TRANSMIT DIVERSITY OVER FREQUENCY-SELECTIVE FADING CHANNEL : A BLIND APPROACH Sebastien Houcke and Ons Benrhouma Deprt Signal et Communication. ENST-Bretagne TAMCIC (CNRS 2658) email:sebastien.houcke@enst-bretagne.fr ABSTRACT In this article, we introduce a novel blind space time processing allowing the transmission of dig- ital communication over a frequency-selective fad- ing channel. We show that it is relevant to use trans- mit diversity in such a context. Our scheme uses 2 transmit antennae and K (K 2) received anten- nae. We call our method Turbo deflation because it is based on results from the field of blind sources separation of convolutive mixture (i.e. deflation ap- proach [1]) and from principle of iterative turbo de- coding [2]. Furthermore it is a blind approach which means that the receiver does not need any training se- quence. Our novel method could for instance be used for underwater communications where blind equalization scheme have already been introduced with really convincing performances [3]. 1. INTRODUCTION Let us consider the complex envelope yt of the continuous-time signal transmitted by a communi- cation system using two transmit antennae and K received antennae. Denote by y p the contribution in y of the signal emitted by antenna number p. Thus y can be seen as a linear mixture of 2 sources y y 1 y 2 . In the telecommunication framework, y p may be a linear process modeled as : y p t ∑ m s p mh p t mT where s p m m is an i.i.d. se- quence of discrete Q-PSK symbols, T is the symbol period and h p denotes the impulse response of the channel relative to source p, i.e. a filter stemming from the cascade of a band-limited pulse-shaping filter and multi-path transmission effects. At the receiver side, y is observed through an array of K sensors and thus yt and h p t are vector-valued. We assume that the symbols emitted by antenna 2 are an interleaved version of the one emitted by an- tenna 1. 1 n s 1 nN s 1 nN N 1 T and 2 n s 2 nN s 2 nN N 1 T have the following relation : 2 n Π N 1 n (1) where Π N is a N N pseudo-random interleaver. We also assume that the channel is stationary over the duration NT . We address here the following blind prob- lem that consists in restoring the symbol sequence 1 n . Note that neither training sequences, nor prior knowledge about the filters are available at the receiver side. In fact, this problem has obvious con- nections with the framework of blind source sepa- ration. We remind that the standard requirements in this field are: the sources are mutually indepen- dent, centered, ergodic and stationary. In our con- text, S 1 n and S 2 n do not strictly obey the inde- pendence assumption. However for large enough interleavers, we can assume mutual independence between the sources. In order to extract the sources, we use the defla- tion approach [1] that is based on the minimization of a contrast function [4]. We recall that a contrast function is a function of the statistics of the received signal and its minimization allows the extraction of one source. Section 2.1 reviews the deflation pro- cedure in details. By re-itering the deflation procedure and ex- ploiting the relation (1) between the sources, we can use the information obtained from the estimate of the first extracted source as a priori information for the second one. This allows us to improve the estimate of the sequence of symbols 1 n . 2. THE TURBO DEFLATION 2.1 Description of the iterative procedure First of all, we describe the deflation procedure for two sources which is the key-stone of our reception scheme. This procedure can be splitted into two stages: Stage 1 : 1. The observation y is sampled at rate 1 T and passed through a digital K 1 vector-filter G 1 z . The coefficients of G 1 z are adapted by minimization of a contrast function. The min- imum is reached iif z 1 n the output of G 1 z equals the symbols of one of the source up to a delay and a complex multiplicative factor. 2. By an adaptive subtraction procedure, we com- pute from z 1 n the contribution on each captor of the source currently estimated and we sub- tract this contribution from the observed signal. More precisely, we search t 1 z of size K 1 that minimizes yn t 1 z z 1 n 2 1861