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

power adaptive network coding for a non orthogonal multiple access relay channel in this paper we propose a novel power adaptive network coding panc for a non orthogonal multiple access relay channel marc where two sources transmit their information simultaneously to the destination with the help of a relay in contrast to the conventional xor based network coding cxnc the relay in panc generates network coded symbols by considering the coefficients of the source to relay channels and forwards each symbol with a pre optimized power level specifically by defining a symbol pair as two symbols from the two sources we first derive the expression of symbol pair error rate sper for the system noting that deriving the exact sper are complex due to the irregularity of the decision regions caused by random channel coefficients we propose a coordinate transform ct method on the received constellation to simplify the derivations of the sper next we obtain the optimal power level by decomposing it as a multiplication of a power scaling factor and a power adaptation factor we prove that with the power scaling factor at the relay our panc scheme can achieve a full diversity gain i e an order of two diversity gain while the cxnc can achieve only an order of one diversity gain in addition we optimize the power adaptation factor at the relay to minimize the sper at the destination by considering of the relationship between sper and minimum euclidean distance of the received constellation resulting in an improved coding gain simulation results show that 1 the sper derived based on our ct method can well approximate the exact sper with a much lower complexity 2 the panc scheme with power adaptation optimizations and power scaling factor design can achieve a full diversity and obtain a much higher coding gain than other network coding schemes

space time codes for high data rate wireless communication performance criteria in the presence of channel estimation errors mobility and multiple paths space time coding is a bandwidth and power efficient method of communication over fading channels that realizes the benefits of multiple transmit antennas specific codes have been constructed using design criteria derived for quasi static flat rayleigh or rician fading where channel state information is available at the receiver it is evident that the practicality of space time codes will be greatly enhanced if the derived design criteria remain valid in the absence of perfect channel state information it is even more desirable that the design criteria not be unduly sensitive to frequency selectivity and to the doppler spread this paper presents a theoretical study of these issues beginning with the effect of channel estimation error here it is assumed that a channel estimator extracts fade coefficients at the receiver and for constellations with constant energy it is proved that in the absence of ideal channel state information the design criteria for space time codes is still valid the analysis also demonstrates that standard channel estimation techniques can be used in conjunction with space time codes provided that the number of transmit antennas is small we also derive the maximum likelihood detection metric in the presence of channel estimation errors next the effect of multiple paths on the performance of space time codes is studied for a slowly changing rayleigh channel it is proved that the presence of multiple paths does not decrease the diversity order guaranteed by the design criteria used to construct the space time codes similar results hold for rapid fading channels with or without multiple paths the conclusion is that the diversity order promised by space time coding is achieved under a variety of mobility conditions and environmental effects

one sided complete stable minimal surfaces we prove that there are no complete one sided stable minimal surfaces in the euclidean 3 space we classify least area surfaces in the quotient of mathbb r 3 by one or two linearly independent translations and we give sharp upper bounds of the genus of compact two sided index one minimal surfaces in non negatively curved ambient spaces finally we estimate from below the index of complete minimal surfaces in flat spaces in terms of the topology of the surface

linear decoupled and quasi decoupled space time codes space time transmit diversity results in coupling of transmitted symbols across different antennas which increases the complexity of maximum likelihood decoding symbol coupling can be completely or partially avoided if the space time code stc satisfies specific decoupling conditions examples of such codes are orthogonal space time block codes and quasi orthogonal codes in this letter we study decoupling conditions for a linear full diversity stc quasi decoupled codes are proposed as a partially decoupled full diversity stc of any rate for any number of transmit antennas with minimum decoding delay by optimizing the coding gain of quasi decoupled codes it is shown that quasi orthogonal codes have competitive performance with respect to the alamouti code and the more recent threaded algebraic space time tast codes and abba codes a general full diversity decoupling condition is considered and the general solution to this case which also encompasses previously known orthogonal stcs is derived

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

fourth order statistics for blind classification of spatial multiplexing and alamouti space time block code signals blind signal classification a major task of intelligent receivers has important civilian and military applications this problem becomes more challenging in multi antenna scenarios due to the diverse transmission schemes that can be employed e g spatial multiplexing sm and space time block codes stbcs this paper presents a class of novel algorithms for blind classification of sm and alamouti stbc al stbc transmissions unlike the prior art we show that signal classification can be performed using a single receive antenna by taking advantage of the space time redundancy the first proposed algorithm relies on the fourth order moment as a discriminating feature and employs the likelihood ratio test for achieving maximum average probability of correct classification this requires knowledge of the channel coefficients modulation type and noise power to avoid this drawback three algorithms have been further developed their common idea is that the discrete fourier transform of the fourth order lag product exhibits peaks at certain frequencies for the al stbc signals but not for the sm signals and thus provides the basis of a useful discriminating feature for signal classification the effectiveness of these algorithms has been demonstrated in extensive simulation experiments where a nakagami m fading channel and the presence of timing and frequency offsets are assumed

