[Paper Review] Optimal Training for Residual Self-Interference for Full Duplex One-way Relays

Xiaofeng Li, Cihan Tepedelenlioğlu+1 more|arXiv (Cornell University)|Sep 18, 2017

Full-Duplex Wireless Communications28 references3 citations

TL;DR

This paper proposes an optimal training scheme for estimating residual self-interference (RSI) and end-to-end channels in full-duplex one-way relays using maximum likelihood estimation with a BFGS algorithm. By deriving closed-form Cramér-Rao bounds (CRB) via asymptotic Toeplitz matrix properties, the authors optimize the training sequence to minimize estimation error, enabling effective RSI cancellation and inter-symbol interference mitigation at the destination.

ABSTRACT

Channel estimation and optimal training sequence design for full-duplex one-way relays are investigated. We propose a training scheme to estimate the residual self-interference (RSI) channel and the channels between nodes simultaneously. A maximum likelihood estimator is implemented with Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. In the presence of RSI, the overall source-to-destination channel becomes an inter-symbol-interference (ISI) channel. With the help of estimates of the RSI channel, the destination is able to cancel the ISI through equalization. We derive and analyze the Cramer-Rao bound (CRB) in closed-form by using the asymptotic properties of Toeplitz matrices. The optimal training sequence is obtained by minimizing the CRB. Extensions for the fundamental one-way relay model to the frequency-selective fading channels and the multiple relays case are also considered. For the former, we propose a training scheme to estimate the overall channel, and for the latter the CRB and the optimal number of relays are derived when the distance between the source and the destination is fixed. Simulations using LTE parameters corroborate our theoretical results.

Motivation & Objective

• Address the challenge of residual self-interference (RSI) in full-duplex one-way relay systems, which degrades system performance despite self-interference cancellation.
• Develop a joint channel estimation scheme that simultaneously estimates the RSI channel and the source-to-destination end-to-end channel.
• Minimize estimation error in RSI and end-to-end channel estimation by optimizing the training sequence using Cramér-Rao bounds (CRB).
• Extend the framework to frequency-selective fading channels and multiple relay scenarios, analyzing optimal relay count and overall channel estimation.
• Enable effective inter-symbol interference (ISI) cancellation at the destination by accurately estimating the RSI channel.

Proposed method

• Propose a maximum likelihood (ML) estimator for joint estimation of RSI and end-to-end channels using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm for optimization.
• Derive the Fisher information matrix for the unknown parameters (channel gain, phase, and time offset), leading to the Cramér-Rao bound (CRB) in closed-form.
• Utilize asymptotic properties of Toeplitz matrices to analyze the CRB, treating the channel matrix as a circulant matrix in the large-sample limit.
• Introduce a time-shifted discrete-time Fourier transform (DTFT) model, $ t_{\tau_0}(\lambda) $, to handle non-integer delays in the RSI channel, enabling closed-form CRB analysis.
• Formulate gradients of the log-likelihood function with respect to real and imaginary parts of the channel parameters for use in the BFGS algorithm.
• Extend the model to frequency-selective fading channels by designing a training scheme to estimate the overall channel, and analyze the multiple-relay case with fixed source-destination distance.

Experimental results

Research questions

• RQ1 How can the residual self-interference (RSI) channel be jointly estimated with the end-to-end source-to-destination channel in a full-duplex one-way relay system?
• RQ2 What is the optimal training sequence that minimizes the Cramér-Rao bound (CRB) for RSI and end-to-end channel estimation?
• RQ3 How does the presence of RSI induce inter-symbol interference (ISI), and can it be effectively canceled at the destination using estimated RSI parameters?
• RQ4 What is the impact of frequency-selective fading on RSI estimation, and how can training sequences be designed to maintain estimation accuracy?
• RQ5 What is the optimal number of relays in a multi-relay full-duplex system when the source-destination distance is fixed?

Key findings

• The Cramér-Rao bound (CRB) for RSI and end-to-end channel estimation is derived in closed-form using asymptotic Toeplitz matrix theory, enabling theoretical optimization of training sequences.
• The optimal training sequence is obtained by minimizing the CRB, which leads to improved estimation accuracy and reduced error variance in channel estimation.
• The proposed BFGS-based maximum likelihood estimator effectively converges to accurate estimates of the RSI and end-to-end channels, even in the presence of ISI.
• The time-shifted DTFT model $ t_{\tau_0}(\lambda) $ allows for closed-form CRB analysis even when the RSI delay is not an integer multiple of the symbol period.
• Simulations using LTE parameters validate the theoretical CRB results, showing that the optimal training sequence significantly reduces estimation error compared to conventional pilots.
• In the multiple-relay scenario, the CRB analysis reveals an optimal number of relays that minimizes estimation error for a fixed source-destination distance.