Larry L. Horowitz

Performance advantage of complex LMS for controlling narrow-band adaptive arrays

In narrow-band adaptive-array applications, the mean-square convergence of the discrete-time real least mean-square (LMS) algorithm is slowed by image-frequency noises generated in the LMS loops. The complex LMS algorithm proposed by Widrow et al. is shown to eliminate these noises, yielding convergence of the mean-squared error (MSE) at slightly over twice the rate. This paper includes a comprehensive analysis of the MSE of adaptation for LMS. The analysis is based upon the method developed in the 1968 dissertation by K. D. Senne, and it represents the most complete treatment of the subject published to date.

Controlling Adaptive Antenna Arrays with the Sample Matrix Inversion Algorithm

Considerations are given leading to the selection of the samplematrix inversion algorithm for the control of an airborne narrowbandand adaptive receiving array for use in omnidirecti com communications. Performance is measured for a laboratory nulling system which implements this design concept. This performance ance is compared with predictions based on the component tolerances of the laboratory system.

Adaptive Main-Beam Nulling for Narrow-Beam Antenna Arrays

Narrow-beam, low-sidelobe antennas may be used to enhance communication in the presence of sidelobe interferers. Protection against main-beam interferers as well can be obtained through the use of an adaptive multibeam antenna. Such an antenna, suitable for time-multiplexed, multichannel signals is described here. The objective is to permit successful communication and signal direction-of-arrival tracking in the presence of a large number of sidelobe interferers and a small number of main-beam interferers.

The effects of spline interpolation on power spectral density

This paper discusses the power spectral effects of spline interpolators. A general technique is given for finding the steady-state spectral effects of splines of all orders, when applied following uniform sampling of the input function. The following observations are made: 1) the even order splines that were examined (second and fourth order) possessed divergent steady-state frequency transfer functions, 2) the degree of preservation of the power spectral density of the input process increased with the order of the (odd order) spline used for interpolation, and 3) the reconstruction of a stationary random process over a finite record length will, on the average, have less power than indicated by the steady-state transfer function.

Parameter Bounds on Estimation Accuracy Under Model Misspecification

When the assumed data distribution differs from the true distribution, the model is said to be misspecified or mismatched. Model misspecification at some level is an inevitability of engineering practice. While Hubers celebrated work assesses maximum-likelihood (ML) performance under misspecification, no simple theory for bounding parameter estimation exists. The class of parameter bounds emerging from the covariance inequality, or equivalently the minimum norm theorem is revisited. The expectation operator is well-known to form an inner product space. Flexibility in the choice of expectation integrand and measure for integration exists, however, to establish a class of parameter bounds under a general form of model misspecification, i.e., distribution mismatch. The Cramér-Rao bound (CRB) primarily, and secondarily the Barankin/Hammersley-Chapman-Robbins, Bhattacharyya, and Bobrovsky-Mayer-Wolf-Zakai bounds under misspecification are considered. Hubers sandwich covariance is readily established as a special case of the misspecified CRB subject to ML constraints, and generalizations of the Slepian and Bangs formulae under misspecification are obtained.

Benefits of aspect diversity for SAR ATR: fundamental and experimental results

This paper continues the study reported in Ref. 1 and Ref. 2 trading off the fundamental ATR performance capability (i.e., algorithm-independent) of various SAR design options. The previous papers considered the performance impact of SAR range/cross-range resolution and compared the use of 1-D HRR (high-range-resolution radar) versus 2-D SAR, versus multisensor, 3-D SAR. The work reported here extends the SAR and HRR results of Ref. 2 to include aspect diversity in the SAR measurements. We show that SAR and HRR are benefited by multi-aspect measurements mostly because multiple views add diversity: poorer views benefit from having better views combined in a multi-aspect classifier. Finally, as a proof of concept, multi-aspect diversity is incorporated into an existing SAR ATR classifier; performance of an MSTAR 10-class MSE classifier is shown to improve substantially. A major tenet is verified by the experimental results: added measurement domains, such as aspect diversity, which separate the target signature vectors in the observation space, make it easier to obtain better target classification, enhanced false- alarm rejection, and robustness to unknown statistics.

Convergence Rate of the Extended SMI Algorithm for Narrowband Adaptive Arrays

An extended sample matrix inversion (SMI) algorithm can be used for minimizing the mse (mean-squared error) between the output of an N-element adaptive array and a desired reference signal. This algorithm is shown to yield mse within 3 dB of minimum (on the average) after (2N - 1) observations of the antenna element outputs.

Fundamental SAR ATR performance predictions for design trade-offs: 1D HRR versus 2D SAR versus 3D SAR

This paper continues the development of a fundamental, algorithm-independent view of the ATR performance that can be achieved using SAR data. Such ATR performance predictions are intended to enable evaluation of performance tradeoffs for SAR designs, including both parameter selections (e.g., bandwidth and transmit power) and added domains of SAR observation, such as 3-D, full polarimetry, aspect diversity, and/or frequency diversity. Using a Bayesian framework, we show target classification performance predictions for two tactical targets (either stationary with radar netting assumed deployed, or moving) using three different domains of observation: 1-D HRR (high-range-resolution radar), 2-D SAR, and 3-D SAR. Comparisons of the three domains are made at 3m, 1m, 0.5m and 0.3m range and cross-range resolutions. The discussion of 3-D SAR includes parameter tradeoffs of various height resolutions at the target, and various numbers of sensors. For each measurement modality, we list some of the unique sensitivities which could cause performance degradations.

Aspects of threshold region mean squared error prediction: Method of interval errors, bounds, Taylor's theorem and extensions

The method of interval errors (MIE) predicts mean-squared error (MSE) performance at low signal-to-noise ratios (SNR) where global errors dominate. It is algorithm specific and enabled by an estimate of asymptotic MSE performance and sidelobe error probabilities. Parameter bounds are adequate representations of the asymptotic MSE in absence of signal model mismatch, but Taylor theorem can account for this mismatch. Herein limitations of bounds versus Taylors theorem to represent the asymptotic MSE of nonlinear schemes like maximum-likelihood are discussed. Use of first-order Taylor expansions for the purpose of improved approximation of sidelobe error probability is likewise explored.

Coherent Square Wave Demodulation of Ideal Limiter Output

An ideal limiter may be used to single-bit quantize a noisy sinusoidal signal. This digitization is particularly economical if the signal is to be recorded. lt might then be desired to obtain phase coherence with the limited input signal. A single-bit digital phase-locked loop. utilizing a square wave reference, could be used for this purpose. The effects of coherent square wave demodulation on the signal-to-noise ratio and the (signal-to-noise spectral density) ratio are discussed. The latter result is directly applicable to the performance of the digital phase-locked loop.