Multivariate regression estimation of continuous-time processesfrom sampled data: local polynomial fitting approach

Let (Y,X)={Y(t),X(t),-∞j) be a renewal point processes on (0,∞), with a finite mean rate, independent of (Y,X). We consider the estimation of regression function r(x₀, x₁,...,x_m-1; τ₁,...,τ_m) of ψ(Y(τ_m)) given (X(0)=x₀, X(τ₁)=x₁,...,X(τ_m-1)=_x-1 ) for arbitrary lags 0<τ₁<...< τ_m on the basis of the discrete-time observations {Y(t_j),X(t_j),t_j)_j=1ⁿ . We estimate the regression function and all its partial derivatives up to a total order p⩾1 using high-order local polynomial fitting. We establish the weak consistency of such estimates along with rates of convergence. We also establish the joint asymptotic normality of the estimates for the regression function and all its partial derivatives up to a total order p⩾1 and provide explicit expressions for the bias and covariance matrix (of the asymptotically normal distribution)     

Statistical characterization of sample fourth-order cumulants of anoisy complex sinusoidal process

The paper deals with the statistical characterization of sample estimates of the fourth-order cumulants of a random process consisting of multiple complex sinusoids and additive colored Gaussian noise. In particular, it presents necessary and sufficient conditions for strong consistency of the sample cumulants of arbitrary orders, and derives expressions for the asymptotic covariance of the sample estimates of the fourth-order cumulants. It is shown that the fourth-order cumulant C_4y (τ₁,...,τ₄) can be written as a function of a single argument τ=τ₃+τ₄ -τ₁-τ₂, which implies large flexibility in estimating the cumulant. It is recommended that the estimate be based upon lags such that τ₁ is distant from τ₂ and τ₃ is distant from τ₄, and/or as a linear combination of such terms. The asymptotic variance of a cumulant-based frequency estimator is shown to have the form c₂·SNR^-2+c₃·SNR^-3 +c₄·SNR^-4, where the coefficient c ₂ may possibly vanish. The theory is illustrated via numerical examples. The results of this paper will be useful in analyzing the performance of various cumulant-based frequency estimation algorithms     

Three space-economical algorithms for calculatingminimum-redundancy prefix codes

The minimum-redundancy prefix code problem is to determine, for a given list W=[ω₁,..., ω_n] of n positive symbol weights, a list L=[l₁,...,l_n] of n corresponding integer codeword lengths such that Σ_i=1 ⁿ 2^-li⩽1 and Σ_i=1ⁿ ω_il_i is minimized. Let us consider the case where W is already sorted. In this case, the output list L can be represented by a list M=[m₁,..., m_H], where m_l, for l=1,...,H, denotes the multiplicity of the codeword length l in L and H is the length of the greatest codeword. Fortunately, H is proved to be O(min(log(1/p₁),n)), where p₁ is the smallest symbol probability, given by ω₁/Σ _i=1ⁿ ω_i. We present the Fast LazyHuff (F-LazyHuff), the Economical LazyHuff (E-LazyHuff), and the Best LazyHuff (B-LazyHuff) algorithms. F-LazyHuff runs in O(n) time but requires O(min(H², n)) additional space. On the other hand, E-LazyHuff runs in O(n+nlog(n/H)) time, requiring only O(H) additional space. Finally, B-LazyHuff asymptotically overcomes, the previous algorithms, requiring only O(n) time and O(H) additional space. Moreover, our three algorithms have the advantage of not writing over the input buffer during code calculation, a feature that is very useful in some applications     

Capacity of the Gaussian arbitrarily varying channel

The Gaussian arbitrarily varying channel with input constraint Γ and state constraint Λ admits input sequences x=(x₁,---,X_n) of real numbers with Σx_i²⩽nΓ and state sequences s=(S₁,---,s_n ) of real numbers with Σs_i²⩽nΛ; the output sequence x+s+V, where V=(V₁,---,V_n) is a sequence of independent and identically distributed Gaussian random variables with mean 0 and variance σ². It is proved that the capacity of this arbitrarily varying channel for deterministic codes and the average probability of error criterion equals 1/2 log (1+Γ/(Λ+σ²)) if Λ<Γ and is 0 otherwise     

Emission cross sections and spectroscopy of Ho3+ laserchannels in KGd(WO4)2 single crystal