a weighted combining algorithm for spatial multiplexing mimo df relaying systems jointly detecting the signals from the source and relay in a spatial multiplexing sm multiple input multiple output mimo relaying system improves the transmit reliability significantly however the existing joint detection schemes for sm mimo relaying systems which achieve full diversity such as the near maximum likelihood ml decoder suffer from high complexity in this paper we propose a weighted combining wc algorithm which is applied before the detector in the sm mimo decode and forward relaying system the proposed algorithm merges the received signal vectors from the source and relay into a combined signal without expanding their dimension and formulates an equivalent mimo channel matrix for the combined signal resulting in a lower complexity for the subsequent detection we analyze the performance of the proposed wc algorithm with ml detection in terms of the diversity order and computational complexity an approximate upper bound on the symbol error probability sep for the proposed algorithm is also derived simulation results show that in symmetric networks the proposed wc algorithm achieves substantially lower complexity while maintaining an sep performance similar to that of the benchmark nml decoder the consistency of the derived upper bound on the sep is also verified by simulations

on mimo beamforming systems using quantized feedback we propose the hadamard matrix as a codebook for multiple input multiple output mimo beamforming systems and show that a quantized equal gain transmission qegt scheme using the hadamard codebook has the same symbol error probability performance as a receiver selection diversity combining scheme operating in independent generalized rayleigh fading channels we show that a mimo beamforming system using quantized feedback over rician fading channels can be analyzed by considering a corresponding receiver selection combining scheme operating in single input multiple output simo systems over correlated generalized rician fading channels also we propose a greedy cophasing scheme for mimo beamforming systems using quantized feedback the greedy cophasing scheme provides 3 2 db power gain over an orthogonal space time block code when the number of transmit antennas is four the number of receive antennas is one and the number of feedback bits is three

differential space time modulation space time coding and modulation exploit the presence of multiple transmit antennas to improve the performance on multipath radio channels thus far most work on space time coding has assumed that perfect channel estimates are available at the receiver in certain situations however it may be difficult or costly to estimate the channel accurately in which case it is natural to consider the design of modulation techniques that do not require channel estimates at the transmitter or receiver we propose a general approach to differential modulation for multiple transmit antennas based on group codes this approach ran be applied to any number of transmit and receive antennas and any signal constellation we also derive low complexity differential receivers error bounds and modulator design criteria which we use to construct optimal differential modulation schemes for two transmit antennas these schemes can be demodulated with or without channel estimates this permits the receiver to exploit channel estimates when they are available the performance degrades by approximately 3 db when estimates are not available

invariance principles for random bipartite planar maps it is conjectured in the physics literature that properly rescaled random planar maps when conditioned to have a large number of faces should converge to a limiting surface whose law does not depend up to scaling factors on details of the class of maps that are sampled previous works on the topic starting with chassaing schaeffer have shown that the radius of a random quadrangulation with n faces converges in distribution once rescaled by n 1 4 to the diameter of the brownian snake up to a scaling constant using a bijection due to bouttier di francesco guitter between bipartite planar maps and a family of labeled trees we show the corresponding invariance principle for a class of random maps that follow a boltzmann distribution the radius of such maps conditioned to have n faces or n vertices and under a criticality assumption converges in distribution once rescaled by n 1 4 to a scaled version of the diameter of the brownian snake convergence results for the so called profile of maps are also provided as well as convergence of rescaled bipartite maps to the brownian map as introduced by marckert mokkadem the proofs of these results rely on a new invariance principle for two type spatial galton watson trees

distributed differential space time coding for wireless relay networks distributed space time coding is a cooperative transmission scheme for wireless relay networks with this scheme antennas of the distributive relays work as transmit antennas of the sender and generate a space time code at the receiver it achieves the maximum diversity although the scheme needs no channel information at relays it does require full channel information both the channels from the transmitter to relays and the channels from relays to the receiver at the receiver in this paper we propose a differential transmission scheme which requires channel information at neither relays nor the receiver for wireless relay networks as distributed space time coding can be seen as the counterpart of space time coding in the network setting this scheme is the counterpart of differential space time coding compared to coherent distributed space time coding the differential scheme is 3db worse in addition we show that alamouti square real orthogonal and sp 2 codes can be used differentially in networks with corresponding numbers of relays we also propose distributed differential space time codes that work for networks with any number of relays using circulant matrices

blind stbc identification for multiple antenna ofdm systems this paper addresses the problem of space time block code stbc identification for multiple antenna ma orthogonal frequency division multiplexing ofdm systems operating over frequency selective channels for the first time in literature previous investigations published on the topic of stbc identification were restricted to single carrier systems operating over frequency flat channels ofdm systems make this topic more challenging to handle since the identifiers work in frequency selective channels with little or no knowledge of the beginning of the ofdm blocks ofdm parameters and frequency selective channel coefficients we show that by taking advantage of the space time redundancy stbc identification can be performed by exploiting the cross correlation of the signals received from different antennas as a discriminating feature using this feature we develop a binary hypothesis test for decision making the proposed method does not require information about the channel coefficients modulation format noise power or timing of the ofdm and stbc blocks moreover it does not need accurate knowledge of either clock timing information or ofdm parameters including the number of sub carriers and cyclic prefix length extensive simulation experiments have verified the effectiveness of the proposed method

