## Signals, Information, Inference, and Learning (SIIL) Group

*[I’ve recently moved to Duke University. New website forthcoming.]*

The Signals, Information, Inference, and Learning (SIIL) Group focuses on the theory, application, and practice of statistical signal and array processing. Our goal is to advance technology for existing and emerging next generation systems through innovative algorithm development, solid theory and analysis, performance bounding, and experimental validation of concepts. Multisensor / multichannel applications and topics of interest include but are not limited to:

- Cooperative Radar-Communications (Shared-Spectrum / RF Convergence)
- Cognitive MIMO Radar / Sonar
- Machine and Deep Learning
- Bayesian Sparse Vector Recovery
- Information Theory–Estimation Theory Interplay
- Geolocation (positioning, navigation, and timing (PNT))
- Robust Adaptive Filtering / Beamforming
- Adaptive Radar Detection and Estimation
- Synthetic Aperture Radar (SAR) Image Change Detection
- Robust Parameter Estimation and Bounds Under Model Misspecification
- Communication Over Dynamic Channels
- Adaptive MIMO Communications

#### Christ D. Richmond

Associate Professor Director of SIIL Group

### Shared-Spectrum / RF Convergence

The limited availability of frequency spectrum requires greater spectral efficiency to meet the increasing demands for communication (comm.) and data services. Thus, exploring the possibility of diverse RF systems coexisting within the same frequency band is a means of improving spectral efficiency. Radars coexisting in the same frequency band as comm. systems presents a set of new challenges for system design and analysis. We are exploring both the fundamental theory enabling such coexistence, and the development of algorithms to realize new capabilities to support emerging technologies. Military, civilian, and industrial systems potentially will be affected by this move toward shared-spectrum. Coexistence also will be essential to facilitate the required comm. needs of self-driving automotive vehicles.

Recent Papers:

- A. S. Bondre and C. D. Richmond, “Asymptotic Distribution of Generalized Likelihood Ratio Test Under Model Misspecification with Application to Cooperative Radar-Communications,” Proceedings of the ICASSP, June 6—11, 2021, pp. 8463-8467.
**[Invited Paper**, Special Session: Robust Sensing and Detection in Congested Spectrum] - A. Coluccia, G. Ricci, and C. D. Richmond, “Adaptive Radar Detection Without Secondary Data for Uncooperative Spectrum Sharing Scenarios,” IEEE Transactions on Signal Processing, vol. 69, pp. 3206—3219, June 2021.
- A. Herschfelt, A. Chiriyath, D. W. Bliss, C. D. Richmond, U. Mitra, and S. D. Blunt, “Vehicular RF Convergence: Simultaneous Radar, Communications, and PNT for Urban Air Mobility and Automotive Applications,” IEEE Radar Conference, Florence, Italy, September 21—25, 2020.
- T. Ali, A. S. Bondre, C. D. Richmond, “On Wilks’ Theorem for Generalized Likelihood Ratio Test Performance of Cooperative Radar-Communications,” IEEE Radar Conference, Florence, Italy, September 21—25, 2020, pp. 1—6.
**[Invited Paper]** - A. Chiriyath, C. D. Richmond, D. W. Bliss, “Multiple-Channel Multiple-User Normalized Matched Filter Detector for RF Convergence,” Proceedings of the 53rd Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, November 3—6, 2019.
**[Invited Paper,**Special Session Spectrum Sharing]. - C. D. Richmond, “Generalized Likelihood Ratio Test Performance for Cooperative Radar-Communications,” Proceedings of the 52nd Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, October 28—31, 2018, pp. 957—961.
**[Invited Paper**, Special Session on Radar-Communications RF Convergence]. - C. D. Richmond and P. Basu, “Architectures for Cooperative Radar-Communications: Average vs. Generalized Likelihood Ratio Tests,” Proceedings of the IEEE Radar Conference, Oklahoma City, OK, April 2018, pp. 1—6.
**[Invited Paper**, Special Session on RF and Communications Convergence] - C. D. Richmond, P. Basu, R. E. Learned, J. Vian, A. Worthen, and M. Lockard, “Performance Bounds on Cooperative Radar and Communication Systems Operation,” Proceedings of the IEEE Radar Conference, Philadelphia, PA, May 2016, pp. 1—6.
**[Invited Paper**, Special Session on Radar-Communications Cooperation]

### Cognitive Radar / Sonar

Bats and dolphins are known to use echo location to find food and navigate their environments, and likely inspired the original concept of radar and sonar. Closer examination reveals that bats and dolphins actually adapt their chirp waveform emissions as their task evolves. The concept of cognitive radar / sonar builds on this observation by instituting multiple levels of system agility that allow adapting waveform characteristics, integration times, transmit powers, platform geometries, etc. as the mission evolves. Such agility has demonstrated improved performance over conventional radar/sonar. When coupled with layers of artificial intelligence, cognitive systems are expected to pave the way toward the next generation of radar / sonar technology. We are working to develop meaningful performance bounds for such systems, and exploring the incorporation of deep learning methods to better leverage the benefits of AI.

