Low-delay, high-rate, non-square STBCs from scaled complex orthogonal designs

Space-time block codes (STBCs) obtained from non-square complex orthogonal designs are bandwidth efficient compared to those from square real/complex orthogonal designs for colocated coherent MIMO systems and has other applications in (i) non-coherent MIMO systems with non-differential detection, (ii) Space-Time-Frequency codes for MIMO-OFDM systems and (iii) distributed space-time coding for relay channels. Liang (IEEE Trans. Inform. Theory, 2003) has constructed maximal rate non-square designs for any number of antennas, with rates given by [(a+1)/(2a)] when number of transmit antennas is 2a-1 or 2a. However, these designs have large delays. When large number of antennas are considered this rate is close to 1/2. Tarokh et al (IEEE Trans. Inform. Theory, 1999) have constructed rate 1/2 non-square CODs using the rate-1 real orthogonal designs for any number of antennas, where the decoding delay of these codes is less compared to the codes constructed by Liang for number of transmit antennas more than 5. In this paper, we construct a class of rate-1/2 codes for arbitrary number of antennas where the decoding delay is reduced by 50% when compared with the rate-1/2 codes given by Tarokh et al. It is also shown that even though scaling the variables helps to lower the delay it can not be used to increase the rate.

Rheology of dense sheared granular flows

Rapid granular flows are defined as flows in which the time scales for the particle interactions are small compared to the inverse of the strain rate, so that the particle interactions can be treated as instantaneous collisions. We first show, using Discrete Element simulations, that even very dense flows of sand or glass beads with volume fraction between 0.5 and 0.6 are rapid granular flows. Since collisions are instantaneous, a kinetic theory approach for the constitutive relations is most appropriate, and we present kinetic theory results for different microscopic models for particle interaction. The significant difference between granular flows and normal fluids is that energy is not conserved in a granular flow. The differences in the hydrodynamic modes caused by the non-conserved nature of energy are discussed. Going beyond the Boltzmann equation, the effect of correlations is studied using the ring kinetic approximation, and it is shown that the divergences in the viscometric coefficients, which are present for elastic fluids, are not present for granular flows because energy is not conserved. The hydrodynamic model is applied to the flow down an inclined plane. Since energy is not a conserved variable, the hydrodynamic fields in the bulk of a granular flow are obtained from the mass and momentum conservation equations alone. Energy becomes a relevant variable only in thin 'boundary layers' at the boundaries of the flow where there is a balance between the rates of conduction and dissipation. We show that such a hydrodynamic model can predict the salient features of a chute flow, including the flow initiation when the angle of inclination is increased above the 'friction angle', the striking lack of observable variation of the volume fraction with height, the observation of a steady flow only for certain restitution coefficients, and the density variations in the boundary layers.

Semigroups on Frechet spaces and equations with infinite delays

In this paper, we show existence and uniqueness of a solution to a functional differential equation with infinite delay. We choose an appropriate Frechet space so as to cover a large class of functions to be used as initial functions to obtain existence and uniqueness of solutions.

On the duality between rate and power optimizations

Sequence design problems are considered in this paper. The problem of sum power minimization in a spread spectrum system can be reduced to the problem of sum capacity maximization, and vice versa. A solution to one of the problems yields a solution to the other. Subsequently, conceptually simple sequence design algorithms known to hold for the white-noise case are extended to the colored noise case. The algorithms yield an upper bound of 2N - L on the number of sequences where N is the processing gain and L the number of non-interfering subsets of users. If some users (at most N - 1) are allowed to signal along a limited number of multiple dimensions, then N orthogonal sequences suffice.

On the maximal rate of non-square STBCs from complex orthogonal designs

A Linear Processing Complex Orthogonal Design (LPCOD) is a p x n matrix epsilon, (p >= n) in k complex indeterminates x(1), x(2),..., x(k) such that (i) the entries of epsilon are complex linear combinations of 0, +/- x(i), i = 1,..., k and their conjugates, (ii) epsilon(H)epsilon = D, where epsilon(H) is the Hermitian (conjugate transpose) of epsilon and D is a diagonal matrix with the (i, i)-th diagonal element of the form l(1)((i))vertical bar x(1)vertical bar(2) + l(2)((i))vertical bar x(2)vertical bar(2)+...+ l(k)((i))vertical bar x(k)vertical bar(2) where l(j)((i)), i = 1, 2,..., n, j = 1, 2,...,k are strictly positive real numbers and the condition l(1)((i)) = l(2)((i)) = ... = l(k)((i)), called the equal-weights condition, holds for all values of i. For square designs it is known. that whenever a LPCOD exists without the equal-weights condition satisfied then there exists another LPCOD with identical parameters with l(1)((i)) = l(2)((i)) = ... = l(k)((i)) = 1. This implies that the maximum possible rate for square LPCODs without the equal-weights condition is the same as that or square LPCODs with equal-weights condition. In this paper, this result is extended to a subclass of non-square LPCODs. It is shown that, a set of sufficient conditions is identified such that whenever a non-square (p > n) LPCOD satisfies these sufficient conditions and do not satisfy the equal-weights condition, then there exists another LPCOD with the same parameters n, k and p in the same complex indeterminates with l(1)((i)) = l(2)((i)) = ... = l(k)((i)) = 1.

