spectral precoding for rectangularly pulsed ofdm spectrally precoded orthogonal frequency division multiplexing ofdm is a promising rectangularly pulsed ofdm signaling format which can provide very small power spectral sidelobes while allowing for efficient implementation by fast fourier transform and guard interval insertion in this paper general constraints on spectral precoding are developed for ofdm signals with zero padding zp ofdm or cyclic prefix cp ofdm to warrant the desirable spectral property that the power spectral sidelobes decay asymptotically as f 2k 2 where k is a preassigned positive integer in accordance with the constraints block partitioning is adopted to construct a general signaling format to facilitate the precoder design of the spectrally precoded cp ofdm that can provide fast decaying sidelobes new correlative and orthogonal precoders are also devised so that the desirable spectral property of fast sidelobe decaying is achieved with spectrally precoded zp ofdm and cp ofdm signals

synchronization requirements for multi user ofdm on satellite mobile and two path rayleigh fading channels the performance of multi user orthogonal frequency division multiplexing ofdm with raised cosine time domain pulse shaping is studied on the satellite mobile channel smc and the two path rayleigh fading channel a multi user time and carrier frequency synchronization scheme is discussed the relationship between the synchronization requirement and the roll off rate spl beta of the pulse shaping is explored in gaussian and typical rician k 10 channels multi user ofdm with spl beta 0 2 requires timing and carrier frequency synchronization accuracies of 4 and 2 respectively in order to avoid severe degradation due to multi user adjacent channel interference while on the two path rayleigh channel these values must be better than 2 for error floors less than 10 sup 3 timing and carrier frequency accuracies are normalized to t and 1 t respectively where t is the symbol duration multi user ofdm is less affected by the multipath time delay and slightly more severely affected by the doppler frequency shift than traditional fdm with root nyquist filtering fdm rnf for the same value of spl beta

the poincare algebra in rank 3 simple lie algebras we classify embeddings of the poincare algebra p 3 1 into the rank 3 simple lie algebras up to inner automorphism we show that there are exactly two embeddings of p 3 1 into sl 4 c which are however related by an outer automorphism of sl 4 c next we show that there is a unique embedding of p 3 1 into so 7 c up to inner automorphism but no embeddings of p 3 1 into sp 6 c all embeddings are explicitly described as an application we show that each irreducible highest weight module of sl 4 c not necessarily finite dimensional remains indecomposable when restricted to p 3 1 with respect to any embedding of p 3 1 into sl 4 c

n continuous sc fdma and its polarized transmission and reception this paper investigates the application of n continuous spectral projection precoding design to single carrier frequency division multiple access sc fdma it first considers a general orthogonal projection based precoded system with an improved iterative receiver and analyzes its ultimate performance in an additive white gaussian noise channel both in terms of achievable throughput and symbol error rates for n continuous sc fdma the distribution of the symbol errors is very much asymmetric a few base pulses carry the lion share of the self induced interference resulting in a zero throughput we show that an optimized transmission and reception scheme based on a polarized use of the base pulses can satisfactorily deal with this asymmetry and the end to end throughput can be recovered to be close to optimal applying a similar scheme to n continuous ofdm enables also an improved performance in the high snr regime where the interference effect strikes the most

on the cohen macaulay type of s lines in an 1 abstract let a be the coordinate ring of s lines through the origin in a n 1 k we discuss what it means for these lines to be in sufficiently general position and then with this restriction on the lines we attempt to verify our belief that the cohen macaulay type of a depends only on s and n we characterize those s and n for which a is a gorenstein ring i e of c m type 1 and explicitly calculate the cohen macaulay type in several other cases we then extend some of our results to the case of an arbitrary reduced curve whose tangent cone consists of lines in sufficiently general position finally we calculate the hubert samuel polynomials of the curves we have been considering

regular subalgebras and nilpotent orbits of real graded lie algebras abstract for a semisimple lie algebra over the complex numbers dynkin 1952 developed an algorithm to classify the regular semisimple subalgebras up to conjugacy by the inner automorphism group for a graded semisimple lie algebra over the complex numbers vinberg 1979 showed that a classification of a certain type of regular subalgebras called carrier algebras yields a classification of the nilpotent orbits in a homogeneous component of that lie algebra here we consider these problems for graded semisimple lie algebras over the real numbers first we describe an algorithm to classify the regular semisimple subalgebras of a real semisimple lie algebra this also yields an algorithm for listing up to conjugacy the carrier algebras in a real graded semisimple real algebra we then discuss what needs to be done to obtain a classification of the nilpotent orbits from that such classifications have applications in differential geometry and theoretical physics our algorithms are implemented in the language of the computer algebra system gap using our package corelg we report on example computations

