a numerical scheme for shock propagation in three dimensions a numerical scheme for shock propagation in three space dimensions is presented the motion of the leading shock surface is calculated by using whitham s theory of geometrical shock dynamics the numerical scheme is used to examine the focusing of initially curved shock surfaces and the diffraction of shocks in a pipe with a 90 bend numerical and experimental results for the corresponding two dimensional or axisymmetrical cases are used to compare with the new and more complicated three dimensional results

tomlinson harashima precoding in mimo systems a unified approach to transceiver optimization based on multiplicative schur convexity this paper deals with the design of a multicarrier multiple input multiple output system which performs nonlinear tomlinson harashima precoding at the transmitter and linear equalization at the receiver the goal is the joint optimization of the processing matrices at both ends of the wireless link assuming a constraint on the overall transmit power we consider different design criteria which require the maximization minimization of objective functions that depend on the mean square errors over the individual data streams a unified framework for the solution of a great number of optimization problems is developed based on the concept of multiplicative schur convexity we show that many widely used design criteria can be easily accommodated in our framework our analysis is centered on two theorems which in the case of cooperative processing among the different subcarriers provide closed form solutions to a number of optimization problems on the other hand when an independent processing is assumed at each subcarrier closed form solutions may not exist nonetheless exploiting the results of the two theorems we show that for a variety of cost functions the optimization problem can be efficiently solved theoretical analysis and computer simulations are used to assess the performance of the proposed schemes and make comparisons with linear transceiver architectures it turns out that nonlinear precoding provides better results than linear prefiltering when the cost function is multiplicatively schur convex in contrast when the cost function is multiplicatively schur concave the nonlinear scheme is equivalent to the linear one

cohomology for frobenius kernels of sl2 abstract let sl 2 r be the r th frobenius kernels of the group scheme sl 2 defined over an algebraically closed field of characteristic p 0 in this paper we give for r 1 a complete description of the cohomology groups for sl 2 r we also prove that the reduced cohomology ring h sl 2 r k red is cohen macaulay geometrically we show for each r 1 that the maximal ideal spectrum of the cohomology ring for sl 2 r is homeomorphic to the fiber product g b u r finally we adapt our calculations to obtain analogous results for the cohomology of higher frobenius lusztig kernels of quantized enveloping algebras of type sl 2

zero forcing dfe transceiver design over slowly time varying mimo channels using st gtd this paper considers the optimization of transceivers with decision feedback equalizers dfe for slowly time varying memoryless multi input multi output mimo channels the data vectors are grouped into space time blocks st blocks for the spatial and temporal precoding to take advantage of the diversity offered by time varying channels the space time generalized triangular decomposition st gtd is proposed for application in time varying channels under the assumption that the instantaneous channel state information at the transmitter csit and receiver csir and the channel prediction are available we also propose the space time geometric mean decomposition st gmd system based on st gtd under perfect channel prediction the system minimizes both the arithmetic mse at the feedback detector and the average un coded bit error rate ber in moderate high signal to noise ratio snr region for practical applications a novel st gtd based system which does not require channel prediction but shares the same asymptotic ber performance with the st gmd system is also proposed at the moderate high snr region our analysis and numerical results show that all the proposed systems have better ber performance than the conventional gmd based systems over time varying channels the average bers of the proposed systems are non increasing functions of the st block size

accounting for transverse flow in the theory of geometrical shock dynamics the theory of geometrical shock dynamics is deduced as a formal approximation to the equations of gas dynamics in two dimensions thus overcoming the approximation of quasi one dimensional flow utilized in the original derivation successive approximations may be obtained by using the truncation scheme developed by best 1991 for considering shock propagation down a tube of slowly varying cross section the zero order approximation yields the theory as developed by whitham 1957 the first order approximation includes a term which is additional to those appearing in the equations derived by best 1991 the characteristic speeds for disturbances propagating on the shock are computed and a hierarchical wave structure is evident in view of this structure comment is made upon the problem of blast diffraction by a convex corner

extensions of simple modules for finite chevalley groups let g be an almost simple algebraic group over an algebraically closed field k of positive characteristic p we assume that g is defined and split over the prime field 5 for it 3 1 we denote by g n the finite group consisting of the points of g over the field with p elements our first result states that for a certain class of simple modules for g n the only extensions that can occur are those which are restrictions of g extensions see theorem 2 8 the full story about g extensions is not known yet except for a few rather small groups however much more is known about extensions for the algebraic group than about those for the finite group for instance the linkage principle l gives an upper bound for which g extensions may occur moreover a proof of the lusztig conjecture on the irreducible characters for g also implies strong statements about g extensions see 3 proposition 2 81 it is an open question whether all extensions between simple g n modules can be found via the extension theory for g we prove that in generic cases this is in fact so see theorem 3 2 moreover for the groups x 3 p and sp 4 p we are able to determine completely all extensions between simple modules from the corresponding known results for the algebraic groups x 3 k and sp 4 k our results extend previous results by cline parshall and scott s 91 who consider extensions of the trivial module by a minimal module and smith ls who considers extensions between certain minimal modules the method we use is a generalization of the one used by humphreys 131 who proves the existence of certain selfextensions for sp 4 p it should be pointed out that our methods do not work for p small on the other hand everything we do generalizes easily to the twisted chevalley groups see theorem 3 4 we demonstrate this by working out all extensions for su 3 p see section 4 3

