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

new results on selection diversity the performances of selection diversity receiver structures in a slow flat rayleigh fading environment are assessed a number of new and interesting results are obtained binary digital signaling using noncoherent frequency shift keying ncfsk differential phase shift keying dpsk coherent phase shift keying cpsk and coherent frequency shift keying cfsk is considered the traditional analysis the traditional selection diversity model of a selection diversity system is based on choosing the branch with the largest signal to noise snr power ratio while assuming that the noise power is constant across all branches however many practical selection systems choose the branch based on a largest signal plus noise s n selection sample of a filter output this paper comprises accurate analyses of such s n selection systems results show that s n selection systems perform better than predicted by the traditional selection diversity model this is because the former includes the statistical nature of the noise whereas the latter does not the performance difference between the two models increases as the number of diversity branches increases for each of dpsk and cpsk the dual diversity equal gain eg combining and s n selection systems perform identically for each of ncfsk and cfsk receiver structures which are equivalent when there is no diversity perform differently in a diversity environment certain dual diversity s n selection systems give the same performances as eg combining or square law combining the results are contingent upon perfect cophasing for the eg combining in systems where estimates of the combining carrier phases contain noise s n selection outperforms eg combining for dual diversity

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

s n energy selection combining for mpsk and 16 qam signaling in nakagami m and rician fading channels a signal plus noise s n energy selection diversity combining s n esc scheme for m ary phase shift keying mpsk in rayleigh fading channels is mathematically analyzed also the s n esc scheme for mpsk and 16 quadrature amplitude modulation 16 qam signaling in nakagami m and rician fading channels is studied by computer simulations the s n esc selects the branch with the maximum s n energy for detection the advantage of the s n esc scheme is that it requires no explicit channel estimation for diversity branch selection we show that the symbol error probability sep of the s n esc is the same as that of classical selection combining sc for mpsk signaling in independent and identically distributed i i d rayleigh fading channels also we show that the sep of a weighted s n esc scheme is the same as that of classical sc for mpsk signaling in independent and nonidentically distributed i n d rayleigh fading channels it is shown by computer simulations that the s n esc scheme provides a smaller sep than classical sc for mpsk signaling in nondispersive fading channels such as nakagami m fading channels with nakagami parameter m 1 and rician fading channels with rician parameter k 0 on the other hand the s n esc scheme is shown by computer simulations to have a larger sep than classical sc for 16 qam signaling in nakagami m and rician fading channels

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

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

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

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

a formula on the wiener hermite expansion two mathematical formulas are given in an explicit form one develops a product of two different multiple wiener integrals in a series of wiener hermite expansions the other one develops a product of two random variables each of which is described by a wiener hermite expansions in a series of another wiener hermite expansion

scattering of a scalar wave from a slightly random surface scalar wave scattering from a slightly random surface is analyzed by a probabilistic method we make use of the homogeneity of an infinite random surface that is the shift invariance property of the strictly homogeneous random field by the group theoretic consideration of such a shift invariance property the wave solution proves to be a homogeneous random field multiplied by an exponential function then such a homogeneous random field is approximately solved for a slightly random surface to yield a wave solution involving multiple scattering several statistical properties of the scattering are calculated and shown in the figures the accuracy of the approximate solution is examined in terms of the error of the boundary value equation

a noncommutative analogue of the odlyzko bounds and bounds on performance for space time lattice codes this paper considers space time coding over several independently rayleigh faded blocks in particular we will concentrate on giving upper bounds for the coding gain of lattice space time codes as the number of blocks grow this problem was previously considered in the single antenna case by bayer fluckiger et al in 2006 crucial to their work was odlyzko s bound on the discriminant of an algebraic number field as this provides an upper bound for the normalized coding gain of number field codes in the mimo context natural codes are constructed from division algebras defined over number fields and the coding gain is measured by the discriminant of the corresponding noncommutative algebra in this paper we will develop analogues of the odlyzko bounds in this context and show how these bounds limit the normalized coding gain of a very general family of division algebra based space time codes these bounds can also be used as benchmarks in practical code design and as tools to analyze asymptotic bounds of performance as the number of independently faded blocks increases

on z_ 2 k dual binary codes a new generalization of the gray map is introduced the new generalization phi z2 kn rarr z2 2k 1n is connected with the known generalized gray map phi in the following way if we take two dual linear z2 k codes and construct binary codes from them using the generalizations phi and phi of the gray map then the weight enumerators of the binary codes obtained will satisfy the macwilliams identity the classes of z2 k linear hadamard codes and co z2 k linear extended 1 perfect codes are described where co z2 k linearity means that the code can be obtained from a linear z2 k code with the help of the new generalized gray map

