Covert, or low probability of detection (LPD), communications clearly has significant application, from scenarios ranging from covert military operations and the organization of social unrest, to the protection of users from having their movements tracked on an everyday basis. In addition, encrypted data or even just the transmission of a signal can arouse suspicion, and even the most theoretically robust low probability of intercept (LPI) or cryptographic security scheme can often be defeated by a determined adversary using non-computational methods such as side-channel analysis. The topic of LPD communications for wireless communication systems has laid largely dormant since its study in classical spread-spectrum systems.

The goal of this project is to embark on a comprehensive study of LPD wireless communications, asking: (1) what are the fundamental limits of LPD communication?, (2) how do we achieve those limits?, and (3) what are the barriers to the implementation of those results?

The University of Massachusetts at Amherst is teaming with Raytheon/BBN Technology to investigate these questions.

This work is supported by the National Science Foundation under Grant Number ECCS-1309573 and CNS-1525642. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

In addition to the research below, we are active in ** undergraduate education and K-12 outreach **.
Prof. Goeckel advised a senior capstone project that developed an intuitive 3-D modeling interface at
both the input and output; most notable is an output that is a true 3-D hologram. Prof. Goeckel and
the team have begun to take the "hologram machine" on the road, visiting a local elementary school on
May 8th, 2014 to engage young students in math and science. You can see a video of the
project here .

We gave a ** keynote ** at the Workshop on Wireless Physical Layer Security at ICC 2016:

The original formulation of the low probability of detection (LPD) problem for additive white Gaussian noise (AWGN) channels was presented at the IEEE International Symposium on Information Theory (ISIT) 2012, with a more complete version appearing in IEEE JSAC in September 2013. An extension to the practical case when the Warden Willie does not know the timing of the transmission was presented at the IEEE International Symposium on Information Theory (ISIT) 2014 and later appeared in the IEEE Transactions on Wireless Communications.

We have extended the work to optical channels, where the consideration of quantum mechanical effects must be considered. This work appeared in the IEEE International Symposium on Information Theory (ISIT) in 2013:

We know from our early work on covert communications that, if the warden Willie knows the statistics of the noise affecting his receiver, Alice can transmit no more than O(sqrt(n)) covert bits reliably to Bob in n channel uses of an additive white Gaussian noise (AWGN) channel. However, other authors have recently considered the case where Willie has some uncertainty about his noise statistics, in particular the average power of the noise impacting his receiver. These authors have shown that, if Willie does not know his noise statistics exactly but rather only knows that the average noise power falls in some range, Alice can covertly transmit O(n) bits in n channel uses. Here, we take a different approach. Rather than abstracting the error in Willie's estimation process to parametric uncertainty in his statistical model, we provide Willie with the full collection of channel observations and allow him to use them in whatever manner he chooses (e.g. for first channel estimation and then detection of Alice). In particular, we assume that Willie lacks knowledge of his channel statistics but observes T(n) length-n codeword periods, one of which may be used by Alice to attempt covert transmission. Under most operating conditions, we show that the warden Willie, even without a priori knowledge of his channel statistics, can limit Alice to the same covert performance scaling as when he knows his channel statistics, hence pointing in a different direction from the recent work of other researchers for this important problem. (Paper in preparation for * IEEE Wireless Communication Letters *).

Motivated by Willie's inability to detect transmission by Alice if we can somehow keep him from understanding the background noise power he should be observing when Alice is not transmitting, we consider the case where a single jammer, whom we term ``uninformed'' because he does not know when Alice might transmit, simply varies the power of the random noise that he puts into the environment. We consider various environments (AWGN, fading) and constructions for the jammer's strategy under which we are able to demonstrate that Alice can transmit O(n) bits in n channel uses. (Paper submitted to the Allerton Conference on Signals, Systems, and Computers.)

Finally, we have written a review article of this important area: