An Advanced Tree Algorithm with Interference Cancellation in Uplink and Downlink

TL;DR

ATIC extends SICTA by enabling interference cancellation at both the AP and users, achieving an asymptotic MST of $0.924$, about a $0.231$ increase over SICTA’s $0.693$ and approaching the collision-channel limit. The analysis provides a closed-form expression for the CRI length $L_n$, proves the asymptotic throughput bound $\frac{4}{3}\ln 2$, and shows gating as the best CAP for ATIC while windowed access offers no advantage. The approach reduces mean packet delay at high loads and lowers AP memory requirements despite a higher downlink feedback burden that scales with packet size $B$. Practically, these results are most applicable to systems with robust feedback channels (e.g., LTE) and dense IoT deployments where many devices contend for uplink access.

Abstract

In this paper, we propose Advanced Tree-algorithm with Interference Cancellation (ATIC), a variant of binary tree-algorithm with successive interference cancellation (SICTA) introduced by Yu and Giannakis. ATIC assumes that Interference Cancellation (IC) can be performed both by the access point (AP), as in SICTA, but also by the users. Specifically, after every collision slot, the AP broadcasts the observed collision as feedback. Users who participated in the collision then attempt to perform IC by subtracting their transmissions from the collision signal. This way, the users can resolve collisions of degree 2 and, using a simple distributed arbitration algorithm based on user IDs, ensure that the next slot will contain just a single transmission. We show that ATIC reaches the asymptotic throughput of 0.924 as the number of initially collided users tends to infinity and reduces the number of collisions and packet delay. We also compare ATIC with other tree algorithms and indicate the extra feedback resources it requires.

Figures (7)

• Figure 1: An example visualization of different tree algorithms. At each collision of more than 2 signals, the users independently split into two groups the users that selected the left group transmit once again. The skipped slots in SICTA are drawn with dotted lines. In ATIC, collisions of degree two (skipped or not) are resolved deterministically. ATIC is able to skip slot $4$, as $A$ and $B$ can infer that they are in a collision of degree two. Slot $4$ and $5$ hence become deterministic and so do $10$ and $11$.
• Figure 2: Simulated normalized collision degree distribution for SICTA with blocked access for 100000 collision slots. The packet arrival rate in the network is 0.693 which is the MST for this scheme. We see that more than half the collisions have a multiplicity of 2.
• Figure 3: The throughput conditioned on a collision of $\nuser$ users. The conditional throughput is 1 when $0<\nuser\leq2$ and tends to $\frac{4}{3}\ln{2}$ as $\nuser\longrightarrow\infty$. The lowest conditional throughput of $0.9$ is achieved for $n=3$.
• Figure 4: Throughput for windowed access with ATIC as function of the expected number of arrivals per window $\lambda \Delta$. We see that gated access is the best CAP to be used along with ATIC.
• Figure 5: The mean packet delay of BTA, SICTA, and ATIC. The packets arrive in the network independently with a Poisson distribution with mean $\lambda$. Even for arrival rates theoretically supported by SICTA in the interval (0.6, 0.693] packets per slot, the delay becomes very large. In such cases, ATIC provides a much lower packet delay.

Theorems & Definitions (3)

• Theorem 1
• proof
• Theorem 2