Minimax estimation of deterministic parameters in linear models with a random model matrix

We consider the problem of estimating an unknown deterministic parameter vector in a linear model with a random model matrix, with known second-order statistics. We first seek the linear estimator that minimizes the worst-case mean-squared error (MSE) across all parameter vectors whose (possibly weighted) norm is bounded above. We show that the minimax MSE estimator can be found by solving a semidefinite programming problem and develop necessary and sufficient optimality conditions on the minimax MSE estimator. Using these conditions, we derive closed-form expressions for the minimax MSE estimator in some special cases. We then demonstrate, through examples, that the minimax MSE estimator can improve the performance over both a Baysian approach and a least-squares method. We then consider the case in which the norm of the parameter vector is also bounded below. Since the minimax MSE approach cannot account for a nonzero lower bound, we consider, in this case, a minimax regret method in which we seek the estimator that minimizes the worst-case difference between the MSE attainable using a linear estimator that does not know the parameter vector, and the optimal MSE attained using a linear estimator that knows the parameter vector. For analytical tractability, we restrict our attention to the scalar case and develop a closed-form expression for the minimax regret estimator.     

1/f noise in large-area Hg<Subscript>1−x</Subscript>Cd<Subscript>x</Subscript>Te photodiodes

The 1/f noise in photovoltaic (PV) molecular-beam epitaxy (MBE)-grown Hg_1−xCd_xTe double-layer planar heterostructure (DLPH) large-area detectors is a critical noise component with the potential to limit sensitivity of the cross-track infrared sounder (CrIS) instrument. Therefore, an understanding of the origins and mechanisms of noise currents in these PV detectors is of great importance. Excess low-frequency noise has been measured on a number of 1000-μm-diameter active-area detectors of varying “quality” (i.e., having a wide range of I-V characteristics at 78 K). The 1/f noise was measured as a function of cut-off wavelength under illuminated conditions. For short-wave infrared (SWIR) detectors at 98 K, minimal 1/f noise was measured when the total current was dominated by diffusion with white noise spectral density in the mid-10⁻¹⁵A/Hz^1/2 range. For SWIR detectors dominated by other than diffusion current, the ratio, α, of the noise current in unit bandwidth i_n(f = 1 Hz, V_d = −60 mV, and Δf = 1 Hz) to dark current I_d(V_d = −60 mV) was α_SW-d = i_n/I_d ∼ 1 × 10⁻³. The SWIR detectors measured at 0 mV under illuminated conditions had median α_SW-P = i_n/I_ph ∼ 7 × 10⁻⁶. For mid-wave infrared (MWIR) detectors, α_MW-d = i_n/I_d ∼ 2 × 10⁻⁴, due to tunneling current contributions to the 1/f noise. Measurements on forty-nine 1000-μm-diameter MWIR detectors under illuminated conditions at 98 K and −60 mV bias resulted in α_MW-P = i_n/I_ph = 4.16 ± 1.69 × 10⁻⁶. A significant point to note is that the photo-induced noise spectra are nearly identical at 0 mV and 100 mV reverse bias, with a noise-current-to-photocurrent ratio, α_MW-P, in the mid 10⁻⁶ range. For long-wave infrared (LWIR) detectors measured at 78 K, the ratio, α_LW-d = i_n/I_d ∼ 6 × 10⁻⁶, for the best performers. The majority of the LWIR detectors exhibited α_LW-d on the order of 2 × 10⁻⁵. The photo-induced 1/f noise had α_LW-P = i_n/I_ph ∼ 5 × 10⁻⁶. The value of the noise-current-to-dark-current ratio, α appears to increase with increasing bandgap. It is not clear if this is due to different current mechanisms impacting 1/f noise performance. Measurements on detectors of different bandgaps are needed at temperatures where diffusion current is the dominant current. Excess low-frequency noise measurements made as a function of detector reverse bias indicate 1/f noise may result primarily from the dominant current mechanism at each particular bias. The 1/f noise was not a direct function of the applied bias.     

Characteristic Features of the Optimal Processing of the Results of Measurements in the Case of a Random Observation Function

An analysis is made of the characteristic features and problems of the optimal processing of the results of measurements in the case of a random observation function utilizing a nonlinear Kalman filter. A method is proposed for increasing the convergence domain of the filter with additional processing of measurements in the frequency domain.     

