Capacity of wireless channels and networks
One of the fundamental issues in the design of a wireless communication system is how fast data can be transmitted reliably. The theoretical upper bound for speed of data transmission over a channel is called the channel capacity. The capacity of time-varying channels depends on what is known about the channel at the transmitter and/or receiver. It also depends on whether rate can be adaptive or constant, as well as whether or not service outage can be tolerated. We have investigated capacity and capacity regions of time-varying multiuser channels, cellular systems, and ad-hoc networks with one or more antennas at the transmitter(s) and receiver(s).
We consider massive MIMO systems, i.e. systems with a large number of transmitter and/or receiver antennas, and look into the benefits achievable in the asymptotic regime of large antennas. Our work focuses on low-complexity transmission and detection of uncoded symbols reliably through the said systems. Our research focuses on exploiting the spatial diversity inherent in large antenna systems to provide noncoherent communication schemes, i.e. schemes where the transmitter and the receiver do not know the instantaneous communication channel, but know the statistics. Based on a characterization of the finite antenna behaviour of such systems, we propose encoding and decoding schemes and investigate the competitiveness of these schemes with schemes exploiting instantaneous channel knowledge. Our investigations use techniques from optimization, error exponent analysis, space-time coding, and robust design. We also have developed novel cryptographic schemes based on large dimensional random matrices. In these schemes the complexity involved in decoding massive MIMO systems is used to provide low-complexity physical-layer encryption commensurate with the most sophisticated forms of application-layer encryption.
Green wireless system design
A large chunk of the wireless system infrastructure in place today was not built with energy efficiency in mind. However, with ever increasing demands for wireless services, this is a significant bottleneck to future expansion. We take a cross-layer approach to studying energy efficiency in the entire communication chain. We investigate the fundamental limits of energy involved in transporting bits from one point to another. We develop models of bit transport interactions across the entire communication system chain, from the circuits of the baseband processing blocks to the networks of communicating agents that they support. This allows us to investigate the tradeoffs among QoS, power consumption and cooperation requirements on wireless networks at different layers of the communication chain.
Cognitive radio networks
Spectrum is a very scarce resource in commercial deployments of wireless networks. This has led to interest in intelligent or cognitive radios which would be able to make opportunistic use of spectrum not licensed to it, thereby coexisting with legacy systems. Our research focuses on developing enabling schemes for this technology, right from coding techniques optimal for different regimes of operation to techniques which allow smarter interference management under very general conditions.
Wireless sensor networks
A special challenge of sensor networks is that they are energy limited (which is stricter than power limitations) and hence the conventional techniques of designing layers of the communication network protocol often does not carry over into such regimes. Our research takes a cross layer approach and looks into energy conscious design starting right from the physical layer to the network and transport layer.
Compressed sensing in wireless systems
While the Shannon-Nyquist sampling theorem has made possible the representation of real world signals in digital domain, and is one of the most prominent theoretical foundations of the digital age, the frequency domain restriction on signals is often too restrictive. We investigate the limits of communication system design outside this paradigm and look at exploiting other prior knowledge of real world systems and channels to come up with design insights for the practicing engineer.
Distributed sensing, communications, and control
This area of research focuses on the interplay between control and communications, optimal sparse sensing and state estimation for high-dimensional control systems, as well as sensor placement, outage detection, and cyber-physical security for the smart grid.
Communications and signal processing in bioengineering and neuroscience
One of our major focus areas is the use of the information theoretic notion of directed information to improve detection of neural connectivity. Current methods of inferring the connectivity of neurons generalize notions of Granger causality and find the directed information of a pair of neurons’ spike trains. These methods can lead to a few major false positive scenarios. These false positives have been shown to be avoidable if all vital neurons in the network are recorded and included in the directed information measure. In practice, however, it is restrictive and expensive to capture the signal from all such vital neurons. To address this issue, we propose a modified method that uses the spike trains of only the two neurons as well as side information readily available to the experimenter to detect neural connectivity with fewer false positives.
We have also applied signal processing methods to separate gene expression microarray mixed cell tissue samples. For example, tumor biopsy tissues that are profiled using microarrays contain a mixture of tumor cells, infiltrating immune cells and additional microenvironmental cells such as fibroblasts. Previous studies have shown that microarray measurements are well modeled as a linear mixture of multiple signatures from different cell types. This problem is almost identical to signal processing of hyper-spectral imaging. Thus, by incorporating state of the art signal processing tools we successfully identify the cell types in the mixture, extract their individual signatures and relative proportions per sample (Zuckerman et al. PLoS Comput Biol. 2013;9(8):e1003189). Application of this method to the abundance of gene expression microarray samples that exist in publicly available repositories can be a powerful tool for the discovery of phenomena otherwise not detected in the mixed tissue samples of individual experiments.
Reliability and security of modern power grid
Economic and social loss due to power grid outages and blackouts have been huge due to the lack of effective sensing, communications, data processing and control over the grid. As the grid becomes increasingly complex and dependent on modern information technology, its security against cyber-physical attacks is another critical issue. We provide solutions to these urgent issues by leveraging the advancement in sensing devices and developing efficient and real-time power network monitoring, analysis and control systems.
Information limits of analog to digital schemes
Although most of the information stored in today's machines is digital, real world physical systems assume a continuum of states. This implies that analog to digital conversion and possible information loss is an inherent part of any practical wireless communication system. This information loss can be associated with both sampling and quantization errors. Although the sampling error can be eliminated by sampling at the Nyquist rate, technology limitations may preclude us from doing so and sub-Nyquist sampling techniques have to be employed. We study the performance loss due to sub-Nyquist sampling from an information theoretic framework. Specific metrics include capacity loss in channels with sampling at the receiver end and the minimal distortion in rate-limited descriptions of sampled processes.