[Paper Review] Cloud-Edge Non-Orthogonal Transmission for Fog Networks with Delayed CSI at the Cloud

Jingjing Zhang, Osvaldo Simeone|arXiv (Cornell University)|May 25, 2018

Caching and Content Delivery8 references4 citations

TL;DR

This paper proposes a cloud-edge non-orthogonal transmission scheme for fog radio access networks (F-RANs) with delayed channel state information (CSI) at the cloud. By superimposing cloud-precoded signals and edge-precoded cached content using superposition coding and zero-forcing beamforming, the scheme achieves a normalized delivery time (NDT) of $\delta = \min\left(\frac{1-\mu}{r} + 1, \frac{1-\mu}{\alpha} + \frac{1}{r}\right)$, significantly improving latency over orthogonal schemes under imperfect CSI.

ABSTRACT

In a Fog Radio Access Network (F-RAN), the cloud processor (CP) collects channel state information (CSI) from the edge nodes (ENs) over fronthaul links. As a result, the CSI at the cloud is generally affected by an error due to outdating. In this work, the problem of content delivery based on fronthaul transmission and edge caching is studied from an information-theoretic perspective in the high signal-to-noise ratio (SNR) regime. For the set-up under study, under the assumption of perfect CSI, prior work has shown the (approximate or exact) optimality of a scheme in which the ENs transmit information received from the cloud and cached contents over orthogonal resources. In this work, it is demonstrated that a non-orthogonal transmission scheme is able to substantially improve the latency performance in the presence of imperfect CSI at the cloud.

Motivation & Objective

• To address the latency degradation caused by outdated CSI at the cloud in F-RANs with fronthaul-constrained edge caching.
• To investigate whether non-orthogonal transmission can outperform traditional orthogonal schemes under imperfect CSI at the cloud.
• To characterize the normalized delivery time (NDT) in the high-SNR regime for a cloud-edge transmission strategy combining fronthaul and edge caching.
• To establish the optimality of non-orthogonal transmission in terms of latency when CSI at the cloud is delayed.

Proposed method

• The cloud precodes content for users and transmits it over fronthaul links using superposition coding, with power allocation based on CSI error scaling $\mathbb{E}[|h_k^i - \hat{h}_k^i|^2] \doteq P^{-\alpha}$.
• Edge nodes cache subfiles and cooperatively precoded them using zero-forcing (ZF) beamforming to null interference from other users, exploiting perfect CSI at the edge.
• The transmitted signal at each edge node is the superposition of the cloud-precoded signal and the edge-precoded signal, enabling non-orthogonal multiple access.
• User decoding proceeds in two stages: first decoding the edge-precoded signal treating interference as noise, then decoding the cloud-precoded signal after cancellation.
• The scheme uses a time-division structure where edge and cloud signals are transmitted in sequence, with decoding order determined by signal strength and latency constraints.
• The normalized delivery time (NDT) is derived in two regimes: when edge decoding dominates ($\mu \geq 1 - \alpha$) and when cloud decoding dominates ($\mu \leq 1 - \alpha$).

Experimental results

Research questions

• RQ1 Can non-orthogonal transmission outperform orthogonal schemes in F-RANs when the cloud has delayed CSI?
• RQ2 What is the optimal trade-off between fronthaul and edge transmission in terms of delivery latency under imperfect CSI?
• RQ3 How does the scaling of CSI error ($P^{-\alpha}$) affect the achievable diversity and multiplexing gain in the high-SNR regime?
• RQ4 Under what conditions does edge-based ZF beamforming combined with cloud superposition coding minimize the normalized delivery time (NDT)?
• RQ5 Is there a regime where the latency is dominated by cloud transmission, and when is it dominated by edge transmission?

Key findings

• The proposed non-orthogonal transmission scheme achieves a normalized delivery time (NDT) of $\delta = \frac{1-\mu}{r} + 1$ when $\mu \geq 1 - \alpha$, indicating that edge transmission dominates latency.
• When $\mu \leq 1 - \alpha$, the NDT is $\delta = \frac{1-\mu}{\alpha} + \frac{1}{r}$, showing that cloud transmission latency dominates due to imperfect CSI.
• The scheme achieves a diversity gain of $\alpha$ from the CSI error scaling, which is exploited via superposition coding to mitigate interference.
• The edge-precoded signals are decoded first at rate $(1 - \alpha)\log P$, treating interference and noise as a single term with power $\mathbb{E}[|z_k|^2] \doteq 1$.
• After decoding the edge signal, the cloud-precoded signal is decoded at rate $\alpha \log P$, with the interference-plus-noise term $\mathbb{E}[|\tilde{\boldsymbol{h}}_k^T \sum \boldsymbol{v}_{d_{k'}} s_{d_{k'}}|^2] \doteq P^\alpha$.
• The total NDT is minimized compared to orthogonal schemes, especially in the high-SNR regime, due to the efficient use of non-orthogonal multiplexing and ZF beamforming.