1. Fundamental Limits for Cognitive Radios
We are exploring the basic constraints on the operation of opportunistic radios that take advantage of the gaps in spectrum utilization that currently exist, while preserving the operation of legacy systems. The goal is to provide the appropriate technical perspective for a roadmap for spectrum regulation in the medium to long term. Our initial results indicate that there might be substantial advantages to building out non-frequency-specific infrastructure (whether ad-hoc or otherwise). This suggests that the conventional wisdom behind exclusive property-rights in spectrum could be missing half the story since such a right to exclude would discourage, rather than encourage, investments in the potentially most useful infrastructure.
So far, our technical focus has been on quantifying the limits on the sensing side. While in standard data communication, it is possible to engineer systems that typically operate at medium-to-high SNRs, the opportunistic case is fundamentally limited by low SNR behavior since that is the typical case when a band is free for opportunistic use! Opportunistic systems are thus more sensitive to uncertainties and unmodeled characteristics of the environment, and we have begin to quantify how cooperative diversity might be required to overcome some of these sensitivies. While many multiuser data communication systems are interference limited and require power control and MAC protocols to maintain data throughput, in the opportunistic case, power control and MAC protocols must also be used to preserve the sensitivity required to guarantee non-interference with potential legacy systems.
2. Delay Universality in Channel and Source Coding
Rather than fixing the message set and letting the block-length vary with the source, we explore fixing the input rate and letting the target delay vary with the application. This sort of delay universality turns out to be required in the relevant separation theorems for certain unstable processes. So far, we have explored these ideas in distributed lossless source coding, point-to-point channel coding, as well as multiterminal channel coding problems like MAC and degraded broadcast channels. The ultimate goal of the multiterminal work is to understand what the right architecture is for delay-sensitive and rate-sensitive applications to share a common communication medium. Preliminary results are already questioning the conventional wisdom holding that delay-sensitive applications need to operate within a clean band without external interference.
3. Feedback, Reliability, and Control
We are exploring the use of feedback to improve the reliability of communication systems. So far, we have developed a new upper bound (the "focusing bound") that quantifies the substantial improvements in the fixed-delay reliability function with feedback, and showed that this bound is asymptotically achievable for certain classes of channels given noiseless feedback by using appropriate flow control. This improved reliability with feedback is particularly surprising given that fixed-block reliability functions can achieve no such gain.
The fixed-delay reliability functions with feedback are particularly important since delay-universal (anytime) communication problems are intimately connected to remote stabilization problems in which a control system must operate over a noisy communication link. This connection is just one example of our larger research program in which we attempt to build an appropriate heirarchy of communication problems partially ordered by the channel resources they require.
In addition to the fixed-delay reliability functions, we are also interested in both fixed and variable block schemes. For fixed blocks, we have shown that generic Gaussian multiuser schemes can achieve arbitrarily high reliability improvements with feedback, as long as they operate under an average power constraint. For variable blocks, we have been exploring the limits on the feedback required to get reliability gains. So far, we have considered average-rate-limited noiseless feedback as well as high-quality, but noisy, feedback.