spine of outer space is an isomorphism

mapping class groups and outer automorphism groups of free groups are c simple abstract we prove that the reduced c algebras of centerless mapping class groups and outer automorphism groups of free groups are simple as are the irreducible pure subgroups of mapping class groups and the analogous subgroups of outer automorphism groups of free groups

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

space time coding techniques with bit interleaved coded modulations for mimo block fading channels the space time bit interleaved coded modulation st bicm is an efficient technique to obtain high diversity and coding gain on a block fading multiple input multiple output mimo channel its maximum likelihood ml performance is computed under ideal interleaving conditions which enables a global optimization taking into account channel coding thanks to a diversity upper bound derived from the singleton bound an appropriate choice of the time dimension of the space time coding is possible which maximizes diversity while minimizing complexity based on the analysis an optimized interleaver and a set of linear precoders called dispersive nucleo algebraic dna precoders are proposed the proposed precoders have good performance with respect to the state of the art and exist for any number of transmit antennas and any time dimension with turbo codes they exhibit a frame error rate which does not increase with frame length

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

on the design of multidimensional signal sets for ofdm systems an orthogonal frequency division multiplexing ofdm system operating over a wireless communication channel effectively forms a number of parallel frequency nonselective fading channels thereby obviating the need for complex equalization and thus greatly simplifying equalization decoding however the ofdm system also exhibits two weaknesses relative to its single carrier counterparts 1 the diversity achieved by the ofdm system can be less than a single carrier system employing the same error control code in a signaling environment rich in diversity and 2 the baseband transmitted signal can exhibit significant amplitude fluctuation over time thereby precluding efficient transmit amplifier operation in this paper nonstandard multidimensional signal sets matched to the ofdm framework are prescribed that address both of these issues the proposed signal sets are chosen to maximize the diversity achieved by an uncoded system under a constraint to control the peak to mean envelope power ratio pmepr of the baseband transmitted waveform the cost of employing the proposed signal sets is an increase in decoding complexity as essentially a small amount of controlled equalization has been added to the receiver thus the resulting system can be viewed as a hybrid between an ofdm system and a standard single carrier system numerical results are presented which suggest that 1 the system can provide an attractive alternative to a standard ofdm system in terms of required average transmitted snr versus receiver complexity and 2 the system yields a modest reduction in pmepr versus a standard ofdm system

algebraic lattice constellations bounds on performance in this work we give a bound on performance of any full diversity lattice constellation constructed from algebraic number fields we show that most of the already available constructions are almost optimal in the sense that any further improvement of the minimum product distance would lead to a negligible coding gain furthermore we discuss constructions minimum product distance and bounds for full diversity complex rotated z i sup n lattices for any dimension n which avoid the need of component interleaving

construction methods for asymmetric and multiblock space time codes in this paper the need for the construction of asymmetric and multiblock space time codes is discussed above the trivial puncturing method i e switching off the extra layers in the symmetric multiple input multiple output mimo setting two more sophisticated asymmetric construction methods are proposed the first method called the block diagonal method bdm can be converted to produce multiblock space time codes that achieve the diversity multiplexing tradeoff dmt it is also shown that maximizing the density of the newly proposed block diagonal asymmetric space time ast codes is equivalent to minimizing the discriminant of a certain order a result that also holds as such for the multiblock codes an implicit lower bound for the density is provided and made explicit for an important special case that contains e g the systems equipped with 4tx 2rx antennas further an explicit scheme achieving the bound is given another method proposed here is the smart puncturing method spm that generalizes the subfield construction method proposed in earlier work by hollanti and ranto and applies to any number of transmitting and lesser receiving antennas the use of the general methods is demonstrated by building explicit sphere decodable codes using different cyclic division algebras cdas computer simulations verify that the newly proposed methods can compete with the trivial puncturing method and in some cases clearly outperform it the conquering construction exploiting maximal orders improves upon the punctured perfect code and the djabba code as well as the icosian code also extensive dmt analysis is provided