on the sphere decoding algorithm i expected complexity the problem of finding the least squares solution to a system of linear equations where the unknown vector is comprised of integers but the matrix coefficient and given vector are comprised of real numbers arises in many applications communications cryptography gps to name a few the problem is equivalent to finding the closest lattice point to a given point and is known to be np hard in communications applications however the given vector is not arbitrary but rather is an unknown lattice point that has been perturbed by an additive noise vector whose statistical properties are known therefore in this paper rather than dwell on the worst case complexity of the integer least squares problem we study its expected complexity averaged over the noise and over the lattice for the sphere decoding algorithm of fincke and pohst we find a closed form expression for the expected complexity both for the infinite and finite lattice it is demonstrated in the second part of this paper that for a wide range of signal to noise ratios snrs and numbers of antennas the expected complexity is polynomial in fact often roughly cubic since many communications systems operate at noise levels for which the expected complexity turns out to be polynomial this suggests that maximum likelihood decoding which was hitherto thought to be computationally intractable can in fact be implemented in real time a result with many practical implications

trees and spatial topology change in causal dynamical triangulations generalized causal dynamical triangulations generalized cdt is a model of two dimensional quantum gravity in which a limited number of spatial topology changes is allowed to occur we solve the model at the discretized level using bijections between quadrangulations and trees in the continuum limit scaling limit the amplitudes are shown to agree with known formulas and explicit expressions are obtained for loop propagators and two point functions it is shown that from a combinatorial point of view generalized cdt can be viewed as the scaling limit of planar maps with a finite number of faces and we determine the distance function on this ensemble of planar maps finally the relation with planar maps is used to illuminate the mysterious identity of certain continuum cylinder amplitudes

a network coding approach to cooperative diversity this paper proposes a network coding approach to cooperative diversity featuring the algebraic superposition of channel codes over a finite field the scenario under consideration is one in which two ldquopartnersrdquo node a and node b cooperate in transmitting information to a single destination each partner transmits both locally generated information and relayed information that originated at the other partner a key observation is that node b already knows node a s relayed information because it originated at node b and can exploit that knowledge when decoding node a s local information this leads to an encoding scheme in which each partner transmits the algebraic superposition of its local and relayed information and the superimposed codeword is interpreted differently at the two receivers i e at the other partner and at the destination node based on their different a priori knowledge decoding at the destination is then carried out by iterating between the codewords from the two partners it is shown via simulation that the proposed scheme provides substantial coding gain over other cooperative diversity techniques including those based on time multiplexing and signal euclidean space superposition

multiuser detection of alamouti signals in a mimo multiple access channel where users employ space time block codes stbc interference cancellation can be used to suppress co channel interference and recover the desired signal of each user at the receiver leveraging the special properties of alamouti matrices we first show that spatial multiplexing of alamouti signals retains the space time diversity gain of alamouti signaling using our proposed low complexity alamouti blast mmse a blast algorithm next in contrast to traditional transmit diversity that focuses on stbc construction at the transmitter this paper looks at transmit diversity from the perspective of the receiver in other words the receiver gets to choose the stbciquests which are favourable to the channel assuming a fixed blast receive algorithm in a multiusermac setting we first present a systematic methodology to exploit different decomposition structure in alamouti matrices each with different tradeoff between performance and decoding complexity using possibly different mimo receive algorithms we then demonstrate that the notion of angles the inner product of two quaternionic vectors between multiuser channels determines the performance of mimo receive algorithms as an application of the general theory we transform the decoding problem for several types of quasi orthogonal stbc qostbc into multiuser detection of virtual alamouti users building upon our a blast algorithm we propose new algorithms for decoding single user and multiuser qostbc in particular we show that bit error probability is a function of the quaternionic angle between virtual users for a single user or multiple users this angle varies with the type of qostbc and leads to a new form of adaptive modulation called code diversity where feedback instructs the transmitter how to choose from a plurality of codes

inequivalent complexity criteria for free boundary minimal surfaces abstract we obtain a series of results in the global theory of free boundary minimal surfaces which in particular provide a rather complete picture for the way different complexity criteria such as area topology and morse index compare beyond the regime where effective estimates are at disposal

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

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

renormalizable models in rank d geq 2 tensorial group field theory classes of renormalizable models in the tensorial group field theory framework are investigated the rank d tensor fields are defined over d copies of a group manifold g d u 1 d or g d su 2 d with no symmetry and no gauge invariance assumed on the fields in particular we explore the space of renormalizable models endowed with a kinetic term corresponding to a sum of momenta of the form p 2a a in 0 1 this study is tailored for models equipped with laplacian dynamics on gd case a 1 but also for more exotic nonlocal models in quantum topology case 0 a 1 a generic model can be written dim g d phi k d a where k is the maximal valence of its interactions using a multi scale analysis for the generic situation we identify several classes of renormalizable actions including matrix model actions in this specific instance we find a tower of renormalizable matrix models parametrized by k geq 4 in a second part of this work we study the uv behavior of the models up to maximal valence of interaction k 6 all rank d geq 3 tensor models proved renormalizable are asymptotically free in the uv all matrix models with k 4 have a vanishing function at one loop and very likely reproduce the same feature of the grosse wulkenhaar model commun math phys 256 305 2005

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

mimo antenna subset selection with space time coding this paper treats multiple input multiple output mimo antenna subset selection employing space time coding we consider two cases differentiated based on the type of channel knowledge used in the selection process we address both the selection algorithms and the performance analysis we first consider the case when the antenna subsets are selected based on exact channel knowledge eck our results assume the transmission of orthogonal space time block codes with emphasis on the alamouti see ieee j select areas commun vol 16 p 1451 68 oct 1998 code next we treat the case of antenna subset selection when statistical channel knowledge sck is employed by the selection algorithm this analysis is applicable to general space time coding schemes when eck is available we show that the selection algorithm chooses the antenna set that maximizes the channel frobenius norm leading to both coding and diversity gain when sck is available the selection algorithm chooses the antenna set that maximizes the determinant of the covariance of the vectorized channel leading mostly to a coding gain in case of eck based selection we provide analytical expressions for average snr and outage probability improvement for the case when sck based selection is used we derive expressions for coding gain we also present extensive simulation studies validating our results

integer forcing linear receivers linear receivers are often used to reduce the implementation complexity of multiple antenna systems in a traditional linear receiver architecture the receive antennas are used to separate out the codewords sent by each transmit antenna which can then be decoded individually although easy to implement this approach can be highly suboptimal when the channel matrix is near singular this paper develops a new linear receiver architecture that uses the receive antennas to create an effective channel matrix with integer valued entries rather than attempting to recover transmitted codewords directly the decoder recovers integer combinations of the codewords according to the entries of the effective channel matrix the codewords are all generated using the same linear code which guarantees that these integer combinations are themselves codewords provided that the effective channel is full rank these integer combinations can then be digitally solved for the original codewords this paper focuses on the special case where there is no coding across transmit antennas and no channel state information at the transmitter s which corresponds either to a multiuser uplink scenario or to single user v blast encoding in this setting the proposed integer forcing linear receiver significantly outperforms conventional linear architectures such as the zero forcing and linear minimum mean squared error receiver in the high signal to noise ratio regime the proposed receiver attains the optimal diversity multiplexing tradeoff for the standard multiple input multiple output mimo channel with no coding across transmit antennas it is further shown that in an extended mimo model with interference the integer forcing linear receiver achieves the optimal generalized degrees of freedom

local convergence of large random triangulations coupled with an ising model we prove the existence of the local weak limit of the measure obtained by sampling random triangulations of size n decorated by an ising configuration with a weight proportional to the energy of this configuration to do so we establish the algebraicity and the asymptotic behaviour of the partition functions of triangulations with spins for any boundary condition in particular we show that these partition functions all have the same phase transition at the same critical temperature some properties of the limiting object called the infinite ising planar triangulation are derived including the recurrence of the simple random walk at the critical temperature

low complexity detection scheme for cooperative mimo systems with decode and forward relays in this paper we study low complexity detection schemes for cooperative multiple input multiple output mimo systems with decode and forward df relays in fixed df protocols the error propagation effect that limits the diversity gain can be overcome by using joint maximum likelihood jml detection but its complexity increases exponentially with the number of streams and modulation orders to develop a low complexity detection scheme we first extend the cooperative maximum ratio combining c mrc scheme to mimo relay networks and then investigate the diversity order of the system we show that c mrc achieves full diversity gain for orthogonal space time code but its diversity gain is limited when the deployed space time code is non orthogonal to address this problem we propose an effective detection scheme that is applicable to arbitrary space time codes on the basis of pairwise error probability approximation max log approximation and the chernoff bound we construct an equivalent point to point mimo signal model and then apply tree search detection techniques compared to jml the proposed detection scheme significantly reduces the detection complexity while preserving diversity gain moreover it can be readily extended to complex field network coding systems whose performance is superior to that of galois field network coding systems analysis and simulation results confirm the efficiency of the proposed scheme

performance of bicm sc and bicm ofdm systems with diversity reception in non gaussian noise and interference in this paper we present a general mathematical framework for performance analysis of single carrier sc and orthogonal frequency division multiplexing ofdm systems employing popular bit interleaved coded modulation bicm and multiple receive antennas the proposed analysis is applicable to bicm systems impaired by general types of fading including rayleigh ricean nakagami m nakagami q and weibull fading and general types of noise and interference with finite moments such as additive white gaussian noise awgn additive correlated gaussian noise gaussian mixture noise co channel interference narrowband interference and ultra wideband interference we present an approximate upper bound for the bit error rate ber and an accurate closed form approximation for the asymptotic ber at high signal to noise ratios for viterbi decoding with the standard euclidean distance branch metric for the standard rate 1 2 convolutional code the proposed approximate upper bound and the asymptotic approximation become tight at bers of 10 6 and 10 12 respectively however if the code is punctured to higher rates e g 2 3 or 3 4 the asymptotic approximation also becomes tight at a ber of 10 6 exploiting the asymptotic ber approximation we show that the diversity gain of bicm systems only depends on the free distance of the code the type of fading and the number of receive antennas but not on the type of noise in contrast their coding gain strongly depends on the noise moments our asymptotic analysis shows that as long as the standard euclidean distance branch metric is used for viterbi decoding bicm systems optimized for awgn are also optimum for any other type of noise and interference with finite moments

performance and optimization of network coded cooperative diversity systems in this paper we study network coded cooperative diversity nccd systems comprising multiple sources one relay and one destination where the relay detects the packets received from all sources and performs galois field gf network coding over rm gf 2 m before forwarding a single packet to the destination assuming independent rayleigh fading for all links of the network we derive simple and accurate closed form approximations for the asymptotic symbol and bit error rates of nccd systems the derived error rate expressions are valid for arbitrary numbers of sources arbitrary modulation schemes and arbitrary constellation mappings and provide significant insight into the impact of various system and channel parameters on performance moreover these expressions can be exploited for optimization of the constellation mapping as well as for formulation of various nccd system optimization problems including optimal power allocation relay selection and relay placement

multiple antenna signaling over fading channels with estimated channel state information performance analysis multiple antenna concepts for wireless communication systems promise high spectral efficiency and low error rates by proper exploitation of the randomness in multipath propagation in this paper we investigate the impact of channel uncertainty caused by channel estimation errors on the error rate performance we consider a training based multiple antenna system that reserves a portion of time to sound the channel training symbols are used to estimate the channel by means of an arbitrary linear filter at the receiver no channel state information csi is assumed at the transmitter we present a new framework to analyze training based multiple antenna systems by introducing an equivalent system model that specifies the channel by the estimated and hence known channel coefficients and an uncorrelated data dependent multiplicative noise we derive the maximum likelihood ml detector and highlight its behavior in the limiting cases of perfect csi and no csi and its relation to several mismatched detectors we deduce new exact expressions and chernoff bounds of the pairwise error probability pep used to assess word error and bit error rate bounds for ml and mismatched detection finally we review the code design guidelines in terms of the deleterious effect of channel uncertainty for coherent and noncoherent signaling schemes and present numerical results

closest point search in lattices in this semitutorial paper a comprehensive survey of closest point search methods for lattices without a regular structure is presented the existing search strategies are described in a unified framework and differences between them are elucidated an efficient closest point search algorithm based on the schnorr euchner 1995 variation of the pohst 1981 method is implemented given an arbitrary point x spl isin spl ropf sup m and a generator matrix for a lattice spl lambda the algorithm computes the point of spl lambda that is closest to x the algorithm is shown to be substantially faster than other known methods by means of a theoretical comparison with the kannan 1983 1987 algorithm and an experimental comparison with the pohst 1981 algorithm and its variants such as the viterbo boutros see ibid vol 45 p 1639 42 1999 decoder modifications of the algorithm are developed to solve a number of related search problems for lattices such as finding a shortest vector determining the kissing number computing the voronoi 1908 relevant vectors and finding a korkine zolotareff 1873 reduced basis

compact brownian surfaces i brownian disks we show that under certain natural assumptions large random plane bipartite maps with a boundary converge after rescaling to a one parameter family mathrm bd l 0 l infty of random metric spaces homeomorphic to the closed unit disk of mathbb r 2 the space mathrm bd l being called the brownian disk of perimeter l and unit area these results can be seen as an extension of the convergence of uniform plane quadrangulations to the brownian map which intuitively corresponds to the limit case where l 0 similar results are obtained for maps following a boltzmann distribution in which the perimeter is fixed but the area is random

the topological structure of scaling limits of large planar maps we discuss scaling limits of large bipartite planar maps if p 2 is a fixed integer we consider for every integer n 2 a random planar map mn which is uniformly distributed over the set of all rooted 2p angulations with n faces then at least along a suitable subsequence the metric space consisting of the set of vertices of mn equipped with the graph distance rescaled by the factor n 1 4 converges in distribution as n towards a limiting random compact metric space in the sense of the gromov hausdorff distance we prove that the topology of the limiting space is uniquely determined independently of p and of the subsequence and that this space can be obtained as the quotient of the continuum random tree for an equivalence relation which is defined from brownian labels attached to the vertices we also verify that the hausdorff dimension of the limit is almost surely equal to 4

an efficient detector for combined space time coding and layered processing group layered space time architecture glst combines space time block coding and layered space time processing where the transmit stream is partitioned into different groups and in each group space time block coding is applied in the traditional receiver of glst group detection is applied first to suppress the interference from other groups and then decoding is performed for the desired group in this letter a novel detector is proposed in which the entire groups are decoded first and then group detection is performed next theoretical analysis will demonstrate that the new detector can achieve a significant capacity gain compared with the traditional one simulation results will further show that the proposed detector can obtain at least 4 db gain at a frame error rate of 10 sup 2 for instance

