| PhD Seminar

Name of the Speaker: Mr. Prashant N (EE18D202)
Guide: Prof. Lakshmi Narasimhan
Venue: ESB-244 (Seminar Hall)
Date/Time: 18th September 2024 (Wednesday), 11:00 AM
Title: Decentralised and Invariant Resource Allocation Policies for Multiple Access Channels

Abstract :

In wireless communications, the fading multiple access channel (MAC) serves as a model for systems in which multiple users transmit information over fading channels to a single receiver. Our research focuses on exploring optimal power allocation policies to maximize the sum rate for non-cooperative users with individual transmit power constraints for various MAC wireless systems. This optimization of power allocation for various wireless systems may be a non-convex problem. We provide an alternating maximization algorithm to compute near-optimal policies for non-convex problems and optimal policies for convex problems.

In this system, a phenomenon, that we refer to as invariance, is observed when the number of transmitting users in the system is sufficiently large. Under invariance, the optimal power allocation policy of a user becomes independent of the other users. This enables decentralized computation of optimal power allocation strategies. Further, when new users get added to the system or a few current users drop out of the system, re-computation of the optimal power allocation scheme would not be required under invariance. We analyze this invariance phenomenon and provide conditions under which invariance occurs. We also derive the optimal power allocation strategy under invariance. The power allocation policies thus derived are shown to achieve the global maxima of the sum-rate optimization problems.

We perform the above analysis for the following MAC models. 1) Indoor Optical Wireless MAC: The indoor optical wireless MAC has multiple mobile users communicating using infrared to an access point. The wireless optical channel is non-negative real-valued and the exact capacity of it is not known. We use a tight lower bound on the sum rate to formulate the power allocation optimization problem with per-user average and peak transmit power constraints. This optimization problem turns out to be non-convex. Here, the conditions under which invariance occurs and the invariant power allocation policy are derived.

2) Gaussian MAC: This MAC is the standard model of RF wireless communication systems. A non-convex power allocation optimization problem is formulated using the Gaussian sum-rate expression with per-user average power constraint. The conditions for the existence of invariance are derived. Further, we show that, under certain conditions, the invariant power allocation strategy is a greedy policy.

3) Generalized Gaussian (GG) MAC: In contrast to previous MAC models where the additive noise follows a Gaussian distribution, the GG-MAC has additive noise that follows the generalized Gaussian distribution. The GG distribution can accurately model the additive noise in multiple systems such as ultrawide numbers and RF communications, acoustic communications, etc. First, we derive a tight lower bound on the capacity of this system and its sum rate with per-user average and peak transmit power constraints. Next, we formulate a convex power allocation problem using a lower bound on the sum rate. Finally, as before, we obtain the conditions for the existence of invariance and show that the greedy policy is the invariant power allocation strategy when there are sufficiently large numbers of users in the system.