No regrets: Distributed power control under time-varying channels and QoS requirements

Abstract

The problem of power control in wireless networks consists of adjusting transmit power in order to achieve a target SINR level in the presence of noise and interference from other users. In this paper, we examine the performance of the seminal Foschini-Miljanic (FM) power control scheme in networks where channel conditions and users' quality of service (QoS) requirements vary arbitrarily with time (e.g. due to user mobility, fading, etc.). Contrary to the case of static and/or ergodic channels, the system optimum power configuration may evolve over time in an unpredictable fashion, so users must adapt to changes in the wireless medium (or their own requirements) "on the fly", without being able to anticipate the system evolution. To account for these considerations, we provide a formulation of power control as an online optimization problem and we show that the FM dynamics lead to no regret in this dynamic context. Specifically, in the absence of maximum transmit power constraints, we show that the FM power control scheme performs at least as well as (and typically outperforms) any fixed transmit profile, irrespective of how the system varies with time; finally, to account for maximum power constraints that occur in practice, we introduce an adjusted version of the FM algorithm which retains the convergence and no-regret properties of the original algorithm in this constrained setting.

Learning to Be Green: Robust Energy Efficiency Maximization in Dynamic MIMO–OFDM Systems

“…This guarantee is key for massive MIMO systems (where the number of transmit/receive antennas can grow to be quite large) because it provides a worst-case estimate for the system's equilibration time. That being said, (30) only becomes tight in adversarial environments (e.g. in the presence of jamming); in typical scenarios, the user's regret usually decays much faster and the system attains a stable, no-regret state within a few iterations, even for large numbers of antennas per user -cf.…”

“…A regret-based approach was recently employed by the authors of [27] who studied the problem of power control in infrastructureless wireless networks and proposed an algorithm that minimizes the users' (internal) regret to attain the system's equilibrium. In a similar vein, [28] studied the transient phase of the Foschini-Miljanic (FM) power control algorithm in static environments and used the notion of swap regret [29] to propose alternative convergent power control schemes; even more recently, [30] showed that the FM dynamics lead to no regret, so they retain their optimality properties in dynamic environments. Finally, [31] and [32] used online optimization techniques and a methodology based on matrix exponential learning [7,8,33,34] to derive a no-regret adaptive transmit policy for power control and throughput maximization in cognitive radio networks respectively.…”

Power allocation over time‐varying multiple‐access interference channels

“…For instance, in , the authors propose distributed low‐complexity adaptive stochastic algorithms for joint power and admission control, such that multiple network nodes can simultaneously transmit while maintaining a desired SINR. In , the authors examine a Foschini–Miljanic‐based distributed power control scheme for time‐varying channels under QoS requirements. Particularly, an online power control optimization problem—based on perfect knowledge of the instantaneous SINR—is formulated leading to a performance that is at least as well (if not better) than any fixed transmit power scheme.…”

Resource-sharing cognitive radio networks in commercial and military environments

“…One such scheme is the traditional water-filling power assignment [57] that inversely relates the power adaptation to the channel power gain to effectively fill the capacity of the channel. However, as pointed out by the authors in [58], mobility and fading in communication networks can cause the channel conditions and user QOS requirements to vary arbitrarily over time, requiring the system to adapt its power configuration. For such dynamic networks, the FoschiniMiljanic power control scheme proposed in [58], allows the SU to anticipate and adapt to changes on the fly, based on an online optimization methodology that outperforms previous fixed transmit profile strategies.…”

“…However, as pointed out by the authors in [58], mobility and fading in communication networks can cause the channel conditions and user QOS requirements to vary arbitrarily over time, requiring the system to adapt its power configuration. For such dynamic networks, the FoschiniMiljanic power control scheme proposed in [58], allows the SU to anticipate and adapt to changes on the fly, based on an online optimization methodology that outperforms previous fixed transmit profile strategies. Other notable work on distributed power control is the GADIA scheme (greedy asynchronous distributed interference avoidance algorithm) [59] where interference mitigation as the optimization objective allows the network to match the performance of a centralized allocation strategy.…”