Influence of device engineering on the analog and RF performances of SOI MOSFETs

This work presents a systematic comparative study of the influence of various process options on the analog and RF properties of fully depleted (FD) silicon-on-insulator (SOI), partially depleted (PD) SOI, and bulk MOSFET's with gate lengths down to 0.08 /spl mu/m. We introduce the transconductance-over-drain current ratio and Early voltage as key figures of merits for the analog MOS performance and the gain and the transition and maximum frequencies for RF performances and link them to device engineering. Specifically, we investigate the effects of HALO implantation in FD, PD, and bulk devices, of film thickness in FD, of substrate doping in SOI, and of nonstandard channel engineering (i.e., asymmetric Graded-channel MOSFETs and gate-body contacted DTMOS).     

An improved statistical analysis of the least mean fourth (LMF) adaptive algorithm

The paper presents an improved statistical analysis of the least mean fourth (LMF) adaptive algorithm behavior for a stationary Gaussian input. The analysis improves previous results in that higher order moments of the weight error vector are not neglected and that it is not restricted to a specific noise distribution. The analysis is based on the independence theory and assumes reasonably slow learning and a large number of adaptive filter coefficients. A new analytical model is derived, which is able to predict the algorithm behavior accurately, both during transient and in steady-state, for small step sizes and long impulse responses. The new model is valid for any zero-mean symmetric noise density function and for any signal-to-noise ratio (SNR). Computer simulations illustrate the accuracy of the new model in predicting the algorithm behavior in several different situations.     

2-D symmetry: theory and filter design applications

In this comprehensive review article, we present the theory of symmetry in two-dimensional (2-D) filter functions and in 2-D Fourier transforms. It is shown that when a filter frequency response possesses symmetry, the realization problem becomes relatively simple. Further, when the frequency response has no symmetry, there is a technique to decompose that frequency response into components each of which has the desired symmetry. This again reduces the complexity of two-dimensional filter design. A number of filter design examples are illustrated.     

High-performance MIM capacitor using ALD high-k HfO/sub 2/-Al/sub 2/O/sub 3/ laminate dielectrics

For the first time, we successfully fabricated and demonstrated high performance metal-insulator-metal (MIM) capacitors with HfO/sub 2/-Al/sub 2/O/sub 3/ laminate dielectric using atomic layer deposition (ALD) technique. Our data indicates that the laminate MIM capacitor can provide high capacitance density of 12.8 fF//spl mu/m/sup 2/ from 10 kHz up to 20 GHz, very low leakage current of 3.2 /spl times/ 10/sup -8/ A/cm/sup 2/ at 3.3 V, small linear voltage coefficient of capacitance of 240 ppm/V together with quadratic one of 1830 ppm/V/sup 2/, temperature coefficient of capacitance of 182 ppm//spl deg/C, and high breakdown field of /spl sim/6 MV/cm as well as promising reliability. As a result, the HfO/sub 2/-Al/sub 2/O/sub 3/ laminate is a very promising candidate for next generation MIM capacitor for radio frequency and mixed signal integrated circuit applications.     

Low-temperature poly-SiGe alloy growth of high gain/speed pin infrared photosensor with gold-induced lateral crystallization (Au-ILC)

The hydrogenated poly-silicon germanium (poly-SiGe:H) epitaxial film has been investigated using gold-induced lateral crystallization (Au-ILC) technology on a-SiGe:H layers at 10-h 350/spl deg/C annealing temperature and 60-sccm hydrogen (H/sub 2/) content. Using this optimal condition, the growth rate of the induced Au was as large as 15.9 /spl mu/m/h. With a low annealing temperature (/spl les/400/spl deg/C) and large growth rate, this novel technology will be noticeably useful for poly-SiGe:H pin IR-sensing fabrication on a conventional precoated indium tin oxide (ITO)-glass substrate. Under a 1-/spl mu/W IR-LED incident light (with peak wave length at 710 nm) and at a 5-V biased voltage, the poly-SiGe:H pin IR sensor developed by the Au-ILC technology, i.e., an Al (anode)/n poly-SiGe:H/i poly-SiGe:H/p poly-SiGe:H/ITO (cathode)/glass-substrate structure allowed for maximum optical gain and response speed. The optical gains and the response speeds were almost 600 and 130%, respectively, better than that of a traditional pin type. Meanwhile, the FWHM of a poly-SiGe:H pin sensor with Au-ILC technology was reduced from 280 to 150 nm. This reveals excellent IR-sensing selectivity. These IR-sensing trials demonstrated again that the proposed Au-ILC technology has very useful application in the field of low cost integrated circuits on optoelectronic applications.