Theoretical Mean Square Research Articles

Performance Analyses of OFDM–CDMA Receivers in Multipath Fading Channels

Orthogonal frequency-division multiplexing (OFDM) is a promising scheme for multicarrier (MC) transmission. The combination of OFDM and code-division multiple access (CDMA) which is referred to as OFDM-CDMA, has recently attracted much research interest in wireless communications. In this paper, we evaluate the downlink performance for two forms of adaptive OFDM-CDMA receivers in multipath fading channels: 1) MC-CDMA and 2) MC-direct sequence (DS)-CDMA. We propose theoretical minimum mean square errors (MMSEs) for MC-CDMA and MC-DS-CDMA to compare the performances in different situations. Moreover, one drawback of OFDM schemes is the rate reduction due to the cyclic prefix (CP) overhead, which significantly affects the channel utilization in MC-DS-CDMA systems. We propose adaptive receiver structures with both subcarrier- and code-interval equalizations to improve the performance of MC-DS-CDMA systems with shorter or no CP. Simulation results demonstrate the effectiveness of the proposed receivers and the correctness of the theoretical derivations.

On the Optimality of the Null Subcarrier Placement for Blind Carrier Offset Estimation in OFDM Systems

Liu and Tureli proposed a blind carrier frequency offset (CFO) estimation method for orthogonal frequency-division multiplexing (OFDM) systems, making use of null subcarriers. The optimal subcarrier placement that minimizes the Cramer-Rao bound (CRB) of the CFO estimation was reported by Ghogho. In this paper, we study the optimality of the null subcarrier placement from another perspective. We first show that the SNR of the CFO estimation using null subcarriers is a function of the null subcarrier placement. We then formulate the CFO-SNR optimization for the null subcarrier placement as a convex optimization problem for small CFO values and derive the optimal placement when the number of subcarriers is a multiple of the number of null subcarriers. In addition, we show that the SNR-optimal null subcarrier placement also minimizes the theoretical mean square error in the high SNR region. When the number of subcarriers is not a multiple of the number of null subcarriers, we propose a heuristic method for the null subcarrier placement that still achieves good performance in the CFO estimation. We also discuss the optimality of the null subcarrier placement in practical OFDM systems, where guard bands are required at both ends of the spectrum.

Average Performance Analysis of Circular and Hyperbolic Geolocation

A comparative performance analysis of four geolocation methods in terms of their theoretical root mean square positioning errors is provided. Comparison is established in two different ways: strict and average. In the strict type, methods are examined for a particular geometric configuration of base stations (BSs) with respect to mobile position, which determines a given noise profile affecting the respective time-of-arrival (TOA) or time-difference-of-arrival (TDOA) estimates. In the average type, methods are evaluated in terms of the expected covariance matrix of the position error over an ensemble of random geometries, so that comparison is geometry independent. Exact semianalytical equations and associated lower bounds (depending solely on the noise profile) are obtained for the average covariance matrix of the position error in terms of the so-called information matrix specific to each geolocation method. Statistical channel models inferred from field trials are used to define realistic prior probabilities for the random geometries. A final evaluation provides extensive results relating the expected position error to channel model parameters and the number of base stations.

Blind identification of autoregressive system using chaos

The problem of identifying an autoregressive (AR) model using chaos is investigated here. Based on the Cramer-Rao bound (CRB) analysis, it is proved here that when chaos is used to drive an AR system, identification using only the output signal can be as good as that based on using both input and output signals, that is, blind identification is equivalent to nonblind identification. A deterministic maximum likelihood (ML) is, therefore, developed to blindly identify an AR system driven by chaos. Combined with the global search technique genetic algorithm (GA), the proposed GA-ML method is found to achieve the optimal identification performance imposed by the CRB. The theoretical mean square error (MSE) performance of the proposed GA-ML method is derived, and the result is validated using computer simulations. Compared to conventional methods based on white Gaussian driving signal, the chaos approach is shown to have superior performance. The improvement is proved to be the result of the positive and finite Lyapunov exponent of the chaotic signal. The proposed chaos identification method is applied to blind equalization of a spread spectrum (SS) communication system where chaos is used to modulate the information signal. Computer simulations show that the proposed chaos approach has a satisfactory equalization performance even under strong channel effects.

Decision-feedback interference suppression in CDMA systems: a ML-based semiblind approach

This paper addresses the problem of interference suppression in direct sequence code division multiple access systems. We propose a novel semiblind decision feedback (DF) receiver based on the maximum likelihood principle that simultaneously exploits the transmission of training sequences and the statistical information of the unknown transmitted symbols. Both iterative and adaptive implementations of the proposed receiver, derived within the framework of the expectation maximization algorithm, are presented. Computer simulations show that the resulting multiuser detectors attain practically the same performance as the theoretical DF minimum mean square error receiver.

Modified leaky LMS algorithm for channel estimation in DS-CDMA systems

A simple adaptive least mean square (LMS) type algorithm for channel estimation is developed based on certain modifications to finite-impulse response (FIR) Wiener filtering. The proposed algorithm is nearly blind since it does not require any training sequence or channel statistics, and it can be implemented using only noise variance knowledge. A condition guaranteeing the convergence of the algorithm and theoretical mean square error (MSE) values are also derived. Computer simulation results demonstrate that the proposed algorithm can yield a smaller MSE than existing techniques, and that its performance is close to that of optimal Wiener filtering.

