SEIZIÈME COLLOQUE GRETSI — 15-19 SEPTEMBRE 1997 — GRENOBLE 127 Regularized Semi-blind Estimation of spatio-temporal Filter coefficients for mobile radio communications A.M.Kuzminskiy Ɇ , L.Féty É , P.Forster É , S.Mayrargue ‡ É Laboratoire d’Electronique, CNAM, 292, rue Saint-Martin, 75141 Paris Cedex 03, FRANCE, tel: 33 01 40 27 24 85, fax: 33 01 40 27 27 79, e-mail:kuzminsk@cnam.fr ‡ FRANCE TELECOM CNET 38-40 rue du Général Leclerc 92131 Issy-les-Moulineaux, FRANCE, tel. 33 01 45 29 60 51, fax. 33 01 45 29 41 94, e-mail Sylvie.Mayrargue@issy.cnet.fr † Odessa State Polytechnic University, DB “Diskret", 270044, av.Shevchenko 1, Odessa, UKRAINE, tel: 38 04 82 28 87 25, e-mail:kuzm@diskret.opu.odessa.ua RÉSUMÉ On étudie l’adaptation des coefficients du filtre spatio-temporel utilisé à la station de base pour l’égalisation du canal et la réjection des brouilleurs, quand la longueur de la séquence d’apprentissage est insuffisante pour faire appel aux estimateurs classiques. Un critére semi-aveugle et l’algorithme de traitement correspondant sont proposés, en exploitant la présence d’une séquence d’apprentissage courte et la propriété de module constant des signaux. En fait, c’est une nouvelle version de l’estimateur régularisé, adapté aux particularités des radiocommunications mobiles numé riques. ABSTRACT The solved problem is the adjustment of the spatio-temporal filter at the base station, for channel equalization and jammer rejection, when the length of a training sequence is not sufficient to use standard estimators. A semi-blind criterion and processing algorithm are proposed, which exploit the presence of a short training sequence and the constant modulus property of the signals. It is a new version of the regularized estimator, which is adapted to the features of digital mobile radio communications. Introduction In digital mobile radio communications the data are transmit- ted in bursts and a training sequence of short duration is at- tached to each burst. The length of this sequence (26 symbols for the GSM) may not be sufficient to adjust the coefficients of the spatio-temporal filter to equalize the channel and reject the jammers when an array of sensors together with temporal filters are used in the base station. This difficulty can be over- come with the help of suboptimal [1] or blind algorithms [2, 3]. Both approaches have known disadvantages. For example, a global convergence of the popular blind fractionally spaced constant modulus (CM) algorithm is established only for an infinite number of data (mathematical expectation in CM cri- terion) [3 and others]. It has been pointed out in [4,5] that com- bining training and blind techniques can be effective, and semi blind criterions and algorithms for single input multiple out- put channel identification based on maximum likelihood (ML) principle have been proposed. The necessity of complete mod- elling for ML approach limits the aplication area of these al- gorithms. A semi-blind approach based on a least squares (LS) criterion regularized by means of the CM function is proposed here to find the coefficients of the spatio-temporal filter in the general case, with jammers and unknown lengths of propagation channels. It is shown that it allows to reduce the dimension of the optimized CM function by the length of the training sequence. An algorithm for the minimization of the proposed criterion is derived. Its efficiency is demonstrated by simulations, in situations where the length of the training sequence is not sufficient to use the standard regularized LS estimator and the limited volume of data in one burst is not sufficient to use the least squares CM algorithm (LSCMA) [6]. Problem formulation The signal model and the general spatio-temporal filter struc- ture are shown in Fig.1.The notations are the following: K : number of antenna array elements; s n : desired signal; M: num- ber of jammers d in , i D 1::: M; x in , i D 1::: K : antenna array outputs; ò ln , l D 1::: K : additive uncorrelated noise with vari- ance õ 2 ò ; G: propagation channels; O s nÄD D W É X n : desired signal estimator; X T n DfX T 1n ;:::; X T Kn g: . KL Ç 1/ input sig- nal vector, where X T in Dfx in ;:::; x i .nÄL C1/ g for i D 1::: K ; L : number of coefficients of FIR filter in each spatial channel W T i Dfw i 1 ;:::;w iL g; W T DfW T 1 ;:::; W T K g: . KL Ç 1/ vec- tor of weight coefficients; D: delay. All signals assumed zero mean. The features of this signal model in mobile radio commu- nications application are the following: 1. Propagation channels G can be approximated by FIR filters of length L g [3]. Both G and L g are unknown. 2. The desired signal s n has the following temporal struc- ture: data are transmitted in bursts of length N b ; the training sequence of length N < N b is transmitted inside each burst.