the generalized triangular decomposition given a complex matrix h we consider the decomposition h qrp where r is upper triangular and q and p have orthonormal columns special instances of this decomposition include the singular value decomposition svd and the schur decomposition where r is an upper triangular matrix with the eigenvalues of h on the diagonal we show that any diagonal for r can be achieved that satisfies weyl s multiplicative majorization conditions k k k k i 1 r i i 1 1 k k k i 1 r i i 1 i where k is the rank of h i is the i th largest singular value of h and r i is the i th largest in magnitude diagonal element of r given a vector r which satisfies weyl s conditions we call the decomposition h qrp where r is upper triangular with prescribed diagonal r the generalized triangular decomposition gtd a direct nonrecursive algorithm is developed for computing the gtd this algorithm starts with the svd and applies a series of permutations and givens rotations to obtain the gtd the numerical stability of the gtd update step is established the gtd can be used to optimize the power utilization of a communication channel while taking into account quality of service requirements for subchannels another application of the gtd is to inverse eigenvalue problems where the goal is to construct matrices with prescribed eigenvalues and singular values

second cohomology groups for frobenius kernels and related structures abstract let g be a simple simply connected affine algebraic group over an algebraically closed field k of characteristic p for an odd prime p let b be a borel subgroup of g and u be its unipotent radical in this paper we determine the second cohomology groups of b and its frobenius kernels for all simple b modules we also consider the standard induced modules obtained by inducing a simple b module to g and compute all second cohomology groups of the frobenius kernels of g for these induced modules also included is a calculation of the second ordinary lie algebra cohomology group of lie u with coefficients in k

group detection for synchronous gaussian code division multiple access channels the concept of group detection is introduced to address the design of suboptimum multiuser detectors for code division multiple access cdma channels a group detection scheme consists of a bank of p group detectors one each for detecting the information symbols of users in each group of a p group partition of the k simultaneously transmitting users in a parallel group detection scheme these group detectors operate independently whereas in a sequential scheme each group detector uses the decisions of the previous group detectors to successively cancel the interference from those users group detectors based on the generalized likelihood ratio test glrt are obtained for the synchronous gaussian cdma channel the complexity of these detectors is exponential in the group size whereas that of the optimum detector is exponential in k since the partition of users is a design parameter group sizes can be chosen to satisfy a wide range of complexity constraints a key performance result is that the glrt group detectors are optimally group near far resistant furthermore upper and lower bounds on the asymptotic efficiency of the sequential group detectors are derived these bounds reveal that the sequential group detectors can under certain conditions perform as well as glrt group detectors of much larger group sizes group detection provides a unifying approach to multiuser detection when the users are partitioned into k single user groups the glrt a modified form of glrt and the sequential group detectors reduce to previously proposed suboptimal detectors namely the decorrelator the two stage detector and the decorrelating decision feedback detector respectively for the other nontrivial partitions the group detectors are new and have a performance that is commensurate with their complexity

high order essentially nonsocillatory schemes for hamilton jacobi equations hamilton jacobi h j equations are frequently encountered in applications e g in control theory and differential games h j equations are closely related to hyperbolic conservation laws in one space dimension the former is simply the integrated version of the latter similarity also exists for the multidimensional case and this is helpful in the design of difference approximations in this paper high order essentially nonoscillatory eno schemes for h j equations are investigated which yield uniform high order accuracy in smooth regions and sharply resolve discontinuities in the derivatives the eno scheme construction procedure is adapted from that for hyperbolic conservation laws the schemes are numerically tested on a variety of one dimensional and two dimensional problems including a problem related to control optimization and high order accuracy in smooth regions good resolution of discontinuities in the derivatives and convergence to viscosity solutions are observed

extensions of modules for algebraic groups let g be a connected semi simple and simply connected algebraic group over an algebraically closed field k of prime characteristic p in this paper we show how one can obtain the extensions of any two simple g modules if one knows the socles of all the g modules extg l l where g1 denotes the kernel of the frobenius endomorphism on g and l as well as l are simple g1 modules alternatively we prove how all such g extensions can be found once one knows the extensions of any two simple g modules belonging to a specified finite set of simple modules with small highest weight such information is available in certain low rank cases it should also be pointed out that it is possible from lusztig s conjecture on irreducible characters 11 to derive the dimensions of ext l1 l2 when l1 and l2 are simple with such small highest weights to obtain our results on exth we need to know that there exists no g1 extension of a simple module by itself this turns out to be somewhat

block diagonal gmd for zero padded mimo frequency selective channels in the class of systems with linear precoder and decision feedback equalizers dfe for zero padded zp multiple input multiple output mimo frequency selective channels existing optimal transceiver designs present two drawbacks first the optimal systems require a large number of feedback bits from the receiver to encode the full precoding matrix second the full precoding matrix leads to complex computations these disadvantages become more severe as the bandwidth bw efficiency increases in this paper we propose using block diagonal geometric mean decomposition bd gmd to design the transceiver two new bd gmd transceivers are proposed the zf bd gmd system where the receiver is a zero forcing dfe zf dfe and the mmse bd gmd system where the receiver is a minimum mean square error dfe mmse dfe the bd gmd systems introduced here have the following four properties a they use the block diagonal unitary precoding technique to reduce the required number of encoding bits and simplify the computation b for any block size the bd gmd systems are optimal within the family of systems using block diagonal unitary precoders and dfes as block size gets larger the bd gmd systems produce uncoded bit error rate ber performance similar to the optimal systems using unitary precoders and dfes c for the two zf transceivers zf optimal and zf bd gmd and the two mmse transceivers mmse optimal and mmse bd gmd the average ber degrades as the bw efficiency increases d in the case of single input single output siso channels the bd gmd systems have the same performance as those of the lazy precoder transceivers these properties make the proposed bd gmd systems more favorable designs in practical implementation than the optimal systems

