Massive wireless random access : a group testing approach
Keywords: Electrical Engineering.

Next generation wireless systems are widely expected to connect a massive number of low-energy wireless devices that form the fabric of smart technologies and cyberphysical systems. The resultant ``Internet of Things" is expected to be one of the major drivers of technological growth over the next decade. However, its design presents new challenges to wireless engineers. One of the key challenges is how to enable a massive number of low-energy wireless devices to sporadically access the scarce spectrum with minimal coordination and channel estimation overheads. In this dissertation, we focus on this fundamental question. We describe a mathematical framework to study this problem and show how this framework relates to a seemingly unrelated problem in theoretical computer science called group testing. Inspired by this connection, we develop novel group testing codes that are optimal under constraints on the number of tests each item can participate in, or the number of items each test can include. We show that these codes can be translated to innovative energy-efficient random-access protocols which embrace sensor collisions and thus eliminate the complexity and energy cost of collision resolution and retransmissions. We then extend our results in a number of different directions. We incorporate the channel noise in our model and develop both combinatorial and statistical group testing codes that are resilient to errors. We further consider the asynchronous case by removing the assumption that the users' transmissions are aligned, which may not necessarily hold in practical applications. We let the users' transmissions within a frame be received with arbitrary and unknown delays at the receiver. We show that such delays can be accommodated by designing cyclic group testing codes without introducing any additional penalty in transmission length with respect to the synchronous case. We further contribute to the group testing literature by introducing an order-optimal explicit construction in the statistical setting. We show that a famous construction introduced by Kautz and Singleton for the combinatorial group testing problem (which is known to be suboptimal for combinatorial group testing in general) achieves the order optimal tests in the statistical group testing problem. We provide a novel analysis of the probability of a non-defective item being covered by a random defective set directly, rather than arguing from combinatorial properties of the underlying code, which has been the main approach in the literature. Finally, we focus on energy harvesting wireless devices as energy harvesting is expected to be one of the key technologies for building self-sufficient, self-sustainable wireless transceivers for IoT networks. Due to the challenging nature of the problem, as a starting point we focus on the multiple access problem rather than random access, where a fixed and known set of transmitters communicate to a central receiver in a synchronous setting. In this setting, the transmitters are powered by an exogenous stochastic energy harvesting process and equipped with finite batteries. We characterize the capacity region of this channel as an $-letter mutual information rate and develop inner and outer bounds that differ by a constant gap. An interesting conclusion that emerges from our results is that the sum-capacity approaches that of a standard AWGN MAC (with only an average constraint on the transmitted power), as the number of users in the MAC becomes large. Therefore, our results show that with carefully designed power control schemes and coding strategies, the random energy dynamics at the transmitters do not impose any significant penalty on the communication performance