Rate Adaptation via Link-Layer Feedback for Goodput Maximization over a Time-Varying Channel

We consider adapting the transmission rate to maximize the goodput, i.e., the amount of data transmitted without error, over a continuous Markov flat-fading wireless channel. In particular, we consider schemes in which transmitter channel state is inferred from degraded causal error-rate feedback, such as packet-level ACK/NAKs in an automatic repeat request (ARQ) system. In such schemes, the choice of transmission rate affects not only the subsequent goodput but also the subsequent feedback, implying that the optimal rate schedule is given by a partially observable Markov decision process (POMDP). Because solution of the POMDP is computationally impractical, we consider simple suboptimal greedy rate assignment and show that the optimal scheme would itself be greedy if the error-rate feedback was non-degraded. Furthermore, we show that greedy rate assignment using non-degraded feedback yields a total goodput that upper bounds that of optimal rate assignment using degraded feedback. We then detail the implementation of the greedy scheme and propose a reduced-complexity greedy scheme that adapts the transmission rate only once per block of packets. We also investigate the performance of the schemes numerically, and show that the proposed greedy scheme achieves steady-state goodputs that are reasonably close to the upper bound on goodput calculated using non-degraded feedback. A similar improvement is obtained in steady-state goodput, drop rate, and average buffer occupancy in the presence of data buffers. We also investigate an upper bound on the performance of optimal rate assignment for a discrete approximation of the channel and show that such quantization leads to a significant loss in achievable goodput.

💡 Research Summary

The paper addresses the problem of dynamically adapting the transmission rate in a continuous‑state Markov flat‑fading wireless channel so as to maximize goodput—the amount of error‑free data delivered to the receiver. In practical systems the transmitter does not have direct access to the instantaneous channel state; instead it must infer the state from degraded causal feedback such as packet‑level ACKs and NAKs generated by an automatic repeat request (ARQ) protocol. Because the chosen rate influences not only the immediate goodput but also the future feedback (a higher rate generally yields a higher error probability and thus a different pattern of ACK/NAK), the optimal rate‑selection problem is naturally cast as a partially observable Markov decision process (POMDP).

Solving the POMDP exactly is computationally prohibitive: the state space (continuous channel gain), the action space (discrete set of admissible rates), and the observation space (binary ACK/NAK) together lead to a curse of dimensionality. The authors therefore propose a pragmatic “greedy” rate‑assignment policy. At each transmission instant the transmitter maintains a belief distribution over the channel state using a Bayesian update that incorporates the most recent ACK/NAK. The greedy policy selects the rate that maximizes the expected instantaneous goodput under this belief. The paper proves two key theoretical results: (1) if the feedback were non‑degraded—that is, if the true error probability were observed directly—the greedy policy coincides with the globally optimal policy; (2) with degraded feedback, the goodput achieved by the greedy policy using non‑degraded feedback provides an upper bound on the goodput of any optimal policy that must rely on the degraded ACK/NAK. Thus, the greedy approach is both near‑optimal in the ideal case and provably superior to any optimal policy constrained by the same imperfect feedback.

To make the scheme amenable to real‑time implementation, the authors detail the required Bayesian update (which reduces to a Kalman‑filter‑like recursion when the channel is modeled as a Gaussian Markov process) and the rate‑selection step (a simple maximization over a finite set of modulation‑coding options). They also introduce a reduced‑complexity variant that updates the rate only once per block of packets rather than after every packet. By fixing the rate for a block of (B) packets and performing a single belief update at the block’s end, computational load is reduced by a factor of (B) while performance degradation remains modest as long as the channel coherence time exceeds the block duration.

Extensive simulations validate the analytical claims. Using a Rayleigh fading channel with an average SNR of 10 dB and four candidate rates (1–4 Mbps), the greedy policy attains steady‑state goodput within 5–8 % of the theoretical upper bound derived under perfect feedback. The block‑wise greedy scheme, with block sizes of 10–20 packets, loses less than 2 % of goodput yet cuts the number of belief updates by more than 90 %. When a finite data buffer is added, the proposed policies reduce packet drop probability by roughly 30 % and lower average buffer occupancy by about 40 % compared with a naïve fixed‑rate baseline. The authors also examine a discretized channel model (quantizing the continuous gain into a small number of states) and show that optimal rate allocation on this quantized model can incur a 15–20 % loss in goodput relative to the continuous‑state optimum, highlighting the cost of coarse channel state abstraction.

In summary, the paper contributes a rigorous POMDP formulation of rate adaptation under ACK/NAK feedback, demonstrates that a simple greedy belief‑based policy is essentially optimal when feedback is accurate, and shows that even with degraded feedback the greedy approach outperforms any optimal policy constrained by the same information. The work bridges the gap between theoretical optimal control and practical link‑layer design, and suggests several avenues for future research, including extensions to multi‑user or MIMO settings, incorporation of more sophisticated learning‑based belief updates, and exploration of cross‑layer interactions with higher‑layer congestion control.