Calibration of radars using polarimetric techniques

A method that uses the properties of rain medium itself to obtain accurate weather radar system gain calibration is discussed. This technique is based on the principle that the rainfall rate measured using absolute reflectivity (Z) and differential reflectivity ( Z_DR) is the same as that obtained from specific differential phase (K_DP). The measurements required for this technique are Z, Z_DR, and K _DP. The rainfall rate estimates obtained from Z and Z_DR are compared with the estimates obtained from K_DP. The scatter plot between the two rainfall estimates should lie close to a 1:1 line, and any systematic deviation from this line can be removed by appropriately adjusting the system gain. It is noted that Z_DR can be calibrated accurately because it is a differential power measurement, and K_DP is obtained from differential phase measurement, which is unaffected by system calibration. The sensitivity and accuracy of this technique are studied, and theoretical and simulation results for C-band frequencies are presented     

Potential uses of the differential propagation phase constant toestimate raindrop and hailstone size distributions

One of the Doppler radars operated by the National Severe Storms Laboratory can measure the difference between propagation phase constants K_Dp at horizontal and vertical polarization. This study examines the use of this parameter K _Dp in addition to the reflectivity factor Z_H and the differential reflectivity Z_DR, to obtain information about rain and hail. It is shown from theory and experiments that a third parameter of the drop size distribution, obtained from K_DP, can be used to support Z _DR measurement and/or to point out mixed-phase hydrometeors. Quantitative information on hail size distribution can be obtained for small hailstones when their major axes are nearly vertically aligned, giving rise to negative Z_DR and K_DP values     

Secret key agreement by public discussion from common information

The problem of generating a shared secret key S by two parties knowing dependent random variables X and Y, respectively, but not sharing a secret key initially, is considered. An enemy who knows the random variable Z, jointly distributed with X and Y according to some probability distribution P_XYZ, can also receive all messages exchanged by the two parties over a public channel. The goal of a protocol is that the enemy obtains at most a negligible amount of information about S. Upper bounds on H(S) as a function of P_XYZ are presented. Lower bounds on the rate H (S)/N (as N→∞) are derived for the case in which X=[X₁, . . ., X _N], Y=[Y₁, . . ., Y_N] and Z=[Z₁, . . ., Z_N] result from N independent executions of a random experiment generating X_i, Y_i and Z_i for i=1, . . ., N. It is shown that such a secret key agreement is possible for a scenario in which all three parties receive the output of a binary symmetric source over independent binary symmetric channels, even when the enemy's channel is superior to the other two channels     

Conservation of complex power technique for waveguide junctionswith finite wall conductivity

Scattering at the junction of two waveguides with finite wall conductivity is rigorously treated using E-field mode matching and the conservation of complex power technique. At the transverse junction discontinuity between the two waveguides, the complex power absorbed by the junction wall is taken into account along with the usual transfer of complex power from one guide to the other. This leads to a generalized form of the scattering matrix [S] of the lossy junction which incorporates the surface impedance Z_m of the transverse metallic wall, assumed to be a good conductor. The specific case of a copper transverse diaphragm with centered circular iris in an X-band guide is considered and the equivalent TE₁₀ shunt admittance is computed. Numerical results are also given for lossy X-band cavity resonators with circular coupling holes     

A model for fast switching transients in power systems: the nearzone concept

The author presents a simple time-domain model which makes it possible to predict the order of magnitude of the highest di/ dt values generated by closing switches in electrical power systems. The model is based on traveling-wave analysis. It is demonstrated that two different approaches must be applied, according to whether (a) the closing time, T_s, of the switch is faster than twice the traveling time to the first reflection point or (b) T_s is much slower. Under condition (b) the well-known quasistationary approach di/dt_max=U₀/L can be used, where U₀ is the switched voltage and L is the self-inductance of the line between the stray capacitances located to the left and the right of the switching device. Under condition (a) a new formula must be applied: di/dt _max≈2 U₀/ZT_s, where Z is the line impedance of the line in which the switching device is installed and T_s is the time during which the voltage across the switch collapses from U₀ to zero. Experimental results are given from both fast and slow closing switches     