constructing semisimple subalgebras of semisimple lie algebras abstract algorithms are described that help with obtaining a classification of the semisimple subalgebras of a given semisimple lie algebra up to linear equivalence the algorithms have been used to obtain classifications of the semisimple subalgebras of the simple lie algebras of ranks 8 these have been made available as a database inside the sla package of gap 4 the subalgebras in this database are explicitly given as well as the inclusion relations among them

torsion free aluffi algebras abstract a pair of ideals j i r has been called aluffi torsion free if the aluffi algebra of i j is isomorphic to the corresponding rees algebra we give necessary and sufficient conditions for the aluffi torsion free property in terms of the first syzygy module of the form ideal j in the associated graded ring of i for two pairs of ideals j 1 j 2 i such that j 1 j 2 i 2 we prove that if one pair is aluffi torsion free the other one is so if and only if the first syzygy modules of j 1 and j 2 have the same form ideals we introduce the notion of strongly aluffi torsion free ideals and present some results on these ideals

ideals generated by quadrics our purpose is to study the cohomological properties of the rees algebras of a class of ideals generated by quadrics for all such ideals i r k x y z we give the precise value of depthr it and decide whether the corresponding rational maps are birational in the case of dimension d 3 when k r we give structure theorems for all ideals of codimension d minimally generated by d 12 1 quadrics for arbitrary fields k we prove a polarized version

low complexity fft structures for ofdm transceivers orthogonal frequency division multiplexing is a multiple access technique with modulation and demodulation implemented by an inverse discrete fourier transform dft and a dft respectively in a downlink uplink environment an individual receiver transmitter may only use a small number of subchannels at any given time in which case it does not make sense to require full dft demodulation inverse dft modulation several existing low complexity techniques for computing a partial dft or inverse dft with power of two size are examined low complexity fast fourier transform structures for full few input and few output nonpower of two transforms are derived

spectral precoding for constant envelope ofdm spectrally precoded orthogonal frequency division multiplexing ofdm and constant envelope ofdm ce ofdm are two modified ofdm formats that enhance the signaling features of ofdm while allowing for the efficient implementation by discrete fourier transform and the insertion of guard intervals to counteract channel dispersion the spectrally precoded ofdm signal provides very small power spectral sidelobes decaying asymptotically as f 2j 2 with j integer valued design parameter thereby suppressing sidelobe powers effectively and achieving higher spectral efficiency than nonprecoded rectangularly pulsed ofdm which has power spectral sidelobes decaying asymptotically as f 2 the ce ofdm signal exhibits a unity peak to average power ratio and thus enables the efficient use of transmitter s power amplifier in this paper a specific ce ofdm block signaling format is proposed to incorporate spectral precoding with an aim to suppressing sidelobe powers more effectively than conventional nonprecoded ce ofdm the general constraint on spectral precoding is developed to ensure that the power spectral sidelobes of the spectrally precoded ce ofdm block signal with arbitrary data statistics decay asymptotically as f 2j 2 some spectral codes previously found for spectrally precoded ofdm are shown to meet the constraint and thus suited for spectrally precoded ce ofdm specifically spectral performance is analyzed for the spectrally precoded ce ofdm block signal with independent and identically distributed data to illustrate the prevailing spectral advantage the corresponding receiver is also developed to demodulate the spectrally precoded ce ofdm block signal over dispersive channels

cremona transformations and some related algebras abstract one proves a general characteristic free criterion for a rational map between projective varieties to be birational in terms of ideal theoretic and modulo theoretic conditions this criterion is more inclusive than that of f russo a simis compositio math 126 2001 335 358 and moreover differs from previous criteria in its nature in that the syzygies of the base ideal of the map are not directly involved in its formulation however a great deal of the consequences are phrased by means of those very syzygies avoided in the formulation of the criterion in any case the criterion is stated in effective terms so it yields an efficient computable test of birationality one also introduces a so called linear obstruction principle for base ideals of linear type thus raising a basic question concerning the structure of a certain related bilinear algebra

spectrally precoded ofdm by bilinearly transforming the rectangularly pulsed multicarrier basis signals new basis sets containing full response continuous basis signals are developed for constructing spectrally efficient orthogonal frequency division multiplexing ofdm signals with or without cyclic prefix cp or zero padding zp both multiple product and linear combination formats are presented for these basis sets in the multiple product format the developed full response basis signals are shown to be zero valued at interval edges and thus can be used to construct continuous phase ofdm signals it is analytically shown that the constructed continuous phase ofdm signals exhibit relatively small power spectral sidelobes which fall off as f 4 and can thus provide much higher spectral efficiency than the traditional rectangularly pulsed ofdm signal in the linear combination format the proposed basis signals are shown to be the linear combinations of rectangularly pulsed multicarrier basis signals and thereby allow for the efficient realization of fast fourier transform fft specifically a spectrally precoded signaling structure is developed in conjunction with inverse fft and guard insertion to construct continuous phase ofdm signals with or without cp or zp the corresponding spectral decoders are also developed to enable zero forcing zf demodulation for spectrally precoded ofdm with the zero forcing demodulation the spectrally precoded ofdm schemes are shown to outperform in average error rate characteristics the conventional rectangularly pulsed and correlatively coded ofdm schemes on various delay spread channels

asymptotic performance of successive interference cancellation in the context of linear precoded ofdm systems recent results on the asymptotic empirical eigenvalue distribution of random matrices have enabled the study of the asymptotic limits of linear precoded orthogonal frequency division multiplexing systems with minimum mean square error mmse equalization in this letter we extend these results to the mmse successive interference cancellation detector and quantify the nonlinearity gain for certain type of precoding matrices

precoded and vector ofdm robust to channel spectral nulls and with reduced cyclic prefix length in single transmit antenna systems the performance of orthogonal frequency division multiplexing ofdm systems may be degraded when intersymbol interference isi channels have spectral nulls also when isi channels have many taps the data rate overhead due to the insertion of the cyclic prefix is high we first propose a precoded ofdm system that may improve the performance of the ofdm systems for spectral null channels we also propose size k spl times x1 vector ofdm vofdm systems that reduce the cyclic prefix length by k times compared to the conventional ofdm systems the precoding scheme is simply to insert one or more zeros between each two sets of k consecutive information symbols although it can be generalized to a general form this precoding scheme may be able to remove the spectral nulls of an isi channel without knowing the isi channel when no zero is inserted between each two sets of k consecutive information symbols and only each k consecutive symbols are blocked together we obtain vofdm systems both theoretical performance analysis and simulation results are presented finally we compare the combination of the vofdm systems and the unitary matrix modulation with the conventional ofdm systems and the phase shift keying modulation where both differential noncoherent and coherent modulations and demodulations are considered

2 generation of simple lie algebras and free dense subgroups of algebraic groups abstract we construct generating pairs of simple lie algebras in characteristic zero we apply this construction to exhibit infinite series of 2 generator zariski dense subgroups that are free of rank 2 of the simple algebraic groups sl n c sp n c g 2 c

optimal orthogonal precoding for power leakage suppression in dft based systems a solution to the power leakage minimization problem in discrete fourier transform dft based communication systems is presented in a conventional dft based system modulated subcarriers exhibit high sidelobe levels which leads to significant out of band power leakage existing techniques found in the literature either do not achieve sufficient sidelobe suppression or suffer from significant spectral efficiency loss precoding can be seen as a general linear processing method for power leakage reduction however how to design the optimal linear precoder is still an open problem in this paper the power leakage suppression is first treated as a matrix frobenius norm minimization problem and then the optimal orthogonal precoding matrix design for the power leakage suppression is proposed based on singular value decomposition svd by further exploiting the extra degrees of freedom in the precoding matrix two kinds of optimized precoding matrices one with multi carrier property and the other with single carrier property are developed to take the advantages of orthogonal frequency division multiplexing ofdm and single carrier frequency division multiple access sc fdma respectively simulation results show that both the multi carrier and the single carrier precoding schemes achieve significant power leakage suppression and have similar peak to average power ratio papr and bit error rate ber to those of ofdm and sc fdma systems respectively

analysis and design of short block ofdm spreading matrices for use on multipath fading channels we consider the use of block spreading in a multicarrier system to gain diversity advantage when employed over multipath fading channels the main idea is to split the full set of subcarriers into smaller blocks and spread the data symbols across these blocks via unitary spreading matrices in order to gain multipath diversity across each block at the receiver we pose the problem of designing the spreading matrix as a finite dimensional optimization problem in which the asymptotic error is minimized this formulation allows us to find explicit solutions for the optimal spreading matrices the performance is validated for the uncoded channel as well as for the coded channel employing turbo iterative decoding we further demonstrate that suboptimal linear complexity equalization strategies for spread orthogonal frequency division multiplexing ofdm do not gain any diversity advantage over traditional diagonal ofdm

