Anil M. Rao

A denoising approach to multisensor signal estimation

Multisensor array processing of noisy measurements has received considerable attention in many areas of signal processing. The optimal processing techniques developed so far usually assume that the signal and noise processes are at least wide sense stationary, yet a need exists for efficient, effective methods for processing nonstationary signals. Although wavelets have proven to be useful tools in dealing with certain nonstationary signals, the way in which wavelets are to be used in the multisensor setting is still an open question. Based on the structure for optimal linear estimation of nonstationary multisensor data and statistical models of spatial signal coherence, we propose a multisensor denoising algorithm that fully exploits, in a statistically optimal fashion, the additional information afforded by multisensor measurements. Under certain conditions, we show that the proposed estimator can be realized efficiently and robustly in a completely blind fashion, employing only wavelet and discrete Fourier transforms while entailing only a small loss in performance.

Efficient detection with arrays in the presence of angular spreading

The spatial channel in applications such as radar, sonar, and wireless communications is typically characterized by complex signal scattering leading to multiple signal components arriving at the array from a spread of angles. This multipath angle spread is well known to lead to loss of spatial signal coherence, requiring complicated combining schemes to achieve optimal performance, particularly when the signal is partially coherent across the receiving array. We show that the discrete Fourier transform serves as an efficient, robust, and asymptotically optimal spatial combiner for uniform linear arrays (ULAs) in multipath channels. In addition, the proposed spatial processing allows for convenient integration of conventional frequency-domain methods for angle-of-arrival searches. Simulation results show that the proposed combining scheme provides near-optimal performance at significantly less computation, even for arrays of moderate size.

A denoising approach to multichannel signal estimation

Multichannel sensor array processing has received considerable attention in many important areas of signal processing. Almost all data recorded by multisensor instruments contain various amounts of noise, and much work has been done in developing optimal processing structures for estimating the signal source from the noisy multichannel observations. The techniques developed so far assume the signal and noise processes are at least wide-sense-stationary so that optimal linear estimation can be achieved with a set of linear, time-invariant filters. Unfortunately, nonstationary signals arise in many important applications and there is no efficient structure with which to optimally deal with them. While wavelets have proven to be useful tools in dealing with certain nonstationary signals, the way in which wavelets are to be used in the multichannel setting is still an open question. Based on the structure for optimal linear estimation of nonstationary multichannel data and statistical models of spatial signal coherence, we propose a method to obtain an efficient multichannel estimator based on the wavelet transform.

Nonstationary array signal detection using time-frequency and time-scale representations

Quadratic time-frequency representations (TFRs) and time-scale representations (TSRs) have been shown to be very useful for detecting nonstationary signals in the presence of nonstationary noise. The theory developed thus far is only for the single observation case; however, in many situations involving signal detection, there are advantages in using an array of receiving sensors. Sensor arrays allow for target or source localization and can provide a large gain in the SNR. We show that time-frequency and time-scale representations provide a natural structure for the detection of a large class of nonstationary signals in the presence of nonstationary noise using an array of sensors. That is, time-frequency and time-scale provide a detection structure that is both optimal and allows for efficient implementation. In developing the TFR/TSR-based optimal quadratic array processor, we consider several types of array environments including those with full, partial, and no coherence.

Efficient quadratic detection in perturbed arrays via Fourier transform techniques

Matched-field beamforming used in combination with a generalized likelihood ratio test is the most common detector structure in array processing situations. Unfortunately, various array perturbations caused by phase, calibration, propagation effects, or modeling errors can cause the sensor observations to become only partially correlated, limiting the performance of traditional matched-field beamformers that assume perfect coherence of the signal wavefronts. Quadratic array processing is optimal for many perturbed array problems; however, direct implementation poses a significant computational burden. We show that under certain conditions, the optimal quadratic detector for dealing with perturbed arrays can be approximately realized efficiently and robustly employing only discrete Fourier transforms to deal with spatial processing. In addition, we show that the proposed spatial processing allows for convenient integration of conventional frequency-domain methods for angle-of-arrival searches. Our proposed array detection structure provides the robustness and performance benefits of complicated quadratic processing at a computational cost comparable with that of traditional matched-field beamforming.

