Saleem A. Kassam

Distributed detection with multiple sensors II. Advanced topics

Following the foundational work that established basic ideas for optimum distributed defection schemes using multiple sensors (as reviewed in Part I of this two-part review), further work on distributed detection has developed many useful and interesting extensions of the basic concepts. These more recent developments parallel those that arose from the early work on centralized, classical signal detection, resulting in new ideas of asymptotically optimum nonparametric, robust, and sequential centralized detection. Recent developments on these topics in the setting of distributed signal detection are reviewed in the present paper. Results in these directions are important in practice because they allow cases of modeling uncertainty to be addressed, and they provide more efficient detection schemes by optimizing more general performance criteria.

Finite-state Markov model for Rayleigh fading channels

We form a finite-state Markov channel model to represent Rayleigh fading channels. We develop and analyze a methodology to partition the received signal-to-noise ratio (SNR) into a finite number of states according to the time duration of each state. Each state corresponds to a different channel quality indicated by the bit-error rate (BER). The number of states and SNR partitions are determined by the fading speed of the channel. Computer simulations are performed to verify the accuracy of the model.

Robust techniques for signal processing: A survey

In recent years there has been much interest in robustness issues in general and in robust signal processing schemes in particular. Robust schemes are useful in situations where imprecise a priori knowledge of input characteristics makes the sensitivity of performance to deviations from assumed conditions an important factor in the design of good signal processing schemes. In this survey we discuss the minimax approach for the design of robust methods for signal processing. This has proven to be a very useful approach because it leads to constructive procedures for designing robust schemes. Our emphasis is on the contributions which have been made in robust signal processing, although key results of other robust statistical procedures are also considered. Most of the results we survey have been obtained in the past fifteen years, although some interesting earlier ideas for minimax signal processing are also mentioned. This survey is organized into five main parts, which deal separately with robust linear filters for signal estimation, robust linear filters for signal detection and related applications, nonlinear methods for robust signal detection, nonlinear methods for robust estimation, and robust data quantization. The interrelationships among many of these results are also discussed in the survey.

Generalized median filtering and related nonlinear filtering techniques

We consider some generalizations of median filters which combine properties of both the linear and median filters. In particular, L filters and M filters are considered, motivated by robust estimators which are generalizations of the median as a location estimator. A related filter, which we call the modified trimmed mean (MTM) filter, is also described. The filters are evaluated for their performance on noisy signals containing sharp discontinuities or edges. It is shown that M filters can offer a more favorable combination of the running mean and median filters than can L filters, while MTM filters generally have better characteristics than M filters. We also show that an MTM filter is a data-dependent modification of L filters. The concept of double-window filtering is introduced as a refinement of MTM filtering. One representative set of filtered sequences of a test input using these filters are presented to illustrate the performance characterisics of these filters.

The unifying role of the coarray in aperture synthesis for coherent and incoherent imaging

Systems of two-dimensional (2-D) imaging arrays and apertures are considered from the point of view of their performance in the imaging of spatially incoherent as well as coherent source distributions. Such systems find applications in radar, sonar, and ultrasound imaging, as well as in applications such as seismology and radio astronomy. For linear imaging techniques related to beamforming and based on the Fourier transform relationship between the source distribution and the aperture plane measurements, the point spread function of the system completely characterizes its performance. This function is determined by the geometry of the physical aperture or array as well as the weighting that can be applied to measurements. It is shown that the introduction of the concept of coarray, both for receive apertures in incoherent imaging and for transmit/receive systems in reflection-mode coherent imaging, provides a convenient and elegant framework within which many apparently isolated techniques for point-spread function or aperture synthesis can be understood. In addition to this unifying role, coarray concept gives new insight into the aperture synthesis process, which allows interesting new imaging techniques to be developed, especially in coherent imaging. >

Synthetic aperture beamformer for imaging through a dielectric wall

A coarray-based aperture synthesis scheme using subarrays and postdata acquisition beamforming is presented for through-the-wall wideband microwave imaging applications. The wall causes wave refraction and a change in the propagation speed, both effects alter the travel time between the transmitter, the target, and the receiver. Coherent combining of the pulse waveforms emitted by the different transmitters and incident at the receivers through reflections from targets and clutter requires incorporation of wall effects into the beamformer design. Simulation results verifying the proposed synthetic aperture technique for a through-the-wall imaging (TWI) system are presented. The impact of the wall ambiguities or incorrect estimates of the wall parameters, such as thickness and dielectric constant, on performance is considered.

Channel equalization using adaptive complex radial basis function networks

It is generally recognized that digital channel equalization can be interpreted as a problem of nonlinear classification. Networks capable of approximating nonlinear mappings can be quite useful in such applications. The radial basis function network (RBFN) is one such network. We consider an extension of the RBFN for complex-valued signals (the complex RBFN or CRBFN). We also propose a stochastic-gradient (SG) training algorithm that adapts all free parameters of the network. We then consider the problem of equalization of complex nonlinear channels using the CRBFN as part of an equalizer. Results of simulations we have carried out show that the CRBFN with the SG algorithm can be quite effective in channel equalization. >

Optimum Quantization for Signal Detection

Optimum quantization of data, primarily for signal detection applications, is considered. It is shown that two useful detection criteria lead to quantization which gives the minimum mean-squared error between the quantized output and the locally optimum nonlinear transform for each data sample. This criterion is an extension of the usual minimum distortion criterion for optimum quantizers. Numerical results show that it leads to optimum quantizers which can be considerably better in their performance for non-Guassian inputs than the minimum-distortion quantizers.

Hybrid ARQ with selective combining for fading channels

We propose and analyze a hybrid automatic repeat request (ARQ) with a selective combining scheme using rate-compatible punctured convolutional (RCPC) codes for fading channels. A finite-state Markov channel model is used to represent the Rayleigh fading channels. We show that the hybrid ARQ with selective combining yields better performance than the generalized type-II ARQ scheme for fading channels. Furthermore, simulation results of real-time video time division multiple access (TDMA) transmission system are given. Better video quality can be obtained by our proposed scheme, with a bounded delay. Analytical results of throughput and packet error rate (PER) are compared to the simulated results. Our analysis based on a finite-state Markov channel model, is shown to give good agreement with simulations.

Robust Wiener filters

Abstract The performance of minimum mean-square-error estimation filters for signals in additive noise can deteriorate considerably for deviations of the actual signal and noise power spectral densities (PSDs) from assumed, nominal densities. We consider two classes of PSDs which are useful models for the signal and noise when their PSDs are not precisely known. For these classes, robust filters which are saddlepoints for mean-square- error performance are derived. The robust filters achieve their worst performance for pairs of least-favorable signal and noise PSDs for which they are the optimum filters. It is shown by a numerical example that the robust filter can be very useful in maintaining a reasonable error performance over the whole of the classes of PSDs.