A rate-one full-diversity low-complexity space-time-frequency block code (STFBC) for 4-Tx MIMO-OFDM

It is known that by employing space-time-frequency codes (STFCs) to frequency selective MIMO-OFDM systems, all the three diversity viz spatial, temporal and multipath can be exploited. There exists space-time-frequency block codes (STFBCs) designed using orthogonal designs with constellation precoder to get full diversity (Z.Liu, Y.Xin and G.Giannakis IEEE Trans. Signal Processing, Oct. 2002). Since orthogonal designs of rate one exists only for two transmit antennas, for more than two transmit antennas STFBCs of rate-one and full-diversity cannot be constructed using orthogonal designs. This paper presents a STFBC scheme of rate one for four transmit antennas designed using quasi-orthogonal designs along with co-ordinate interleaved orthogonal designs (Zafar Ali Khan and B. Sundar Rajan Proc: ISIT 2002). Conditions on the signal sets that give full-diversity are identified. Simulation results are presented to show the superiority of our codes over the existing ones.

A systematic design of high-rate full-diversity space-frequency codes for MIMO-OFDM systems

This paper presents a systematic construction of high-rate and full-diversity space-frequency block codes for MIMO-OFDM systems. While all prior constructions offer only a maximum rate of one complex symbol per channel use, our construction yields rate equal to the number of transmit antennas and simultaneously achieves full-diversity. The proposed construction works for arbitrary number of transmit antennas and arbitrary channel power delay profile. A key step in this construction is the generalization of the stacked matrix code design criteria given by Bolcskei et.al., (IEEE WCNC 2000). Explicit equivalence of our generalized code design criteria with the Hadamard-product based criteria of W. Su et.al., (lEEE Trans. Sig. Proc. Nov 2003) is established and new high-rate codes are constructed using our criteria.

A unified construction of space-time codes with optimal rate-diversity tradeoff

The problem of constructing space-time (ST) block codes over a fixed, desired signal constellation is considered. In this situation, there is a tradeoff between the transmission rate as measured in constellation symbols per channel use and the transmit diversity gain achieved by the code. The transmit diversity is a measure of the rate of polynomial decay of pairwise error probability of the code with increase in the signal-to-noise ratio (SNR). In the setting of a quasi-static channel model, let n(t) denote the number of transmit antennas and T the block interval. For any n(t) <= T, a unified construction of (n(t) x T) ST codes is provided here, for a class of signal constellations that includes the familiar pulse-amplitude (PAM), quadrature-amplitude (QAM), and 2(K)-ary phase-shift-keying (PSK) modulations as special cases. The construction is optimal as measured by the rate-diversity tradeoff and can achieve any given integer point on the rate-diversity tradeoff curve. An estimate of the coding gain realized is given. Other results presented here include i) an extension of the optimal unified construction to the multiple fading block case, ii) a version of the optimal unified construction in which the underlying binary block codes are replaced by trellis codes, iii) the providing of a linear dispersion form for the underlying binary block codes, iv) a Gray-mapped version of the unified construction, and v) a generalization of construction of the S-ary case corresponding to constellations of size S-K. Items ii) and iii) are aimed at simplifying the decoding of this class of ST codes.

BER analysis of space-time block codes from generalized complex orthogonal designs for M-PSK

In this paper, we present an analysis for the bit error rate (BER) performance of space-time block codes (STBC) from generalized complex orthogonal designs for M-PSK modulation. In STBCs from complex orthogonal designs (COD), the norms of the column vectors are the same (e.g., Alamouti code). However, in generalized COD (GCOD), the norms of the column vectors may not necessarily be the same (e.g., the rate-3/5 and rate-7/11 codes by Su and Xia in [1]). STBCs from GCOD are of interest because of the high rates that they can achieve (in [2], it has been shown that the maximum achievable rate for STBCs from GCOD is bounded by 4/5). While the BER performance of STBCs: from COD (e.g., Alamouti code) can be simply obtained from existing analytical expressions for receive diversity with the same diversity order by appropriately scaling the SNR, this can not be done for STBCs from GCOD (because of the unequal norms of the column vectors). Our contribution in this paper is that we derive analytical expressions for the BER performance of any STBC from GCOD. Our BER analysis for the GCOD captures the performance of STBCs from COD as special cases. We validate our results with two STBCs from GCOD reported by Su and Xia in [1], for 5 and 6 transmit antennas (G(5) and G(6) in [1]) with rates 7/11 and 3/5, respectively.

Parallel and antiparallel aggregation of alpha-helices. Crystal structures of two apolar decapeptides X-Trp-Ile-Ala-Aib-Ile-Val-Aib-Leu-Aib-Pro-OMe (X = Boc, Ac)

An apolar helical decapeptide with different end groups, Boc- or Ac-, crystallizes in a completely parallel fashion for the Boc-analog and in an antiparallel fashion for the Ac-analog. In both crystals, the packing motif consists of rows of parallel molecules. In the Boc-crystals, adjacent rows assemble with the helix axes pointed in the same direction. In the Ac-crystals, adjacent rows assemble with the helix axes pointed in opposite directions. The conformations of the molecules in both crystals are quite similar, predominantly alpha-helical, except for the tryptophanyl side chain where chi 1 congruent to 60 degrees in the Boc- analog and congruent to 180 degrees in the Ac-analog. As a result, there is one lateral hydrogen bond between helices, N(1 epsilon)...O(7), in the Ac-analog. The structures do not provide a ready rationalization of packing preference in terms of side-chain interactions and do not support a major role for helix dipole interactions in determining helix orientation in crystals. The crystal parameters are as follow. Boc-analog: C60H97N11O13.C3H7OH, space group Pl with a = 10.250(3) A, b = 12.451(4) A, c = 15.077(6) A, alpha = 96.55(3) degrees, beta = 92.31(3) degrees, gamma = 106.37(3) degrees, Z = 1, R = 5.5% for 5581 data ([F] greater than 3.0 sigma(F)), resolution 0.89 A. Ac-analog: C57H91N11O12, space group P2(1) with a = 9.965(1) A, b = 19.707(3) A, c = 16.648(3) A, beta = 94.08(1), Z = 2, R = 7.2% for 2530 data ([F] greater than 3.0 sigma(F)), resolution 1.00 A.

Signal set design for full-diversity low-decoding-complexity differential scaled-unitary STBCs

The problem of designing high rate, full diversity noncoherent space-time block codes (STBCs) with low encoding and decoding complexity is addressed. First, the notion of g-group encodable and g-group decodable linear STBCs is introduced. Then for a known class of rate-1 linear designs, an explicit construction of fully-diverse signal sets that lead to four-group encodable and four-group decodable differential scaled unitary STBCs for any power of two number of antennas is provided. Previous works on differential STBCs either sacrifice decoding complexity for higher rate or sacrifice rate for lower decoding complexity.

BER analysis of space-time block codes from generalized complex orthogonal designs for M-PSK

In this paper, we present an analysis for the bit error rate (BER) performance of space-time block codes (STBC) from generalized complex orthogonal designs for M-PSK modulation. In STBCs from complex orthogonal designs (COD), the norms of the column vectors are the same (e.g., Alamouti code). However, in generalized COD (GCOD), the norms of the column vectors may not necessarily be the same (e.g., the rate-3/5 and rate-7/11 codes by Su and Xia in [1]). STBCs from GCOD are of interest because of the high rates that they can achieve (in [2], it has been shown that the maximum achievable rate for STBCs from GCOD is bounded by 4/5). While the BER performance of STBCs: from COD (e.g., Alamouti code) can be simply obtained from existing analytical expressions for receive diversity with the same diversity order by appropriately scaling the SNR, this can not be done for STBCs from GCOD (because of the unequal norms of the column vectors). Our contribution in this paper is that we derive analytical expressions for the BER performance of any STBC from GCOD. Our BER analysis for the GCOD captures the performance of STBCs from COD as special cases. We validate our results with two STBCs from GCOD reported by Su and Xia in [1], for 5 and 6 transmit antennas (G(5) and G(6) in [1]) with rates 7/11 and 3/5, respectively.