generalized geometric mean decomposition and dfe transceiver design part ii performance analysis in a companion paper the generalized geometric mean decomposition ggmd was proposed and used to design ggmd decision feedback equalizer dfe transceivers for arbitrary multiple input multiple output mimo channels without zero forcing constraint for the application to cyclic prefix cp systems the ggmd dfe transceiver has the most advantage over the gmd dfe mmse transceiver in terms of design and implementation complexity this paper presents the performance analysis for the ggmd dfe transceiver implementation proposed in part i the arithmetic mean square error mse symbol error rate ser and gaussian mutual information of the proposed system are investigated the performance advantages of ggmd dfe transceiver over popular orthogonal frequency division multiplexing ofdm and single carrier cp mmse systems are shown analytically and verified by numerical simulations

new precoding for intersymbol interference cancellation using nonmaximally decimated multirate filterbanks with ideal fir equalizers in this paper we propose a new precoding method for intersymbol interference isi cancellation by using non maximally decimated multirate filterbanks unlike the existing preceding methods such as the th and trellis precodings the new preceding i may be independent of the isi channel ii is linear and does not have to implement any modulo operation iii gives the ideal fir equalization at the receiver for any fir isi channel including spectral null channels iv expands the transmission bandwidth in a minimum amount the precoding is built on non maximally decimated multirate filterbanks based on multirate filterbank theory we present a necessary and sufficient condition on an fir isi transfer function in terms of its zero set such that there is a linear fir n spl times m precoder so that an ideal fir equalizer exists where the integers k and n are arbitrarily fixed the condition is easy to check as a consequence of the condition for any given fir isi transfer function not identically 0 there always exist such linear fir precoders moreover for almost all given fir isi transfer functions there exist linear fir precoders with size n spl times n 1 i e the bandwidth is expanded by 1 n in addition to the conditions on the isi transfer functions a method for the design of the linear fir precoders and the ideal fir equalizers is also given numerical examples are presented to illustrate the theory

joint unitary triangularization for gaussian multi user mimo networks the problem of transmitting a common message to multiple users over the gaussian multiple input multiple output broadcast channel is considered where each user is equipped with an arbitrary number of antennas a closed loop scenario is assumed for which a practical capacity approaching scheme is developed by applying judiciously chosen unitary operations at the transmit and receive nodes the channel matrices are triangularized so that the resulting matrices have equal diagonals up to a possible multiplicative scalar factor this along with the utilization of successive interference cancellation reduces the coding and decoding tasks to those of coding and decoding over the single antenna additive white gaussian noise channel over the resulting effective channel any off the shelf code may be used for the two user case it was recently shown that such joint unitary triangularization is always possible in this paper it is shown that for more than two users it is necessary to carry out the unitary linear processing jointly over multiple channel uses i e space time processing is employed it is further shown that exact triangularization where all resulting diagonals are equal is still not always possible and appropriate conditions for the existence of such are established for certain cases when exact triangularization is not possible an asymptotic construction is proposed that achieves the desired property of equal diagonals up to edge effects that can be made arbitrarily small at the price of processing a sufficiently large number of channel uses together

extensions for finite chevalley groups i let g be a connected semisimple algebraic group defined and split over the field fp with p elements and k be the algebraic closure of fp assume further that g is almost simple and simply connected and let g fq be the finite chevalley group consisting of fq rational points of g where q pr for a non negative integer r in this paper formulas are found relating extensions between simple kg fq modules and extensions over g considered as an algebraic group over k one of these formulas which only holds for primes p 3 h 1 where h is the coxeter number of g is then used to show the vanishing of self extensions between simple kg fq modules except for certain simple modules when r 1 and the underlying root system is of type a1 or cn

improved linear transmit processing for single user and multi user mimo communications systems in this paper we propose a novel linear transmit precoding strategy for multiple input multiple output mimo systems employing improper signal constellations in particular improved zero forcing zf and minimum mean square error mmse precoders are derived based on modified cost functions and are shown to achieve a superior performance without loss of spectrum efficiency compared to the conventional linear and nonlinear precoders the superiority of the proposed precoders over the conventional solutions are verified by both simulation and analytical results the novel approach to precoding design is also applied to the case of an imperfect channel estimate with a known error covariance as well as to the multi user scenario where precoding based on the nullspace of channel transmission matrix is employed to decouple multi user channels in both cases the improved precoding schemes yield significant performance gain compared to the conventional counterparts