The spectroscopic properties of Ho³⁺ laser channels in KGd(WO₄)₂ crystals have been investigated using optical absorption, photoluminescence, and lifetime measurements. The radiative lifetimes of Ho³⁺ have been calculated through a Judd-Ofelt (JO) formalism using 300-K optical absorption results. The JO parameters obtained were Ω₂=15.35×10^-20 cm², Ω ₄=3.79×10^-20 cm², Ω₆ =1.69×10^-20 cm². The 7-300-K lifetimes obtained in diluted (8·10¹⁸ cm^-3) KGW:0.1% Ho samples are: τ(⁵F₃)≈0.9 μs, τ( ⁵S₂)=19-3.6 μs, and τ(⁵F₅ )≈1.1 μs. For Ho concentrations below 1.5×10²⁰ cm^-3, multiphonon emission is the main source of non radiative losses, and the temperature independent multiphonon probability in KGW is found to follow the energy gap law τ_ph ^-1(0)=βexp(-αΔE), where β=1.4×10^-7 s^-1, and α=1.4×10³ cm. Above this holmium concentration, energy transfer between Ho impurities also contributes to the losses. The spectral distributions of the Ho³⁺ emission cross section σ_EM for several laser channels are calculated in σ- and π-polarized configurations. The peak a σ_EM values achieved for transitions to the ⁵I₈ level are ≈2×10^-20 cm² in the σ-polarized configuration, and three main lasing peaks at 2.02, 2.05, and 2.07 μm are envisaged inside the ⁵I₇→⁵I₈ channel     

The dynamics of group codes: state spaces, trellis diagrams, andcanonical encoders

A group code C over a group G is a set of sequences of group elements that itself forms a group under a component-wise group operation. A group code has a well-defined state space Σ_k at each time k. Each code sequence passes through a well-defined state sequence. The set of all state sequences is also a group code, the state code of C. The state code defines an essentially unique minimal realization of C. The trellis diagram of C is defined by the state code of C and by labels associated with each state transition. The set of all label sequences forms a group code, the label code of C, which is isomorphic to the state code of C. If C is complete and strongly controllable, then a minimal encoder in controller canonical (feedbackfree) form may be constructed from certain sets of shortest possible code sequences, called granules. The size of the state space Σ_k is equal to the size of the state space of this canonical encoder, which is given by a decomposition of the input groups of C at each time k. If C is time-invariant and ν-controllable, then |Σ_k|=Π_1⩽j⩽v|F_j/F _j-1|^j, where F₀ ⊆···⊆ Fν is a normal series, the input chain of C. A group code C has a well-defined trellis section corresponding to any finite interval, regardless of whether it is complete. For a linear time-invariant convolutional code over a field G, these results reduce to known results; however, they depend only on elementary group properties, not on the multiplicative structure of G. Moreover, time-invariance is not required. These results hold for arbitrary groups, and apply to block codes, lattices, time-varying convolutional codes, trellis codes, geometrically uniform codes and discrete-time linear systems     

On minimal α-mean error parameter transmission over a Poissonchannel

We consider the problem of one-dimensional parameter transmission over a Poisson channel when the input signal (intensity) obeys a peak energy constraint. We show that it is possible to choose input signals and an estimator in such a way that the mean-square error of parameter transmission will decrease exponentially with transmission time T→∞ and we find the best possible exponent. For more general loss functions of the type |x|α we find the best possible exponent if α⩾α₀=(1+√5)/2≈1.618. If 0<α<α₀ then some lower and upper bounds for the best possible exponent are established     

Measurement and behavior of dual-polarization vegetation opticaldepth and single scattering albedo at 1.4- and 5-GHz microwavefrequencies

A measurement procedure has been developed and tested to determine horizontal and vertical polarization radiative transfer properties, i,e., single scattering albedo (ω) and optical depth (τ), of vegetation under field conditions. The procedure was applied to a wheat crop for a series of biomass densities. The measurements were done using two different radiometers (1.4 and 5 GHz) and for different view angles. The measurements and calculations indicated that the ratios of horizontal and vertical polarization radiative transfer properties (α=Γ_h/Γ_ν, α'=τ_h/τ_ν and β=ωh/ω_ν) are slightly dependent on view angle. However, no significant dependence on biomass density could be discerned     

The Kolmogorov complexity, universal distribution, and codingtheorem for generalized length functions

A function h(w) is said to be useful for the coding theorem if the coding theorem remains to be true when the lengths |w| of codewords w in it are replaced with h(w). For a codeword w=a₀a₁...a_m-1 of length m and an infinite sequence Q=(q₀, q₁, q₂, ...) of real numbers such that 0n⩽½, let |w|_Q denote the value Σ_n=0^m-1 (if a_n =0 then -log₂q_n, else -log₂(1-q _n)), that is, -log₂, (the probability that flippings of coins generate x) assuming that the (i+1)th coin generates a tail (or 0) with probability q_i. It is known that if 0n→∞ q_n then |w|_Q is useful for the coding theorem and if lim_n→∞ q _n/(1/(2ⁿ))=0 then |w|_Q is not useful. We introduce several variations of the coding theorem and show sufficient conditions for h(w) not to be useful for these variations. The usefulness is also defined for the expressions that define the Kolmogorov complexity and the universal distribution. We consider the relation among the usefulness for the coding theorem, that for the Kolmogorov complexity, and that for the universal distribution     