Maan magneettikentän dipolimallin toimivuus inklinaatiojakauman perusteella

The magnetic field of the Earth is 99 % of the internal origin and generated in the outer liquid core by the dynamo principle. In the 19th century, Carl Friedrich Gauss proved that the field can be described by a sum of spherical harmonic terms. Presently, this theory is the basis of e.g. IGRF models (International Geomagnetic Reference Field), which are the most accurate description available for the geomagnetic field. In average, dipole forms 3/4 and non-dipolar terms 1/4 of the instantaneous field, but the temporal mean of the field is assumed to be a pure geocentric axial dipolar field. The validity of this GAD (Geocentric Axial Dipole) hypothesis has been estimated by using several methods. In this work, the testing rests on the frequency dependence of inclination with respect to latitude. Each combination of dipole (GAD), quadrupole (G2) and octupole (G3) produces a distinct inclination distribution. These theoretical distributions have been compared with those calculated from empirical observations from different continents, and last, from the entire globe. Only data from Precambrian rocks (over 542 million years old) has been used in this work. The basic assumption is that during the long-term course of drifting continents, the globe is sampled adequately. There were 2823 observations altogether in the paleomagnetic database of the University of Helsinki. The effect of the quality of observations, as well as the age and rocktype, has been tested. For comparison between theoretical and empirical distributions, chi-square testing has been applied. In addition, spatiotemporal binning has effectively been used to remove the errors caused by multiple observations. The modelling from igneous rock data tells that the average magnetic field of the Earth is best described by a combination of a geocentric dipole and a very weak octupole (less than 10 % of GAD). Filtering and binning gave distributions a more GAD-like appearance, but deviation from GAD increased as a function of the age of rocks. The distribution calculated from so called keypoles, the most reliable determinations, behaves almost like GAD, having a zero quadrupole and an octupole 1 % of GAD. In no earlier study, past-400-Ma rocks have given a result so close to GAD, but low inclinations have been prominent especially in the sedimentary data. Despite these results, a greater deal of high-quality data and a proof of the long-term randomness of the Earth's continental motions are needed to make sure the dipole model holds true.

Charge distribution in and electric moments of some aliphatic acids

Using the treatment of Smith et al., charge distribution in and consequently the dipole moments of several aliphatic acids have been evaluated. The electric moments of chloro (2·86 D), bromo (2·90 D), iodo (2·06 D) and trichloro (3·00 D) acetic acids have been measured in dioxan solution at 35°. The experimental values are compared with those calculated theoretically and discussed in terms of the various possible structures.

BER analysis of space-time block codes from generalized complex orthogonal designs for M-PSK

In this paper, we present an analysis for the bit error rate (BER) performance of space-time block codes (STBC) from generalized complex orthogonal designs for M-PSK modulation. In STBCs from complex orthogonal designs (COD), the norms of the column vectors are the same (e.g., Alamouti code). However, in generalized COD (GCOD), the norms of the column vectors may not necessarily be the same (e.g., the rate-3/5 and rate-7/11 codes by Su and Xia in [1]). STBCs from GCOD are of interest because of the high rates that they can achieve (in [2], it has been shown that the maximum achievable rate for STBCs from GCOD is bounded by 4/5). While the BER performance of STBCs: from COD (e.g., Alamouti code) can be simply obtained from existing analytical expressions for receive diversity with the same diversity order by appropriately scaling the SNR, this can not be done for STBCs from GCOD (because of the unequal norms of the column vectors). Our contribution in this paper is that we derive analytical expressions for the BER performance of any STBC from GCOD. Our BER analysis for the GCOD captures the performance of STBCs from COD as special cases. We validate our results with two STBCs from GCOD reported by Su and Xia in [1], for 5 and 6 transmit antennas (G(5) and G(6) in [1]) with rates 7/11 and 3/5, respectively.

On the maximal rate of (n+1) x n and (n+2) x n complex orthogonal designs

For p x n complex orthogonal designs in k variables, where p is the number of channels uses and n is the number of transmit antennas, the maximal rate L of the design is asymptotically half as n increases. But, for such maximal rate codes, the decoding delay p increases exponentially. To control the delay, if we put the restriction that p = n, i.e., consider only the square designs, then, the rate decreases exponentially as n increases. This necessitates the study of the maximal rate of the designs with restrictions of the form p = n+1, p = n+2, p = n+3 etc. In this paper, we study the maximal rate of complex orthogonal designs with the restrictions p = n+1 and p = n+2. We derive upper and lower bounds for the maximal rate for p = n+1 and p = n+2. Also for the case of p = n+1, we show that if the orthogonal design admit only the variables, their negatives and multiples of these by root-1 and zeros as the entries of the matrix (other complex linear combinations are not allowed), then the maximal rate always equals the lower bound.

Intermolecular interactions in pi -conjugated systems: Application to polyenes

A computational scheme has been developed for strongly interacting systems wherein the intermolecular interaction is introduced as a charge-induced-dipole term. Within this approximation, the model Hamiltonian is exactly solved using a valence-bond basis. The validity of the scheme has been checked by use of exact calculations on small model systems. The method has been applied to finite polyenes to study the shifts in the ground-state energies and dipole-allowed excited-state energies in the presence of neighbors. Our calculations show a red shift in the optical gap of the infinite polyene by 0.124 eV, which is rather small compared to the experimental red shift. This is traced to the larger inaccuracy in the calculated shift in the excited state. The calculated shift in the ground-state energies are more accurate and hence the method is better suited for studying the effect of intermolecular interactions on the properties of the ground state.

Photophysics of conjugated polymers: interplay between Forster energy migration and defect concentration in shaping a photochemical funnel in PPV

Recent single molecule experiments have suggested the existence of a photochemical funnel in the photophysics of conjugated polymers, like poly[2-methoxy-5-(2'-ethylhexyl)oxy-1,4-phenylenevinylene] (MEH-PPV). The funnel is believed to be a consequence of the presence of conformational or chemical defects along the polymer chain and efficient non-radiative energy transfer among different chromophore segments. Here we address the effect of the excitation energy dynamics on the photophysics of PPV. The PPV chain is modeled as a polymer with the length distribution of chromophores given either by a Gaussian or by a Poisson distribution. We observe that the Poisson distribution of the segment lengths explains the photophysics of PPV better than the Gaussian distribution. A recently proposed version of an extended particle-in-a-box' model is used to calculate the exciton energies and the transition dipole moments of the chromophores, and a master equation to describe the excitation energy transfer among different chromophores. The rate of energy transfer is assumed to be given here, as a first approximation, by the well-known Forster expression. The observed excitation population dynamics confirms the photochemical funneling of excitation energy from shorter to longer chromophores of the polymer chain. The time scale of spectral shift and energy transfer for our model polymer, with realistic values of optical parameters, is in the range of 200-300 ps. We find that the excitation energy may not always migrate towards the longest chromophore segments in the polymer chain as the efficiency of energy transfer between chromophores depends on the separation distance between the two and their relative orientation.

Exotic dielectric behavior of polar liquids

We present a report of our analysis of wave vector dependence of the static dielectric function of a dipolar liquid obtained by a microscopic calculation. At low values of the wave vector (k), the longitudinal dielectric function ϵ(k) increases with k, in contradiction to some assumptions reported in the literature. As the value of k is increased, ϵ(k) diverges at a critical value kc which depends on the value of the long wavelength static dielectric constant (ϵ0) of the liquid. The dielectric function is negative for values of k greater than kc. At large values of k, the calculated ϵ(k) fails to attain the limiting value of unity. We attribute this result to the failure of the point dipole assumption made in the evaluation of the polarization correlation function required by the theory. The behavior of ϵ(k) for the dipolar liquid is compared with that of one component plasma for which reliable results can be obtained over the full range of wave vectors. For both systems, the stability conditions are fulfilled at all values of k. A plausible explanation of this rather exotic behavior of ϵ(k) is given.

A Novel Construction of Complex Orthogonal Designs with Maximal Rate and Low-PAPR

Space-time block codes based on orthogonal designs are used for wireless communications with multiple transmit antennas which can achieve full transmit diversity and have low decoding complexity. However, the rate of the square real/complex orthogonal designs tends to zero with increase in number of antennas, while it is possible to have a rate-1 real orthogonal design (ROD) for any number of antennas.In case of complex orthogonal designs (CODs), rate-1 codes exist only for 1 and 2 antennas. In general, For a transmit antennas, the maximal rate of a COD is 1/2 + l/n or 1/2 + 1/n+1 for n even or odd respectively. In this paper, we present a simple construction for maximal-rate CODs for any number of antennas from square CODs which resembles the construction of rate-1 RODs from square RODs. These designs are shown to be amenable for construction of a class of generalized CODs (called Coordinate-Interleaved Scaled CODs) with low peak-to-average power ratio (PAPR) having the same parameters as the maximal-rate codes. Simulation results indicate that these codes perform better than the existing maximal rate codes under peak power constraint while performing the same under average power constraint.