extensions for frobenius kernels 1 1 let g be a simple algebraic group over an algebraically closed field k of characteristic p 0 for r 1 let gr be the rth frobenius kernel of g it is well known that the representations for g1 are equivalent to the restricted representations for lie g historically the cohomology for frobenius kernels has been best understood for large primes friedlander and parshall fp first computed the cohomology ring h g1 k for p 3 h 1 where h is the coxeter number of the underlying root system they proved that the cohomology ring can be identified with the coordinate algebra of the nullcone andersen and jantzen aj later verified this fact for p h furthermore they generalized this calculation by looking at h g1 h0 where h0 indb for p h their results had some restrictions on the type of root system involved kumar lauritzen and thomsen klt removed the restrictions on the root systems through the use of frobenius splittings the cohomology ring h g1 k modulo nilpotents can be identified in general with the coordinate algebra of the restricted nullcone n1 x lie g x p 0 for good primes nakano parshall and vella npv proved that this variety is irreducible and can be identified with the closure of some richardson orbit recently carlson lin nakano and parshall clnp have given an explicit description of n1 these recent results provide some indication that one can systematically study extensions of frobenius kernels for small primes by using general formulas which exhibit generic behavior for large primes

equal diagonal qr decomposition and its application to precoder design for successive cancellation detection in multiple input multiple output mimo multiuser detection theory the qr decomposition of the channel matrix h can be used to form the back cancellation detector in this paper we propose an optimal qr decomposition which we call the equal diagonal qr decomposition or briefly the qrs decomposition we apply the decomposition to precoded successive cancellation detection where we assume that both the transmitter and the receiver have perfect channel knowledge we show that for any channel matrix h there exists a unitary precoder matrix s such that hs qr where the nonzero diagonal entries of the upper triangular matrix r in the qr decomposition of hs are all equal to each other the precoder and the resulting successive cancellation detector have the following properties a the minimum euclidean distance between two signal points at the channel output is equal to the minimum euclidean distance between two constellation points at the precoder input up to a multiplicative factor that equals the diagonal entry in the r factor b the superchannel hs naturally exhibits an optimally ordered column permutation i e the optimal detection order for the vertical bell labs layered space time v blast detector is the natural order c the precoder s minimizes the block error probability of the qr successive cancellation detector d a lower and an upper bound for the free distance at the channel output is expressible in terms of the diagonal entries of the r factor in the qr decomposition of a channel matrix e the precoder s maximizes the lower bound of the channel s free distance subject to a power constraint f for the optimal precoder s the performance of the qr detector is asymptotically at large signal to noise ratios snrs equivalent to that of the maximum likelihood detector mld that uses the same precoder further we consider two multiplexing schemes time division multiple access tdma and orthogonal frequency division multiplexing ofdm we d

second cohomology groups for algebraic groups and their frobenius kernels let g be a simple simply connected algebraic group scheme defined over an algebraically closed field of characteristic p 0 let t be a maximal split torus in g b t be a borel subgroup of g and u its unipotent radical let f g g be the frobenius morphism for r 1 define the frobenius kernel gr to be the kernel of f iterated with itself r times define ur respectively br to be the kernel of the frobenius map restricted to u respectively b let x t be the integral weight lattice and x t be the dominant integral weights the computations of particular importance are h2 u1 k h2 br for x t h2 gr h0 for x t and h2 b for x t the above cohomology groups for the case when the field has characteristic 2 are computed in this paper these computations complete the picture started by bendel nakano and pillen 2007 5 for p 3 furthermore the computations show h2 gr h0 has a good filtration

frobenius splitting of cotangent bundles of flag varieties let g be a semisimple and simply connected algebraic group over an algebraically closed field of characteristic p 0 let u be the unipotent radical of a borel subgroup b g and u the lie algebra of u springer 16 has shown for good primes that there is a b equivariant isomorphism u u where b acts through conjugation on u and through the adjoint action on u for g sln one has the well known equivariant isomorphism a 7 a i between unipotent and nilpotent upper triangular matrices let p be a good prime for g then there is an isomorphism of homogeneous bundles x g b u g b u where the latter can be identified with the cotangent bundle t g b of g b motivated in part by 12 we establish a link between the g invariant form on the steinberg module st h0 g b p 1 cf 1 8 and frobenius splittings 15 of the cotangent bundle of g b the representation h0 g b 2 p 1 is a quotient of the space of functions h x ox on x here h0 g b m denotes the g module induced from the b module m and half the sum of the roots r opposite to the roots

extensions for finite chevalley groups ii let g be a semisimple simply connected algebraic group defined and split over the field fp with p elements let g fq be the finite chevalley group consisting of the fq rational points of g where q p r and let g r be the rth frobenius kernel the purpose of this paper is to relate extensions between modules in mod g f q and mod g r with extensions between modules in mod g among the results obtained are the following for r 2 and p 3 h 1 the g f q extensions between two simple g f q modules are isomorphic to the g extensions between two simple p r restricted g modules with suitably twisted highest weights for p 3 h 1 we provide a complete characterization of h 1 g f q h0 where h 0 ind g b a and a is p r restricted furthermore for p 3 h 1 necessary and sufficient bounds on the size of the highest weight of a g module v are given to insure that the restriction map h 1 g v h 1 g f q v is an isomorphism finally it is shown that the extensions between two simple p r restricted g modules coincide in all three categories provided the highest weights are close together