Recent Papers:

- T. Ali and C. D. Richmond, “Optimal Target Detection for Random Channel Matrix-Based Cognitive Radar / Sonar,” IEEE Radar Conference, Atlanta, GA, May 10-14, 2021.
- C. D. Richmond, “Optimal Target Detection for Cognitive MIMO Radar/Sonar,” 2019 IEEE Underwater Acoustic Signal Processing Workshop, West Greenwich, Rhode Island, October 2019, p. 24.

### Machine and Deep Learning

The increase in large amounts of stored labeled data (sometimes called “big data”) by many technology companies (e.g. Google, Facebook, Amazon, etc.) has set the stage for techniques such as machine and deep learning to extract incredible amounts of useful information and provide new and exciting capabilities. Such techniques are amazingly adept at finding and exploiting hidden structure within data. We are very interested in applying these learning techniques to classical problems in radar/sonar and communications.

### Bayesian Sparse Vector Recovery

Many engineering applications involve signals residing in a low dimensional subspace, or sometimes signals are intentionally transformed into a lower dimensional subspace (e.g. via compressed sensing). Sparse vector recovery aims to determine this low dimensional subspace from noisy data measurements, and knowledge of a much larger (underdetermined) space known to include the lower dimensional signal subspace. When cast within a Bayesian estimation framework, a selection of the prior distribution can be made to reflect desired signal sparsity. Variational Bayesian methods attempt to improve computations by using a misspecified prior distribution, but one that yields better computational efficiency. We are interested in quantifying the performance loss suffered versus the gains in computational savings. Emerging techniques based on message passing appear to achieve better computational efficiency, while not using a misspecified model. So, we are also exploring the potential of applying such techniques to other areas.

Recent Papers:

### Information Theory-Estimation Theory Interplay

New intimate relationships between Information Theory and Parameter Estimation have surfaced over the last twenty years. Perhaps the most prominent is the I-MMSE that relates mutual information and the mean squared error (MSE) of the minimum MSE estimator. Such relationships provide new insights and perspectives on signal processing, and may hold the key to achieving true spectral efficiency in shared-spectrum / RF convergence systems.

### Robust Adaptive Filtering / Beamforming

The optimal adaptive beamformer (ABF) maximizing output signal-to-interference plus noise ratio has filter weights that depend on the data covariance and signal array response vector. The effectiveness of practical application of this optimal beamformer, however, is limited by (i) data stationarity (needed for covariance estimation), and (ii) knowledge of the true signal array response vector. Robust ABF (RABF) methods embrace these two critical issues by reformulation of the ABF weight optimization to account for them and minimize their effects. We are interested in various aspects of robust ABF including insights from random matrix theory, application of machine / deep learning methods, and the implications of information theory based universal schemes.

Recent papers:

- C. D. Richmond, “Signal-to-Interference-plus-Noise Ratio Loss Constrained Robust Adaptive Beamformer Inpsired by Random Matrix Theory,” Proceedings of the 179th Meeting of the Acoustical Society of America, December 7—11, 2020. [
**Invited Talk,**Special Session: Random Matrix Theory in Acoustics] - C. D. Richmond, “Capon-Bartlett Cross Spectrum and A Perspective on Robust Adaptive Filtering,” Special Issue on Robust Multi-Channel Signal Processing and Applications: On the Occasion of the 80th Birthday of Johann F. Bohme,
*Signal Processing*, Elsevier, Vol. 171, June 2020. - S. Krishnamurthy, D. W. Bliss, C. D. Richmond, V. Tarokh, “Peak Sidelobe Level Gumbel Distribution of Antenna Arrays with Random Phase Centers,”
*IEEE Transactions on Antennas and Propagation*, Vol. 67, No. 8, August 2019, pp. 5399—5410.

### Adaptive Radar Detection and Estimation

Adaptive radar detection and estimation make use of multiple data measurements collectively to accomplish the tasks of target detection and parameter estimation in the presence of additive clutter, jamming, and noise of unknown covariance. Several algorithms have been developed and studied in detail, and continue to find wide use in many adaptive radar systems, including the adaptive matched filter (AMF), the generalized likelihood ratio test (GLRT), and the adaptive coherence estimation (ACE). We are interested in applying these techniques in new areas and using them in the context of transfer learning.