Effect of process parameters on transport phenomena during solidification in the presence of electromagnetic stirring

In the present work, a numerical study is performed to predict the effect of process parameters on transport phenomena during solidification of aluminium alloy A356 in the presence of electromagnetic stirring. A set of single-phase governing equations of mass, momentum, energy and species conservation is used to represent the solidification process and the associated fluid flow, heat and mass transfer. In the model, the electromagnetic forces are incorporated using an analytical solution of Maxwell equation in the momentum conservation equations and the slurry rheology during solidification is represented using an experimentally determined variable viscosity function. Finally, the set of governing equations is solved for various process conditions using a pressure based finite volume technique, along with an enthalpy based phase change algorithm. In present work, the effect of stirring intensity and cooling rate are considered. It is found that increasing stirring intensity results in increase of slurry velocity and corresponding increase in the fraction of solid in the slurry. In addition, the increasing stirring intensity results uniform distribution of species and fraction of solid in the slurry. It is also found from the simulation that the distribution of solid fraction and species is dependent on cooling rate conditions. At low cooling rate, the fragmentation of dendrites from the solid/liquid interface is more.

Unsteady MHD mixed convection flow over an impulsively stretched permeable vertical surface in a quiescent fluid

The unsteady mixed convection flow of an incompressible laminar electrically conducting fluid over an impulsively stretched permeable vertical surface in an unbounded quiescent fluid in the presence of a transverse magnetic field has been investigated. At the same time, the surface temperature is suddenly increased from the surrounding fluid temperature or a constant heat flux is suddenly imposed on the surface. The problem is formulated in such a way that for small time it is governed by Rayleigh type of equation and for large time by Crane type of equation. The non-linear coupled parabolic partial differential equations governing the unsteady mixed convection flow under boundary layer approximations have been solved analytically by using the homotopy analysis method as well as numerically by an implicit finite difference scheme. The local skin friction coefficient and the local Nusselt number are found to decrease rapidly with time in a small time interval and they tend to steady-state values for t* >= 5. They also increase with the buoyancy force and suction, but decrease with injection rate. The local skin friction coefficient increases with the magnetic field, but the local Nusselt number decreases. There is a smooth transition from the unsteady state to the steady state. (C) 2010 Elsevier Ltd. All rights reserved.

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.

Boundary value problems for third-order nonlinear ordinary differential equations

In this paper, we describe how to analyze boundary value problems for third-order nonlinear ordinary differential equations over an infinite interval. Several physical problems of interest are governed by such systems. The seminumerical schemes described here offer some advantages over solutions obtained by using traditional methods such as finite differences, shooting method, etc. These techniques also reveal the analytic structure of the solution function. For illustrative purposes, several physical problems, mainly drawn from fluid mechanics, are considered; they clearly demonstrate the efficiency of the techniques presented here.

Existence and approximations of solutions to some fractional order functional integral equations

In this paper we shall study a fractional order functional integral equation. In the first part of the paper, we proved the existence and uniqueness of mile and global solutions in a Banach space. In the second part of the paper, we used the analytic semigroups theory oflinear operators and the fixed point method to establish the existence, uniqueness and convergence of approximate solutions of the given problem in a separable Hilbert space. We also proved the existence and convergence of Faedo-Galerkin approximate solution to the given problem. Finally, we give an example.

Semigroups on Frechet spaces and equations with infinite delays

In this paper, we show existence and uniqueness of a solution to a functional differential equation with infinite delay. We choose an appropriate Frechet space so as to cover a large class of functions to be used as initial functions to obtain existence and uniqueness of solutions.

Sequence design for symbol-asynchronous CDMA with power or rate constraints

Sequence design and resource allocation for a symbol-asynchronous chip-synchronous code division multiple access (CDMA) system is considered in this paper. A simple lower bound on the minimum sum-power required for a non-oversized system, based on the best achievable for a non-spread system, and an analogous upper bound on the sum rate are first summarised. Subsequently, an algorithm of Sundaresan and Padakandla is shown to achieve the lower bound on minimum sum power (upper bound on sum rate, respectively). Analogous to the synchronous case, by splitting oversized users in a system with processing gain N, a system with no oversized users is easily obtained, and the lower bound on sum power (upper bound on sum rate, respectively) is shown to be achieved by using N orthogonal sequences. The total number of splits is at most N - 1.