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

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

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

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

coset codes i introduction and geometrical classification practically all known good constructive coding techniques for bandlimited channels including lattice codes and various trellis coded modulation schemes can be characterized as coset codes a coset code is defined by a lattice partition lambda lambda and by a binary encoder c that selects a sequence of cosets of the lattice lambda the fundamental coding gain of a coset code as well as other important parameters such as the error coefficient the decoding complexity and the constellation expansion factor are purely geometric parameters determined by c lambda lambda the known types of coset codes as well as a number of new classes that systematize and generalize known codes are classified and compared in terms of these parameters

error performance of multidimensional lattice constellations part ii evaluation over fading channels this is the second part of a two part series of papers where the error performance of multidimensional lattice constellations with signal space diversity ssd is investigated in part i following a novel combinatorial geometrical approach which is based on parallelotope geometry we have presented an exact analytical expression and two closed form bounds for the symbol error probability sep in additive white gaussian noise awgn in the present part ii we extend the analysis and present a novel analytical expression for the frame error probability fep of multidimensional lattice constellations over nakagami m fading channels as the fep of infinite lattice constellations is lower bounded by the sphere lower bound slb we propose the sphere upper bound sub for block fading channels furthermore two novel bounds for the fep of multidimensional lattice constellations over block fading channels named multiple sphere lower bound mslb and multiple sphere upper bound msub are presented the expressions for the slb and sub are given in closed form while the corresponding ones for mslb and msub are given in closed form for unitary block length numerical and simulation results illustrate the tightness of the proposed bounds which can be efficiently used to set the performance limits on the fep of lattice constellations of arbitrary structure dimension and rank

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

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

new algebraic constructions of rotated z sup n lattice constellations for the rayleigh fading channel in this correspondence we present various families of full diversity rotated z sup n lattice constellations based on algebraic number theory constructions we are able to give closed form expressions of their minimum product distance using the corresponding algebraic properties

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

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

error performance of multidimensional lattice constellations part i a parallelotope geometry based approach for the awgn channel multidimensional lattice constellations which present signal space diversity ssd have been extensively studied for single antenna transmission over fading channels with focus on their optimal design for achieving high diversity gain in this two part series of papers we present a novel combinatorial geometrical approach based on parallelotope geometry for the performance evaluation of multidimensional finite lattice constellations with arbitrary structure dimension and rank in part i we present an analytical expression for the exact symbol error probability sep of multidimensional signal sets and two novel closed form bounds named multiple sphere lower bound mlsb and multiple sphere upper bound msub part ii extends the analysis to the transmission over fading channels where multidimensional signal sets are commonly used to combat fading degradation numerical and simulation results show that the proposed geometrical approach leads to bounds that can be used for the performance evaluation and the design of multidimensional lattice constellations both in additive white gaussian noise awgn and fading channels

wiener analysis of a binary hysteresis system nonlinear transformation of an independent gaussian sequence by a binary hysteresis is studied by wiener s method nonlinear problems in random theory mit cambrige ma 1958 the output sequence of the hysteresis is represented by a series of wiener hermite functionals which are random and orthogonal uncorrelated to each other from the hysteresis equation a set of linear equations for the wiener hermite functionals is derived without approximation the equations directly show that the hysteresis is decomposed into equivalent subsystems consisting of static nonlinear elements multipliers adders and linear filters they are solved by use of random numbers generated in a computer in order to get a sample output sequence approximated by a finite sum of the wiener hermite functionals another set of equations is derived for the mean square values of the wiener hermite functionals in terms of its numerical solutions the convergence property of the wiener hermite functional series is discussed

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

trellis coded modulation with multidimensional constellations trellis coded modulation schemes using four eight or 16 dimensional constellations have a number of potential advantages over the usual two dimensional schemes a smaller constituent two dimensional constellation easier tolerance to phase ambiguities and a better trade off between complexity and coding gain a number of such schemes are presented and evaluated starting with a variety of multidimensional lattices we show how to select multidimensional constellations how to partition them into subsets how to construct trellis codes using those subsets and how to map hits to constellation points simplifications of the viterbi decoding algorithm are presented we conclude that there are multidimensional trellis coded modulation schemes that perform better for the same complexity than do two dimensional schemes

precoding by pairing subchannels to increase mimo capacity with discrete input alphabets we consider gaussian multiple input multiple output mimo channels with discrete input alphabets we propose a non diagonal precoder based on the x codes in to increase the mutual information the mimo channel is transformed into a set of parallel subchannels using singular value decomposition svd and x codes are then used to pair the subchannels x codes are fully characterized by the pairings and a 2 2 real rotation matrix for each pair parameterized with a single angle this precoding structure enables us to express the total mutual information as a sum of the mutual information of all the pairs the problem of finding the optimal precoder with the above structure which maximizes the total mutual information is solved by i optimizing the rotation angle and the power allocation within each pair and ii finding the optimal pairing and power allocation among the pairs it is shown that the mutual information achieved with the proposed pairing scheme is very close to that achieved with the optimal pre coder by cruz et al and is significantly better than mercury waterfllling strategy by lozano et al our approach greatly simplifies both the precoder optimization and the detection complexity making it suitable for practical applications