on nilpotent commuting varieties and cohomology of frobenius kernels abstract the paper studies the dimensions of irreducible components of commuting varieties of restricted nilpotent r tuples in a classical lie algebra g defined over an algebraically closed field k as applications we obtain some new results on the structure of the even cohomology ring of frobenius kernels g r for each r 1 where g is the simply connected simple algebraic group such that lie g g explicit calculations for rank two groups are also presented

analysis on the diversity multiplexing tradeoff for ordered mimo sic receivers the diversity multiplexing tradeoff for multiple input multiple output mimo point to point channels and multiple access channels were first proposed and studied by zheng and tse recently while the optimal tradeoff curves for mimo channels have been explicitly explored those corresponding to some suboptimal and practical mimo schemes are still open one such important problem is the diversity multiplexing tradeoff for a v blast type system employing ordered successive interference cancellation sic receivers with zero forcing zf or minimum mean square error mmse processing at each stage in this paper we take a novel geometrical approach and rigorously verify that under general settings the optimal ordering rule for a v blast sic receiver will not improve its performance regarding diversity multiplexing tradeoff in point to point channels the same geometrical tool is then applied to mimo spatial division multiple access channels leading to some first results in this area particularly we reveal that when the rates of data streams are fixed i e zero spatial multiplexing gain the diversity order is not improved by user ordering

structure of an optimum linear precoder and its application to ml equalizer the structure of an optimum linear precoder for a rotation invariant performance measure is obtained subject to the constraint of limited input power for a block transmission scheme it is shown that several known performance measures of a communication system are rotation invariant the rotation invariant property provides a unified framework for obtaining the structure of an optimum linear precoder for several criteria such as 1 maximization of minimum distance 2 maximization of channel capacity and 3 optimization of different performance measures such as bit error rate ber mean square error signal to noise ratio of optimum equalizers linear minimum mean square error zero forcing maximum likelihood ml zero forcing block decision feedback minimum mean square error block decision feedback etc this framework provides a method for obtaining the structure of an optimum linear precoder for ber performance measure of the ml equalizer the structure turns out to be a channel diagonalizing structure after a prerotation of the input constellation using this structure the properties of the optimum precoder that minimize the ber of the ml equalizer for two binary phase shift keying symbols transmission under input power constraint are studied

the dirty mimo multiple access channel in the scalar dirty multiple access channel in addition to gaussian noise two additive interference signals are present each known non causally to a single transmitter it was shown by philosof et al that for strong interferences an independent identically distributed ensemble of codes does not achieve the capacity region rather a structured codes approach was presented that was shown to be optimal in the limit of high signal to noise ratios where the sum capacity is dictated by the minimal bottleneck channel gain in this paper we consider the multiple input multiple output mimo variant of this setting in order to incorporate structured codes in this case one can utilize matrix decompositions that transform the channel into effective parallel scalar dirty multiple access channels this approach however suffers from a bottleneck effect for each effective scalar channel and therefore the achievable rates strongly depend on the chosen decomposition it is shown that a recently proposed decomposition where the diagonals of the effective channel matrices are equal up to a scaling factor is optimal at high signal to noise ratios under an equal rank assumption this approach is then extended to any number of transmitters finally an application to physical layer network coding for the mimo two way relay channel is presented

generalized triangular decomposition in transform coding a general family of optimal transform coders tcs is introduced here based on the generalized triangular decomposition gtd developed by jiang this family includes the karhunen loeve transform klt and the generalized version of the prediction based lower triangular transform plt introduced by phoong and lin as special cases the coding gain of the entire family with optimal bit allocation is equal to that of the klt and the plt even though the original plt introduced by phoong is not applicable for vectors that are not blocked versions of scalar wide sense stationary processes the gtd based family includes members that are natural extensions of the plt and therefore also enjoy the so called minlab structure of the plt which has the unit noise gain property other special cases of the gtd tc are the geometric mean decomposition gmd and the bidiagonal decomposition bid transform coders the gmd tc in particular has the property that the optimum bit allocation is a uniform allocation this is because all its transform domain coefficients have the same variance implying thereby that the dynamic ranges of the coefficients to be quantized are identical

a fast marching like algorithm for geometrical shock dynamics we develop a new algorithm for the computation of the geometrical shock dynamics gsd model the method relies on the fast marching paradigm and enables the discrete evaluation of the first arrival time of a shock wave and its local velocity on a cartesian grid the proposed algorithm is based on a first order upwind finite difference scheme and reduces to a local nonlinear system of two equations solved by an iterative procedure reference solutions are built for a smooth radial configuration and for the 2d riemann problem the link between the gsd model and p systems is given numerical experiments demonstrate the efficiency of the scheme and its ability to handle singularities

transmit antenna selection for multiple input multiple output spatial modulation systems the benefits of transmit antenna selection tas invoked for spatial modulation sm aided multiple input multiple output mimo systems are investigated specifically we commence with a brief review of the existing tas algorithms and focus on the recently proposed euclidean distance based tas ed tas schemes due to their high diversity gain then a pair of novel ed tas algorithms termed as the improved qr decomposition qrd based tas qrd tas and the error vector magnitude based tas evm tas are proposed which exhibit an attractive system performance at low complexity moreover the proposed ed tas algorithms are amalgamated with the low complexity yet efficient power allocation pa technique termed as tas pa for the sake of further improving the system s performance our simulation results show that the proposed tas pa algorithms achieve signal to noise ratio snr gains of up to 9 db over the conventional tas algorithms and up to 6 db over the tas pa algorithm designed for spatial multiplexing systems

generalized geometric mean decomposition and dfe transceiver design part i design and complexity this paper considers a new matrix decomposition which decomposes a complex matrix as a product of several sets of semi unitary matrices and upper triangular matrices in an iterative manner the inner most triangular matrix has its diagonal elements equal to the geometric mean of the singular values of the target complex matrix the complexity defined in terms of the number of floating point operations of the new decomposition generalized geometric mean decomposition ggmd depends on its parameters but is always less than or equal to that of geometric mean decomposition gmd the optimal parameters which yield the minimal complexity are derived the paper also shows how to use ggmd to design an optimal decision feedback equalizer dfe transceiver for multiple input multiple output mimo channels without zero forcing constraint a novel iterative receiving detection algorithm for the specific receiver is also proposed for the application to cyclic prefix systems in which the svd of the equivalent channel matrix can be easily computed the proposed ggmd transceiver has k log2 k times complexity advantage over the gmd transceiver where is the number of data symbols per data block and is a power of 2 in a companion paper performance analyses of the proposed ggmd transceiver in terms of arithmetic mean square error mse symbol error rate ser and gaussian mutual information are performed and comparisons with well known transceivers are made the results show that the proposed transceiver reaches the same optimality that a gmd mmse transceiver can possibly achieve

the multitone channel the maximum bit rate of multitone qam quadrature amplitude modulation over a general linear channel is found first the overall bit rate for an awgn channel with a two level transfer function is maximized using a multitone qam system the power distribution between the tones and the number of bits symbol per tone is optimized for a given symbol error rate extending these results to the general channel it is shown that the optimum power division for multitone signals is similar to the water pouring solution of information theory furthermore multitone qam performance is about 9 db worse than the channel capacity independent of the channel characteristics the multitone results throughout are compared to those of an equivalent single tone linearly equalized system the comparison shows that the multitone system is useful for some channels e g those with deep nulls in the transfer function the maximum bit error rate over a twisted pair channel which is performance dominated by near end crosstalk next is also found

decision feedback multiuser detection a systematic approach a systematic approach to decision feedback multiuser detection is introduced for the joint detection of symbols of k simultaneously transmitting users of a synchronous correlated waveform multiple access cwma channel with gaussian noise a new performance criterion called symmetric energy is defined which is a low noise indicator of the joint error rate that at least one user is detected erroneously even the best linear detectors can perform poorly in terms of symmetric energy compared to the maximum likelihood detector a general class of decision feedback detectors dfds is defined with o k implementational complexity per user the symmetric energy of arbitrary dfd and bounds on their asymptotic effective energy aee performance are obtained along with an exact bit error rate and aee analysis for the decorrelating dfd the optimum dfd that maximizes symmetric energy is obtained each one of the k optimum decorrelating and conventional dfds that correspond to the k orders in which the users can be detected are shown to outperform the linear optimum decorrelating and conventional detectors respectively in terms of symmetric energy moreover algorithms are obtained for determining the choice of order of detection for the three dfds which guarantee that they uniformly user wise outperform their linear counterparts in addition to optimality in symmetric energy it is also shown that under certain conditions the optimum dfd achieves the aee performance of the exponentially complex maximum likelihood detector for all users simultaneously none of the results of this paper make the perfect feedback assumption the implications of our work on power control for multiuser detection are also discussed

infinitesimal fixed points in modules with good filtration let g be the lie algebra of the connected semisimple algebraic group g defined over an algebraically closed field k of characteristic p p 0 if m is a g module with good filtration d we consider the module m g of fixed points under g as a module for the image of g under the frobenius homomorphism g g this module is denoted m g 1 cf j and it has been conjectured that it also has a good filtration d we will give an example to show that this is too optimistic in the other direction we prove something stronger in rank 1 namely we show that if b is a borel subgroup in sl2 or psl2 and m is a b module with relative schubert filtration cf vdk then so is mb 1 some preliminary work was done at the university of virginia where i much enjoyed the hospitality of brian parshall and leonard scott

optimal precoder design for correlated mimo communication systems using zero forcing decision feedback equalization we consider the design of the precoder for a multi input multi output mimo communication system equipped with a decision feedback equalizer dfe receiver for such design problems perfect knowledge of the channel state information csi at both the transmitter and the receiver is usually required however in the environment of wireless communications it is often difficult to provide sufficiently timely and accurate feedback of csi from the receiver to the transmitter for such designs to be practically viable in this paper we consider the optimum design of a precoder for a wireless communication link having m transmitter antennas and n receiver antennas m n in which the channels are assumed to be flat fading and may be correlated we assume that full knowledge of csi is available at the receiver at the transmitter however only the first and second order statistics of the channels are available our goal here is to come up with an efficient design of the optimal precoder for such a mimo system by minimizing the average arithmetic mean squared error mse of zero forcing zf decision feedback detection subject to a constraint on the total transmitting power applying some of the properties of the matrix parameters this nonconvex optimization problem can be transformed into a convex geometrical programming problem which can then be efficiently solved using an interior point method the performance of the mimo system equipped with this optimum precoder and a zf dfe has also been found to be comparable and in some cases superior to that of v blast which necessitates optimally ordered successive interference cancellation based on the largest postdetection signal to noise ratio snr in terms of tradeoff between performance and implementation simplicity our new system is certainly an attractive alternative

