[Paper Review] The Degrees of Freedom of the $K$-pair-user Full-Duplex Two-way Interference Channel with and without a MIMO Relay

Zhiyu Cheng, Natasha Devroye|arXiv (Cornell University)|Nov 27, 2013

Full-Duplex Wireless Communications30 references4 citations

TL;DR

This paper analyzes the degrees of freedom (DoF) in a K-pair-user full-duplex two-way interference channel (TWIC), showing that full-duplex operation doubles the DoF to K, but interaction among users does not further increase it. With a non-causal MIMO relay having 2K antennas, the DoF can be doubled again to 2K via a one-shot interference mitigation scheme, while a causal relay cannot increase DoF beyond K.

ABSTRACT

In a $K$-pair-user two-way interference channel (TWIC), $2K$ messages and $2K$ transmitters/receivers form a $K$-user IC in the forward direction ($K$ messages) and another $K$-user IC in the backward direction which operate in full-duplex mode. All nodes may interact, or adapt inputs to past received signals. We derive a new outer bound to demonstrate that the optimal degrees of freedom (DoF, also known as the multiplexing gain) is $K$: full-duplex operation doubles the DoF, but interaction does not further increase the DoF. We next characterize the DoF of the $K$-pair-user TWIC with a MIMO, full-duplex relay. If the relay is non-causal/instantaneous (at time $k$ forwards a function of its received signals up to time $k$) and has $2K$ antennas, we demonstrate a one-shot scheme where the relay mitigates all interference to achieve the interference-free $2K$ DoF. In contrast, if the relay is causal (at time $k$ forwards a function of its received signals up to time $k-1$), we show that a full-duplex MIMO relay cannot increase the DoF of the $K$-pair-user TWIC beyond $K$, as if no relay or interaction is present. We comment on reducing the number of antennas at the instantaneous relay.

Motivation & Objective

• To characterize the degrees of freedom (DoF) in a K-pair-user two-way interference channel (TWIC) with full-duplex operation and user interaction.
• To investigate whether interaction among users or the presence of a MIMO relay can further increase DoF beyond what full-duplex operation alone achieves.
• To determine the DoF gain from a full-duplex MIMO relay under non-causal and causal forwarding constraints.
• To explore the minimum number of antennas required at a non-causal relay to achieve the maximum DoF of 2K.
• To establish fundamental limits on DoF in bidirectional multi-user interference networks under practical full-duplex operation.

Proposed method

• Derives a new outer bound on DoF for the K-pair-user TWIC to show that interaction does not increase DoF beyond K.
• Proposes a one-shot transmission scheme using a non-causal MIMO relay with 2K antennas to achieve 2K DoF by fully mitigating interference.
• Uses a transformed network model with user 2K-1 as a virtual relay to simplify DoF analysis and derive converse bounds.
• Applies information-theoretic inequalities, including entropy and mutual information bounds, to analyze signal dependencies and interference cancellation.
• Distinguishes between non-causal (instantaneous) and causal (delayed) relay forwarding models to compare DoF performance.
• Employs a symmetric transformation of the channel to isolate key interference terms and derive sum-rate bounds that lead to DoF conclusions.

Experimental results

Research questions

• RQ1 What is the maximum degrees of freedom (DoF) achievable in a K-pair-user full-duplex two-way interference channel with user interaction?
• RQ2 Can interaction among users in a full-duplex TWIC increase the DoF beyond the doubling effect of full-duplex operation?
• RQ3 What is the DoF gain from introducing a full-duplex MIMO relay in a K-pair-user TWIC, and how does relay causality affect this gain?
• RQ4 Can a non-causal MIMO relay with fewer than 2K antennas still achieve the full 2K DoF, or is 2K the minimum required?
• RQ5 Does the presence of a causal MIMO relay increase the DoF beyond K in a K-pair-user full-duplex TWIC?

Key findings

• The DoF of the K-pair-user full-duplex TWIC without a relay is K, indicating that full-duplex operation doubles the DoF compared to half-duplex, but interaction does not further increase it.
• For a non-causal MIMO relay with 2K antennas, the DoF can be increased to 2K via a one-shot scheme that fully cancels interference.
• A causal MIMO relay cannot increase the DoF beyond K, even with full-duplex operation, meaning it provides no DoF gain over a system without a relay.
• The converse proof for the causal relay case shows that interference from all 2K-1 other users, including cross-directional signals, limits DoF to K.
• The DoF result is robust to network asymmetry, as shown by summing over arbitrary rate pairs without loss of generality.
• Reducing the number of antennas at a non-causal relay may reduce the achievable DoF or require additional cognition, and the DoF limit for such cases remains open.