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

s n energy selection combining for bpsk signaling in rayleigh fading channels a signal plus noise s n energy selection combining s n esc scheme and a weighted s n esc scheme for binary phase shift keying bpsk signaling are studied the s n esc selects the branch with the maximum s n energy for detection the advantage of the s n esc and the weighted s n esc is that they require no explicit channel estimation for diversity branch selection the bit error rate ber performances of the s at esc and the weighted s n esc are analyzed for bpsk signaling in independent and nonidentically distributed i n d rayleigh fading channels we show that the average error rate performance of the s n esc is the same as classical signal to noise ratio selection combining snr sc which requires the estimation of fading amplitudes for branch selection in independent and identically distributed i i d rayleigh fading channels we also show that the weighted s n esc has the same ber performance as the classical snr sc for i n d rayleigh fading channels

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

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

an algebraic coding scheme for wireless relay networks with multiple antenna nodes we consider the problem of coding over a half duplex wireless relay network where both the transmitter and the receiver have respectively several transmit and receive antennas whereas each relay is a small device with only a single antenna since in this scenario requiring the relays to decode results in severe rate hits we propose a full rate strategy where the relays do a simple operation before forwarding the signal based on the idea of distributed space time coding our scheme relies on division algebras an algebraic object which allows the design of fully diverse matrices the code construction is applicable to systems with any number of transmit receive antennas and relays and has better performance than random code constructions with much less encoding complexity finally the robustness of the proposed distributed space time codes to node failures is considered

a family of generalized constant modulus algorithms for blind equalization by generalizing the definition of complex modulus this letter presents a family of generalized constant modulus algorithms whose special examples includes not only the well known constant modulus algorithm but also the recently proposed sign godard algorithm square contour algorithm sca generalized sca and sign sca

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

geometrically uniform codes a signal space code c is defined as geometrically uniform if for any two code sequences in c there exists an isometry that maps one sequence into the other while leaving the code c invariant geometrical uniformity a strong kind of symmetry implies such properties as a the distance profiles from code sequences in c to all other code sequences are all the same and b all voronoi regions of code sequences in c have the same shape it is stronger than ungerboeck zehavi wolf symmetry or calderbank sloane regularity nonetheless most known good classes of signal space codes are shown to be generalized coset codes and therefore geometrically uniform including a lattice type trellis codes based on lattice partitions lambda lambda such that z sup n lambda lambda 4z sup n is a lattice partition chain and b phase shift keying psk type trellis codes based on up to four way partitions of a 2 sup n psk signal set

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

constellations matched to the rayleigh fading channel we introduce a new technique for designing signal sets matched to the rayleigh fading channel in particular we look for n dimensional n spl ges 2 lattices whose structure provides nth order diversity our approach is based on a geometric formulation of the design problem which in turn can be solved by using a number geometric approach specifically a suitable upper bound on the pairwise error probability makes the design problem tantamount to the determination of what is called a critical lattice of the body s x x sub 1 spl middot spl middot spl middot x sub n spl isin r sup n spl pi sub i 1 sup n x sub i spl les 1 the lattices among which we search for an optimal solution are the standard embeddings in r sup n of the number ring of some totally real number field of degree n over q simulation results confirm that this approach yields lattices with considerable coding gains

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

almost universal codes achieving ergodic mimo capacity within a constant gap this paper addresses the question of achieving capacity with lattice codes in multi antenna block fading channels when the number of fading blocks tends to infinity a design criterion based on the normalized minimum determinant is proposed for division algebra multi block space time codes over fading channels this plays a similar role to the hermite invariant for gaussian channels under maximum likelihood decoding it is shown that this criterion is sufficient to guarantee transmission rates within a constant gap from capacity both for deterministic channels and ergodic fading channels moreover if the number of receive antennas is greater than or equal to the number of transmit antennas the same constant gap is achieved under naive lattice decoding as well in the case of independent identically distributed rayleigh fading the error probability vanishes exponentially fast in contrast to the standard approach in the literature which employs random lattice ensembles the existence results in this paper are derived from the number theory first the gap to capacity is shown to depend on the discriminant of the chosen division algebra then class field theory is applied to build families of algebras with small discriminants the key element in the construction is the choice of a sequence of division algebras whose centers are number fields with small root discriminants

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

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

the design of trellis coded mpsk for fading channels performance criteria it has been well established that the appropriate criterion for optimum trellis coded modulation design on the additive white gaussian noise channel is maximization of the free euclidean distance it is shown that when the trellis coded modulation is used on a rician fading channel with interleaving deinterleaving the design of the code of optimum performance is guided by other factors in particular the length of the shortest error event path and the product of branch distances possibly normalized by the euclidean distance of the path along the path although maximum free distance d sub free is still an important consideration it plays a less significant role the more severe the fading is on the channel these considerations lead to the definition of a new distance measure of optimization of trellis codes transmitted over rician fading channels if no interleaving deinterleaving is used then once again the design of the trellis code is guided by maximizing d sub free