Bandwidth and rise time calculations for digital multimode fiber-optic data links

The use of multimode fiber in digital fiber-optic data links requires simple and accurate procedures for the calculation of data line component bandwidth and rise time responses. The author investigates source/fiber/detector interactions, to develop a simple model for multimode fiber system information capacity. Simplified expressions for the baseband impulse and frequency responses of each component are given along with relationships between the theoretical impulse response root mean square (RMS) width and the component rise time or bandwidth. The application of the central limit theorem to the system yields expressions for the composite system rise time and bandwidth which contain correction factors to those that would be obtained using the normal Gaussian assumptions.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The analysis of molecular dynamics with a range of microwave/far infrared spectra

A Mori approximant for zero-THz absorptions of dipolar solutes is tested thoroughly with several examples. A number of points emerge from the data correlation. (i)It is advantageous to analyse the complicated theoretical expressions before attempting a best fit analysis. Curve matching should be performed in both time and frequency domains. (ii)The theory is sufficient at short and long times but the evolution at intermediate times is not followed satisfactorily. This shows up clearly in the 10–50 cm-1 region of the far infrared. (iii)The far infrared peak frequency is not related straightforwardly to the theoretical mean square torque, but via parameters grouped about 2·6 for the two dozen or so systems studied. (iv)The measured Debye relaxation times (this work) are reproduced theoretically from the far infrared to within about 30 per cent of their values for most solutes, but progressively poorer results are obtained as the molecular size increases, and as the molecules become more anisotropic. (v)It is essential to consider in detail the effects of collision-induced absorptions and other mechanisms of permanent dipole enhancement. The failure of the Gordon sum rule cannot be attributed solely to this cause and rototranslational interaction probably plays a significant role.

Optical-model potential in finite nuclei from Reid's hard core interaction

Starting from the Brueckner-Hartree-Fock approximation and Reid's hard core nucleon-nucleon interaction, we calculate and parametrize the energy---and the density---dependence of the isoscalar, isovector, and Coulomb components of the complex optical-model potential in infinite nuclear matter, for energies up to 160 MeV. We then construct the optical-model potential in a finite nucleus. In a first step, we adopt a local density approximation which implies that the value of the complex potential at each point of the nucleus is the same as in a uniform medium with the local density. We compute the corresponding volume integrals per nucleon and mean square radii of the real and of the imaginary parts of the optical-model potential, in particular for protons scattered by $^{12}\mathrm{C}$, $^{16}\mathrm{O}$, $^{27}\mathrm{Al}$, $^{40}\mathrm{Ca}$, $^{58}\mathrm{Ni}$, $^{120}\mathrm{Sn}$, and $^{208}\mathrm{Pb}$. We compare these results with a compilation of empirical values and find that the calculated and experimental volume integrals are in good agreement but that the theoretical mean square radii are too small. We ascribe this discrepancy to the fact that our local density approximation does not include accurately the effect in a nonuniform medium of the range of the effective interaction. We include this range in a semiphenomenological way suggested by the Hartree approximation. With a reasonable value for this range parameter, which is the only one occurring in our work, good agreement is obtained between the theoretical and the empirical values of the volume integrals and mean square radii of the real and, to a lesser extent, of the imaginary parts of the optical-model potential, for mass numbers $12\ensuremath{\le}A\ensuremath{\le}208$ and for energies $E$ up to 160 MeV. Our results are given in analytic form and can thus be used in analyses of experimental data. We also discuss the difference between the optical-model potentials for protons and for neutrons.[NUCLEAR REACTIONS Calculation of the complex optical-model potential for finite nuclei from Reid's hard core interaction; comparison with a compilation of empirical potentials.]

Polystyrenes of known structure: Part 3. Polymers with long-chain branching

The melt- and solution viscosity behaviour of some polystyrenes with long-chain branching is described. These polymers, which were prepared by reacting chloromethylated polystyrene with potassium polystyryl, are distinguishable from the comb-shaped polystyrenes previously described in having longer branches and lower branching frequencies. (The number-average molecular weight of the branches is greater than 4.6 × 10 4 and in some cases greater than that of the backbone.) Their low shear melt viscosities and intrinsic viscosities in tetrahydrofuran and cyclohexane are above those of the backbone polymer and increase as the branch length increases for a given branching frequency, the rate of increase being greater the lower the branching frequency. In each solvent the intrinsic viscosities of the branched polymers are below those of linear polymers of comparable molecular weights. The melt viscosities of the majority of the branched polymers are also below those of linear polymers of the same molecular weights, but for a few, those with the longest branches in the series with the lowest branching frequency, the opposite is true. Another outcome of this work is the finding that for these branched polymers the low-shear melt viscosities and the intrinsic viscosities in solution are given by: viscosity ∝〈S 2 0〉 a where 〈S 2 0〉 is the theoretical mean square unperturbed radius of gyration. The exponents a for the branched polymers in the melt and in tetrahydrofuran differ from those for linear polystyrenes for which a similar relation holds, but are about equal for branched and linear polystyrenes in cyclohexane. The behaviour shown by the branched polystyrenes described here is considered in relation to the behaviour of the comb-shaped polystyrenes reported earlier and that of the branched polystyrenes studied by Decker and by Fujimoto et al.

Theoretical Mean-Square Displacements for Surface Atoms in Face-Centered Cubic Lattices with Applications to Nickel

The mean-square displacements of atoms in a face-centered cubic crystal have been calculated as a function of distance from a free surface using the harmonic approximation in the high-temperature limit. The procedure is based on the inversion of the dynamical matrix. Calculations have been made for the (100), (110), and (111) surfaces using a nearest-neighbor central-force model for crystals up to 30 layers thick. The force constants for surface atoms are assumed to be the same as those in the interior. The mean-square displacements increase monotonically from the middle of the crystal to the surface. Anisotropy of the meansquare displacement components is found for the surface atoms in each plane considered. The theoretical results are compared with recent low-energy electron-diffraction data on nickel single crystals.