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

systematic and optimal cyclotomic lattices and diagonal space time block code designs in this correspondence a new and systematic design of cyclotomic lattices with full diversity is proposed by using some algebraic number theory this design provides infinitely many full diversity cyclotomic lattices for a given lattice size based on the packing theory and the concrete form of the design optimal cyclotomic lattices are presented by minimizing the mean transmission signal power for a given minimum diversity product or equivalently maximizing the minimum product for a given mean transmission signal power the newly proposed cyclotomic lattices can be applied to both space time code designs for multi antenna systems and linear precode design for signal space diversity in single antenna systems over fast rayleigh fading channels although there are some cyclotomic lattices space time codes existing in the literature most of them are not optimal

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

superimposed training based noncoherent mimo systems the training based scheme constitutes an efficient method for noncoherent multiantenna communications in this paper we propose a superimposed training based linear dispersion stld transmission scheme where the transmitted symbols are superposition of the training pilots and the data symbols the stld system enjoys simple encoding and efficient suboptimal decoding since for noncoherent multiple input multiple output systems employing the stld scheme analytical expressions of block or bit error probabilities do not exist deterministic optimization methods cannot be used to design the optimal stld system we therefore propose to design the optimal stld systems using simulation based optimization techniques together with gradient estimation simulation results show that with either maximum likelihood or suboptimal decoding the stld systems obtained by the proposed design algorithm generally outperform the conventional training based scheme employing space time codes designed for coherent channels

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

low ml decoding complexity stbcs via codes over the klein group in this paper we give a new framework for constructing low ml decoding complexity space time block codes stbcs using codes over the klein group k almost all known low ml decoding complexity stbcs can be obtained via this approach new full diversity stbcs with low ml decoding complexity and cubic shaping property are constructed via codes over k for number of transmit antennas n 2m m 1 and rates r 1 complex symbols per channel use when r n the new stbcs are information lossless as well the new class of stbcs have the least known ml decoding complexity among all the codes available in the literature for a large set of n r pairs

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

delay tolerant distributed tast codes for cooperative diversity in cooperative networks using a decode and forward strategy the multiple relays effectively transmit a distributed space time code the performance of which can be severely degraded when timing synchronization among the relays is not assured e g in cases of broadcast to dispersed recipients or in networks without a shared high quality timing reference recent work by xia and hammons have investigated the design of distributed space time codes that are delay tolerant in the sense that full spatial diversity is achieved regardless of timing offsets in general the previously known space time block codes belonging to the class of c linear codes however which are important because they achieve full spatial diversity and admit near optimal lattice decoding algorithms are not delay tolerant in this paper we present a new family of such codes that are fully delay tolerant the new codes generalize the threaded algebraic space time tast codes introduced by el gamal and damen like their brethren the new distributed tast codes are effective and flexible enabling use of different signaling constellations transmission rates numbers of transmit and receive antennas and decoders of varying levels of complexity

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

on the lattices of l topologies certain properties of the lattices of l topologies determined by the families of scott continuous functions for a given topological space are investigated the authors disprove certain known theorems on the above lattices and the correct results are provided using the concept of strict chain join generability in lattices

a new family of unitary space time codes with a fast parallel sphere decoder algorithm in this paper we propose a new design criterion and a new class of unitary signal constellations for differential space time modulation for multiple antenna systems over rayleigh flat fading channels with unknown fading coefficients extensive simulations show that the new codes have significantly better performance than existing codes we have compared the performance of our codes with differential detection schemes using orthogonal design cayley differential codes fixed point free group codes and product of groups and for the same bit error rate our codes allow smaller signal to noise ratio snr by as much as 10 db the design of the new codes is accomplished in a systematic way through the optimization of a performance index that closely describes the bit error rate as a function of the snr the new performance index is computationally simple and we have derived analytical expressions for its gradient with respect to constellation parameters decoding of the proposed constellations is reduced to a set of one dimensional closest point problems that we solve using parallel sphere decoder algorithms this decoding strategy can also improve efficiency of existing codes