Efficient structures for quadratic time-frequency and time-scale array processors

Sensor arrays are able to enhance desired signal reception while simultaneously suppressing undesired components through the use of directionality. In many important applications, the return signal is best modeled as being nonstationary and may lose coherence between sensors, severely limiting the performance of traditional array processors based on matched-field beamforming. Quadratic array processing is optimal for many stochastic signals of interest, but direct implementation poses a significant computational burden making it impractical in many situations. It has been shown that quadratic time-frequency representations and time-scale representations (TFRs and TSRs) provide a structured detection framework for detecting certain nonstationary signals in the presence of nonstationary noise using a partially coherent sensor array, making quadratic array processing a viable alternative to suboptimal matched-filter techniques. In this paper we discuss restrictions on the decorrelation between sensors which lead to efficient TFR/TSR-based processors known as banded and subarray beamformers.

Efficient signal detection in perturbed arrays

The use of sensor arrays in signal processing applications has received considerable attention. Various array perturbations caused by phase, calibration, or modeling errors often cause the sensor observations to become only partially correlated, limiting the application of traditional matched-field beamformers. Quadratic array processing is optimal for many randomly perturbed array problems; however, direct implementation poses a significant computational burden. We propose a highly efficient, asymptotically optimal method of implementing quadratic array processors suitable for detection problems in randomly perturbed arrays. Specifically, we show that under certain conditions the optimal array processor can be approximately realized efficiently and robustly employing only discrete Fourier transforms to deal with spatial processing while entailing only a small loss in performance.

Multi-Sensor and Time-Space Processing: Quadratic Detection in Arrays Using TFDs

This chapter discusses the multi-sensor and time-space processing. It presents time–frequency methods suitable for multi-sensor and time-space processing. In underwater acoustics and telecommunications, separation of signal mixtures is traditionally based on methods such as independent component analysis (ICA) or blind source separation (BSS). These are formulated using time frequency distributions (TFDs) for dealing with the case when the signals are non-stationary. Multi-sensor data are processed with TFDs for channel estimation and equalization. In BSS and Direction of Arrival (DOA) estimation problems, the time–frequency approach to array signal processing leads to improved spatial resolution and source separation performances. The methods under this include time–frequency MUSIC, AD-MUSIC, and TFD-based BSS. In sensor array processing, for source localization, TFDs provide a good framework for hypothesis testing as they possess additional degrees of freedom provided by the t and f parameters. TFD-based array detection is formulated using the Weyl correspondence. The TFD-based structure allows the optimal detector to be implemented naturally and efficiently.

Efficient detection in the presence of angular spreading

The spatial channel in applications such as radar, sonar, and wireless communications is typically characterized by complex signal scattering leading to multiple signal components arriving at the array from a spread of angles. This multipath angle spread is well known to lead to loss of spatial signal coherence across a receiving sensor array, requiring complicated combining schemes to achieve optimal performance, particularly when the signal is only partially coherent across the array. We show that the discrete Fourier transform serves as an efficient, robust, and asymptotically optimal spatial combiner for uniform linear arrays in multipath channels. In addition, the proposed spatial processing allows for convenient integration of conventional frequency-domain methods for angle-of-arrival searches. Simulation results show that the proposed combining scheme provides near-optimal performance at significantly less computation, even for arrays of modest size.

Denoising multisensor data

Multisensor array processing of noisy measurements has received considerable attention in many areas of signal processing. The optimal processing techniques developed so far usually assume the signal and noise processes are at least wide-sense-stationary, yet a need exists for efficient, effective methods for processing nonstationary signals. While wavelets have proven to be useful tools in dealing with certain nonstationary signals, the way in which wavelets are to be used in the multisensor setting has only recently been considered. In this work we show how multisensor denoising can be carried out in perturbed, narrowband arrays even in the absence of the signal sources direction of arrival. We show that our proposed blind estimator can be implemented efficiently and robustly employing only wavelet and discrete Fourier transforms while entailing only a small loss in performance.