mimo transceiver optimization with linear constraints on transmitted signal covariance components this correspondence revisits the joint transceiver optimization problem for multiple input multiple output mimo channels the linear transceiver as well as the transceiver with linear precoding and decision feedback equalization are considered for both types of transceivers in addition to the usual total power constraint an individual power constraint on each antenna element is also imposed a number of objective functions including the average bit error rate are considered for both of the above systems under the generalized power constraint it is shown that for both types of systems the optimization problem can be solved by first solving a class of mmse problems am mmse or gm mmse depending on the type of transceiver and then using majorization theory the first step under the generalized power constraint can be formulated as a semidefinite program sdp for both types of transceivers and can be solved efficiently by convex optimization tools the second step is addressed by using results from majorization theory the framework developed here is general enough to add any finite number of linear constraints to the covariance matrix of the input

extension of the pisarenko method to sparse linear arrays when applied to array processing the pisarenko harmonic decomposition phd method is limited to linear equispaced arrays we present an approach that allows us to extend it to general arrays although for the ease of exposition we consider only sparse linear arrays we exploit the fact that the phd can be seen as a deconvolution or model fitting approach that minimizes an t sub 1 norm and can thus be implemented as a standard linear program looking at the phd from this point of view has two advantages it allows us to extend its applicability to arbitrary arrays and by diverging slightly from the basic philosophy it allows us to improve its performance which is often quite poor in its original version

on the proximity factors of lattice reduction aided decoding lattice reduction aided decoding lrad features reduced decoding complexity and near optimum performance in multiinput multioutput communications in this paper a quantitative error rate analysis of lrad is presented to this aim the proximity factors are defined to measure the worst case losses in decoding distances associated with the decision region relative to infinite lattice decoding ild namely closest point search in an infinite lattice upper bounds on the proximity factors are derived which are functions of the dimension n of the lattice alone the study is then extended to the dual basis reduction it is found that the bounds for dual basis reduction may be smaller reasonably good bounds are derived in many cases proximity factors not only imply the same diversity order in fading channels but also relate the error probabilities of ild and lrad

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

extensions for finite chevalley groups iii rational and generic cohomology abstract let g be a connected reductive algebraic group and b be a borel subgroup defined over an algebraically closed field of characteristic p 0 in this paper the authors study the existence of generic g cohomology and its stability with rational g cohomology groups via the use of methods from the authors earlier work new results on the vanishing of g and b cohomology groups are presented furthermore vanishing ranges for the associated finite group cohomology of g f q are established which generalize earlier work of hiller in addition to stability ranges for generic cohomology which improve on seminal work of cline parshall scott and van der kallen

mmse decision feedback equalizers finite length results this paper extends a number of results on the infinite length minimum mean square error decision feedback equalizer mmse dfe reported by cioffi dudevoir eyuboglu and forney see ieee trans commun 1995 to the finite length case cholesky factorization and displacement structure theory are demonstrated to be two powerful analytical tools for analyzing the finite length mmse dfe our objective throughout the paper is to establish finite length analogs of the well known infinite length mmse dfe results similarities and differences between the two cases are examined and delineated finally convergence of our derived finite length results to their well established infinite length counterparts is shown

mmse dfe transceiver design over slowly time varying mimo channels using st gtd in a companion paper we have studied the zero forcing zf transceiver with decision feedback equalizer dfe over slowly time varying narrowband multiinput multioutput mimo channels the space time generalized triangular decomposition st gtd was used for the design of zf dfe transceivers the space time geometric mean decomposition st gmd zf transceiver minimizes both the arithmetic mean square error mse at the feedback detector and the average uncoded bit error rate ber in moderate high signal to noise ratio snr this paper addresses the design problem of dfe transceiver without zero forcing constraint in the first part a channel independent temporal precoder is superimposed on the conventional block wise gmd based minimum mean square error mmse dfe transceiver to take advantage of the temporal diversity in the second part st gtd is applied for the design of mmse dfe transceivers with accurate channel prediction and space time powerloading the proposed st gmd mmse transceiver minimizes the arithmetic mse at the feedack detector and maximizes gaussian mutual information for practical applications the st gtd mmse transceiver which does not require channel prediction but shares the same asymptotic ber performance with the st gmd mmse system is also developed in the convex region our analysis shows that the proposed mmse transceivers has better ber performance than the conventional gmd based mmse transceiver the average bers of the proposed systems are nonincreasing functions of the st block size the superior performance of st gmd mmse transceiver over the st gmd zf transceiver is also verified analytically

discrete multiple tone modulation with coset coding for the spectrally shaped channel a discrete approach to multiple tone modulation is developed for digital communication channels with arbitrary intersymbol interference isi and additive gaussian noise multiple tone modulation is achieved through the concatenation of a finite block length modulator based on discrete fourier transform dft code vectors and high gain coset or trellis codes symbol blocks from an inverse dft idft are cyclically extended to generate isi free channel output symbols that decompose the channel into a group of orthogonal and independent parallel subchannels asymptotic performance of this system is derived and examples of asymptotic and finite block length coding gain performance for several channels are evaluated at different values of bits per sample this discrete multiple tone technique is linear in both the modulation and the demodulation and is free from the effects of error propagation that often afflict systems employing bandwidth optimized decision feedback plus coset codes

