Closed-form solution for underground impedance calculations

Recently, a closed-form solution for the self-impedance of a conductor directly buried in the earth has been conjectured through analogy with other closed-form approximations for overhead conductors. This letter provides a mathematical development for the equation and extends the results to the more general case of a conductor contained in a dielectric tunnel deep within a medium of arbitrary relative permeability. The derivation shows the mathematical approximations which are needed in obtaining the desired result and introduces a new simple, yet surprisingly accurate approximation for the ratio of Kelvin functions which is superior to the one-term approximation currently in use.     

Closed-form expressions for interconnection delay, coupling, andcrosstalk in VLSIs

A closed-form formula for a waveform of the RC interconnection line with practical boundary conditions is derived. Expressions are also derived for the voltage slope and transition time of the RC interconnection and for coupling capacitance and crosstalk voltage height, which can be used in VLSI designs. Using the expressions, the optimum linewidth that minimizes RC delay and the trend of RC delay in the scaled-down VLSIs are discussed     

Closed-form expressions for distribution of sum of exponentialrandom variables

In many systems which are composed of components with exponentially distributed lifetimes, the system failure time can be expressed as a sum of exponentially distributed random variables. A previous paper mentions that there seems to be no convenient closed-form expression for all cases of this problem. This is because in one case the expression involves high-order derivatives of products of multiple functions. The authors prove a simple intuitive multi-function generalization of the Leibnitz rule for high-order derivatives of products of two functions and use this to simplify this expression, thus giving a closed form solution for this problem. They similarly simplify the state-occupancy probabilities in general Markov models     

Closed-form solution for parametric second Stokes generation inRaman amplifiers

The efficiency of a first Stokes Raman amplifier can be seriously reduced by the generation of a second Stokes beam. The dominating process for this generation is often a Raman four-wave mixing interaction which couples the pump and second Stokes beams. A one-dimensional model for this effect has a closed-form solution, simply described in terms of an equivalent input, under conditions where high first Stokes conversion efficiency is possible. Excellent agreement with numerical integration results has been obtained. Use of the model for maximizing conversion efficiency of pump beams with large temporal or spatial intensity nonuniformity is described, with an example worked out for a triangular pulse shape     

Closed-form solution for circle pose estimation using binocular stereo vision

A simple method for pose estimation of a circle, with known circle radius, on the basis of binocular stereo vision is presented. The method is based on the projective equation of a circle, into which the stereo vision constraints are incorporated. The estimated pose parameters are compared with the ground truth and excellent performance is reported.     

Closed-form solution for a line source at the edge of anisorefractive wedge

A closed-form solution is given for the radiation of an electric or magnetic line source located at the edge of an isorefractive wedge. The solution is valid for any wedge angle if the line source is isotropic. For certain nonisotropic line sources, the solution is valid only if the wedge angle is commensurable to π radians     

Closed-form expressions for the outage and ergodic Shannon capacity of MIMO MRC systems

Transmit-beamforming (TB) over multiple-input multiple-output (MIMO) fading channels steers the transmit power in the receiver's direction, so as to maximize the output signal-to-noise ratio (SNR) after maximal ratio combining (MRC) at the receiver. This letter proposes a simple algorithm that allows evaluating an exact and tractable expression for the probability density function of the SNR at the output of the TB receiver, subject to Rayleigh fading. The latter enables the derivation of closed-form expressions for the outage and ergodic capacity of MIMO MRC systems under Rayleigh fading, thereby avoiding the need for time-consuming numerical integrations or Monte Carlo simulations.     

Closed-form analytical results for interference rejection ofnonlinear prediction filters in DS-SS systems

Closed-form analytical expressions for narrow-band interference rejection of nonlinear prediction filters in direct-sequence spread-spectrum (DS-SS) systems are established. It is shown that nonlinear prediction filters outperform linear ones     

Correlation of electromigration lifetime distribution to failure mode in dual Damascene Cu/SiLK interconnects

The electromigration cumulative percent lifetime probability of dual Damascene Cu/SiLK interconnects was fitted using three, individual lognormal functions where the functional populations were grouped by void growth location determined from focused ion beam failure analysis of all 54 of the stressed structures. The early, first mode failures were characterized by small voids in the bottom of the vias. The intermediate mode failures had voids in the line and via bottom while the late mode failures had voids that formed in the line only. The three, individual lognormal functions provided good fits of the data. Failure mode population separation using comprehensive failure analysis suggested that only the first mode failures should be used in the prediction of the chip design current.     

The solution of the general equation for public key distribution systems (Corresp.)

A generalization of the public key distribution is derived. It is shown that the public key of any two members must obey a functional equation, which can be solved in a closed mathematical form.     

Closed-form BER results for multiple-chip-rate CDMA systems based on the simplified improved gaussian approximation

We consider very general code-division-multiple- access (CDMA) systems, namely multiple-chip-rate CDMA systems, where signals can be transmitted at different chip rates, carrier frequencies, processing gains, and transmitted powers to satisfy the given quality of service (QoS) requirements. Also, nonzero and possibly different carrier frequency offsets are assumed for different users. For these systems, a closed-form bit error rate (BER) expression is derived based on the simplified improved Gaussian approximation. Numerical result demonstrates that the proposed method provides much more accurate BER values compared to the standard Gaussian approximation.     

Randomized cyclic delay code for cooperative communication systems

We deal here with distributed cooperative communication systems in which a single source transmits its information with the help of multiple relays to a destination. Specifically, we consider decode and forward relay networks based on orthogonal frequency division multiplexing (OFDM). Most previous work needs a priori information for antenna allocation to obtain cooperative diversity advantages. We propose a simple method that does not require additional information in order to coordinate relay transmission. Our main proposal is to retransmit randomly cyclic-shifted sequences of the received symbol at relays. Simulation results verify that full gain in diversity is achieved when the number of subcarriers is sufficiently large.     

Adaptive observer for systems with pure time delay

This note is concerned with the application of adaptive techniques for simultaneous parameter identification and state estimation to the design of an adaptive observer for systems having unknown pure time delay and parameters.     

Analysis of MUSIC-based delay estimators for direct-sequencecode-division multiple-access systems

Most receiver designs for asynchronous direct-sequence code-division multiple-access (DS-CDMA) systems exploit timing information to simultaneously detect the desired signal and suppress the interference. In this paper, a previously proposed MUSIC delay estimation algorithm is considered which requires no initial information and no exhaustive search of the delays. Based on a Taylor series expansion, approximations of the first and second moments of the delay estimation error are derived for this MUSIC algorithm. The analysis is alternative and further to that previously performed     

Closed-form design and efficient implementation of variable digital filters with simultaneously tunable magnitude and fractional delay

This paper proposes a closed-form solution for designing variable one-dimensional (1-D) finite-impulse-response (FIR) digital filters with simultaneously tunable magnitude and tunable fractional phase-delay responses. First, each coefficient of a variable FIR filter is expressed as a two-dimensional (2-D) polynomial of a pair of parameters called spectral parameters; one is for independently tuning the cutoff frequency of the magnitude response, and the other is for independently tuning fractional phase-delay. Then, the closed-form error function between the desired and actual variable frequency responses is derived without discretizing any design parameters such as the frequency and the two spectral parameters. Finally, the optimal solution for the 2-D polynomial coefficients can be easily determined through minimizing the closed-form error function. We also show that the resulting variable FIR filter can be efficiently implemented by generalizing Farrow structure to our two-parameter case. The generalized Farrow structure requires only a small number of multiplications and additions for obtaining any new frequency characteristic, which is particularly suitable for high-speed tuning.     

On the quasi-stationary distribution of the residual lifetime

This work establishes the sufficiency conditions for the existence of the conditional limit distribution of the residual lifetime for arbitrary systems. Explicit expressions are derived     

Reconfigurable antenna solution for MIMO-OFDM systems

A reconfigurable microstrip dipole antenna solution for multiple-input multiple-output (MIMO) communication systems making use of orthogonal frequency division multiplexing (OFDM) is presented. When applied to closely spaced antenna arrays, this method can increase link capacity. The benefits of this novel antenna solution are demonstrated by channel capacity measurements taken in an indoor environment with a 2/spl times/2 MIMO system.     

Angle and delay estimation of space-time channels for TD-CDMA systems

In mobile communications the antenna arrays make it possible to estimate the path delay, angle of arrival (or angle), and amplitude for the multipath propagation channel. This paper considers the problem of joint angle and delay estimation (JADE) in a time-division code-division multiple access system. The angle/delay estimation is made from multiple slots by exploiting the angle/delay invariance of the channel regardless of the fast faded amplitude variation (i.e., angle/delay is assumed quasistatic). JADE can be approximated by methods that estimate the frequencies of the two-dimensional complex sinusoids where the faded amplitudes act as sources. The shift invariance method (JADE-ESPRIT) is chosen for its capacity to pair delay and angle for each path and each user. The consistency of JADE-ESPRIT for a large enough number of slots guarantees the feasibility of the method for spatially correlated noise. The performance of the JADE method for channel estimation is evaluated analytically and numerically in propagation environments with increasing complexity.     

室内分布系统TD-SCDMA改造方案

从TD SCDMA室内分布系统特点出发，得出了TD SCDMA室内分布系统建设的基本原则，分析了TD SCDMA与其他2G系统共享室内分布系统的可能性，从而提出了微型、小型、中型和大型四种典型2G颁布系统的ID SCDMA改造方案。     

All-digital multipoint adaptive delay compensation circuit for lowskew clock distribution

The authors describe an all-digital circuit for automatically controlling skew in the distribution of a clock or data signal over a single line. The circuit derives a compensating delay for any location such that a signal applied at one end emerges at the same global time at all sites. This is an alternative to delay-equalised hierarchical trees for use in large ICs, computers, and digital switches. A 3 μm CMOS prototype at eight sites spread over 16 m shows adaptive skew control to within +/- 1.5 primitive buffer delays of the process employed. A novel technique for accommodating metastability is involved in the design