Comunicaciones Inalámbricas

VANDERMONDE FREQUENCY DIVISION MULTIPLEXING FOR COGNITIVE RADIO
Leonardo S.Cardoso t , Mari Kobayashi t , @yvind Ryan*, and Merouane Debbah t

t SUPELEC, Gif-sur-Yvette, France
* University of Oslo, Oslo, Norway

E-mail: {leonardo.cardoso,mari.kobayashi,merouane.debbah}@supelec.fr, oyvindry@ifi.uio.no

ABSTRACT
We consider a cognitive radio scenario where a primary
and a secondary userwish to communicate with their corresponding receivers simultaneously over frequency selective channels. Under realistic assumptions that the primary
user is ignorant of the secondary user's presence and that the
secondary transmitter has no side information about the primary's message, we propose a Vandermonde precoder that
cancels the interference from the secondary user by exploiting theredundancy of the cyclic prefix and the frequency
selectivity of the channel. Our numerical examples show
that VFDM, with an appropriate design of the input covariance, enables the secondary user to achieve a non-negligible
rate while generating zero interference to the primary user.
1. MOTIVATION
We consider a 2 x 2 cognitive radio model where both a
primary (licensed) transmitter and asecondary (unlicensed)
transmitter wish to communicate with their corresponding
receivers simultaneously as illustrated in Fig.l. When both
transmitters do not share each other's message, the information theoretic model falls into the Gaussian interference
channel [I, 2] whose capacity remains open in the general
case. A significant number of recent works have aimed
at characterizing theachievable rates of the cognitive radio channel, i.e. the interference channel with some knowledge of the primary's message at the secondary transmitter
[3, 4, 5, 6]. These include the pioneering work of [3], the
works of [4], [5] for the case of weak, strong Gaussian interference, respectively, and finally a recent contribution of
[6] with partial knowledge at the secondary transmitter. In
all theseworks, the optimal transmission scheme is based
on dirty-paper coding that pre-cancels the known interference to the secondary receiver and helps the primary user's
transmission. Unfortunately, this optimal strategy is very
complex to implement in practice and moreover based on
rather unrealistic assumptions: a) the secondary transmitter has full or partial knowledge of the primary message,This work was partially supported by Alcatel-Lucent.

978-1-4244-2046-9/08/$25.00 ©2008 IEEE

primary

Tx 1 k - - - - - - - - . . . . l Rx 1

secondary Tx 2 I"'--------~ Rx 2
h(22)

Fig. 1. 2 x 2 cognitive model
b) both transmitters know all the channels perfectly. Despite its cognitive capability, the assumption a) seems very
difficult (if not impossible) to hold, because in practicethe
secondary transmitter has to decode the message of the primary transmitter in a causal manner by training over a noisy,
faded or capacity-limited link. The assumption b) requires
both transmitters to perfectly track all channels (possibly
by an explicit feedback from two receivers) and thus might
be possible only if the underlying fading channel is quasistatic.
The above observationmotivates us to design a practical transmission scheme under more realistic assumptions.
First, we consider no cooperation between two transmitters. The primary user is ignorant of the secondary user's
presence and furthermore the secondary transmitter has no
knowledge on the primary transmitter's message. Second,
we assume that transmitter I knows perfectly h (11), while
transmitter 2 knows itslocal channels h(21) and h(22). This
assumption is rather reasonable when the channel reciprocity
can be exploited for time division duplexing systems. Also,
each receiver i is assumed to estimate perfectly its direct
channel h (ii). Finally, assuming frequency selective fading
channels, we consider OFDM transmission. The last assumption has direct relevance to the current OFDM-based...