mimo transceivers with decision feedback and bit loading theory and optimization this paper considers mimo transceivers with linear precoders and decision feedback equalizers dfes with bit allocation at the transmitter zero forcing zf is assumed considered first is the minimization of transmitted power for a given total bit rate and a specified set of error probabilities for the symbol streams the precoder and dfe matrices are optimized jointly with bit allocation it is shown that the generalized triangular decomposition gtd introduced by jiang li and hager offers an optimal family of solutions the optimal linear transceiver which has a linear equalizer rather than a dfe with optimal bit allocation is a member of this family this shows formally that under optimal bit allocation linear and dfe transceivers achieve the same minimum power the dfe transceiver using the geometric mean decomposition gmd is another member of this optimal family and is such that optimal bit allocation yields identical bits for all symbol streams no bit allocation is necessary when the specified error probabilities are identical for all streams the qr based system used in vblast is yet another member of the optimal family and is particularly well suited when limited feedback is allowed from receiver to transmitter two other optimization problems are then considered a minimization of power for specified set of bit rates and error probabilities the qos problem and b maximization of bit rate for fixed set of error probabilities and power it is shown in both cases that the gtd yields an optimal family of solutions

a new numerical method for shock wave propagation based on geometrical shock dynamics in this paper a new numerical method for calculating the motion of shock waves in two and three dimensions is presented the numerical method is based on whitham s theory of geometrical shock dynamics which is an approximate theory that determines the motion of the leading shockfront explicitly the numerical method uses a conservative finite difference discretization of the equations of geometrical shock dynamics these equations are similar to those for steady supersonic potential flow and thus the numerical method developed here is similar to ones developed for that context numerical results are presented for shock propagation in channels and for converging cylindrical and spherical shocks the channel problem is used in part to compare this new numerical method with ones developed earlier converging cylindrical and spherical shocks are calculated to analyse their stability

efficiently computed reduced parameter input aided mmse equalizers for ml detection a unified approach a unified approach for computing the optimum settings of a length n sub f input aided equalizer that minimizes the mean square error between the equalized channel impulse response and a target impulse response of a given length n sub b is presented this approach offers more insight into the problem easily accommodates correlation in the input and noise sequences leads to significant computational savings and allows us to analyze a variety of constraints on the target impulse response besides the standard unit tap constraint in particular we show that imposing a unit energy constraint results in a lower mean square error at a comparable computational complexity furthermore we show that under the assumed constraint of finite length filters the relative delay between the equalizer and the target impulse response plays a crucial role in optimizing performance we describe a new characterization of the optimum delay and show how to compute it finally we derive reduced parameter pole zero models of the equalizer that achieve the high performance of a long all zero equalizer at a much lower implementation cost

filterbank transceivers optimizing information rate in block transmissions over dispersive channels optimal finite impulse response fir transmit and receive filterbanks are derived for block based data transmissions over frequency selective additive gaussian noise agn channels by maximizing mutual information subject to a fixed transmit power constraint both fir and pole zero channels are considered the inherent flexibility of the proposed transceivers is exploited to derive as special cases zero forcing zf and minimum mean square error receive filterbanks the transmit filterbank converts transmission over a frequency selective fading channel affected by additive colored noise into a set of independent flat fading subchannels with uncorrelated noise samples two loading algorithms are also developed to distribute transmit power and number of bits across the usable subchannels while adhering to an upper bound on the bit error rate ber reduction of the signal to noise ratio snr margin required to satisfy the prescribed ber is achieved by coding each subchannel s bit stream the potential of the proposed transceivers is illustrated and compared to discrete multitone dmt with simulated examples

differential feedback of geometrical mean decomposition precoder for time correlated mimo systems for a time correlated channel we consider the differential feedback of the geometrical mean decomposition gmd precoder which is known to be optimal for a number of criteria when the channel varies slowly we can expect the optimal gmd precoders of consecutive channel uses to be close we consider the feedback of the so called differential precoder and show that it lies in a neighborhood of the identity matrix using matrix perturbation theory furthermore the radius of the neighborhood is shown to be proportional to a time correlation parameter such a characterization allows for subsequent efficient quantization of the differential precoder we show how to design codewords for the prescribed radius by perturbing the identity matrix and applying qr decomposition on the perturbed matrix simulations are given to demonstrate that with a small feedback rate the performance of the proposed differential gmd comes close to the case when perfect channel state information is available to the transmitter for slowly time varying channels like those in indoor and microcellular environments

design of block transceivers with decision feedback detection this paper presents a method for jointly designing the transmitter receiver pair in a block by block communication system that employs intrablock decision feedback detection we provide closed form expressions for transmitter receiver pairs that simultaneously minimize the arithmetic mean squared error mse at the decision point assuming perfect feedback the geometric mse and the bit error rate of a uniformly bit loaded system at moderate to high signal to noise ratios separate expressions apply for the zero forcing and minimum mse mmse decision feedback structures in the mmse case the proposed design also maximizes the gaussian mutual information and suggests that one can approach the capacity of the block transmission system using independent instances of the same gaussian code for each element of the block our simulation studies indicate that the proposed transceivers perform significantly better than standard transceivers and that they retain their performance advantages in the presence of error propagation