[Paper Review] Two-Way Transmission Capacity of Wireless Ad-hoc Networks

Rahul Vaze, Kien T. Truong+2 more|arXiv (Cornell University)|Sep 8, 2010

Advanced MIMO Systems Optimization20 references4 citations

TL;DR

This paper introduces a two-way transmission capacity framework for wireless ad-hoc networks that accounts for bidirectional traffic with asymmetric rate requirements in frequency division duplexing (FDD) systems. It derives tight upper and lower bounds on two-way transmission capacity and identifies an optimal bandwidth allocation strategy that outperforms proportional allocation, especially for asymmetric traffic, while also quantifying the capacity loss due to limited feedback in beamforming systems.

ABSTRACT

The transmission capacity of an ad-hoc network is the maximum density of active transmitters per unit area, given an outage constraint at each receiver for a fixed rate of transmission. Most prior work on finding the transmission capacity of ad-hoc networks has focused only on one-way communication where a source communicates with a destination and no data is sent from the destination to the source. In practice, however, two-way or bidirectional data transmission is required to support control functions like packet acknowledgements and channel feedback. This paper extends the concept of transmission capacity to two-way wireless ad-hoc networks by incorporating the concept of a two-way outage with different rate requirements in both directions. Tight upper and lower bounds on the two-way transmission capacity are derived for frequency division duplexing. The derived bounds are used to derive the optimal solution for bidirectional bandwidth allocation that maximizes the two-way transmission capacity, which is shown to perform better than allocating bandwidth proportional to the desired rate in both directions. Using the proposed two-way transmission capacity framework, a lower bound on the two-way transmission capacity with transmit beamforming using limited feedback is derived as a function of bandwidth, and bits allocated for feedback.

Motivation & Objective

• To extend the concept of transmission capacity to two-way wireless ad-hoc networks, accounting for bidirectional traffic with different rate requirements in each direction.
• To model and analyze the impact of correlated interference in two-way communication, where success in both directions is interdependent.
• To derive tight upper and lower bounds on two-way transmission capacity under frequency division duplexing (FDD), assuming Rayleigh fading and Poisson point process node distribution.
• To determine the optimal bandwidth allocation strategy that maximizes two-way transmission capacity, especially for asymmetric traffic scenarios.
• To quantify the performance loss in two-way transmission capacity when using limited feedback beamforming compared to genie-aided feedback.

Proposed method

• Models transmitter locations as a Poisson point process (PPP) and assumes independent Rayleigh fading on separate frequency bands for uplink and downlink.
• Derives tight upper and lower bounds on the joint two-way success probability, which are shown to differ by only a constant, enabling accurate capacity characterization.
• Uses stochastic geometry and tools from point process theory to analyze interference distribution and derive closed-form bounds on transmission capacity.
• Solves a convex optimization problem in a single variable to find the optimal bandwidth allocation that maximizes two-way transmission capacity.
• Analyzes the impact of limited feedback in beamforming by modeling feedback overhead and deriving a lower bound on two-way transmission capacity as a function of feedback bits and bandwidth.
• Validates theoretical bounds through simulations using standard methodology from one-way network studies, with parameters such as path-loss exponent α=4 and distance d=5m.

Experimental results

Research questions

• RQ1 How does the two-way transmission capacity of an ad-hoc network compare to its one-way counterpart when both directions must succeed?
• RQ2 What is the optimal bandwidth allocation strategy between uplink and downlink that maximizes two-way transmission capacity under asymmetric rate requirements?
• RQ3 How does the use of limited feedback in beamforming affect the two-way transmission capacity compared to perfect (genie-aided) feedback?
• RQ4 To what extent does the correlation between uplink and downlink interference reduce the two-way transmission capacity compared to independent interference models?
• RQ5 Can tight analytical bounds be derived for two-way transmission capacity that capture the true system behavior up to a constant factor?

Key findings

• The two-way transmission capacity is significantly lower than the one-way capacity—at 10% outage probability, it is only half the one-way capacity under the same total bandwidth and data rate.
• For symmetric traffic (equal rates in both directions), proportional bandwidth allocation is optimal, but it performs poorly for asymmetric traffic.
• The optimal bandwidth allocation strategy derived via convex optimization provides a 36% gain over proportional allocation in asymmetric scenarios (e.g., 1.024 kbits vs. 0.056 kbits per direction).
• The derived upper and lower bounds on two-way transmission capacity differ by only a constant, confirming their tightness and enabling accurate capacity characterization.
• With limited feedback beamforming, the two-way transmission capacity is substantially reduced compared to genie-aided feedback, especially when feedback overhead consumes significant bandwidth.
• The lower bound on two-way transmission capacity with limited feedback is derived as a function of bandwidth and feedback bits, showing a clear trade-off between feedback overhead and achievable capacity.