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Linear Precoders for OFDM Wireless Communication

## Merouane Debbah

Degree: Ph.D.

Supervisor: Prof. Philippe Loubaton

Department: Laboratoire Systemes de CommunicationsoInstitution:

Institution: Ecole Normale Superieure de Cachan/Universite de Marne La
Valle
Date of Graduation: October 2003
Contact Information:

Prof. Merouane Debbah

Mobile Communication Group

Institut Eurecom

2229 Route des Cretes

B.P. 193

06904 SOPHIA ANTIPOLIS CEDEX

France

Email: debbah@eurecom.fr

Website: http://www.eurecom.fr/~debbah

Abstract

A multi-carrier {\bf OFDM} (Orthogonal Frequency Division Multiplexing)
system using a Cyclic Prefix for preventing inter-block interference is
known to be equivalent to a system based on multiple flat fading
parallel transmission channels in the frequency domain. In such a
system, the information sent on some carriers might be subject to strong
attenuations and could be unrecoverable at the receiver.
The aim of this thesis is to investigate a transmission scheme known as
{\bf Linear Precoded OFDM} to overcome these drawbacks.

Linear Precoding consists in spreading the information contained in a
$K$-dimensional vector onto $N$ carriers. Therefore , the $K \times 1$
infomation vector to be transmitted is multiplied by an $N \times K$
matrix. The precoder is intended to increase the overall frequency
diversity of the modulator so that unreliable carriers can still be
recovered by taking advantage of the subbands enjoying a high signal to
noise ratio.
Using new tools, borrowed from the so-called {\bf free probability
theory}, the Signal to Interference plus Noise Ratio (SINR) at the
output of linear and non-linear equalizers are derived when $N \to
\infty $ and $K/N \to \alpha$ assuming both ergodic and non ergodic
channels. Based on the assumption of asymptotic Gaussian interference,
the SINR is then used as a benchmark measure of performance for
different criterias.

These asymptotic results aim at adjusting the different parameters
involved in the detection process : nature and impact of the
orthogonality of the precoding matrix columns, optimal amount of
redundancy of the precoding matrix when coding is applied (ratio
$\frac{K}{N}$, values of the coefficients of the non-linear equalizers).
Interestingly, the results have very simple interpretations and
determine the useful parameters to be considered in the design of
these transmissions schemes.
Finally, conclusions are drawn on the future research topics in
connection with our work.