The length of a typical Huffman codeword

If p_i(i=1,···, N) is the probability of the ith letter of a memoryless source, the length l_i of the corresponding binary Huffman codeword can be very different from the value -log p_i. For a typical letter, however, l_i≈-logp_i. More precisely, P_m ^-=Σ/sub j∈{i|l<-logpj-m}/p_j<2^-m and P_m ⁺=Σ/sub j∈{i|li>-logpi+m/}p_j<2^-c(m-2)+2, where c≈2.27     

Reduction of the current gain of the n-p-n transistor component ofa thyristor due to the doping concentration of the p-base

The reduction of the current amplification factor of a wide-base transistor, with growing doping concentration in the base region, is investigated. A method for the determination of the minority-carrier lifetime τ_n in the base region and the emitter Gummel number G_e is developed. The method is based on transistor structures differing only in the base width. It was found that the lifetime τ_n decreases according to the power law τ_n~N^-0.45_A. This result is analyzed for different recombination processes. Good agreement is obtained if shallow impurities acting as recombination centers are assumed. The injection-limited current gain β_γ decreases significantly with an increase in the total number of the doping concentration of the base, reaches a broad maximum, and then falls slowly. The maximum value of G_e is found to be 1.1×10¹⁴ cm^-4-s in good agreement with theoretical results. Finally, the contribution of the injection efficiency γ and the transport factor α_T to the current gain α are determined. It is found that α is limited mainly by the injection efficiency γ     

Propagation characteristics of Schottky contact suspended slow-wavemicrostrip line

The single-layer reduction (SLR) model computes the normalized phase constant (β/β₀), dielectric loss (α_d), and conductor loss (α_c) for the Schottky contact slow-wave microstrip (SCSM) line with accuracy about 2.0% for β/β₀, and within 0.01 dB/mm for the total loss (α_t=α_d+α_c) as compared against the experimental results. The SLR model has been further used to analyze the normal and abnormal characteristics of a proposed Schottky contact suspended slow-wave microstrip (SCSSM) line with 22% increase in β/β₀ over the normal SCSM line. The SCSSM line could be useful in the lower range of RF for the development of compact components     

A new common-emitter hybrid-π small-signal equivalent circuitfor bipolar transistors with significant neutral base recombination

The linear superposition approach to the modeling of small-signal parameters in the presence of substantial base recombination, which involves a virtual transistor without base recombination, is identified to cause incorrect emitter current modeling. All of the terminal current changes can be correctly modeled by using the measured forced-V_BE Early voltage in a new equivalent circuit, which properly accounts for NBR and Early effect in a physically consistent manner. As a result, practical situations of small collector-base resistance (τ _μ) can be properly handled, τ_μ is related to the ac current-drive and ac voltage-drive Early voltages, which facilitates parameter extraction and circuit modeling. Measurements on state-of-the-art UHV/CVD SiGe HBT's show that the conventional assumption that τ_μ is far larger than the forced-V_BE output resistance τ₀ does not apply to devices with significant NBR. In practice, τ_μ can be comparable to (and smaller than) τ₀ depending on the device processing, profiles and operating temperature. Temperature dependent data are presented, and circuit implications are discussed based on the new equivalent circuit     

Strongly consistent online forecasting of centered Gaussianprocesses

An estimator Eˆ(d_n,n) of the conditional expectation E[X_n+1|X_n,...,X(n-d_n+1)] in a centered, stationary, and ergodic Gaussian process {X_i}_i with absolutely summable Wold coefficients is constructed on the basis of having observed X₁,...,X_n . For a suitable choice of the length dn→∞ (n→∞) of the past covered by the conditional expectation, it is established that |Eˆ(d_n,n)-E[X_n+1|X_n ,...,X(n-d_n+1)]|→0 with probability 1. In addition, sufficient conditions for |E[X_n+1|X_n,X _n-1,...]-E[X_n+1|X_n,...,X(n-d_n +1)]| →0 to hold with probability 1 are given, that is, conditions under which Eˆ(d_n,n) can be used as a strongly consistent forecaster for |E[X_n+1|X_n,X _n-1,...]     