the subalgebras of the rank two symplectic lie algebra abstract the semisimple subalgebras of the rank 2 symplectic lie algebra sp 4 c are well known and we recently classified its levi decomposable subalgebras in this article we classify the solvable subalgebras of sp 4 c up to inner automorphism this completes the classification of the subalgebras of sp 4 c more broadly speaking in completing the classification of the subalgebras of sp 4 c we have completed the classification of the subalgebras of the rank 2 semisimple lie algebras

the euclidean algebra in rank 2 classical lie algebras we classify the embeddings of the euclidean algebra e 2 into the rank 2 semisimple classical lie algebras the classifications are up to inner automorphism we also examine the finite dimensional irreducible representations of the rank 2 semisimple classical lie algebras restricted to e 2 with respect to various embeddings all lie algebras and representations are over the complex numbers

time limited orthogonal multicarrier modulation schemes time limited orthogonal tlo multicarrier modulation mcm schemes with waveform shaping are investigated the waveform shaped scheme with no frame overlap is spectrally inefficient an improved scheme is proposed and it is shown that this scheme allows a certain amount of overlap between adjacent frames without destroying the orthogonality the scheme is therefore spectrally efficient the improved tlo mcm scheme can be regarded as a time domain dual form of chang s band limited orthogonal mcm 1966

the aluffi algebra of the jacobian of points in projective space torsion freeness abstract the algebra in the title has been introduced by p aluffi let j i be ideals in the commutative ring r the embedded aluffi algebra of i on r j is an intermediate graded algebra between the symmetric algebra and rees algebra of the ideal i j over r j a pair of ideals has been dubbed an aluffi torsion free pair if the surjective map of the aluffi algebra of i j onto the rees algebra of i j is injective in this paper we focus on the situation where j is the ideal of points in general linear position in projective space and i is its jacobian ideal

levi decomposable algebras in the classical lie algebras abstract we examine embeddings of an important class of levi decomposable algebras into the classical lie algebras in particular we classify the embeddings of a n c n 1 b n c 2 n 1 c n c 2 n and d n c 2 n into the complex simple lie algebras a n 1 b n 1 c n 1 and d n 1 respectively up to inner automorphism

orthogonally multiplexed orthogonal amplitude modulation family a family of coherent orthogonally multiplexed orthogonally amplitude modulated omoam signals is presented the omoam signal is constituted by orthogonally multiplexing ai component signals each constructed by a data chosen group of l orthogonal pulse amplitude modulated basis signals a generalized signal format is proposed to model the omoam signal in a unified way that the family contains not only classical orthogonally multiplexed modulations as special embodiments but also a multitude of new modulations a generalized optimum receiver for coherently demodulating omoam signals is developed and analyzed in terms of the bit error probability for the additive white gaussian noise channel the spectral characteristics of the omoam signals constructed from various time limited and band limited basis sets are studied in terms or the fractional out of band power containment several general trends of error and spectral performance characteristics are exploited

spectral precoding for cyclic prefixed ofdma with interleaved subcarrier allocation spectrally precoded orthogonal frequency division multiple access ofdma using cyclic prefix and interleaved subcarrier allocation iofdma is a useful rectangularly pulsed ofdma signaling format for it exploits high spectral compactness and frequency diversity characteristics in this paper two new spectral precoders of the largest precoding rate are developed for iofdma in order to provide improved spectral compactness and reduce implementation complexity respectively specifically a new correlative precoder is developed and shown to minimize the dominant spectral coefficient among all correlative precoders of the largest precoding rate and thus can construct iofdma signals providing extremely high spectral compactness besides a multiple stage spectral precoding technique is proposed to construct a low complexity orthogonally precoded iofdma with power spectral sidelobes decaying as f 2l 2 for l 1 where l is the number of stages the corresponding orthogonally precoded iofdma signals conveying independent zero mean data are shown to provide the same power spectrum as existing orthogonally precoded iofdma signals of the largest precoding rate while requiring much less complexity

aluffi torsion free ideals abstract a special class of algebras which are intermediate between the symmetric and the rees algebras of an ideal was introduced by p aluffi in 2004 to define characteristic cycle of a hypersurface parallel to conormal cycle in intersection theory these algebras are recently investigated by a nasrollah nejad and a simis who named them aluffi algebras for a pair of ideals j i of a commutative ring r the aluffi algebra of i j is called aluffi torsion free if it is isomorphic to the rees algebra of i j in this paper ideals generated by 2 minors of a 2 n matrix of linear forms and also edge ideals of graphs are considered and some conditions are presented which are equivalent to aluffi torsion free property of them