Non coherent coding for MIMO-OFDM systems Raouia Ayadi Ecole sup´ erieure des communications de Tunis Cit´ e Technologie des Communications, 2083 El Ghazala, Ariana, Tunisia Email : ayadi@telecom-paristech.fr In´ es Kammoun LETI Department, ENIS BPW 3038 Sfax - Tunisia Email : ines.kammoun@ieee.org Mohamed Siala Ecole suprieure des communications de Tunis Cit´ e Technologie des Communications, 2083 El Ghazala, Ariana, Tunisia Email : mohamed.siala@supcom.rnu.tn Georges Rodriguez-Guisantes TELECOM ParisTech 46, rue Barrault, 75634 Paris Cedex 13, France Email : rodriguez@telecom-paristech.fr Abstract— This paper deals with the problem of code design for non-coherent frequency-selective Multiple Input Multiple Output (MIMO)-Orthogonal Frequency Division Multiplexing (OFDM) fading links, where neither the transmitter nor the receiver knows the channel. A simple and classical approach for non coherent (NC) coding for MIMO-OFDM system consists of coding across antennas and time slots on each OFDM subcarrier. Only, this approach does not permit to exploit the diversity of frequency- selective channels. In our aim to exploit this diversity, we propose in this paper a strategy that consists of coding across antennas and OFDM subcarriers (space-frequency coding) within a single OFDM symbol. Our space-frequency (SF) codes are based on NC Grassmann space-time (ST) codes obtained via an exponential map from coherent ST codes. We determine the asymptotic Pairwise Error Probability (PEP) for each scheme in order to evaluate the diversity and the coding gains. Simulations show that compared with the classical approach, our NC-SF codes can get more diversity gain and better symbol error performance. I. I NTRODUCTION The Multiple Input Multiple Output (MIMO) systems are considered as a good candidate for the fourth generation of wireless communications. These systems acheive a full spatial diversity. Several space-time (ST) codes have been developed over the flat fading channels. These codes exploit spatial and temporal diversity, leaving frequency domain unexploited. However, the MIMO channels present a selectivity for high wideband and cause the Inter-Symbol Interference (ISI). The Orthogonal Frequency Division Multiplexing (OFDM) is a powerful technique used in various wireless commu- nication systems that endure the frequency selectivity of channels [1] [2]. Combined with MIMO systems, the OFDM proves a robustness while crossing frequency selective chan- nels [3]. Most of the previous works introduced the space-frequency (SF) code in coherent MIMO-OFDM systems, i.e assume a perfect knowledge of the channel state information (CSI) at the receiver [4] [5]. In [4], some full-diversity SF codes are obtained from ST codes for arbitrary power delay profiles by a simple mapping. A code design criterion for SF-coded MIMO- OFDM systems was derived in [5]. Authors show in [5] that space-time codes introduced to achieve full spatial diversity in narrowand case will in general not achieve full space- frequency diversity. In practice, the knowledge of the CSI, getting via the training sequences, decreases the spectral efficiency of the system. Otherwise, it is sometimes impossible to estimate the channel coefficients and especially in the frequency-selective case due to the presence of multiple paths. To combat this drawback, non coherent (NC) communication, where neither the trans- mitter nor the receiver has CSI, was considered recently [6]. In [6], Borgmann et al adress code design for NC frequency- selective MIMO-OFDM fading channels. They propose design criteria for SF unitary codebook and show that unlike in the coherent case, NC-ST codes designed to achieve full spatial diversity in the frequency-flat fading case can fail completely to exploit not only frequency diversity but also spatial diversity when used in frequency-selective fading environments. In this paper, we propose a non-unitary SF codebook suited for NC MIMO-OFDM links. These codes are based on unitary ST codes proposed in [7] for frequency flat fading channels. The ST codes introduced in [7] are obtained via an exponential map from coherent codes and they were called Grassmann codes since they are set of points in the Grassmannian G T,Mt , the set of the M t -dimensional vector subspaces of C Mt , where T is the coherence time of the channel and M t it the number of transmit antennas. At the receiver the decision is made according to the Generalized Likelihood Ratio Test (GLRT), which does not require the knowledge of the channel statistics. These codes have been designed for flat fading channels and don’t exploit the frequency diversity of a selective channel. Our objective in this paper is to design SF codes for NC communications using the Grassmann NC-ST codes. Compa- rison will be done with a simple approach which consists of tansmitting a Grassmannian NC-ST codeword over each flat fading subcarrier. The rest of this paper is organized as follows. In Section 2, we introduce the system model. We describe the NC-ST coded MIMO-OFDM in section 3 and give its diversity and coding gains. In section 4, we present our approch to design the NC- SF code. In section 5, we provide some simulation results. Finally, section 6 contains our conclusions.