on the cubical geometry of higman s group we investigate the cocompact action of higman s group on a cat 0 square complex associated to its standard presentation we show that this action is in a sense intrinsic which allows for the use of geometric techniques to study the endomorphisms of the group and show striking similarities with mapping class groups of hyperbolic surfaces outer automorphism groups of free groups and linear groups over the integers we compute explicitly the automorphism group and outer automorphism group of higman s group and show that the group is both hop an and co hop an we actually prove a stronger rigidity result about the endomorphisms of higman s group every non trivial morphism from the group to itself is an automorphism we also study the geometry of the action and prove a surprising result although the cat 0 square complex acted upon contains uncountably many ats the higman group does not contain subgroups isomorphic to z finally we show that this action possesses features reminiscent of negative curvature which we use to prove a re ned version of the tits alternative for higman s group higman s group was constructed in 15 as the rst example of a nitely presented in nite group without non trivial nite quotients it is given by the following presentation h ai i z 4z aiai 1a i a 2 i 1 i z 4z if some partial results about higman s group are known the structure of the group and its geometry have remained mostly elusive the group is known to split as an amalgamated product over several non abelian free subgroups and such splittings can be used to derive various properties of the group for instance the group has nite asymptotic dimension by work of bell dranishnikov 1 a property that implies the novikov conjecture and the coarse baum connes conjecture for the group 36 37 such splittings have also been used to show that the higman group admits in a sense many quotients schupp developed small cancellation tools to show that the group is sq universal 30 that is every countable group embeds in a quotient of h minasyan osin used these splittings to show that the group is 2010 mathematics subject classi cation primary 20f65 secondary 20f28

a universal lattice code decoder for fading channels we present a maximum likelihood decoding algorithm for an arbitrary lattice code when used over an independent fading channel with perfect channel state information at the receiver the decoder is based on a bounded distance search among the lattice points falling inside a sphere centered at the received point by judicious choice of the decoding radius we show that this decoder can be practically used to decode lattice codes of dimension up to 32 in a fading environment

frame fuzzy points and membership for a frame l the collection of l fuzzy subsets of a set x forms a locale the localic definition of points gives rise to l fuzzy points x where x x and is a prime element of l membership is defined in terms of a satisfactory local theory of l fuzzy topology emerges from this supplemented for some purposes by continuity of l

linear threaded algebraic space time constellations space time st constellations that are linear over the field of complex numbers are considered relevant design criteria for these constellations are summarized and some fundamental limits to their achievable performances are established the fundamental tradeoff between rate and diversity is investigated under different constraints on the peak power receiver complexity and rate scaling with the signal to noise ratio snr a new family of constellations that achieve optimal or near optimal performance with respect to the different criteria is presented the proposed constellations belong to the threaded algebraic st tast signaling framework and achieve the optimal minimum squared euclidean distance and the optimal delay for systems with one receive antenna these constellations also achieve the optimal peak to average power ratio for quadrature amplitude modulation qam and phase shift keying psk input constellations as well as optimal coding gains in certain scenarios the framework is general for any number of transmit and receive antennas and allows for realizing the optimal tradeoff between rate and diversity under different constraints simulation results demonstrate the performance gains offered by the proposed designs in average power and peak power limited systems

diagonal algebraic space time block codes we construct a new family of linear space time st block codes by the combination of rotated constellations and the hadamard transform and we prove them to achieve the full transmit diversity over a quasi static or fast fading channels the proposed codes transmit at a normalized rate of 1 symbol s when the number of transmit antennas n 1 2 or n is a multiple of four we spread a rotated version of the information symbol vector by the hadamard transform and send it over n transmit antennas and n time periods for other values of n we construct the codes by sending the components of a rotated version of the information symbol vector over the diagonal of an n spl times n st code matrix the codes maintain their rate diversity and coding gains for all real and complex constellations carved from the complex integers ring z i and they outperform the codes from orthogonal design when using complex constellations for n 2 the maximum likelihood ml decoding of the proposed codes can be implemented by the sphere decoder at a moderate complexity it is shown that using the proposed codes in a multiantenna system yields good performances with high spectral efficiency and moderate decoding complexity