Some new constructions for simplex codes

Three constructions for n-dimensional regular simplex codes α_i, 0⩽i⩽n, are proposed, two of which have the property that α_i for 1⩽i⩽n is a cyclic shift of α₁. The first method is shown to work for all the positive integers n=1,2,... using only three real values. It turns out that these values are rational whenever n+1 is a square of some integer. Whenever a (v,k,λ) cyclic (or Abelian) difference set exists, this method is generalized so that a similar method is shown to work with ν=n (the number of dimensions)     

Perfect pseudoperiodic binary arrays

Arrays with good correlation properties are required for code-departure imaging, as well as for other applications of two-dimensional signal processing. Since binary arrays with perfect periodic autocorrelation are rather sparse. `pseudoperiodic' binary arrays are discussed. The transmitted binary array is correlated in the receiver with the same array which is surrounded periodically by similar ternary arrays. A construction method is presented that permits the construction of such `pseudoperiodic' binary arrays with perfect correlation properties for all sizes p₁^a1×p ₂^a2 (p₁, p₂ odd prime, a₁, a₂=1, 2, 3...)     

Two-dimensional weight-constrained codes through enumeration bounds

For a rational α∈(0,1), let 𝒜_n×m,α be the set of binary n×m arrays in which each row has Hamming weight αm and each column has Hamming weight αn, where αm and αn are integers. (The special case of two-dimensional balanced arrays corresponds to α=1/2 and even values for n and m.) The redundancy of 𝒜_n×m,α is defined by ρ_n×m,α=nmH(α)-log₂|𝒜 _n×m,α| where H(x)=-xlog₂x-(1-x)log₂(1-x). Bounds on ρ_n×m,α are obtained in terms of the redundancies of the sets 𝒜_ℒ,α of all binary ℒ-vectors with Hamming weight αℒ, ℒ∈{n,m}. Specifically, it is shown that ρ_n×m,α⩽nρ_m,α+mρ _n,α where ρ_ℒ,α=ℒH(α)-log₂|𝒜 _ℒ,α| and that this bound is tight up to an additive term O(n+log m). A polynomial-time coding algorithm is presented that maps unconstrained input sequences into 𝒜_n×m,α at a rate H(α)-(ρ_m,α/m)     

Combinatorial bounds for list decoding

Informally, an error-correcting code has "nice" list-decodability properties if every Hamming ball of "large" radius has a "small" number of codewords in it. We report linear codes with nontrivial list-decodability: i.e., codes of large rate that are nicely list-decodable, and codes of large distance that are not nicely list-decodable. Specifically, on the positive side, we show that there exist codes of rate R and block length n that have at most c codewords in every Hamming ball of radius H^-1(1-R-1/c)·n. This answers the main open question from the work of Elias (1957). This result also has consequences for the construction of concatenated codes of good rate that are list decodable from a large fraction of errors, improving previous results of Guruswami and Sudan (see IEEE Trans. Inform. Theory, vol.45, p.1757-67, Sept. 1999, and Proc. 32nd ACM Symp. Theory of Computing (STOC), Portland, OR, p. 181-190, May 2000) in this vein. Specifically, for every ε > 0, we present a polynomial time constructible asymptotically good family of binary codes of rate Ω(ε⁴) that can be list-decoded in polynomial time from up to a fraction (1/2-ε) of errors, using lists of size O(ε^-2). On the negative side, we show that for every δ and c, there exists τ < δ, c₁ > 0, and an infinite family of linear codes {C_i}_i such that if n_i denotes the block length of C_i, then C _i has minimum distance at least δ · n_i and contains more than c₁ · n_i^c codewords in some Hamming ball of radius τ · n_i. While this result is still far from known bounds on the list-decodability of linear codes, it is the first to bound the "radius for list-decodability by a polynomial-sized list" away from the minimum distance of the code     

A model for the multipath delay profile of fixed wireless channels

This paper deals with the measurement and modeling of multipath delay on fixed wireless paths at 1.9 GHz in suburban environments. The primary focus is on the delay profile, which is the normalized plot of received power versus delay in response to an RT “impulse.” We describe measurement campaigns in the western suburbs of Chicago, IL, and in suburban north-central New Jersey. Our analysis of the data suggests to us that, for directive terminal antennas, the delay profile can be modeled as having a “spike-plus-exponential” shape, i.e., a strong return (“spike”) at the lowest delay, plus a set of returns whose mean powers decay exponentially with delay. This delay profile can be characterized by just two parameters (both variable over the terrain), namely, the ratio (K₀) of the average powers in the “spike” and “exponential” components and the decay time constant (τ₀) of the “exponential” component. No such simple structure appears to apply for delay profiles using omnidirectional antennas. For a directive antenna with a 32° beamwidth, we find that: (1) the statistical correlation between the profile parameters K₀ and τ₀ is negligible; (2) these parameters are relatively insensitive to antenna height and path length; and (3) over each measured region (Illinois and New Jersey), K₀ and τ₀ have median values close to 8 dB and just below 0.2 μs, respectively. Moreover, we have found simple probability distributions that accurately portray the variability of K₀ and τ₀ over the terrain