Filter bank frame expansions with erasures

We study frames for robust transmission over the Internet. In our previous work, we used quantized finite-dimensional frames to achieve resilience to packet losses; here, we allow the input to be a sequence in l₂(Z) and focus on a filter-bank implementation of the system. We present results in parallel, R^N or C^N versus l₂(Z), and show that uniform tight frames, as well as newly introduced strongly uniform tight frames, provide the best performance     

Microwave measurement of temperature and current dependences ofsurface impedance for high-Tc superconductors

Perturbation formulas for TE₀₁₁-mode dielectric rod resonator and for a TE₀₁₁-mode circular cavity resonator are derived to determine the surface impedance Z_s of superconductors from measured values of resonant frequencies and unloaded Q. The relation between the maximum surface current density of a superconductor, J_s, and output power from a signal generator is derived. On the basis of these analytical results, a measurement technique is proposed to evaluate the temperature and J_s dependencies of Z_s for superconductors. The measured results of the temperature dependence of Z_s for YBCO and copper plates are presented. From these results, it is verified that the dielectric resonator is suitable for measuring the surface reactance for YBCO. From these Z_s values the temperature dependences of the skin depth and the penetration depth and those of the complex conductivity are obtained on the basis of the two-fluid model. These measured values agree well with the theoretical curves     

Stripline resonator measurements of Zs versus Hrf in YBa2Cu3O7-x thin films

A report is presented on measurements of the surface impedance, Z_S, of YBa₂Cu₃O_7-x thin films using a stripline resonator. The films were deposited on LaAlO₃ substrates by off-axis magnetron sputtering. The authors obtained Z_S as a function of frequency from 1.5 to 20 GHz, as a function of temperature from 4 K to the transition temperature (~90 K), and as a function of the RF magnetic field from zero to 300 Oe. At low temperatures the surface resistance, R _S, of the films shows a very weak dependence on the magnetic field up to 225 to 250 Oe. At 77 K, R_S is proportional to the square of the field. The penetration depth shows a much weaker dependence on the field than does R_S. The origins of the magnetic field dependence of Z_S are also discussed     

Rain-induced attenuation effects on C-banddual-polarization meteorological radars

An attenuation correction procedure is proposed and evaluated by simulations using raindrop size distribution obtained from ground-based disdrometer measurements. The results show that under certain conditions it is possible to retrieve C-band reflectivity factor (Z _H) and differential reflectivity (Z_DR) radar observables affected by attenuation along rain-filled propagation paths. Rainfall rates estimated from Z _H and Z_DR with and without attenuation correction are compared to determine the effects of attenuation and the capability of the correction procedure to account for it     

Proton-exchanged optical waveguides in Z-cut LiNbO3 using phosphoric acid

Proton-exchanged Z-cut LiNbO₃ planar waveguides formed using phosphoric acid were characterized optically. The refractive index profile and the diffusion parameters were studied systematically. These waveguides have propagation losses of less than 1 dB/cm and exhibit properties that are different from those obtained using benzoic acid. The index profile is not a simple step function and can be modeled accurately by a polynomial expression. A maximum surface index increase of 0.145 was measured at a 0.633-μm wavelength. The diffusion constant D₀ and the activation energy Q for the proton-exchange process using this acid were found to be 6.43×10⁸ μm²/h and 82.91 kJ/mol, respectively. The annealing properties of these waveguides were also established, and the effects of annealing on surface index change and waveguide depth increase were found to follow a power-law relationship     

A binary analog to the entropy-power inequality

Let {X_n}, {Y_n} be independent stationary binary random sequences with entropy H( X), H(Y), respectively. Let h(ζ)=-ζlogζ-(1-ζ)log(1-ζ), 0⩽ζ⩽1/2, be the binary entropy function and let σ(X)=h^-1 (H(X)), σ(Y)=h^-1 (H(Y)). Let z_n=X_n⊕Y_n , where ⊕ denotes modulo-2 addition. The following analog of the entropy-power inequality provides a lower bound on H(Z ), the entropy of {Z_n}: σ(Z)⩾σ(X)*σ(Y), where σ(Z)=h^-1 (H(Z)), and α*β=α(1-β)+β(1-α). When {Y _n} are independent identically distributed, this reduces to Mrs. Gerber's Lemma from A.D. Wyner and J. Ziv (1973)     

Evaluation of the quantization error in denominator-separable 2-Drecursive filters

The evaluation of the quantization error in two-dimensional (2-D) digital filters involves the computation of the infinite square sum J=Σ^∞_m=φΣ ^∞_n=φy² (m, n). A simple method is presented for evaluating J based on partial fraction expansion and using the residue method provided the Z-transform Y(Z₁, Z₂) of the sequence y(m, n) having quadrant support is a causal bounded input, bounded output (BIBO) stable denominator-separable rational function. The value of J is expressed as a sum of simple integrals which can easily be evaluated. The simple integrals are tabulated for ready reference. The proposed method is suitable for analytical as well as numerical computation and can easily be programmed     

Single frequency electrooptical tuning of an extended cavity diodelaser at 1500 nm wavelength

A wavelength-tunable, single-frequency GaInAsP-InP laser diode using an intracavity electrooptic LiNbO₃ crystal as the wavelength selective component is discussed. Wavelength tuning is achieved by applying a driving voltage on the crystal electrodes. First results indicate a tuning rate of 1 GHz/V over a tuning range of about 4 nm. This performance was obtained using a nonoptimized X-cut, Z-propagating LiNbO₃ crystal. A potential tuning rate of 6.5 GHz/V is possible with reasonable improvements     

Input filter design criteria for switching regulators usingcurrent-mode programming

Design criteria are developed for a constant-frequency current-programmed switching DC-to-DC converter with an input filter to ensure stability and prevent performance degradation. The criteria are given in terms of the filter voltage transfer function H_S , output admittance Y_s, and the y-parameter model of the switching converter. The criteria are listed as four inequalities and illustrated graphically. The criteria may be summarized as follows: assuming a converter that satisfies its loop gain T, line-to-output transfer function A_gf , and output impedance Z_of requirement is given, an input filter with H_s and Y_s can be used to attenuate the noise emissions from the converter without adversely affecting the converter if H_s⩽1 (may be relaxed to 3-6 dB), and Y _s is larger than the curves of the graphical illustration, perhaps using 6 dB as a rule-of-thumb minimum separation     

The Z4-linearity of Kerdock, Preparata, Goethals, andrelated codes

Certain notorious nonlinear binary codes contain more codewords than any known linear code. These include the codes constructed by Nordstrom-Robinson (1967), Kerdock (1972), Preparata (1968), Goethals (1974), and Delsarte-Goethals (1975). It is shown here that all these codes can be very simply constructed as binary images under the Gray map of linear codes over Z₄, the integers mod 4 (although this requires a slight modification of the Preparata and Goethals codes). The construction implies that all these binary codes are distance invariant. Duality in the Z₄ domain implies that the binary images have dual weight distributions. The Kerdock and “Preparata” codes are duals over Z₄-and the Nordstrom-Robinson code is self-dual-which explains why their weight distributions are dual to each other. The Kerdock and “Preparata” codes are Z₄-analogues of first-order Reed-Muller and extended Hamming codes, respectively. All these codes are extended cyclic codes over Z₄, which greatly simplifies encoding and decoding. An algebraic hard-decision decoding algorithm is given for the “Preparata” code and a Hadamard-transform soft-decision decoding algorithm for the I(Kerdock code. Binary first- and second-order Reed-Muller codes are also linear over Z₄ , but extended Hamming codes of length n⩾32 and the Golay code are not. Using Z₄-linearity, a new family of distance regular graphs are constructed on the cosets of the “Preparata” code     

A 2-adic approach to the analysis of cyclic codes

This paper describes how 2-adic numbers can be used to analyze the structure of binary cyclic codes and of cyclic codes defined over Z _2(a), a⩾2, the ring of integers modulo 2^a. It provides a 2-adic proof of a theorem of McEliece that characterizes the possible Hamming weights that can appear in a binary cyclic code. A generalization of this theorem is derived that applies to cyclic codes over Z_2(a) that are obtained from binary cyclic codes by a sequence of Hensel lifts. This generalization characterizes the number of times a residue modulo 2^a appears as a component of an arbitrary codeword in the cyclic code. The limit of the sequence of Hensel lifts is a universal code defined over the 2-adic integers. This code was first introduced by Calderbank and Sloane (1995), and is the main subject of this paper. Binary cyclic codes and cyclic codes over Z_2(a) are obtained from these universal codes by reduction modulo some power of 2. A special case of particular interest is cyclic codes over Z₄ that are obtained from binary cyclic codes by means of a single Hensel lift. The binary images of such codes under the Gray isometry include the Kerdock, Preparata, and Delsart-Goethals codes. These are nonlinear binary codes that contain more codewords than any linear code presently known. Fundamental understanding of the composition of codewords in cyclic codes over Z₄ is central to the search for more families of optimal codes. This paper also constructs even unimodular lattices from the Hensel lift of extended binary cyclic codes that are self-dual with all Hamming weights divisible by 4. The Leech lattice arises in this way as do extremal lattices in dimensions 32 through 48     

Population inversion in the recombination of optically-ionizedplasmas

The possibility of using a high-intensity optical field in conjunction with a gas target to produce a highly ionized plasma filament suitable for recombination XUV lasers in both transient and quasi-steady-state regimes is examined. A distinction is made between low Z ions which can be stripped to the desired ionization state at nonrelativistic intensities and higher Z ions which require relativistic intensities to produce the desired ionization. In the nonrelativistic case (E_i<500 eV), it is shown that electron thermal conduction is extremely effective in cooling ~10-μm diameter filaments imbedded in cold background plasma. In the relativistic case, self-focusing of the ionizing laser radiation may lead to a very small diameter electron-cavitated filaments which will undergo a space-charge-driven expansion (Coulomb explosion) on the time scale of an ion plasma period, resulting in the emission of extremely high currents of moderate energy (E≈1/8 Zm_e c²) ions. The implications of such filamentation for the scaling of the present type of recombination laser to short wavelengths are discussed     

Replacement policies for a cumulative damage model with minimalrepair at failure

The authors apply periodic replacement with minimal repair at failure to cumulative damage models: a unit is replaced at time T , at shock N, or at damage Z and undergoes minimal repair between replacements. The mean cost-rate is obtained, and each optimal T*, N*, and Z* to minimize the cost-rate is discussed. A numerical example is given for an exponential case     

A new organic electrooptic crystal:2,6-dibromo-N-methyl-4-nitroaniline (DBNMNA)

A new organic electrooptic crystal, 2,6-dibromo-N-methyl-4-nitroaniline, is reported. The crystal structure was determined by X-ray diffraction (orthorhombic, space group Fdd2, point group mm2, Z=16, a=11.745 Å, b=29.640 Å, c=10.807 Å). The refractive indexes were measured at several wavelengths between 500 and 1100 nm (at 632.8 nm, n_a=1.90, n_b=1.62, and n_c=1.48) and fit the data to a single oscillator Sellmeier equation. A report is presented on measurements of the linear electrooptic effect, yielding the combined coefficients n_a ³r₁₃-n_c³ r₃₃, as well as the first known measurements of the quadratic electrooptic effect in an organic crystal, yielding the coefficients r₄₂ and r₅₁ at 514.5, 632.8, and 810 nm. Good agreement is found between the observed dispersion in the electrooptic coefficients and that predicted by the simple two-level dispersion model     

Signal sets matched to groups

Recently, linear codes over Z_M (the ring of integers mod M) have been presented that are matched to M -ary phase modulation. The general problem of matching signal sets to generalized linear algebraic codes is addressed based on these codes. A definition is given for the notion of matching. It is shown that any signal set in N-dimensional Euclidean space that is matched to an abstract group is essentially what D. Slepian (1968) called a group code for the Gaussian channel. If the group is commutative, this further implies that any such signal set is equivalent to coded phase modulation with linear codes over Z_M. Some further results on such signal sets are presented, and the signal sets matched to noncommutative groups and the linear codes over such groups are discussed