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

interpolation based transmit beamforming for mimo ofdm with limited feedback transmit beamforming and receive combining are simple methods for exploiting spatial diversity in multiple input multiple output orthogonal frequency division multiplexing mimo ofdm system optimal beamforming requires channel state information in the form of the beamforming vectors for each ofdm subcarrier this paper proposes a limited feedback architecture that combines beamforming vector quantization and smart vector interpolation in the proposed system the receiver sends a fraction of information about the optimal beamforming vectors to the transmitter and the transmitter computes the beamforming vectors for all subcarriers through interpolation a new spherical interpolator is developed that exploits parameters for phase rotation to satisfy the phase invariance and unit norm properties of the transmitted beamforming vectors the beamforming vectors and phase parameters are quantized at the receiver and the quantized information is provided to the transmitter the proposed quantization system provides only a moderate increase in complexity versus over comparable approaches numerical simulations show that the proposed scheme performs better than existing diversity techniques with the same feedback data rate

scaling limits of random planar maps with large faces we discuss asymptotics for large random planar maps under the assumption that the distribution of the degree of a typical face is in the domain of attraction of a stable distribution with index alpha in 1 2 when the number n of vertices of the map tends to infinity the asymptotic behavior of distances from a distinguished vertex is described by a random process called the continuous distance process which can be constructed from a centered stable process with no negative jumps and index alpha in particular the profile of distances in the map rescaled by the factor n 1 2 alpha converges to a random measure defined in terms of the distance process with the same rescaling of distances the vertex set viewed as a metric space converges in distribution as n to infty at least along suitable subsequences towards a limiting random compact metric space whose hausdorff dimension is equal to 2 alpha

reduced feedback mimo ofdm precoding and antenna selection transmitter precoding for multiple input multiple output orthogonal frequency division multiplexing mimo ofdm is an effective way of leveraging the diversity gains afforded by a multiple transmit multiple receive antenna system in a frequency selective environment in the limited feedback scenario optimal precoder representation for narrowband mimo systems using moderately sized codebooks designed on the grassmann manifold has been shown to perform remarkably well in mimo ofdm systems precoder matrices have to be designed for all subcarriers and the amount of feedback can get prohibitively large this is especially true for next generation wireless local area networks and wireless metropolitan area networks which have a large number of subcarriers in this paper we present techniques to reduce this feedback requirement and the performance of these algorithms is numerically shown to provide improvement over existing schemes

more on the o n model on random maps via nested loops loops with bending energy we continue our investigation of the nested loop approach to the o n model on random maps by extending it to the case where loops may visit faces of arbitrary degree this allows us to express the partition function of the o n loop model as a specialization of the multivariate generating function of maps with controlled face degrees where the face weights are determined by a fixed point condition we deduce a functional equation for the resolvent of the model involving some ring generating function describing the immediate vicinity of the loops when the ring generating function has a single pole the model is amenable to a full solution physically such a situation is realized upon considering loops visiting triangles only and further weighting these loops by some local bending energy our model interpolates between the two previously solved cases of triangulations without bending energy and quadrangulations with rigid loops we analyze the phase diagram of our model in details and derive in particular the location of its non generic critical points which are in the universality classes of the dense and dilute o n model coupled to 2d quantum gravity similar techniques are also used to solve a twisting loop model on quadrangulations where loops are forced to make turns within each visited square along the way we revisit the problem of maps with controlled possibly unbounded face degrees and give combinatorial derivations of the one cut lemma and of the functional equation for the resolvent

the brownian map is the scaling limit of uniform random plane quadrangulations we prove that uniform random quadrangulations of the sphere with n faces endowed with the usual graph distance and renormalized by n 1 4 converge as n in distribution for the gromov hausdorff topology to a limiting metric space we validate a conjecture by le gall by showing that the limit is up to a scale constant the so called brownian map which was introduced by marckert mokkadem and le gall as the most natural candidate for the scaling limit of many models of random plane maps the proof relies strongly on the concept of geodesic stars in the map which are configurations made of several geodesics that only share a common endpoint and do not meet elsewhere

the space of embedded minimal surfaces of fixed genus in a 3 manifold iv locally simply connected this paper is the fourth in a series where we describe the space of all embedded minimal surfaces of fixed genus in a fixed but arbitrary closed 3manifold the key is to understand the structure of an embedded minimal disk in a ball in r3 this was undertaken in cm3 cm4 and the global version of it will be completed here see the discussion around figure 12 for the local case and cm15 for some more details our main results are theorem 0 1 the lamination theorem and theorem 0 2 the one sided curvature estimate the lamination theorem is stated in the global case where the lamination is in fact a foliation the first four papers of this series show that every embedded minimal disk is either a graph of a function or is a double spiral staircase where each staircase is a multivalued graph this is done by showing that if the curvature is large at some point and hence the surface is not a graph then it is a double spiral staircase like the helicoid to prove that such a disk is a double spiral staircase we showed in the first three papers of the series that it is built out of n valued graphs where n is a fixed number in this paper we will deal with how the multi valued graphs fit together and in particular prove regularity of the set of points of large curvature the axis of the double spiral staircase the first theorem is the global version of the statement that every embedded minimal disk is a double spiral staircase

achieving full frequency and space diversity in wireless systems via bicm ofdm stbc and viterbi decoding orthogonal frequency division multiplexing ofdm is known as an efficient technique to combat frequency selective channels in this paper we show that the combination of bit interleaved coded modulation bicm and ofdm achieves the full frequency diversity offered by a frequency selective channel with any kind of power delay profile pdp conditioned on the minimum hamming distance dfree of the convolutional code this system has a simple viterbi decoder with a modified metric we then show that by combining such a system with space time block coding stbc one can achieve the full space and frequency diversity of a frequency selective channel with n transmit and m receive antennas bicm stbc ofdm achieves the maximum diversity order of nml over l tap frequency selective channels regardless of the pdp of the channel this latter system also has a simple viterbi decoder with a properly modified metric we verify our analytical results via simulations including channels employed in the ieee 802 11 standards

loop models on random maps via nested loops the case of domain symmetry breaking and application to the potts model we use the nested loop approach to investigate loop models on random planar maps where the domains delimited by the loops are given two alternating colors which can be assigned different local weights hence allowing for an explicit z2 domain symmetry breaking each loop receives a non local weight n as well as a local bending energy which controls loop turns by a standard cluster construction that we review the q n2 potts model on general random maps is mapped to a particular instance of this problem with domain non symmetric weights we derive in full generality a set of coupled functional relations for a pair of generating series which encode the enumeration of loop configurations on maps with a boundary of a given color and solve it by extending well known complex analytic techniques in the case where loops are fully packed we analyze in detail the phase diagram of the model and derive exact equations for the position of its non generic critical points in particular we underline that the critical potts model on general random maps is not self dual whenever q 1 in a model with domain symmetric weights we also show the possibility of a spontaneous domain symmetry breaking driven by the bending energy this article is part of lattice models and integrability a special issue of journal of physics a mathematical and theoretical in honour of f y wu s 80th birthday

random planar lattices and integrated superbrownian excursion in this paper a surprising connection is described between a specific brand of random lattices namely planar quadrangulations and aldous integrated superbrownian excursion ise as a consequence the radius r n of a random quadrangulation with n faces is shown to converge up to scaling to the width r r l of the support of the one dimensional ise or precisely more generally the distribution of distances to a random vertex in a random quadrangulation is described in its scaled limit by the random measure ise shifted to set the minimum of its support in zero the first combinatorial ingredient is an encoding of quadrangulations by trees embedded in the positive half line reminiscent of cori and vauquelin s well labelled trees the second step relates these trees to embedded discrete trees in the sense of aldous via the conjugation of tree principle an analogue for trees of vervaat s construction of the brownian excursion from the bridge from probability theory we need a new result of independent interest the weak convergence of the encoding of a random embedded plane tree by two contour walks to the brownian snake description of ise our results suggest the existence of a continuum random map describing in term of ise the scaled limit of the dynamical triangulations considered in two dimensional pure quantum gravity

space time frequency shift keying frequency shift keying fsk is a popular modulation scheme in power limited communication links this paper introduces space time fsk st fsk which does not require any channel state information at the transmitter and the receiver as in conventional noncoherent fsk st fsk can be viewed as a special unitary st modulation design however st fsk has a number of advantages over existing unitary st modulation designs st fsk is easier to design and enjoys lower decoding complexity furthermore st fsk guarantees full diversity finally st fsk can be adopted in the digital as well as in the analog domain and merges very naturally with frequency hopping multiple access as expected all these advantages come at the cost of a decrease in spectral efficiency

a recursive approach to the o n model on random maps via nested loops we consider the o n loop model on tetravalent maps and show how to rephrase it into a model of bipartite maps without loops this follows from a combinatorial decomposition that consists in cutting the o n model configurations along their loops so that each elementary piece is a map that may have arbitrary even face degrees in the induced statistics these maps are drawn according to a boltzmann distribution whose parameters the face weights are determined by a fixed point condition in particular we show that the dense and dilute critical points of the o n model correspond to bipartite maps with large faces i e whose degree distribution has a fat tail the re expression of the fixed point condition in terms of linear integral equations allows us to explore the phase diagram of the model in particular we determine this phase diagram exactly for the simplest version of the model where the loops are rigid several generalizations of the model are discussed

