Control Overhead Optimization in Wireless Resource Allocation Problems
Authors:   , Ren Jie , Walsh John MacLaren 
Published: July 2021

Under many traditional resource allocation and link adaptation architectures of modern wireless communication systems, such as those utilized in the Long Term Evolution 3GPP standard, channel quality indicators (CQI) and other channel parameters are sent as uplink feedback, and these are utilized to determine which user should get which resource blocks as well as deciding the coding scheme. Then the base station must signal the resource decision on the downlink as overhead control information in addition to the data to be transmitted to the user itself. These resource decisions control information, along with the channel quality feedback utilized to make them, create control overhead in the multiuser OFDMA system that are surprisingly large, with the control information such as resource decisions and reference signals typically occupying roughly a quarter to a third of all downlink transmission in the LTE standard. Inspired by this observation, in this dissertation, we focus on determining how to efficiently encode control information salient for resource allocation from the view of both information theory and communication. In the first section of the dissertation, we model the CQI feedback process as a lossless distributed function computation problem, and consider the special case that there is an infinite backlog of traffic at the basestation that is waiting and destined for each user. Via computation of related fundamental information theoretic limits, we show that, if the basestation is not allowed to interact with the users, a small amount of control information compression beyond that required to simply forward channel quality information is possible. However, the amount of information saved by even the best possible lossless non-interactive scheme is small and does not scale with the number of users. Next, switching to a model in which the resource decisions can be made interactively with the users, we show that substantial control rate compression is possible for this CQI feedback process. In particular, a feedback process that is structured in a similar manner to an auction yields rate savings which are proven to scale proportionally with the number of users. This shows that, provided interaction is included into the model, substantial rate savings relative to simple channel quality information forwarding can be achieved with simple schemes. Next, we improve the model of the resource allocation problem by incorporating downlink traffic arrival statistics into the scheduling, and the signals the basestation sends into the optimization. Including the consideration of the control signals sent into the model enables the optimization of control signals flowing on the downlink, and thus the potential to reduce the footprint of control information in the downlink, which was the problem which originally motivated the research. The incorporation of arrival statistics and the buffer at the basestation involves adding memory into the model, and the problem is no longer one involving simple multiterminal source compression, but one of a distributed Markov decision process (MDP). In particular, the basestation directly observes how much information is currently in the buffer destined for each user, and the users know their individual channel qualities. A MDP framework can be applied to this problem to yield optimal resource controllers, which form the resource allocation decision as a function of both the users' channel qualities and the buffer information. While an omniscient controller having simultaneous access to all of these channel qualities and the buffer information could implement these resource decisions, the fact that the observations are spread throughout the network require coordination between the users in the form of control messages. The final section of the dissertation considers the fundamental limits for such MDP problems where the global state is composed of a series of local states, each observable at a different node in a network. First, using recent results from multiterminal information theory, bounds on the minimum amount of control information required for the nodes to perfectly simulate the omniscient controller are presented, both for one-shot and for interactive control messaging schemes. Next, this control overhead cost is included as a negative term into the reward function for the MDP, and a tradeoff between control overhead and controller performance is defined. The resulting optimization problem is complex, and hence an alternating optimization algorithm is presented to yield candidate messaging and controls schemes. It is shown that the presented algorithm yields a sequence of combined rewards which always converges, and when the associated control map and messaging converge, they always yield a Nash equilibrium for the associated optimization problem. Throughout this final section, each stage of the development is accompanied with a detailed example showing how to apply the framework to the wireless resource allocation problem. The dissertation then concludes with a number of fruitful directions for future research.