[Paper Review] Outage Performance of Two-Hop OFDM Systems with Spatially Random Decode-and-Forward Relays

Shuping Dang, Justin P. Coon+1 more|arXiv (Cornell University)|Aug 10, 2017

Cooperative Communication and Network Coding3 citations

TL;DR

This paper analyzes the outage performance of two-hop OFDM systems with spatially random decode-and-forward relays using a Poisson point process model. It derives exact and asymptotic outage probability expressions for bulk and per-subcarrier relay selection, reveals a ternary diversity gain property (0, 1, or infinite), and formulates a concave optimization problem to maximize system throughput by selecting the optimal number of subcarriers.

ABSTRACT

In this paper, we analyze the outage performance of different multicarrier relay selection schemes for two-hop orthogonal frequency-division multiplexing (OFDM) systems in a Poisson field of relays. In particular, special emphasis is placed on decode-and-forward (DF) relay systems, equipped with bulk and per-subcarrier selection schemes, respectively. The exact expressions for outage probability are derived in integrals for general cases. In addition, asymptotic expressions for outage probability in the high signal-to-noise ratio (SNR) region in the finite circle relay distribution region are determined in closed forms for both relay selection schemes. Also, the outage probabilities for free space in the infinite relay distribution region are derived in closed forms. Meanwhile, a series of important properties related to cooperative systems in random networks are investigated, including diversity, outage probability ratio of two selection schemes and optimization of the number of subcarriers in terms of system throughput. All analysis is numerically verified by simulations. Finally, a framework for analyzing the outage performance of OFDM systems with spatially random relays is constructed, which can be easily modified to analyze other similar cases with different forwarding protocols, location distributions and/or channel conditions.

Motivation & Objective

• To address the lack of analysis on OFDM systems with spatially random relays in realistic network scenarios.
• To model relay locations using a Poisson point process to reflect the dynamic, random nature of real-world deployments.
• To derive exact and asymptotic outage probability expressions for both bulk and per-subcarrier relay selection schemes.
• To investigate key system properties such as diversity gain, performance ratio between selection schemes, and optimal subcarrier allocation.
• To construct a generalizable framework applicable to other protocols, channel models, and relay distributions.

Proposed method

• Models relay locations as a homogeneous Poisson point process (PPP) in a 2D plane, with source and destination at fixed positions.
• Uses a two-hop decode-and-forward (DF) relay protocol where relays decode and forward signals on OFDM subcarriers.
• Derives exact outage probability in integral form using order statistics and PPP properties for general relay density and region.
• Applies asymptotic analysis at high SNR to derive closed-form expressions for finite and infinite relay regions.
• Employs series expansion of the exponential term in the outage expression for small relay density to approximate performance.
• Framed the system throughput maximization as a concave optimization problem over the number of subcarriers, proven to be concave in the number of subcarriers.

Experimental results

Research questions

• RQ1 What is the exact outage probability for bulk and per-subcarrier relay selection in a two-hop OFDM system with spatially random relays?
• RQ2 How does the outage probability behave in the high-SNR regime for finite and infinite relay distribution regions?
• RQ3 What is the diversity gain in a Poisson-distributed relay network, and can it be characterized as a ternary property?
• RQ4 How does the performance ratio between per-subcarrier and bulk selection depend on relay density?
• RQ5 What is the optimal number of subcarriers that maximizes system throughput under a reliability constraint?

Key findings

• The exact outage probability for both bulk and per-subcarrier selection is derived in integral form for general cases.
• Asymptotic outage expressions in closed form are derived for high SNR in finite regions, and exact closed-form expressions are obtained for free-space (infinite) regions.
• The diversity gain in Poisson random networks is proven to be ternary: either 0, 1, or infinite, depending on the relay density and system parameters.
• An approximate relation between the outage probability ratio of the two selection schemes and relay density is derived, showing per-subcarrier selection outperforms bulk selection in sparse networks.
• A concave optimization problem is formulated to maximize system throughput by selecting the optimal number of subcarriers, and it is proven to be concave in the number of subcarriers.
• An approximation for the cut-off relay density is derived, above which the throughput maximization problem is feasible under reliability constraints.