a limit theorem for the contour process of condidtioned galton watson trees in this work we study asymptotics of the genealogy of galton watson processes conditioned on the total progeny we consider a fixed aperiodic and critical offspring distribution such that the rescaled galton watson processes converges to a continuous state branching process csbp with a stable branching mechanism of index 1 2 we code the genealogy by two different processes the contour process and the height process that le gall and le jan recently introduced we show that the rescaled height process of the corresponding galton watson family tree with one ancestor and conditioned on the total progeny converges in a functional sense to a new process the normalized excursion of the continuous height process associated with the stable csbp we deduce from this convergence an analogous limit theorem for the contour process in the brownian case 2 the limiting process is the normalized brownian excursion that codes the continuum random tree the result is due to aldous who used a different method

random stable laminations of the disk we study large random dissections of polygons we consider random dissections of a regular polygon with n sides which are chosen according to boltzmann weights in the domain of attraction of a stable law of index 2 1 2 as n goes to infinity we prove that these random dissections converge in distribution towards a random compact set called the random stable lamination if 2 we recover aldous brownian triangulation however if 2 1 2 large faces remain in the limit and a dierent random compact set appears we show that the random stable lamination can be coded by the continuous time height function associated to the normalized excursion of a strictly stable spectrally positive levy process of index using this coding we establish that the hausdor dimension of the stable random lamination is almost surely 2 1

percolation on random triangulations and stable looptrees we study site percolation on angel and schramm s uniform infinite planar triangulation we compute several critical and near critical exponents and describe the scaling limit of the boundary of large percolation clusters in all regimes subcritical critical and supercritical we prove in particular that the scaling limit of the boundary of large critical percolation clusters is the random stable looptree of index 3 2 which was introduced in curien and kortchemski random stable looptrees arxiv 1304 1044 2014 we also give a conjecture linking looptrees of any index alpha in 1 2 with scaling limits of cluster boundaries in random triangulations decorated with o n models

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

limits of the boundary of random planar maps we discuss asymptotics for the boundary of critical boltzmann planar maps under the assumption that the distribution of the degree of a typical face is in the domain of attraction of a stable distribution with parameter alpha in 1 2 first in the dense phase corresponding to alpha in 1 3 2 we prove that the scaling limit of the boundary is the random stable looptree with parameter 1 alpha 1 2 second we show the existence of a phase transition through local limits of the boundary in the dense phase the boundary is tree like while in the dilute phase corresponding to alpha in 3 2 2 it has a component homeomorphic to the half plane as an application we identify the limits of loops conditioned to be large in the rigid o n loop model on quadrangulations proving thereby a conjecture of curien and kortchemski

multistage iterative decoding with complexity reduction for concatenated space time codes space time encoders exploiting concatenated coding structures are efficient in attaining the high rates available to large dimensional multiple transmitter multiple receiver wireless systems under fading conditions while also providing maximal diversity benefits we present a multistage iterative decoding structure that takes full advantage of the concatenated nature of the transmission path treating the modulator and channel stages as an additional encoder in serial concatenation this iterative decoder architecture allows an encoder employing decoupled coding and modulation to reach the performance of coded modulation systems it also admits reduced complexity decoding with a computational load that is nonexponential in the number of antennas or the transmission bit rate and makes practical decoding for large transmitter arrays possible the performance curves for these methods follow the shape of the fano bound with only a modest power penalty

scaling limits of random planar maps with a unique large face we study random bipartite planar maps defined by assigning nonnegative weights to each face of a map we prove that for certain choices of weights a unique large face having degree proportional to the total number of edges in the maps appears when the maps are large it is furthermore shown that as the number of edges n of the planar maps goes to infinity the profile of distances to a marked vertex rescaled by n 1 2 is described by a brownian excursion the planar maps with the graph metric resealed by n 1 2 are then shown to converge in distribution toward aldous brownian tree in the gromov hausdorff topology in the proofs we rely on the bouttier di francesco guitter bijection between maps and labeled trees and recent results on simply generated trees where a unique vertex of a high degree appears when the trees are large

sub exponential tail bounds for conditioned stable bienayme galton watson trees we establish uniform sub exponential tail bounds for the width height and maximal outdegree of critical bienayme galton watson trees conditioned on having a large fixed size whose offspring distribution belongs to the domain of attraction of a stable law this extends results obtained for the height and width by addario berry devroye and janson in the finite variance case

martingales in self similar growth fragmentations and their connections with random planar maps the purpose of the present work is twofold first we develop the theory of general self similar growth fragmentation processes by focusing on martingales which appear naturally in this setting and by recasting classical results for branching random walks in this framework in particular we establish many to one formulas for growth fragmentations and define the notion of intrinsic area of a growth fragmentation second we identify a distinguished family of growth fragmentations closely related to stable levy processes which are then shown to arise as the scaling limit of the perimeter process in markovian explorations of certain random planar maps with large degrees which are roughly speaking the dual maps of the stable maps of le gall and miermont in ann probab 39 1 69 2011 as a consequence of this result we are able to identify the law of the intrinsic area of these distinguished growth fragmentations this generalizes a geometric connection between large boltzmann triangulations and a certain growth fragmentation process which was established in bertoin et al ann probab accepted