Some Papers:

- C. D. Richmond, “Mean Squared Error and Threshold SNR Prediction of Maximum-Likelihood Signal Parameter Estimation with Estimated Colored Noise Covariances,” IEEE Transactions on Information Theory, Vol. 52, No. 5, May 2006, pp. 2146–2164.
- C. D. Richmond, “Capon Algorithm Mean Squared Error Threshold SNR Prediction and Probability of Resolution,” IEEE Transactions on Signal Processing, Vol. 53, No. 8, August 2005, pp. 2748-2764.
- C. D. Richmond, “Performance of a Class of Adaptive Detection Algorithms in Non-Homogeneous Environments,” IEEE Transactions on Signal Processing, Vol. 48, No. 5., May 2000, pp. 1248-1262.
- C. D. Richmond, “Performance of the Adaptive Sidelobe Blanker Detection Algorithm in Homogeneous Environments,” IEEE Transactions on Signal Processing, Vol. 48, No. 5, May 2000, pp. 1235-1247.

### Synthetic Aperture Radar (SAR) Image Change Detection

Synthetic aperture radar (SAR) exploits the relative motion of the radar platform to synthesize an effective array aperture during a coherent processing interval that in combination with judicious waveforms and signal processing can create photograph-like images of stationary targets and other scatterers in the scenes of interest. SAR is attractive for several reasons, but one advantage is its ability to create these images regardless of weather and lighting conditions. SAR change detection seeks to determine if a scene has changed since last inspection by comparing SAR images taken from the same area at different times. Such can be valuable for agricultural surveys, forest observations, and natural disaster damage assessments. We are interested in developing and applying SAR change detection algorithms to new areas, including synthetic aperture sonar.

Recent Papers:

- A. S. Bondre and C. D. Richmond, “Theoretical Analysis of a Symmetric Two-Stage Change Detector for SAR Images,” IEEE Transactions on Geoscience and Remote Sensing, Early Access June 2021, pp. 1–17, doi: 10.1109/TGRS.2021.3087530.
- A. S. Bondre and C. D. Richmond, “On Threshold Selection for Improved SAR Two-Stage Change Detection,” IEEE Inter. Radar Conference, Washington, D. C., April 28—30, 2020.
- M. Cha, R. D. Phillips, P. J. Wolfe, and C. D. Richmond, “Two-Stage Change Detection for Synthetic Aperture Radar,” IEEE Transactions on Geoscience and Remote Sensing, Vol. 53, No. 12, December 2015, pp. 6547—6560.

### Robust Parameter Estimation and Bounds Under Model Misspecification

Much of signal processing and statistical inference is data model-based. These models, when correct, allow determination of fundamental limits on detection, classification/association, parameter estimation, data compression, and information rate transfer. Data models, however, are rarely specified correctly, as modeling errors often persist at some level. Robust estimation methods provide algorithms and procedures that are less sensitive to modeling errors. Bounds on parameter estimation that account for the possibility that the assumed model could differ from the true data model have also been developed, and are referred to as misspecified parameter bounds. Such bounds yield insight into the complex trade space that robust estimation schemes attempt to navigate. We are interested in developing robust estimation techniques for adaptive communications, and passive sonar.

Recent Papers:

- C. D. Richmond, “On Constraints in Parameter Estimation and Model Misspecification,” Proceedings of the 21st International Conference on Information Fusion (FUSION 2018), Cambridge, United Kingdom, July 10-13th 2018, pp. 1080—1085. [Invited Paper, Special Session on Lower Bounds for Parameter Estimation and Beyond]
- S. Fortunati, F. Gini, M. S. Greco, and C. D. Richmond, “Performance Bounds for Parameter Estimation Under Misspecified Models,” IEEE Signal Processing Magazine, Vol. 34, No. 6, November 2017, pp. 142–157.
- C. D. Richmond and L. L. Horowitz, “Parameter Bounds on Estimation Accuracy Under Model Misspecification,” IEEE Transactions on Signal Processing, Vol. 63, No. 9, May 2015, pp. 2263—2278.

### Communication Over Dynamic Channels

Airborne communication channels can face some major challenges. The general nature of aeronautical channels, the high dynamic mobility of some airborne platforms, the complex scattering encountered over terrains traversed by these airborne platforms, and varied interference challenges (intentional and unintentional) are all central factors contributing to the complexity of some airborne communication networks. Opportunities exist to advance the state-of-the-art for these challenging environments, and we’re pursuing various approaches.

Recent Papers: