Interference Alignment via Precoded Compute-and-Forward Ehsan E. - - PowerPoint PPT Presentation

Interference Alignment via Precoded Compute-and-Forward

Ehsan E. Khaleghi Advisor : Prof. Jean-Claude Belfiore Communication & Electronics Department Telecom ParisTech Paris, France

SP Coding and Information School

January, 19th to 30th, 2015 – Campinas, Brazil

January 2015

Problematic

Interference Alignement via Compute-and-Forward page 2 Ø

Interference is one of the challenges in wireless communication systems.

Ø

Interference alignment (IA) is an interference management technique for increasing the channel capacity.

Ø

IA can be done via Compute-and-Forward (CoF) protocol.

Ø

We are interested to improve the fractal behavior of the achievable sum-rate defined for CoF protocol by [Nazer et al. 2012] and [Ordentlich et al. 2012] for high values of signal-to-noise ratio (SNR).

• Fig. Upper Bound and achievable sum-rate versus

g for 2-User GS-IFC [Ordentlich et al. 2012].

January 2015

Channel model & Lattice structure

Interference Alignement via Compute-and-Forward 3

v Channel Model v Lattice Structure

q The channel model is: The k-user GS-IFC.

q By using a simple lattice IA [Ordentlich et al. 2012]

the K-user GS-IFC case is approximately equivalent

to the 2-user case.

q In this work we consider the Nested lattice framework

[Ordentlich et al. 2012].

q A lattice is a discrete additive subgroup of , i.e.,

Λ

n

ℜ

Λ ∈ − − Λ ∈ + Λ ∈ ∀

2 1 2 1 2 1

, and where , t t t t t t

{ }

n

Ζ ∈ = Α = Λ Z : M.Z

. ¢ M: Generator matrix of a lattice ( ).

n n×

v A Lattice is full-rank when its Gram matrix Is full-rank.

• Fig. 2-User GS-IFC.

Ø All users have the same power constraint:

. with 1 : uses channel For

2

∑

=

= ≤

n j i i i

P P P x n n

January 2015

Compute-and-Forward Transform with n Time-Slots

Interference Alignement via Compute-and-Forward 4

When SNR is infinity, to avoid and reduce deep fadings in interested regimes: v decided to send codewords by using n different Time-slots.

q Our idea is to precode at time-slot i the transmitted codewords by multiplying them, at the transmitters, by a real

number .

v By using this strategy, only one time-slot over n will result in a small sum-rate, for all values

• f ‘g’.

ü No need of Channel Side Information (CSI) at transmitters.

i

η

v The worst choices of ‘g’ are rational numbers. v The best choices for ‘g’ are numbers equivalent to Golden ratio.

∞ → SNR

Ø When :

v The best Choices for is Golden ratio or its equivalent numbers (slightly greater than 1). j

η

January 2015

Compute-and-Forward Transform with n Time-Slots

Interference Alignement via Compute-and-Forward 5 ¢ The performance of our proposed scheme is shown below for 7 and 13 time slots.

• Fig. Upper Bound and achievable sum rate

versus g for a 2-User GS-IFC with using our proposed scheme (Ts=7).

• Fig. Upper Bound and achievable sum rate

versus g for a 2-User GS-IFC with using our proposed scheme (Ts=13).

January 2015 Interference Alignement via Compute-and-Forward 6

Thank you for your attention ... !!

q E. Ebrahimi Khaleghi, J-C. Belfiore, “Compute-and-Forward for the Interference Channel: Diversity Precoding”, In Proceedings of the 2nd international Iran Workshop on Communication and Information Theory (IWCIT), Iran, Tehran, May 2014.